76827804 mechanica wildfire

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"?@ABCCDBDAFor Educa

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For Educa

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Structural and Thermal Simulation with Pro/ENGINEER Wildfire

Module 1: Introduction

Instructor Preparation

(minimum skills listed; additional experience recommended)Before teaching Mechanica, you must have read and thoroughly understand the following materials:

General Information • Review Pro/ENGINEER Wildfire primer site at http://rdweb.ptc.com/primer/

Wildfire Documentation• Review Pro/ENGINEER Wildfire documentation in Windmill, located in /GS Training

Materials/Domain Knowledge/Create/ProENGINEER/Core Concepts• TBD

Pro/ENGINEER Wildfire• Review Pro/ENGINEER Wildfire training materials in Windmill, located in /GS Ed Srvcs

Operations/GS Education Library/Instructor Materials/Instructor Kits/EN/T978-330-Instructor_Kit-EN

Mechanica• TBD

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Lesson Activities: Day One

Demos & Exercises

LecturesSimplifying

Designs usingIdealizations

Introduction

Creating theBracket

Adding MaterialProperties Creating and

Running GlobalSensitivity

Studies

Optimizing theBracket

Applying Mass,Spring, and

BeamIdealizations

Pro/FICIENCYDaily

Assessments

DefiningConstraints

Defining Loads

Idealizing theModel

Running anAnalysis

Applying ShellIdealizations

Applying SolidIdealizations

Applying RigidConnections

ValidatingDesigns using

Mechanica

OptimizingDesigns using

Mechanica

Creating DesignParameters

DisplayingResults

Applying Endand Perimeter

Welds

Duration• Lecture: 1 hour• Demos (0)• Labs (0)• Total: 1 hour

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Objectives

After completing this module, you should be able to:

� Describe Mechanica Structure.

� Describe Mechanica technology.

� Describe how to run design validation processes in Mechanica.

� Describe how to run optimization processes in Mechanica.

Overview

Mechanica allows engineers to test and optimize designs for structural, dynamic, thermal and durability performance before physical prototyping. Mechanica Structure allows design engineers to evaluate and optimize the static and dynamic structural performance of their designs in a real-world environment. Precise representations of CAD geometry and unique adaptive solution technology provide fast, accurate solutions automatically. This results in improved product quality, while decreasing costs associated with extended development times and ineffectual prototypes.

In this module, you will learn the basic process of using Mechanica.• Running Design Validations• Running Design Optimizations

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Mechanica Modules

� Structure�Stress Intensity Factors

�Contact, Buckling Prestress…

� Thermal�Steady State and Transient Thermal

� Motion�2D Cams and Slots, Gears, Contact and Subassemblies

Mechanica Products:These modules “talk” to each other and multi-disciplinary analyses can be performed. For example:

• Reaction forces and inertial loads can be transferred from motion to structure.• Temperature distributions can be transferred from Thermal to Structure for thermal-stress

analysis.• Optimization studies can be done on structural as well as thermal criteria.

There are three main Mechanica modules: Structure, Thermal, and Motion.

• Mechanica Structure – allows the user to perform Static, Modal, Buckling, Contact, Prestress Static, Prestress Modal, and Vibration analyses. (Additionally, it includes Dynamic Time Response, Dynamic Frequency Response, Dynamic Random Response, and Dynamic Shock Response.)

• Mechanica Thermal – allows the user to perform Steady-State Thermal and Transient Thermal analyses. (Note: Conduction and Convection can be modeled but not Radiation.)

• Mechanica Motion – is a rigid body dynamics (Dynamics of Mechanisms) package which allows mechanism modeling, including 2D cams and slots, gears (simplified geometry is used), contact (collisions and impact between parts can be modeled in detail; certain restrictions apply in terms of the type of regions that can come into contact), and subassemblies.

Note: Only Structure and Thermal products will be used in this course.

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Mechanica: Structure

Analyze parts and assemblies to find:

� Deformed shapes.

� Maximum stresses.

� Natural frequencies.

� Temperatures.

� Buckling loads.

� Responses to forcing functions.

Design Optimization Tool

� Part shape and properties can be parameterized (Design Parameters).

� Vary the model parameters to find the best design.

Mechanica: StructureMechanica Structure can be used to analyze parts and assemblies to determine deformed shapes, maximum stresses, natural frequencies, buckling loads, and responses to forcing functions.

• These are the “How Much” questions. Most analysis software will stop here (design validation).

• Being able to answer the “What if ” questions early and often is where Mechanica brings added value.

• Part shapes and properties can be parameterized to quickly generate and evaluate many software prototypes of your design and determine which is the best. This is illustrated here on a belt clip for an electronic pager (note that only half of the model is used for symmetry).

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Mechanica Technology Overview

� What is FEA/GEA?

� How is Mechanica Structure different from other structural analysis tools?

Closed Form Solution• Exact solutions to differential equations are only known for very basic geometries and

boundary conditions (for example: tensile test specimen, simply supported beam). To extract useful information from these solutions, we have to make some simplifying assumptions and then, using an engineering handbook, find the exact solution which best fits the application.

• For complex geometries, the above approach can only yield “ball park” figures. For example, no closed form solution exists for this engine block. If we want accurate answers, we have to resort to mathematical approximations and numerical methods.

• These methods proceed by using a “divide-and-conquer”approach: Break up the engine block into small, manageable elements (for example: elements which deform in known ways). Compute quantities of interest for each element and then put the solution together by gathering results from all elements.

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Closed Form Solution

�δmax = ?

�σvm,max = ?

�Fmode,1 = ?

�f(δ,σ) = ?

Closed Form Solution• Exact solutions to differential equations are only known for very basic geometries and

boundary conditions (for example: tensile test specimen, simply supported beam). To extract useful information from these solutions, we have to make some simplifying assumptions and then, using an engineering handbook, find the exact solution which best fits the application.

• For complex geometries, the above approach can only yield “ball park” figures. For example, no closed form solution exists for this engine block. If we want accurate answers, we have to resort to mathematical approximations and numerical methods.

• These methods proceed by using a “divide-and-conquer”approach: Break up the engine block into small, manageable elements (for example: elements which deform in known ways). Compute quantities of interest for each element and then put the solution together by gathering results from all elements.

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History of Geometric Elements

Demos & Exercises

Lectures

Rayleigh-RitzMethod

Calculus ofVariation

ExactSolution

FiniteDifference

GeometricElementMethod

Finite ElementMethod

EntireStructure

Green’sFunction

(BEM)

Euler-LagrangeDifferential

Hamilton’sVariationalPrinciple

Divide & Conquer

Closed FormSolution

No ClosedForm Solution

Large elementswith polynomialshape functions

Very small elementswith linear shape

functions

History of Geometric ElementsWe therefore have two classes of problems: Those for which we have closed form solutions and those for which we don’t. This chart is a brief history of mathematical formulations for engineering problems. Starting from Hamilton's Variational Principle:

• Calculus of variation leads to the formulation of Euler-Lagrange Differential Equations. Such equations can be formulated for a large class of problems; finding a solution to these differential equations, however, has proven to be extremely difficult for most situations except textbook problems. Other closed form solutions can be derived using Finite Difference Methods and Green’s Functions (boundary element method), but again only for a limited class of problems.

• Faced with the difficulties of solving complex differential equations, engineers have developed alternative methods. One such alternative approach is the Rayleigh-Ritz method which assumes a deformed shape for the loaded body (shape-function) and works backward towards the solution. The success of this method depends largely on how well we have selected the shape function. For complex structures adequate shape-function cannot be found easily.

• This drawback is eliminated by using a “divide and conquer” approach: break a complex structure or body into small, manageable elements (for example: elements for which shape functions are well known), solve equations for each element and then assemble a solution for the complete structure.

• Two methods have been developed. The Finite Element Method (which uses many small elements with linear shape functions) and the Geometric Element Method (which uses larger elements with polynomial shape functions. Mechanica uses the GEM.

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Derivation

Derivation: Basic Assumptions

� One Degree of Freedom (DOF) in x–direction.

� Cross sectional area of bar is constant and bar is in static equilibrium.

P

DerivationThe material in this section is meant to be presented as a derivation. Figures provide a guideline for what should be written on the board.

• The following discussion is meant as an introductory example to demonstrate how Geometric Element Analysis (GEA) works. We will consider a basic engineering problem, a bar loaded in tension, and derive a solution using the FEA formulation

• FEA is a numerical procedure for analyzing systems for which no closed form solution is available. The basic idea is to subdivide the system under consideration into smaller pieces. Each piece is called an element.

• Different types of elements are used to mathematically represent the geometry and the elasticity of systems. The bar (or truss) element is the simplest type and will be used in our discussion.

• Consider the bar element and a linear spring. Linear springs exhibit a linear relationship between force and displacement. This same relationship exists between force, stress, and displacement in a linear isotropic bar (as shown in the Figure A.)

Spring Element Bar Element

Figure A: Linear Relationship

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Derivation: Linear Relationship Assumptions

� Deformations are elastic.

� !"#"$"%

� Governing equation is linear.

� &"#"'"(

Derivation: Basic Assumptions (cont.)• Deformations are elastic. If the load is removed, the bar comes back to its initial length.• The cross-sectional area is constant throughout the bar element.

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Derivation: Equivalent Stiffness of a Bar

Derivations: Stiffness of Bar• Mechanica is called a displacement-based code because it solves for displacements first and

then derives all other results from there: Solving {u} = [K]-1 {F}, where: ° [K] is called the stiffness matrix, by analogy with the spring (this stiffness matrix, as we

will see is derived from material as well as geometric properties).° {u} is the displacement vector.° {F} is the applied load.

• From displacements, Mechanica calculates the strain defined as: εi = dui/di where “ui” is the displacement in a particular direction “i”. For the situation at hand, and assuming a linear variation of displacement along the length of the element, strain reduces to the ratio of displacement “u” over initial length “ l “. ε = u/l.

• Assuming linear material behavior, Hooke’s law is used to calculate stress:

σ = E * ε , where σ is stress, E is Young’s Modulus and ε is strain.

• Now, coming back to the spring analogy, we can derive the equivalent spring constant of the bar in terms of stress and strain.

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Derivations: Computing Global Stiffness Matrix

Force generated due to the unit displacement

Force generated due to the reaction at the nodes

Derivations: Computing Global Stiffness Matrix• As mentioned before, the main idea behind FEA/GEA is to subdivide the system in smaller

manageable elements and then solve for displacements and stresses. • An important step in this process is to assemble the global stiffness matrix of the system,

which includes the stiffness contribution of each element.• Rewriting the linear equation in matrix form, we obtain the global stiffness of the system.• For the case of a system with bar elements the same procedure can be used. In the case of

the bar, “k” is defined as EA/l (where “l” is the length of one element).

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Derivations: Computing Displacements

Derivations: Computing Displacements• In this case, node 0 has a fixed boundary condition and a load is applied at node 2.• We will be solving the equation Ku=P, were K is the stiffness matrix, u is the unknown nodal

displacements and P is nodal load vector. • Because of the fixed boundary condition at node 0, the first row and column of the stiffness

matrix are deleted. This leave us with 2x2-stiffness matrix that we need to invert and multiply by the load vector in order to solve for the nodal displacements.

• The final solution yields u1=Pl/EA and u2=2Pl/EA. Now, considering that “l” is the length of the element and L the total length of the beam, we have L=2l, and therefore u2=PL/AE,which is the closed form solution for uni-axial strain in a constant cross-section rod under tension.

What ‘s a shape function?A shape function is a mathematical function used to describe the variation of displacement along the edge of an element.

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Geometric Element Analysis (GEA)

� Solution Quality� Built-in Convergence.

� Comparison of solution from one polynomial level to next.

� Quality of your solution is known.

� Adaptive - adds computer resources only where needed.

Mechanica Technology OverviewNote: For the more experienced analyst, some of this discussion will appear very basic.

• GEA uses polynomial-order shape functions to calculate displacements. Each edge in ageometric element model is associated with a polynomial order.

• Convergence is defined as the situation where the answer quits changing as a function of mesh characteristics (be it polynomial order or number of elements)

• Illustrated here is a plate with a hole loaded in tension. We will consider the deformation of the highlighted edge as the GEA algorithm proceeds through the analysis.

• On this graph displacement (delta) is plotted as a function of edge length (l). The dashed line represents the exact solution (which, in practice, is of course unknown). The algorithm is said to have “built-in convergence” because it proceeds as follows:1. Perform the analysis with a linear shape function (delta= al+b) and record results.2. Perform analysis with a quadratic shape function (delta= al2+bl+c) and compare

answer with results obtained in step (1). If the answer has changed by more than a given percentage, increase the p-level of the edge to the next order.

3. Iterate until the previous and the current answers are close enough to be considered identical (within a user-defined tolerance). This is what we call a converged solution.

• As a result of the above process:1. The quality of your solution is known. Mechanica will allow you to verify how well or how

poorly your solution has converged. (How is convergence obtained with FEA? By performing mesh refinement studies which are extremely time consuming. As a result, very few analysts actually perform these studies and design decisions are made on un-converged FEA results.)

2. The solution is adaptive: higher order polynomial are only assigned to edges experiencing large deformations. Changing the nature of the problem (by displacing the load for instance) will affect polynomial orders but not necessarily the mesh.

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Finite Element Analysis (FEA) and Geometric Element Analysis (GEA)

� Independent of load cases.� No previous knowledge of the answer is required.

� Larger, more “flexible” elements vs. smaller, more “rigid” ones.

Traditional FEA Shell Mesh Mechanica Structure GEA Shell Mesh

Mechanica Technology OverviewFEA and GEAMechanica uses Geometric Element Analysis (GEA) as opposed to Finite Element Analysis (FEA). This discussion covers the main differences between FEA/GEA as well as how Mechanica is different from other structural analysis tools.

FEA Meshes versus GEA Meshes• An FEA mesh is made of elements with straight edges. As a result many elements are

needed to produce an exact representation of the geometry. GEA elements map the geometry exactly. Only four elements needed in this example.

• FEA uses linear and at best quadratic shape functions to map deformations. Convergence is achieved through successive mesh refinement studies.

• As explained earlier, Mechanica GEA uses polynomial shape functions (up to order 9) and convergence is achieved by increasing the polynomial order of individual edges during a single run.

• Unlike FEA models (where many elements are needed at expected stress concentrations), GEA models are independent of load cases and no previous knowledge of the answer is required (p-levels needed to accommodate large stress gradients are determined during runtime).

• Finally, (and again due to polynomial shape functions), GEA elements are larger and more flexible(they can deform into irregular shapes as each edge can go to order 9). FEA elements are smaller (to map geometry) and more rigid (they can only deform slightly due to the linear shape functions).

• Other advantages of GEA meshes include: No transition regions, fewer element types, results provided everywhere in the mesh (continuous stress field) as opposed to only at nodes for FEA.

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Yielding in Materials

Yielding in Materials• The continuous line on the graph represents a typical stress-strain curve for a ductile metal

(use tensile specimen example). In the linear range of the graph (elastic range), deformations are reversible (ie: remove the load and the body will revert to its initial configuration). The slope of that curve is a constant called Young’s Modulus (E).

• If the body is loaded beyond its yield strength, then non-elastic deformations occur (ie: remove the load and the body will remain in a deformed state) until the ultimate strength is reached.

• Mechanica is a linear analysis code and will compute results according to the linear range of their material stress-strain curve. If the material is loaded beyond its yield point, Mechanica results will deviate from reality (material non- linearity). This means the user must make sure the stress remains below the yield strength.

• Another situation to watch for is the large displacement non-linearity: typical example is a flat plate problem. If deformation is greater than ~½ the thickness of the plate, some nonlinear effects appear in reality (shear becomes an important factor and Mechanica will overestimate displacements).

• Note that Mechanica can handle certain types of non-linearity such as buckling (the load at which buckling will occur is computed, not the post-buckling behavior), contact, and prestress loading.

Note: Large Deformation Analysis is also available…topic to be covered upcoming lesson module.

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Failure Criteria

� von Mises and Tresca:� Specifies Tensile Yield Stress.

� Modified Mohr� Specifies Ultimate Tensile Strength.

� Specifies Ultimate Compressive Strength.

� Produce Fringe Plot of Failure Index Actual Stress/Yield Stress.� < 1: material below yield point

� = 1: material at yield point

� > 1: material past yield point

Yielding in Materials• How do you know when stress has exceeded yield strength? Which component of stress

should you consider? This is what failure criteria are used for. They allow you to consider only one value with which to compare with the yield of your material. Mechanica will provide you with values for several of these criteria. You will have to choose the one that best fits your needs

• For materials whose properties are identical in all directions (isotropy), a general state of stress can be described using 9 components arranged in a 3x3 matrix (stress tensor, see figure below). This stress matrix is symmetric and reduces to 6 independent components: 3 normal-stress components and 3 shear-stress components.

• By combining stresses in all directions into a single figure, failure criteria avoid having to compare each component with the yield strength of the material.

• Using a convenient geometric transform, it is possible to orient the coordinate system such that all shear stresses are reduced to zero (Mohr’s circle for stress). Once this is done, we are left with three normal stress components called principle stresses.

• Mechanica calculates stress criteria based on these principle stresses: The von Mises stress criterion and the principle stress criterion. These values can then be compared with the material yield strength.

• von Mises Stress criteria should be used for ductile metals (ie: most engineering metals). The principle stress criteria should be used for brittle materials (for example: glass, ceramics).

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Summary

After successfully completing this module, you should know how to:

� Describe Mechanica Structure.

� Describe Mechanica technology.

� Describe how to run design validation processes in Mechanica.

� Describe how to run optimization processes in Mechanica.

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Module 2: Validating Designs Using Mechanica





Materials/Domain Knowledge/Create/Pro/ENGINEER/Core Concepts• TBD



Mechanica• TBD

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Demos & Exercises

LecturesSimplifying


Introduction

Creating theBracket



Studies



BeamIdealizations

Pro/FICIENCYDaily

Assessments

DefiningConstraints

Defining Loads

Idealizing theModel

Running anAnalysis





Mechanica


Mechanica


DisplayingResults


Welds

Duration• Lecture: 15 mins• Demos (30)• Labs (2 hours)• Total: 2 hours 45 mins

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Objectives


� Identify design requirements.

� Apply the Mechanica process to basic structure simulations for design validation.

OverviewDesign processes require engineers to calculate the stress distributions and displacement of new designs. These processes allow engineers to validate design intent.

In this module, you will:• Identify the design requirements using the exercise provided in this module. • Use the design validation phase to prepare a model for static (structural) analysis.• Create and run an analysis.• View and interpret the results.

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Process of Using Mechanica

Running Design Validations

� Part Geometry

� Properties

� Constraints

� Loads

� Elements

� Define and Run Analysis

� Interpret Analysis Results

Running Design Optimizations

� Design Parameters

� Sensitivity

� Optimization

Process Overview• A typical structural simulation consists of the design validation and optimization phases.

These two phases consist of ten steps.• The 10 steps listed here define the Mechanica Structure process. This process is reflected

in the menu structure; it is also an outline for the course. This discussion is meant as an overview and each of these topics will be covered in detail in following modules.

• The first seven steps comprise the Design Validation phase. These steps will allow us to answer the “How much” questions (how much stress, displacement…) and validate our design for its intended use:1. Create the Model Create the part or assembly that satisfies the design intent.2. Idealize the Model Prepare the model for automatic mesh generation. This includes

specifying appropriate idealization types and any required idealization properties.3. Set Units and Material Properties Specify the appropriate system of units and assign

material properties.4. Identify Constraints Define realistic constraints that simulate how the model will

function in the real world.5. Set Loads Define loads to simulate how the model is loaded in the real world.6. Define and Run the Analysis Define the appropriate analysis type (static, modal, etc.)

based on the required results. You can also define the convergence settings. Run the defined analysis.

7. View and Interpret the Results The converged results can be visualized by generating graphs, fringe plots, etc.

• This completes the design validation phase of the process. From this point on we want to answer the “what if” questions. What if we wanted to make this design lighter? What would have to change? Can this design be improved? How does the stress vary as a function of this dimension?

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Design Validation

Design Validations

� Part Geometry

� Properties

� Constraints

� Loads

� Elements

� Define and Run Analysis

� Interpret Analysis Results

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Example: Identifying the Design Requirements

� The design objective is to minimize the bracket mass.

� The design must support a 20 pound load at a specific point.� Maximum stress must be less than 93 N/mm² .

�The maximum allowable displacement is 0.04 mm.

�The distance between the two bolt holes and sheet metal thickness must remain fixed.

Identifying the Design RequirementsThis example illustrates a typical structural simulation. The objective is to find a design that is stronger and lighter than the existing system, yet still easy to assemble resulting in these design requirements.

• The maximum stress must be less than 93 N/mm2 (MPa). This maximum allowable stress is calculated using the tensile yield strength of the available steel (231 N/mm2) with a safety factor of 2.5.

• The maximum allowable displacement is 0.04 mm. This is necessary because a small deformation in the bracket can cause large displacement at the end of the rack it carries.

• The distance between the two bolt holes (30 mm) and sheet metal thickness (2.5 mm) must remain fixed. This is necessary due to assembly constraints.

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Example: Validating Designs Using Mechanica

Bracket Design

� Create in Pro/ENGINEER Wildfire.

� Reflect the design intent.

� Dimensioning scheme.

Bracket Dimensioning Scheme

Note: Relations can be used to capture the inter-relationship among the dimensions.

• The four rounds are created as two separate features: the inner and outer rounds. This dimensioning scheme provides the flexibility of altering each feature independently to improve the design.

• According to the design constraints, the dimensions of the hole will remain fixed during the optimization.

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Validating Designs Using Mechanica

Material Properties

Defining Constraints

Loads

� Bracket bearing loads.� Rack Assembly

� Free Body Diagram of Rack

Defining Elements

� Shell model.

Defining LoadsThe bracket load must be calculated using realistic loading conditions. In reality, a rack is attached to the bracket using two bolts. A 20 lb. load is applied to a point as shown in the top figure.

Calculating the Bracket Bearing LoadA Free Body Diagram (FBD) can be created as shown in the bottom figure.Since the system of equations is indeterminate, the assumption Ay = By is made. The static calculation yields the following result:

Ax = -889 N; Ay = 44.5 N; Bx = 889 N; By = 44.5 NThe force components of the bracket bearing load are equal and opposite.

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Define and Run Analysis

� Static Analysis

� Summary File� RPT file

Define and Run Analysis

Running the Analysis• An analysis is the calculation of a model’s response to it’s boundary conditions. Mechanica

Structure provides 12 types of analyses that span a wide range of actual boundary conditions. The analysis type depends on the type of problem. For this problem, a static analysis will be defined with single pass adaptive convergence criteria. A static analysis type is used to find the stress and displacement of a structure.

• A summary file can be used to monitor the progress of the analysis.

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Displaying and Interpreting the Results

� Result Windows �Stress, Displacement …

Displaying and Interpreting the ResultsResult windows can be created to show the stress and displacement of the model. In this example, several result windows can be created:

• An animated fringe plot that shows the von Mises stress of the model. • An animated fringe plot that shows the displacement of the model.• An animated fringe plot that shows the principal stress of the model.• A fringe plot used to dynamically query the stress of the model.

The results will show that the design needs to be improved in order to satisfy the design requirements. Since most of the part has very low stress, this part may be over-designed. This indicates that further improvement can be made to reduce weight.

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Demonstrations

� Creating the Bracket

� Adding Material Properties

� Define Constraints

� Define Loads

� Idealize the Model

� Running an Analysis

� Display Results

Demonstrations (30 minutes)

In this demonstration, I will:

• Create a part called BRACKET in Pro/ENGINEER Wildfire.• Specify the material properties of the bracket as steel.• Define how the bracket is constrained.• Apply a bearing load on the top and bottom hole.• Idealize the model by compressing it to a mid-surface.• Define a static analysis.• Create a result window.

You will repeat the same steps in the lab exercises.

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Summary


� Identify design requirements.

� Apply the Mechanica process to basic structure simulations for design validation.

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Module 3: Optimizing Designs Using Mechanica

Structural and Thermal Simulations with Pro/ENGINEER Wildfire





Materials/Domain Knowledge/Create/Pro/ENGINEER/Core Concepts• TBD



Mechanica• TBD

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© 2002 PTC


Demos & Exercises

LecturesSimplifying


Introduction

Creating theBracket



Studies



BeamIdealizations

Pro/FICIENCYDaily

Assessments

DefiningConstraints

Defining Loads

Idealizing theModel

Running anAnalysis





Mechanica


Mechanica


DisplayingResults


Welds

Duration• Lecture: 15 mins• Demos (3): 15 mins• Labs (3): 1 hour• Total: 1 hr 30 mins

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© 2002 PTC

Objectives


� Create design parameters.

� Create and run a global sensitivity study.

� Create and run an optimization study.

� Display results and optimized models.

OverviewTo further improve a design, engineers may need to determine the key variables that control and influence the design. This information can be used to optimize designs.

In this module, you will use the design optimization phase to:• Optimize the design.• Find design parameters that best meet the design goal.• Run sensitivity studies to determine the sensitivity to a change in the design parameters.• Run optimization studies to find the best design parameters to satisfy the imposed

constraints.

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Design Optimization Tool

� Part shape and properties can be parameterized.

� Design Parameters can be created.

� Vary the design parameters parameters to find the best design.

Optimization Process

� Design Parameters

� Sensitivity

� Optimization

Optimizing Designs Using Mechanica

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Creating Design Parameters

� Pro/ENGINEER Wildfire dimensions or model parameters.

Creating Design ParametersDesign parameters are variables of the model that can potentially affect the design objectives. Design parameters can be Pro/ENGINEER Wildfire dimensions or model parameters.In a design optimization, the system changes the variables within a certain range to find the best values that satisfy the constraints and optimize the design goal. In the example of the bracket, there are eight design parameters.

Maintaining Design Intent Using RelationsIn Pro/ENGINEER Wildfire, relations can be created to capture the inter-relationship among parameters and dimensions. In Mechanica, these relations remain valid and active in the simulation process. Whenever a design parameter is changed, Mechanica will re-evaluate the relations and regenerate the model. This ensures that the model satisfies the design intent.

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© 2002 PTC

Example: Optimizing Designs Using Mechanica

� Maintaining design intent using relations.� Shape of the Bracket Using Relations

● top = 62.5 + (45 – ang ) * 0.5

Shape of the Bracket Using RelationsIn this example, the basic shape of the model should be maintained. When varying the dimension ANG within the allowable range (from 45 degrees to 90 degrees), the dimension top should be adjusted accordingly. To capture this design intent a relation will be created:

top = 62.5 + (45-ang) * 0.5

Because of this relation, the dimension top will change as ANG changes from 45 to 90 degrees. Thus, the bracket model maintains its basic shape, as shown in this figure. The relation is used to maintain design intent during a sensitivity study. As a result, eight independent design parameters can be reduced to seven.

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Running Sensitivity Studies

� Variables�Design Parameters

� Output�Measures

� Global sensitivity studies serve three primary purposes�How measurable quantities are affected by changes in design parameters.

�Eliminate unnecessary parameters.

�Determine initial parameter values for optimization.

Running Sensitivity StudiesSensitivity studies are used to determine whether a certain characteristic or property of the model is sensitive to a change in a design parameter. Specifically, the system calculates the changes in a model's measures (such as stress and displacement) when a parameter varied over a specified range.Sensitivity studies can be performed by varying the parameters within a range (global sensitivity), or at a specific value (local sensitivity).

Global sensitivity studies serve three primary purposes: • To help understand how a measurable quantity is affected as a parameter varies through its

range.• To help eliminate unimportant parameters from an upcoming optimization.• To determine a good initial value for a parameter in an optimization.

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© 2002 PTC


Running Optimization Studies

� Inputs:� Goal

� Optimization Constraints

� Optimization Variables

� Optimization Results� Measures

� Optimized shape

Running Optimization StudiesIn an optimization study, the solver tries to find a set of design parameter values within their specified ranges that maximizes or minimizes a measurable quantity while satisfying all of the imposed constraints.

There are several key elements that need to be defined in an optimization study.• Goal: A goal is a certain measurable quantity of the model that will be maximized or

minimized in an optimization design study. In the case of the bracket, the goal is to minimize the mass of the bracket.

• Optimization Constraints: These are constraints that a model must satisfy. In the case ofthe bracket, the constraints are:

• The maximum von Mises stress must be less than 93 N/mm2 (MPa).• The maximum allowable displacement is 0.04 mm.

• Optimization Variables: In an optimization study, the solver changes the variables within their range to find the best values that satisfy the constraints and optimize the goal. In the case of the bracket, there are 7 variables shown in the figure (the ranges for these variables can be found in the exercise).

Reviewing Optimization ResultsThe types of results that should be reviewed are the plots showing von Mises stress compared to optimization pass. You may also want to review total mass compared to optimization pass.

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Demonstrations

� Create design parameters and relations.

� Create and run global sensitivity studies.

� Optimize the bracket.



• Create design parameters by renaming the dimensions in Pro/ENGINEER Wildfire.• Investigate the parameters with a global sensitivity study.• Create the optimization design study.


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Summary


� Create design parameters.

� Create and run a global sensitivity study.

� Create and run an optimization study.

� Display results and optimized models.

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Module 4: Simplifying Designs Using Idealizations

Instructor Preparation (minimum skills listed; additional experience recommended)Before teaching Mechanica, you must have read and thoroughly understand the following materials:






Mechanica• TBD

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Demos & Exercises

LecturesSimplifying


Introduction

Creating theBracket



Studies



BeamIdealizations

Pro/FICIENCYDaily

Assessments

DefiningConstraints

Defining Loads

Idealizing theModel

Running anAnalysis





Mechanica


Mechanica


DisplayingResults


Welds

Duration• Lecture: 30 mins• Demos (5): 15 mins• Labs (5): 1 hour• Total: 1 hr 45 mins

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Objectives


� Describe the types and applications of idealizations.

� Simplify designs using idealization.

� Describe the purpose of rigid connections.

� Describe the purpose of end and perimeter welds.

Overview

Idealizations are mathematical approximations of the model geometry. Mechanica uses idealizations to simulate the behavior of the design. Mechanica calculates stress, strain and other values for each idealization or element. You can choose from several different types of idealizations to simplify designs when running analyses. In this module, you will examine several ways to idealize Mechanica elements. There are several simplifications of idealizations of Mechanica elements. It is important to understand the various idealization types and how they affect the results you will get for any given analysis.

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Geometry: Generating the Part

Geometry is the foundation of Mechanica models.

� Created in Pro/ENGINEER Wildfire.

� Imported from other CAD products.

Modeling geometry.

� Ease of modeling with Pro/ENGINEER Wildfire.

� Use recommended part generation techniques.

Datum Points & Curves

Dimensioning Scheme

Future Shape Changes

Base Feature

Relations

Loads

Regions

Patterns

Constraints

Optimization

Future Feature Suppression

Sensitivity Studies

Midsurface Compression

?

Geometry: Generating the PartDecisions made early in generating parts with Pro/ENGINEER Wildfire will affect ease of modeling with Mechanica. The key is to plan ahead and to think in terms of analysis from the beginning. You want to generate “analysis friendly” parts. Here are some examples:

1. Selecting an appropriate Base Feature for your model can save you considerable amounts of time. For instance, thin protrusions allow automatic Mid-surface Compression for shell creation (an operation which must be done manually for other features).

2. Including certain features in your sketches instead of later in part mode will prevent you from easily performing Feature Suppression. External rounds (and any nonstructural feature) are generally suppressed before performing an analysis as they increase the number of elements in the mesh without affecting the results.

3. The Dimensioning Scheme will affect your ability to perform Future Shape Changes as well as Optimization and Sensitivity Studies on certain parameters of your part.

4. Managing Relations will also be important as they might affect parameters to be considered in the analysis.

5. Datum Points and Curves are useful to specify areas of local mesh refinements. They will also allow you to create Regions for precise application of Loads and Constraints.

Make use of recommended part generation techniques in the Online Documentation. In particular “Getting Started” and “Working with shell Models”.

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Model Types

� 3-D: Use if any model entity (geometry, properties, constraints, or loads) lies outside the XY plane.

� Plane Stress 2-D: Use if all model entities lie in the XY plane and Z-direction depth is thin.

� 2-D Axisymmetric: Use when all entities are symmetrical about the same axis of revolution.

� Plane Strain (2-D): Use when strain in Z-direction is negligible and Z-direction depth is thick.

Model Types• There are four model types available in Mechanica Independent Mode (3D, Plane Stress,

Plane Strain and 2D Axisymmetric). The choice of model type significantly affects run times. Whenever possible, we want to take advantage of model types other than 3D.Note: Independent Mode will not be used in this course.

• The 3D model type is by far the one that requires the most computer resources. It is used when no simplification can be applied to the model. Note that this is the only model type available in Integrated Mode.

• The 2D-Plane Stress model type is used for thin parts when all model entities (geometry, properties, constraints and loads) lie in one plane. (namely: no gradients exist in the transverse direction). In these cases, doing away with the third dimension will significantly decrease analysis times while accurately representing the physical situation

• The 2D Axisymmetric model type, as its name implies, is used when all model entities(geometry, properties, constraints and loads) are symmetrical about an axis of revolution.

• The 2D-Plane Strain model type is used for thick, extruded parts when all model entities (geometry, properties, constraints and loads) are identical for each cross-section of the structure (for example: dams, underwater pipes). Again, the third dimension in the model is ignored (as any cross-sectional result is valid for the entire structure) and run times are significantly reduced from the 3D representation.

• Elements, properties, loads, and constraints all depend on the model type selected. As a result, if the model type is changed, all that information is lost.

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Idealization Types

� Beam

� Shell and Solid

� Mass and Spring

Idealization Types“Idealizations” is the term used to designate Mechanica elements. This term puts emphasis on the fact that elements constitute mathematical representations of reality; in particular, we will review the assumptions tied to each type of element. The following are the types of idealizations available along with most common uses:

1. Beam Elements are represented as single lines in space. They are extremely economical from a computational point of view and therefore useful to model overall behavior of large structures (typically trusses, bridges and frames made of standard sections).

2. Shell Elements are represented as surfaces with no thickness. They are generally used to represent parts that are thin relative to their other dimensions (plates, shelled solids, pipes, pressure vessels, panels…). Also computationally economical when compared with 3D Elements.

3. Solid Elements can be used to model any type of structure or part, however they are are the most computationally expensive elements

4. Mass Elements are used to represent any component which only contributes mass and no stiffness to a system, structure or part (for example: motor on a robotic arm). This is particularly useful for modal analysis.

5. Spring Elements are used to represent any component which contributes stiffness (or flexibility) but no mass to a system, structure or part (for example:driving belt). Spring elements are linear-elastic elements (double the applied force, you get double displacement), and can connect two points or a point to ground. Stiffness can be defined in translation (force per unit length) as well as torsion (torque).

When deciding on which elements to use, consider the structure that is being modeled and how that structure behaves, rather than the geometry. This will help in selecting the type of elements for your model.

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Terminology Overview

Geometric Entities� Points� Curves � Surfaces� Volumes

Element Entities� Shells� Edges � Faces� Solids

Integrated Entities� Shell = Feature Type� Edges/Curves = Geometry� Faces/Surfaces = Geometry� Solids = Volumes

Terminology Overview• Being familiar with terminology is critical when dealing with the Mechanica user interface.• Terms used interchangeably in common language will mean different things in Mechanica. In

particular, we need to distinguish between Geometric entities and Element entities.

As far as Integrated Mode is concerned:• A Shell is a feature type (not to be confused with shell elements of Mechanica).• Edges/Curves are used to designate geometry.• Faces/Surfaces are used to designate geometry. • Solids and volumes become equivalent.

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Simplifying Designs Using Idealizations

Using Shell Elements

� Constant shell thickness.

� Linear stress distribution through the thickness (t).

� Length to thickness ratio: �10 < l/t < 1000

� Shell radius of curvature (r):�r > (2/3) * t

Using Shell ElementsAssumptions:

• Shell Elements are represented as surfaces with no thickness. They are used to represent parts that are thin relative to their other dimensions (plates, shelled solids, pipes, pressure vessels, panels)

• Shell element results are derived from classical plate theory. Again, you have to ensure underlying assumptions apply: 1. Shell thickness is constant throughout the element.2. Bending, rather than shear is the dominant deformation mode. As a result, a shell

element has a linear stress distribution through the thickness from tension at the top to compression at the bottom.

3. The length to thickness ratio must be greater than 10 and less than 1000. The lower bound (10) because thick parts deviate from the through-thickness linear stress distribution assumption (shear effects become significant), the upper bound (1000) because very thin parts must be handled with particular numerical formulations (to avoid ill-conditioned stiffness matrices).

4. The shell radius of curvature must satisfy r > (2/3) * t (for example, sharp bends can not be handled with shells). Shell elements represent a 3D physical reality; from a geometrical point of view the smallest possible radius is r = t/2. However, for numerical results to be reliable a value of at least 2/3 * t must be used.

• You need curved underlying geometry to create curved shells. • Mechanica allows you to mix elements created manually and elements created by

AutoGEM. Node to node connectivity must be observed to avoid cracks in model (more on this in next lecture). In Integrated Mode, the user can specify where shell elements will be created on a part (at a mid-plane, on a face, on a region or on a datum plane).

• Pro/ENGINEER Wildfire users can hand mesh parts and surfaces by importing geometry.

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Simplifying Designs Using Idealizations (cont.)

Creating the Mid-Surface

� Define pairs.

� Test compression.�Watch for unopposed surfaces.

�Understand multi-constant thickness.

�Understand compression with regions.

�Watch for gaps in structural assemblies.

�Define pairs in part mode (no pairs in assembly mode).

Surfaces to pair

Creating the Mid-SurfaceTo meet Mechanica’s criteria for shell models, a part must have a constant or multi-constant thickness. In other words, a shell model can not be a tapered part, but a part can have multiple constant thickness areas. The thickness of the shell element is always distributed uniformly about the surface on which it is placed. For this reason, it is important that this surface actually represent the “mid-plane” of the model.To go from 3D Pro/ENGINEER Wildfire geometry to 2D surfaces representing shell elements in Mechanica, the user must define pairs (or groups) of surfaces which will be compressed to a mid-plane surface.This is a three step process:

1. Defining shell pairs - define pairs of surfaces which will be compressed. A pair can consist of two or more surfaces on opposite sides of a volume.

2. Verify that the “Use Pairs” option is set – (from the Pro/ENGINEER Wildfire menu, use Applications>Mechanica>Settings and check the “Use Pairs” option) Mechanica uses this setting to determine whether to perform solid or shell meshing.

3. Test Compression – (from Structure Menu use Model>Idealizations>Shells> Compress). Use this option to compress the pairs of surfaces onto their mid-plane and preview the shell “interpretation”of your part. This is important as improperly paired surfaces will cause fatal errors in your analysis run.

For complex parts, the pair definition process can become extremely tedious. This process can be automated using base features that Auto Pair (Model: Idealizations: Shells: Pairs: Auto Pairs). The following features will Auto Pair : Thin Protrusions (Pro/Surface Quilts), Shelled features, Sheetmetal features, Ribs and certain types of drafts (those having parallelograms as cross sections). Tapered solids can not be paired as shells have a constant thickness. In this sense, a general draft will not Auto Pair.

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Beam Elements

� Constant beam cross-section.

� Symmetrical cross-section, but there are Channel and “L” beams.

� Length to X-section ration should be >= 10:1.

� Results available are axial, bending, torsion, and total beam stresses.

� Must be planar (no corkscrews).

Using Beam ElementsAssumptions:

• A beam element is represented as a single line in space. Typically used for modeling large structures such as trusses, bridges and frames.

• Beam element results are derived from classical beam theory. It is the user’s responsibility to ensure that the following assumptions apply when using beam elements: 1. The beam has a constant cross section. 2. The beam has a symmetric cross section and loads are applied along the plane of

symmetry. Torsional effects can become important for highly un-symmetrical sections and are not well handled by classical beam theory. However, note that channels and “L” sections can be handled.

3. The length-to-width and length-to-depth ratios are greater or equal to 10:1. When this assumption is satisfied, the deformation developed in the beam is mainly due to bending stresses, as opposed to shear stresses.

4. Results include axial, bending, torsion, and total beam stresses. Note that shear stresses are not included. Shear effects can not be captured with beam elements.

5. The beam cross-section does not rotate about the neutral axis (no corkscrew).• In Integrated Mode, the mesh is generated at run time by AutoGEM.

Note: You need curved underlying geometry to create curved beams.

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Solid Elements

� 30:1 Aspect ratio.

� Types:�Brick: six quad faces (8 points).

�Wedges: two tri and three quad faces (6 points).

�Tetrahedral: four tri faces (4 points).

� AutoGEM ensures:�Edge and face connectivity.

�Solids do not overlap.

�Adjacent elements have edge-to-edge connectivity.

Solid ElementsA solid model is a part that is modeled using solid elements like tetrahedral, bricks, or wedges. In Integrated Mode, Mechanica uses only tetrahedrals for solid modeling by default. Solid elements should be used when a part is “chunky,” or when a part's width, length or thickness are not sufficiently small enough to assume that it can be modeled with a shell element.

• Being the most expensive in terms of run time, solid elements are used to model parts for which none of the beam, shell or 2D assumptions apply.

• Assumptions: For reliable results, solid elements with aspect ratios greater than 30:1 should not be used.

• The following types of solids can be created:• Brick (or hexahedron) with six quadrilateral faces and eight points.• Wedge (or pentahedron) with two triangular faces, three quadrilateral faces, and six

points.• Tet (or tetrahedron) with four triangular faces and four points.

• In Integrated Mode, mesh generation occurs "behind the scenes", and meshes are created using Tetrahedral elements only.

• Remember to turn off the setting of "Use Pairs“.

Guidelines for Creating Solids• To ensure good point, edge and face connectivity (namely, to avoid cracks in models), hand-

meshed elements should not be mixed with AutoGEM elements.• Solids must not overlap.• Adjacent elements must have edge-to-edge connectivity. Any unmatched edge creates a

crack in your model (discussed in the next lecture). Divide large arc spans into separate segments by placing points along them or by splitting them before selecting them as edges.

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Mass and Spring Elements

� Mass Elements� Point Mass

● Simple● Advanced

� Spring Elements� References

● Point to Point● Point to Point Pairs● Point to Surface● Point to Edge

� Types● Simple● Advanced● Point to Ground

Mass and Spring Elements• Mass - Used to represent a concentrated or point mass without a specified shape(Structure

only).• Spring - Used to represent a linear elastic (six degrees-of-freedom) spring

connection(Structure only).

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Connections

� End Welds� Requires 2 surfaces.

� Perimeter Welds� Requires 2 surfaces and edges.

� Spot Welds� Requirements:

● One surface on each body.● A gap has to exist between the two surfaces.● A datum point for each spot weld location.● Diameter of the weld.● Material of the weld.

Creating ConnectionsA connection is the point of contact between two or more parts or subassemblies. In Mechanica, two kinds of connections can be used—end welds and perimeter welds.

End WeldsEnd welds can be used in assembly models to connect plates. The plates may be curved and placed at oblique or right angles, such as T or L configurations. By using the end weld, the shell mesh from one plate is extended to meet the mesh from the base plate.End welds can be used to join:

• Two thin wall components at a right angle.• Two thin wall components at an oblique angle.• Two offset thin wall components mated at a right angle with a gap between the compressed

surfaces of the components.Two offset thin wall components mated at an oblique angle with no contact between the components.

Perimeter WeldsPerimeter welds can be used in assembly models to connect parallel plates, which may be curved, along the perimeter of one of the plates. During mesh generation, a series of surfaces is automatically created to connect the selected edges of the top plate to the base plate. Mechanica creates shell elements on the selected surfaces. A series of welds on one or more of the perimeter edges of the top plate establishes a connection to the base plate. The resulting compressed surfaces, however, will still be parallel to one another and will not touch.For E

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Creating Rigid Connections

� Requirements� Points, curves and surfaces.

� Impose equal displacement conditions on the reference.

� Identical to placing an infinitely stiff spring between the references.

Creating Rigid ConnectionsA rigid connection connects geometric entities, such as surfaces, curves and points, so that they remain rigidly connected during an analysis. When entities are connected in this way:

• They move together as if part of a single rigid body. • They do not deform, but the rigid body can move as a whole.

Because Mechanica uses linear constraint equations to enforce the rigid rotations, rather than equations with trigonometric functions (such as sine and cosine), rigid connections should only be used for small rotation angles of rigidly connected entities. Rigid connections should always be used in this way, even when modeling for a large deformation analysis. Mechanica supports rigid connections for 3-D models only.

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AutoGEM Limits Settings

� Allowable Edge Angle – Angel created between any two element edges.

�Shells: 25 min – 150 max

�Solids: 5 min – 175 max

� Allowable Edge Turn – Maximum arc which an edge can span.

�Shells: 80

�Solids: 95

� Allowable Aspect Ratio – The longest edge divided by the shortest edge.

�Shells: 10

�Solids: 30

� Allowable Face Angle - Minimum and maximum angle between any two adjacent element faces.

�Solids 5 min – 175 max

AutoGEMThis is the automatic element generation. Underlying geometry is required. Note that in Integrated Mode, the mesh is generated by AutoGEM for the user at runtime. Limits

• The global density of the mesh can be controlled using the AutoGEM Element Limit Settings:• The Allowable Edge Angle defines the minimum and maximum values for the angle

between two edges. Bringing these values closer together creates smaller elements (mesh will be denser).

• The Allowable Face Angle defines the minimum and maximum value for the angle between two faces in a solid. Again, bringing these values closer together will create more and smaller elements.

• The Max Allowable Edge Turn: Geometric Elements map geometry exactly. Therefore elements will span arcs; this setting defines the maximum arc which can spanned by an element edge. A small value will create more elements.

• The Max Allowable Aspect Ratio: The aspect ratio of an element is defined as the ratio of its longest edge to its shortest. A square has an aspect ratio of 1. A smaller aspect ratio will create more elements for the same geometry.

• Note that changing these settings will greatly influence your run times as well as convergence characteristics (more on this when we look at convergence).

• These element settings are accessible in Integrated Mode under Mechanica>Settings> Auto EM Limits.

• Note that the default values are optimized for solid elements and will therefore necessitate changes for most shell models.

• Defaults based on much testing and validation.• Changing the settings may result in longer run times.• Poorly shaped elements may go to higher P-levels.• Element Limits form can be changed - AGEM Settings: Define/Review Element Limits.

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Demonstrations

� Using Mass, Spring, and Beam Idealizations.

� Using Shell Idealizations.

� Using Solid Idealizations.

� Using Rigid Connections.

� Using End and Perimeter Welds.


In this demonstration, I will

• Create beam, mass, spring, shell, and solid elements.• Simplify a design using shell idealizations.• Define rigid connections.• Define end and perimeter welds.


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Daily Skill Checks

Evaluate your progress:

� Achieve the course objectives.

� Use Pro/FICIENCY assessment questions.

� Apply Precision Learning.

Precision Learning• Learn: by listening to lectures, watching demos, and completing lab exercises.• Assess: your progress with Pro/FICIENCY assessment questions.• Improve: The next day the instructor reviews the exam results of the group and reviews

those topics that received the fewest correct answers.

Getting Started• Before lunch on the first day of class, set up the customer accounts. • When the customers are returning from lunch, refer them to the new Appendix. • Have them take the sample exam. • Review the results of the group and use as an icebreaker.

Daily ExamsDescription: For each course, 5 new 10 question Pro/FICIENCY exams based upon the topics covered each day.

How to use it:• Use the customer accounts already setup for the sample exam. • At the end of each day the customers take the 10 question exam relating to that days’ topics. • The next morning, review the results of the group. • Review those topics with the class that obtained the most incorrect answers.For E

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© 2002 PTC

Summary


� Describe the types and applications of idealizations.

� Simplify designs using idealization.

� Describe the purpose of rigid connections.

� Describe the purpose of end and perimeter welds.

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Module 5: Optimizing Models for Analysis







Mechanica• TBD

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Lesson Activities: Day Two

Demos & Exercises

Lectures ApplyingConstraints

Defining Mid-Surface for

Shells Adding NewMaterial to the

Library

Editing andDeletingMaterials

Using EdgeConstraints

Pro/FICIENCYDaily

Assessments

CreatingRegions

Creating VolumeRegions

ModelingStructural

Assemblies

Using PointConstraints

Using SurfaceConstraints

ConstrainingShell Models

ReferencingConstraints to

the User DefinedCoordinate

System

OptimizingModels forAnalysis

AssigningProperties to

Models

AssigningStructural and

Thermal MaterialProperties

Modeling 2-DPlane Stress

SimulatingApplied Loads

Creating CyclicSymmetry

Constraints

ApplyingGeneral Loads

Applying SpatialVariations to

Loads

Pressure andGravity Loads

Creating LoadDistributions

SuppressingCosmeticFeatures

Defining Mid-Surface Using

Auto Detect

Duration• Lecture: 30 mins• Demos (7): 15 mins• Labs (7): 1 hour 30 mins• Total: 2 hours

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Objectives


� Create Pro/ENGINEER Wildfire models for analysis.

� Use shell elements, solid elements, and regions.

� Model structural assemblies.

� Create 2-Dimensional models.

OverviewGeometry must be created in Pro/ENGINEER Wildfire before it can be analyzed and optimized. You must take into consideration the future activities, such as analysis, sensitivity, or optimization as the geometry is created. Therefore, proper modeling techniques must be used. To promote a flexible approach to analysis, a model may be defined with shell or solid elements. The way that a model is defined determines the type of elements Mechanica will use to model the part.

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Optimizing Models for Analysis

Solid Modeling

Solid ModelingA solid model consists of geometry that can be represented by solid elements like tetrahedrals, bricks, or wedges. In Integrated Mode, Mechanica uses only tetrahedrals for solid modeling, by default. As a rule, solid elements should be used when geometry is as thick and wide as it is long. The geometry’s thickness, however, can vary non-uniformly. In Integrated Mode, element creation is automatic and transparent, with the analysis beginning immediately after the mesh is created. The elements cannot be seen in Integrated Mode until after an analysis is complete (when viewing results). Thus, the user must enter the Independent Mode in order to view the elements prior to running an analysis.

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Suppressing Cosmetic Features

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Geometric Symmetry

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Modeling Shells

� Defining Mid-Surfaces�Defining shell pairs.

�Test the pairs compression.

�Verify the Use Pairs setting.

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Modeling Shells (cont.)

� Automatically create the mid-surface.�Auto Detect

�Shell features

�Thin Features

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Creating Regions

� Surface Regions

� Volume Regions

Creating RegionsRegions are used to apply loads and constraints to particular “footprints” on a model. Surface Regions may be created in Mechanica to apply loads and constraints to specific localized surface areas. Surface region creation is a two-step process.

• Defining the region boundary is accomplished either by creating a datum curve feature to represent the boundary or by sketching the datum curve on the fly. A separate datum curve feature can be created for each region that must be defined. Multiple region boundaries cannot be defined with only one datum curve feature.

• Creating the region consists of splitting a model surface into smaller surfaces, or regions, using the datum curve as a boundary.

As of Release 2000i, features such as Datum Points, Curves and Coordinate Systems can be created either in Mechanica or in Pro/ENGINEER Wildfire.Regions must be defined before mid-surfaces for shell modeling, because creating regions can invalidate existing shell pairs.While Surface Regions may be created in Mechanica to apply loads and constraints to specific localized surface areas, similar functionality allows solids to be split into three-dimensional regions. This is accomplished by creating Volume Regions. Creation of the Volume Region simulation feature is similar to that of the Cut feature in Pro/ENGINEER Wildfire. It can be created in parts or assembly models and inherits the material properties from the solid geometry within which they are created. Since results may be viewed by volume, these regions are beneficial in preparing a model for post processing, making it easier to view internal stresses, strains, etc. Since elements must be created within a volume region, they can also be used as an effective means of increasing mesh density when required.

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Structural Assemblies

� Mixed Meshing

� Interfacing Solid and Shell Elements

Structural AssembliesWhile understanding how parts behave individually is important, many times these parts are bolted or welded to other parts in an assembly. Their interaction may require analyzing the parts joined together in a structural assembly. Thus, the user must understand how to prepare an assembly for a shell model and for a solid model, as well understand the differences between shell and solid models.

Layers and GroupsLayer functionality is fundamental to organization and working efficiently in Pro/ENGINEER Wildfire. When a model is transferred to Independent Mode in Mechanica, there is an option for transferring Pro/ENGINEER Wildfire layers into Mechanica groups. The advantages of groups in Independent Mode are numerous. Groups facilitate ease of use when clicking or manipulating entities—especially elements. They are very useful in both model preparation, as well as in post-processing. For example, if a user wanted to view the stress fringe results for only one part in an assembly (as opposed to viewing the results on the entire assembly), the results can be viewed by group.

Mixed MeshingIn some cases, different element types can be combined. This is done simply by providing Mechanica with the geometry associated with the desired element type and by verifying settings. In Mechanica, if Settings> Use Pairs is checked on, any existing shell pairs will be meshed with shell elements, while any remaining unpaired part geometry will be meshed with solid elements. This functionality also works on single parts that are partially paired. Mixing element types is sometimes critical in balancing time savings with required accuracy.For E

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Modeling in 2-D

� Select the model type� Plane Stress (Structure) or 2-D Plate (Thermal)

� Plane Strain (Structure) or 2-D Unit Depth (Thermal)

�2-D Axisymmetric

� Select the geometry and reference coordinate system

� Define loads and constraints

� Define shell properties

Modeling in 2-D It is possible to define 2-D model types in Mechanica Integrated Mode. In Structure, the available 2-D model types are Plane Strain, Plane Stress, and 2-D Axis-symmetric. In the Thermal module the available model types are 2-D Plate, 2-D Unit Depth, and 2-D Axis-symmetric. The default model type is 3-D. The suggested procedure to define a model for a 2-D analysis in Integrated Mode is as follows:

• Define a reference coordinate system - To prepare the model for a 2-D analysis, a reference coordinate system must be created before the model type is changed from 3-D. The coordinate system can be created in Pro/ENGINEER Wildfire or in Mechanica.

• Select the model type - The model type should be selected before any loads, constraints, or material properties are defined on the model. Changing the model type from 3-D to 2-D causes all modeling entities to be deleted. The available model types are:

• 3-D - Use this option if any aspect of the model lies out of the WCS XY plane. Most models will be 3-D. This is the default model type.

• Plane Stress (Structure) or 2-D Plate (Thermal) - Models should be thin and all modeling entities (properties, constraints, loads, and geometry) must lie in the XY plane of the reference coordinate system.

• Plane Strain (Structure) or 2-D Unit Depth (Thermal) - Model should be sufficiently long such that strain in the transverse z-direction is negligible. All modeling entities must lie in the XY plane of the reference coordinate system.

• 2-D Axisymmetric - Geometry and all modeling entities should be symmetric about anaxis. All modeling entities must lie in the positive x portion of the XY plane of the reference coordinate system.

• Select the geometry and reference coordinate system - Once a model type is selected, the user is required to select the geometry and reference coordinate system for the model. If either selection is invalid, the model type will not be changed.For E

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Demonstrations

� Suppressing Cosmetic Features.

� Defining Mid-Surface for Shells.

� Defining Mid-Surface Using Auto Detect.

� Creating Regions.

� Creating Volume Regions.

� Modeling Structural Assemblies.

� Modeling 2-D Plane Stress.



• Suppress structurally insignificant features• Use shell elements, solid elements, and regions in Mechanica.• Define mid-surfaces for shell modeling.• Create a shell model using auto detect.• Create regions.• Create volume regions.• Model simple structural assemblies.• Model a 2-D plane stress plate.


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Summary


� Create Pro/ENGINEER Wildfire models for analysis.

� Use shell elements, solid elements, and regions.

� Model structural assemblies.

� Create 2-Dimensional models.

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Module 6: Assigning Properties to Models







Mechanica• TBD

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Demos & Exercises




Library



Pro/FICIENCYDaily

Assessments


Auto Detect

CreatingRegions


ModelingStructural

Assemblies






System



Models






Constraints



Loads




Duration• Lecture: 15 mins• Demos (3): 15 mins• Labs (3): 30 hour• Total: 1 hour

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Objectives


� Assign structural and thermal properties to parts.

� Define linear and nonlinear properties.

� Create materials libraries.

� Define temperature-dependent material properties.

� Edit and delete material properties.

OverviewBefore running any Mechanica analysis you must have a thorough understanding of some basic of mechanics of materials. This includes structural material properties and engineering units. You should be able to answer some of these questions.• What is the value of density and what are its units? • What is the value of Young's Modulus and what are its units?• What is Poisson's Ratio and what are its units?• What is the coefficient of Thermal Expansion and what are its units.Engineering units and materials must be set before running analyses in Mechanica. If a material does not exist in the Mechanica material library, then you can add additional materials to a custom material library.

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Model Properties

Properties

� Materials

� Beams

� Shells

� Solids

� Mass

� Springs

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© 2002 PTC

Units

Systems of Units

� Principle Unit System� F = ma must be satisfied

� Force = Mass * Length / Time2

� Principle Unit System defined in Pro/ENGINEER Wildfire.

� Custom Units can be created.

� All parts and assemblies need to have same Principal Unit System.

� Mechanica checks for consistency and prompts to convert.

� For IPS and FPS, Mass = (weight density/gc) * volume

� gc = 32.2 (FPS) and gc = 386.4 (IPS)

Systems of Units• Four basic quantities are required to describe a structural system: Force, Length, Time and

Mass. • You must specify units for three out of the four quantities. The units for the fourth quantity is

determined in terms of the three others according to (a dimensional analysis on) Newton’s Law: F = ma . Mechanica has four basic unit systems (MKS, mmNs, FPS, IPS).

• Example: Consider a stress analysis for a computer chip. Assume we select millimeters (mm) for units of Length, Newtons (N) for force and seconds (s) for units of Time. Substituting units in the equation F = m a and recalling that N = kg m/sec2 , we have:

Kg m / sec2 = mass_unit * mm/ sec2 Ð mass_unit = 1000 kg !! or metric TonnesHaving chosen mmNs as a unit system implies that mass for this computer chip will be expressed in metric tonnes.

Principle System

Length

Time

Temp

Mass/Force

Derived Mass/Force

inch lbm second

(Pro/E default)

in sec °F lbm (mass) lbm - in/sec2

(force)

MKS m sec K kg (mass) kg - m/sec2 = N (force)

CGS cm sec °C g (mass) g - cm/sec2 = µN (force)

mmNs mm sec °C N (force) 1000 kg = tonne (mass)

FPS ft sec °F lbf (force) lbf - sec2/ft = slug (mass)

IPS in sec °F lbf (force) lbf - sec2/in (mass)

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Material Properties

Basic Mechanics of Materials

� Young’s Modulus: E�Slope of Stress/Strain curve.

� Poisson’s Ratio�n = e lateral / e axial

Ultimate StressYield Stress

Strain εεεε

Stress σσσσ

P

P

Basic Mechanics of MaterialYoung’s ModulusThis slide shows a sketch of a general stress-strain curve. This curve is created by applying an increasing axial load to a test specimen and by measuring the load and deformation simultaneously. From this data, the stress (the vertical axis) can be plotted against the strain, or percent elongation (the horizontal axis). As the axial load is increased, the strain increases in a linear fashion. The slope of this line is called Young’s Modulus. The units for Young’s Modulus are stress (load/area) over strain (change in length/original length), or in other words, the same units as stress.

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Beam Properties

Beam Properties

� Required Beam Properties:� Beam Section

● Beam Y and Z axes are determined when cross section is defined.● Can be sketched in integrated mode.

� Beam Orientation● X axis is aligned with the supporting curve.● Align beam local Y axis with one of the “Global” axes.● Offset is for beam centroidal axis.

� Beam Release● Can create joints between beams.● Beams which share endpoints are assumed to be welded.

� Material

Z

Y

Beam PropertiesBeam Elements are represented as one-dimensional lines in space. The following properties

must be provided:1. The Beam section defines the cross section geometry and/or properties for beam

elements.2. The Beam orientation specifies the orientation of the section relative to the model.3. Beam release – Allows the definition of joints between beam elements. This option will

be discussed in further detail below.4. A Material must be specified for the element.

• In Integrated Mode, Mechanica displays an icon representing the beam section and orientation as they have been specified.

Beam Sections• Beam Section Properties are specified using the following fields:

1. Section Name: This allows the user to define a library of sections for further reference.

2. Description: Use this field to document the section type for easy reference. 3. Type: Specify the type of section to be defined (for example:Channel, I-Beam).

This will determine which geometric inputs are needed to fully define the section.

• When the “Review Properties” option is selected, Mechanica will calculate and display area and moments of inertia for the specified section.

• The specification of section properties implies the definition of a local coordinate system for the beam element. By default, the X-axis is oriented along the longitudinal direction. The Y and Z axis directions are defined using the “Beam Orientation” element property.

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Shell Properties

Shell Properties

� Required Shell Properties:� Material

� Shell Property● Homogeneous (uniform thickness)● Laminate Stiffness (input “ABD” matrix for composites)● Laminate lay-up (input ply lay-up information, “ABD” matrix is calculated)

� Material Orientation (laminates only)

� Shell thickness is automatically assigned to the mid-surfaces.

Shell PropertiesShell elements require the following properties:

1. Thickness – A shell element must be associated with a thickness in order to be fully defined geometrically. In Integrated mode this is done at the pair definition stage (the thickness of the compressed feature is known). In Independent Mode, the thickness is entered in a shell definition form.

2. Material – In Independent mode, the material property should be placed on surfaces when possible.

3. Shell Property – Shell Elements can be used to model laminates. Additional properties are necessary to define a laminate, namely the equivalent stiffness matrices (A,B,D). These can be entered directly or calculated by Mechanica given a laminate specification (ply thickness, ply material and orientation).

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Solid Properties

Solid Properties

� Required Solid Properties� Isotropic

● (E1 = E2 = E3)

� Orthotropic ● (E1 ≠ E2 ≠ E3)

� Transverse Isotropic● (E1 ≠ E2 = E3)

� Material Orientation �Orthotropic and Transverse Isotropic only.

Solid Properties• Being the most expensive in terms of run time, solid elements are used to model parts

for which none of the beam, shell or 2D assumptions apply.• For reliable results, solid elements with aspect ratios greater than 30:1 should not be

used.• The following types of solids can be created:

• Brick (or hexahedron) with six quadrilateral faces and eight points. • Wedge (or pentahedron) with two triangular faces, three quadrilateral faces, and

six points.• Tet (or tetrahedron) with four triangular faces and four points.

• In Integrated Mode, mesh generation occurs "behind the scenes", and meshes are created using Tetrahedral elements only.

• Remember to turn off the setting of "Use Pairs“.

Guidelines for Creating Solids• To ensure good point, edge, and face connectivity (for example: to avoid cracks in

models), hand meshed elements should not be mixed with Auto GEM elements.• Solids must not overlap. • Adjacent elements must have edge-to-edge connectivity. Any unmatched edge creates a

crack in your model (discussed in the next lecture). Divide large arc spans into separate segments by placing points along them or by splitting them before selecting them as edges.For E

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Mass and Spring Properties

Mass Element Properties

� Properties for masses.� Mass and mass matrix.

Spring Element Properties

� Spring Stiffness

� Spring Orientation� Align Spring local Y axis with one of the global axes; WCS Y axis is the default.

Mass Element Properties• Mass elements are used to simulate components in a system which contribute mass but

no stiffness. A typical example is a motor on a robotic arm.• Two properties can be used to define a mass element:

1. The Mass Value must be entered in appropriate units (remember this is mass, notweight. You must divide weight by gravity to get the appropriate mass value).

2. Values for the Moments of Inertia are used for analyses where inertial loads are considered. Using moments of inertia is an accurate way to simulate the presence of complex parts without modeling their geometry.

• Note that this representation of parts (Mass and Inertia) is similar to the rigid body dynamics representation in Mechanica Motion.

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Demonstrations

� Assigning structural and thermal material properties.

� Adding new materials to the library.

� Editing and deleting materials.


In this demonstration, I will

• Assign Structural and Thermal Material Properties.• Add new Materials to the Mechanica library.• Edit and delete materials.


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Summary


� Assign structural and thermal properties to parts.

� Define linear and nonlinear properties.

� Create materials libraries.

� Define temperature-dependent material properties.

� Edit and delete material properties.

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1

Module

77Applying Constraints

IntroductionConstraints and loads are configurable features within Mechanica that simulate the real-world environment that you expect your model to encounter. Mechanica uses this information to calculate the behavior of your model during analyses and sensitivity studies.

Objectives After completing this module, you will be able to:

Create different types of constraints.

Constrain design models in Mechanica.

Set the active coordinate system.

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Module 7: Applying Constraints







Mechanica• TBD

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Demos & Exercises




Library



Pro/FICIENCYDaily

Assessments


Auto Detect

CreatingRegions


ModelingStructural

Assemblies






System



Models






Constraints



Loads




Duration• Lecture: 30 mins• Demos (6): 15 mins• Labs (6): 1 hour 15 mins• Total: 2 hour

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Objectives


� Create different types of constraints.

� Constrain models in Mechanica.

� Set the active coordinate system.

OverviewConstraints and loads are Mechanica entities that simulate the real-world environment that the model is expected to encounter. A model’s stress and strain distributions depend on the constraints and loads applied to a model.

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Applying Constraints

Constraints

� Constraining Degrees of Freedom

� Utilizing Symmetry

� Example application

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What is the goal?

� Simulate the real world conditions.

� Eliminate rigid-body motion.

Apply Constraints to:

� Points

� Curves

� Surfaces

Degrees of Freedom (DOF)

� Translation & Rotation.

� Beams, Shells, Solids.

� Constrain DOFs or Enforce Displacements.

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Example: Applying Constraints

How do we constrain this model?

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Example: Applying Constraints

� Constraint the hole.

� Constrain the edge.

� Constrain three points of use symmetry.

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x

y


Symmetry

� Use If:� Geometry

� Properties

� Loads

�Constraints

� Are all symmetrical about the same cutting plane?

� Symmetry decreases:� Model size.

� Your time.

� Time to solve.

� Disk space requirements.

Is there a plane of symmetry?

Constraints (cont.)• Mechanica allows the definition of three types of constraints:

• Point• Edge/Curve• Face/Surface

• The constraint definition dialog box contains the following fields:• Constraint Set : Constraints are grouped into constraint sets. This allows the user to

define multiple constraints for the same model. Specify the Set Name to which this constraint belongs (a constraint can only belong to one Set). This is used later on at the analysis definition stage. Only one Constraint Set can be applied to an analysis.

• Fixed: Specify which degrees of freedom are fixed for the selected entity.• Free: Specify which degrees of freedom are free for the selected entity • Displacement: Specify a prescribed displacement for the selected entity. This is useful

when the input to the model is a known displacement. • Based on the above fields, Mechanica will display an icon with flags (free or fixed)

representing each degree of freedom for the selected entity. • Constraints are applied in the current coordinate system. User defined coordinate systems

can be used for complex orientations. • Use regions (Integrated Mode) or surfaces (Independent Mode) to constrain only a portion

of an entity. • In Independent Mode, constraints should be applied to the geometry (the mesh can be

regenerated during sensitivity and optimization runs). Note that in Integrated mode, the mesh is only created at run time, and therefore all modeling is done on the geometry.

• In Integrated Mode, 1. When using shells, some surfaces will be compressed as pairs are defined. These

surfaces can not be constrained. 2. Constraints applied in part mode are not carried over in assembly mode.

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Cyclic Symmetry

� Use if the entire model:�Geometry

�Properties

�Loads

�Constraints

� Can be reproduced by copying a pie shaped wedge about an axis an integer number of times.

� Apply cyclic symmetry constraint before using AutoGEM to create mesh.

� For modal and buckling analysis, any modes that are not cyclically symmetric will not be calculated.

Cyclic SymmetryA cyclic symmetry constraint allows a section of a cyclically symmetric model to be analyzed , while simulating the behavior of the whole part or assembly. This relational constraint greatly reduces meshing and analysis time. The original model (part or assembly) must exhibit cyclic symmetry, that is, the cut section can be copied about a common axis a specified number of times to reproduce the whole model. (The number of times must be an integer.) The model must exhibit cyclic symmetry in all of the following:

• Geometry • Loads • Constraints • Material type and orientation

In Mechanica, a cyclic symmetry constraint prescribes rotation and displacement on two boundaries to be the same. In the Thermal module, a cyclic symmetry constraint prescribes the temperature distribution on two boundaries to be the same.

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� Constraints applied in current coordinate system.

� Use regions to constrain partial surfaces.

� Choose the appropriate level of detail.

� Apply in assembly mode.

� Don’t apply to entities that get compressed away in shell models.

Assume - in the assembly, this bracket is bolted to a large block and a horizontal load is applied to the small tab at the top of the bracket. (a picture of such an assembly would be great)We need to verify that the stress in the fillet will not exceed yield under this loading.How should we constrain this model?One choice – fully constrain inner hole surfaces – what will happen? Is this realistic for the behavior of the hole? No, we will see artificial stress concentrations. But, are we concerned with the stress around the hole? No. So this will probably be fine.Choice two – if we are not concerned with the stress around the holes, we could even suppress the holes and use surface regions to replace them. Constrain the surface regions (perhaps top and bottom). Again, this will create artificial stress concentrations. Are we concerned about these?Choice three – what if we are concerned with the stresses around the holes? How can we model this ‘bolt-type’ constraint?The slide says that constraints are applied in a current coordinate system. Describe or demo what they will do in the exercises. This will allow the hole to flex much like it would in reality. This will reduce artificial stress concentrations around the hole.The choice of which constraint scheme to use is up to you – what are you concerned about?

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Demonstrations

� Using Edge Constraints.

� Using Point Constraints.

� Constraining Shell Models.

� Referencing Constraints to the User Defined Coordinate System.

� Creating Cyclic Symmetry Constraints.


In this demonstration, I will:• Use edge and point constraints.• Constrain a shell model in Mechanica.• Set an active coordinate system.


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Summary


� Create different types of constraints.

� Constrain models in Mechanica.

� Set the active coordinate system.

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Module 8: Simulating Applied Loads







Mechanica• TBD

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Demos & Exercises




Library



Pro/FICIENCYDaily

Assessments


Auto Detect

CreatingRegions


ModelingStructural

Assemblies






System



Models






Constraints



Loads




Duration• Lecture: 30 mins• Demos (5): 15 mins• Labs (5): 45 mins• Total: 1 hour 30 mins

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Objectives


� Create different load types.

� Describe the difference between point, edge, and surface loads.

� Describe when to use each load type.

OverviewMechanica provides a wide variety of load types. Loads must be applied to at least one area of a model in order for Mechanica to perform most types of analyses.

In this module you will:• Create Point, edge, and surface loads.• Apply spatial variations to loads.• Apply varying load directions and magnitude.• Apply pressure and gravity loads.• Apply spatial variations to loads.• Differentiate between point, edge, and surface loads.

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Simulating Applied Loads

Loads

� Distributions�Total load.

�Total load applied at point.● Torsional loads on solids.

�Force per unit area.

� Spatial Variation�Uniform.

� Interpolated over entity.

� Interpolated point loads.

�Function of Coordinates.

Loads• Mechanica allows the definition of a variety of load types: • Point, Edge/Curve, Face/Surface.

• Bearing loads to simulate contact between cylindrical surfaces (Hertzian contact load distribution).

• Centrifugal and gravity loads to simulate body forces.• Pressure loads (always perpendicular to the applied surface).• Temperature loads to compute thermal stresses.

• The load definition dialog box contains the following fields: • Load Set : Loads are grouped into load sets. This allows the user to isolate the effect

on various loads on the model. Specify the Set name to which this load belongs (a load can only belong to one Set). This is used later on at the analysis definition stage. Multiple load sets can be applied to one analysis.

• The Distribution field defines how the load magnitude is interpreted (mathematically): 1. Total load - distributes the load along the length or area of the selected entity such

that the integral of the load over the selected entity equals the total prescribed value.

2. Total load at point (TLAP) – computes and applies the equivalent shear, moment and torsion of a point force acting at a specified distance from a surface.

3. Force per unit area/length – allows the user to specify a load per unit length, or load per unit area.

• The Spatial Variation field specifies how the load is applied over the entity:1. Uniform - The load has no spatial variation.2. Interpolated Over Entity – Interpolation points with an associated scaling factor

are specified3. Function of Coordinates – The load is distributed as a function of a specified

coordinate value in the current coordinate system.

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Loads Types

� Point

� Edge/Curve

� Surface

� Pressure

� Bearing

� Gravity

� Centrifugal�Angular velocity

�Angular acceleration

� Temperature�Global Temp

�MEC/T Temp

�External Temp

Surface Load Applied at a Point Pressure Load

Bearing Load

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Loads

� Loads applied in current coordinate system.

� Do not apply to entities that get compressed away in Integrated Mode shell models.

� Apply loads to assemblies while in Assembly Mode. Loads applied in Part Mode are ignored in assemblies.

� Use regions to load partial surfaces in Integrated Mode.

Loads (cont.)• Loads are applied in the current coordinate system. User defined coordinate systems can

be used for complex load orientations. • Use regions (Integrated Mode) or surfaces (Independent Mode) to load only a portion of an

entity • Unlike the “Force per Unit Area” option, the “Pressure” load type can only act normally to a

surface. • Note that in Integrated mode, the mesh is only created at run time, and therefore all

modeling is done on the geometry. • In Integrated Mode

1. When using shells, some surfaces will be compressed as pairs are defined. These surfaces can not be loaded.

2. Loads applied in part mode are not carried over in assembly mode (since parts are usually loaded to simulate the presence of other components).

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Singularities

� Stress = Force/Area = Infinite (Singular)� If Area = 0 and F ≠≠≠≠ 0

� A load or constraint must act on an AREA to avoid singularity.

OKOKN/ASurface or Edge

NoOKOKCurve or Edge

NoNoOKPoint

SolidsShells BeamsLoad and Constraint Types

Singularities• Stress can be defined as load over area: s = F/A. As a result, if any load is applied on an

entity that has no area, the stress becomes infinite. This is called a singularity.• Notice that singularities can be created by applying loads or constraints (applying a constraint

to an entity creates a reaction force on that entity). We therefore have to ensure that loads and constraints are applied to entities which have area associated to them.

• The table below specifies which load/constraint types are acceptable for each element type.

• Point loads/constraints can only be applied on beam elements, where they are considered to act on the associated cross-section (defined as an element property). A point load on a shell or on a solid will create a singularity.

• Edge loads/constraints can be applied to beam elements (again, the cross-section property can accommodate loads) as well as to shell elements (where they are considered to act on the area defined by the edge and the shell thickness)

• An edge load/constraint on a solid element will create a singularity.• Surface loads can be applied to shell and solid element types (which both have area) but

not to beam elements (no surface to pick).• 3-Point constraints (refer to PCL 12) violate the above rules. Valid 3-Point constraints can get

away with constraining points on solids and shells because they constrain locations where the net force is zero. Therefore, in the equation s = F/A, both F and A are zero and stress goes to zero (no singularity).

FiniteFiniteN/ASurface or Face

∞FiniteFiniteCurve or Edge

∞∞FinitePoint

SolidsShells BeamsLoad/Constraint Type

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Demonstrations

� Applying General Loads.

� Applying Spatial Load Variations.

� Varying Load Direction and Magnitude.

� Applying Pressure and Gravity Loads.

� Creating Load Distributions.


In this demonstration, I will:• Create point, edge, and surface loads.• Apply spatial variations to loads.• Apply varying load directions and magnitude.• Apply pressure and gravity loads.• Apply spatial variations to loads.


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Daily Skill Checks










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Summary


� Create different load types.

� Describe the difference between point, edge, and surface loads.

� Describe when to use each load type.

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Module 9: Creating and Running Structural Analyses







Mechanica• TBD

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Lesson Activities: Day Three

Demos & Exercises

LecturesPro/

FICIENCYDaily

Assessments

ComparingMPA and SPA

Results


EvaluatingAnalysisResults

EvaluatingAnalysis Results

Setup and Run aStatic Analysis

Setup and Run aThermal Analysis

Combine Structuraland Thermal

Analysis

Creating andRunning Structural

and ThermalAnalyses

Duration• Lecture: 1 hour• Demos (3): 30 mins• Labs (3): 1 hour 30 mins• Total: 3 hours

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Objectives


� Setup models for structural and thermal analyses.

� Run structural and thermal analyses and view the results.

� Transfer thermal loads into structure to determine thermal stresses.

� Create thermal/mechanical and gravity loads.

� Create a static analysis with multiple load sets.

� Create results windows with different combinations of load sets.

OverviewA Structural analysis is the calculations of a model’s response to a loading condition and its boundary conditions. Mechanica provides several types of analyses that span a wide range of actual loading and boundary conditions.Static analysis is performed on a structural product to find the stress and displacement distribution over a structure.Mechanica will be used to investigate the performance of an industrial controller module, which has had reliability problems due to the CPU chip overheating.The controller module consists of a printed circuit board (PCB) with a CPU, several ICs, and some on-board power-supply components - an AC power connector, transformer, and a small vertical heat sink for a voltage regulator. Many electrical components are not included in the model - only those that generate, conduct, absorb or dissipate significant amounts of heat are important for the analysis.First, a structural analysis will be performed to evaluate the stress due to the weight.

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Creating and Running Analyses

Analysis Types

� Static

� Modal

� Pre-stress static

� Pre-stress modal

� Buckling

� Dynamic time

� Dynamic frequency

� Dynamic random

� Dynamic shock

� Fatigue

Analysis Types• Static: Calculates deformations, stresses and reactions in response to specified loads and

subject to specified constraints.• Modal: Calculates the natural frequencies and mode shapes of your model.• Pre-Stress Static: Enables the user to account for the presence of pre-stress in a structure

under static load (pre-stress can strengthen or weaken a structure). A Static analysis must be performed prior to the Pre-Stress analysis.

• Pre-Stress Modal: Enables the user to account for the presence of pre-stress in the determination of natural frequencies and mode shapes of a structure.

• Buckling: Uses results from a previously defined static analysis to determine the critical magnitudes of loads at which a structure will buckle, as well as the model’s stresses, strains, and deformations at the onset of buckling. Note that post-buckling behavior can not be modeled using this analysis type.

• Contact: Calculates deformation, stresses, strain, contact pressures and total contact area in response to specified loads and subject to specified constraints. Contact regions must be defined prior to running the analysis. Note that this is a nonlinear analysis as the contact area (and therefore stress) varies with the applied load.

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Analysis Dialog Box

� Assign an analysis name.

� Pick analysis type.

� Pick one constraint set.

� Pick one or more load sets.

� Pick convergence method.

� Set up convergence criteria.

Analysis FormThe analysis definition form requires the following input:

• Analysis Name: This name will be used to create the results directory.• Type: There are ten different analysis types available in Mechanica Structure. These analysis

types are described in the next slide.• Constraint Set: Select a single constraint set for this analysis. Only one constraint set can be

used.• Load Set: Select one ore more load sets for this analysis. • Convergence Method: Pick a convergence method, SPA or MPA. These will be explained

shortly.• Convergence Criteria: Specify a percentage for convergence and a set of quantities on

which to converge. • Excluded Elements: This option is only available in Independent mode. It allows the user to

exclude troublesome elements from the convergence process, thereby ignoring known singularities (high-stress areas).

• Polynomial Order: Specify the minimum and maximum polynomial order for this analysis. This can be used to stop an analysis at a particular p-level, inspect the results and then restart it to complete the convergence process.

• Plotting Grid: Specify the number of intervals along edges at which results will be computed. This topic will be covered in detail in slide A&R-7.

• Calculate: This option allows the user to toggle “off” unwanted results.

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Analyses Types:

� Static

� Calculates deformations, stresses, and reactions in response to specified loads and constraints.

� Modal

� Calculates natural frequencies and mode shapes of model.

� Pre-stress Static

� Pre-stress Modal

High stiffness

Low stiffness

Pre-stress Static Type Analysis• Accounts for the presence of pre-stress in a structure under static load. Must perform a static

analysis first.• Accounts for the presence of pre-stress in the determination of natural frequency and mode

shapes of a structure. Must perform a modal analysis first.

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� Buckling� Uses results from a static analysis to determine the critical magnitudes of loads at which a structure will buckle, as well as the model’s stresses, strains,and deformations at onset of buckling.

� No post-buckling behavior.

displacement

crit

crit

Buckling Type Analysis• Non-linear.• Uses results from a static analysis to determine the critical magnitudes of loads at

which a structure will buckle, as well as the model’s stresses, strains,and deformations at onset of buckling.

• No post-buckling behavior.

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� Contact:� Calculates deformation, stresses, strain, contact pressures, and total contact area in response to specified loads and subject to specified constraints.

� Contact regions must be defined prior to running the analysis.

Load

Contact Area

Contact Area

Load

Contact Type Analysis • Non-linear.• Calculates deformation, stresses, strain, contact pressures, and total contact area in

response to specified loads and subject to specified constraints.• Contact regions must be defined prior to running the analysis.• As load increases, contact area changes non-linearly.

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�Large Deformation Analysis

� Use if:● Deformation due to load is large ● Small Strain

� Only available for Static analysis.

� Must use 3D or 2D solid elements.

� Only models with isotropic material properties allowed.� No temperature dependent properties are allowed.� Loads must be with respect to WCS.� No bearing loads or loads as a function of coordinates are allowed.� Loads should not be near critical buckling loads.

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Dynamic Type Analyses

� Dynamic Time� Calculates displacements, velocities, accelerations, and stresses in the model in response to time-varying loads (transient response).

� Dynamic Frequency� Calculates amplitude and phase displacements, velocities, accelerations, and stresses in response to cyclic loading.

� Dynamic Random� Calculates RMS (root-mean square) responses based on loading conditions which use a statistical random function. Input is Power Spectral Density plot.

� Dynamic Shock� Calculates maximum values of displacements and stresses in response to base excitation (seismic).

Dynamic Analysis Type• Dynamic Time - Calculates displacements, velocities, accelerations, and stresses in the

model in response to time-varying loads (transient response).• Frequency - Calculates amplitude and phase displacements, velocities, accelerations, and

stresses in response to cyclic loading.• Random – Calculates RMS (root-mean square) responses based on loading conditions

which use a statistical random function. Input is power spectral density plot.• Shock - Calculates maximum values of displacements and stresses in response to base

excitation (seismic).

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Thermal Analyses

� Steady State Thermal� Calculates temperatures through a structure given heat loads, convection conditions.

Analysis Type: Thermal• Steady State Thermal - Calculates temperatures through a structure given heat loads,

convection conditions, and known temperatures.

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Thermal Analyses (cont.)

� Transient Thermal� Calculates time varying temperatures through a structure given time-varying heat loads and/or convection conditions.

T

time

Analysis Type: Thermal• Transient Thermal - Calculates temperatures through a structure given time-varying heat

loads and/or convection conditions.

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Demonstrations

� Setup and Run a Static Analysis.

� Setup and Run a Thermal Analysis.

� Combine Static and Thermal Analysis.


In this demonstration, I will:• Setup and run a static analysis.• Setup and run a thermal analysis.• Combine static and thermal analysis.


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Summary


� Setup models for structural and thermal analyses.

� Run structural and thermal analyses and view the results.

� Transfer thermal loads into structure to determine thermal stresses.

� Create thermal/mechanical and gravity loads.

� Create a static analysis with multiple load sets.

� Create results windows with different combinations of load sets.

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Module 10: Comparing MPA and SPA Results







Mechanica• TBD

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Demos & Exercises

LecturesPro/FICIENCY

DailyAssessments


Results







Analysis


and ThermalAnalyses

Duration• Lecture: 15 mins• Demos (1): 30 mins• Labs (1): 1 hour• Total: 1 hour 45 mins

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Objectives


� Create a Single-Pass Adaptive analysis.

� Create a Multi-Pass Adaptive analysis.

� Describe the difference between Single-Pass Adaptive (SPA) and Multi-Pass Adaptive (MPA) analyses.

OverviewThere are two methods Mechanica can use to elevate these polynomials in order to converge the solution: the MPA approach, and the SPA approach.SPA convergence applies to static, modal, buckling, and contact analyses of all element types. Models may consist of isotropic and/or orthotropic materials. While the single-pass adaptive option is available for contact analysis, we do not normally recommend its use because it can increase run time.Mechanica runs a first pass at p=3 and determines a local estimate of stress error. Using this error estimate, Mechanica determines a new p-order distribution and performs a final pass.In general, use SPA convergence when it is available. Larger models run with SPA convergence typically require less disk space. Also, SPA convergence yields comparable results to MPA convergence of 10% with generally shorter run times.With SPA analysis, you do not control the convergence tolerance, but you do need to examine the stress error estimates reported in the run summary. If these error estimates are acceptable, then continue to use single-pass adaptive convergence for efficiency.If the error estimates from the SPA convergence tolerance are not acceptable—for example, the stress error estimates are too large—then switch to the MPA convergence strategy for subsequent design studies.When you run a design study, using MPA, Mechanica performs calculations and increases the polynomial order for each element edge until the convergence criteria are satisfied. (The polynomial level for edges on which beams and 2-D shells lie begins with either the third order or the order you enter on the analysis definition dialog box, whichever is higher). An analysis converges when the difference in the results of the current pass and the previous pass is within the percentage you specify under Convergence.This module will discuss the difference between the two methods Mechanica can use to elevate the solution, the MPA approach, and the SPA approach.

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Comparing MPA and SPA Results

Convergence: Single-Pass Adaptive

� Significantly faster than multi-pass adaptive.

� Requires fewer resources.

� Proven accuracy.

� Less feedback on solution quality.

Convergence: Single-Pass Adaptive• Solid and shell element types.• Beams, if a shell or solid is present.• Multiple may include both orthotropic and isotropic materials. • All analysis types except pre-stress static.• Steady State Thermal.

• The SPA is significantly faster than MPA, requires fewer computer resources and provides results within 10% of MPA.

• The drawback of SPA is that the user has less information on the quality of the solution and must therefore rely on experience to detect improperly converged results.

• The convergence process for SPA is described below:1. Mechanica solves the problem at p-level 3 and estimates local stress errors. 2. New polynomial orders are assigned to edges based on the magnitude of local stress

errors.3. The problem is solved with the updated polynomial orders and results are outputted.

• The local stress errors are determined based on the difference between stress values computed using two different methods (super-converged stress and single element stress results).

• A percentage is then defined for each element and compared to a target internal error estimator. The target error estimator % is set internally and has been determined experimentally.

• Based on the ratio between actual and target stress error, the number of degrees of freedom (DOF’s) needed to accurately solve for the stress can be determined. The p-level is then increased to the level required to solve the number of DOF’s.

• This method of improving stress accuracy and estimating stress error is based on the work by Zienkiewicz and Zhu ( "The Superconvergent Patch Recovery and A Posteriori Error Estimates. Part 1: The Recovery Technique", International Journal for Numerical Methods in Engineering, Vol. 33, p. 1331 (1992)).

• The final RMS stress error reported in the summary file is calculated by sampling the local error estimates (the same as those used to update polynomial orders).

• If the iterative solver is used, Mechanica first solves the problem at polynomial order 2 with the block solver, then uses the iterative solver for the p-level 3 pass and for the final pass where edge p-levels have been updated to their final values.

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Convergence: Multi-Pass Adaptive (MPA)

p-pass 1All Edges atp = 1

p-pass 2All Edges atp = 2

p-pass 3Various Edgep-levels

p-pass 7Various Edgep-levels

P-pass continues until percentage change is satisfied or until maximum p-order is reached.

Convergence: Multi-Pass Adaptive• A solution is considered to have converged when the results are independent of mesh

density and p-levels. More specifically, in the context of Mechanica, a solution is considered converged when results from the current and previous pass only differ by a user-defined percentage.

• Two convergence methods are available in Mechanica: Single-Pass Adaptive (SPA) and Multi-Pass Adaptive (MPA).

• The process of a Multi-Pass Adaptive run is described in the following example. Consider a static analysis on a plate with a hole and assume we have selected the MPA Convergence Method with 5% convergence on Displacement, Strain Energy and RMS Stress.1. In the first pass, the analysis is performed with all edges at p-level 1 (linear shape

function). Results for displacement, Strain Energy and RMS Stress are stored. 2. In the second pass, the analysis is performed with all edges at p-level 2 (quadratic

shape function). Results are compared with the previous pass. A convergence check is now performed on edges and elements. Edges for which previous and current results defer by more than 5% are upgraded to p-level 3. Elements for which previous and current results defer by more than 5% have all their edges upgraded to p-level 3.

3. The p-passes are repeated until the convergence percentage is satisfied for all specified quantities or until the maximum p-level is reached.

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Checking Convergence Information for SPA

� Check summary file (*.rpt).� Look at the last pass % convergence values.

� Maximum Edge Order should be less than 9.

� Resultant loads should equal the applied load.

� View Fringe Plots� View plots with Average and Continuous Tone OFF.

� Look for discontinuities between elements.

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Checking Convergence Information: MPA

� Check summary file (*.rpt)�Look at the last pass % convergence values specially for measures of interest.

�Maximum Edge Order should be less then 9.

�Resultant loads should equal the applied load.

� Check Convergence Plots�Generate P-plots for all quantities of interest/concern.

�Graph should asymptotically approach a single value. The last two values should be nearly identical.

� View Fringe Plots�View plots with Average and Continuous Tone OFF.

�Look for discontinuities between elements.

Checking Convergence InformationHow do we know if the solution is converged? Evaluating the quality of a solution is critical. The following procedure is recommended for MPA convergence:

1. From the Run Menu, select “Summary” (also available by editing the *.rpt file). Scrolling the file to the last p-pass, you want to verify the following: a) The maximum edge order in the model. A value of 9 indicates that at least one edge

went to the maximum edge order. This is a potentially un- converged result.b) A message indicates whether the analysis has converged within the specified

tolerance. This message is not sufficient to determine the quality of the solution. The table of convergence percentages should have all values close to ~10%.

c) The resultant force on the model should be equal to the applied load.

2. Generating Convergence Graphs is the best way to determine the quality of the solution. You need to create a graph for each quantity on which convergence-checks were performed. Convergence graphs can be generated by plotting quantities of interest (for example: max. displacement, max. stress) against p- ass. A good convergence graph has both of the following characteristics:a) Clear trend approaching a value. b) Ends with a zero slope (for example: last two passes results are identical).

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Demonstration

� Compare MPA and SPA Results.

Demonstrations ( minutes)


• Create a static analysis.• Choose SPA as integration method.• Create another static analysis.• Choose MPA as integration method.• Run both analyses and compare the results.


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Summary


� Create a Single-Pass Adaptive analysis.

� Create a Multi-Pass Adaptive analysis.

� Describe the difference between Single-Pass Adaptive (SPA) and Multi-Pass Adaptive (MPA) analyses.

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Module 11: Evaluating Analysis Results







Mechanica• TBD

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© 2002 PTC


Demos & Exercises

LecturesPro/FICIENCY

DailyAssessments


Results







Analysis


and ThermalAnalyses


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© 2002 PTC

Objectives

After completing this module, you should know how to:

� Describe the basic steps for building a Pro/ENGINEER Wildfire model for analysis.

� Set up and run a thermal analysis and a structural analysis, simultaneously.

� Set up and run a modal analysis and an optimization design study.

OverviewWhen you begin applying Mechanica, you may select large, complex models to analyze.

However, it is recommended that you initially attempt to apply Mechanica to simple, basic models in order to learn the process of building and analyzing Mechanica models.

Analyzing ModelsYou must apply the following steps when running Mechanica analyses:

1. Create or import geometry2. Assign material properties.3. Define loads.4. Apply constraints.5. Create elements.6. Define the analysis. 7. Run the analysis.8. Review the results.9. Assign design parameters.10. Run a sensitivity study.11. Run an optimization study.12. Update the part geometry.

Steps 1 through 8 define an engineering analysis in order to understand how a model behaves under certain boundary conditions. Steps 9 through 12 enable you to improve a design.

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Evaluating Analysis Results

Running Analysis

� Start - Begins calculations.

� Batch - Creates a batch file called mechbatch.bat. Calculations start when the batch file is executed.

� Restart Continues from last successfully completed p-pass.

� Summary - Monitor the run’s progress.

� Output & Temporary Engine Files - Defaults to the directory where you started Mechanica.

� RAM Allocations - 50% of Physical RAM.

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File Structure

� Mech_trl� Captures button picks like trail file for Pro/ENGINEER Wildfire.

� *.prt� Contains geometry, regions, surface pairs, and design parameters.

� config.pro� Configuration options.

File StructureUse the following for an example and assume that the following conditions apply:

• The working directory where Pro/ENGINEER Wildfire was started is mech_stuff.• The model name is test_model.• The analysis name is static_test.

Then, the following files are created:• The mechevnt file (which provides a record of all commands in Mechanica) is appended to

the current Pro/ENGINEER Wildfire trail file.• The files test_model.prt.* and test_model.mdb (Mechanica database) are created upon the

first File:Save. The .prt file contains all of the Pro/ENGINEER Wildfire geometry plus regions, surface pairs and design parameters. The .mdb file contains all Mechanica entities (loads, constraints, properties, and all analysis forms).

• The files test_model.mbk is created upon the second File:Save and can be used as a backup.

• The directory static_test is created when running the analysis. In this directory, the following files are saved: (1) a copy of the *.mdb and *.prt file is kept here for future reference, (2) the *.rpt is a text file containing the model and analysis summary, (3) the *.pas file contains a time log of various analysis and file operations, (4) the *.err file records any error messages occurring during the run 5. The directory static_test.tmp is created when running the analysis. This directory contains temporary files (typically the stiffness matrix) and is deleted upon analysis completion. Disk space requirements must be addressed.

Note: The config.mech file contains user defined configuration options for the Mechanica entities.For E

ducatio

nal Use

Only

© 2002 PTC


Defining a Result Window

1. New result window

2. Window name

3. Highlight study directory� Do NOT double click

4. Desired results� Quantity

� Location

� Display

5. Accept and Show

1

2

3

5

4

Notes to Instructor:• This crossed slide is for your reference. • You will be displaying the next slide, which is a duplicate of this slide without the screen

shots.• Demonstrate the process using the screen shots.

Defining a Result WindowDefining a Result window is a four-step process:

• Select “Create” from the Result Window Menu.• Enter a name for the window to be created.• Highlight the study directory where the desired results are stored and accept the window.

Note: When selecting the study directory, do not double-click on the directory name. This will access the next level in the directory structure.

• Define the result window (Quantity, Location, Display).

• Results from any directory are accessible independently of the model currently displayed.

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© 2002 PTC


Defining a Result Window

1. New result window

2. Window name

3. Highlight study directory

� Do NOT double click

4. Desired results

� Quantity

� Location

� Display

5. Accept and Show

Defining a Result WindowDefining a Result window is a four-step process:

1. Select “Create” from the Result Window Menu.2. Enter a name for the window to be created.3. Highlight the study directory where the desired results are stored and accept the window.

Note: When selecting the study directory, do not double-click on the directory name. This will access the next level in the directory structure.

4. Define the result window (Quantity, Location, Display).

• Results from any directory are accessible independently of the model currently displayed.

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Using a Result Window

� Show �Display a result window.

� Edit�Review the contents of a result window.

● Format: Gives additional display options, Edit Legend, Toggles on/off labels….● Dynamic Query: Use the mouse to get values directly off the display. Locate view and

model maximums and minimums.● Cutting Surf: Make an intersecting cut and view results on cutting surface only.● Capping Surf: Make an intersecting cut and view results on remaining exterior surfaces.

� Save�Store all currently defined result windows.

� Load�Recall previously stored result windows.

Using a Result WindowTaking a closer look at the Result Window:

• Note that the Create, Review, Copy, Delete, Change, Save and Load options only apply to the Edit column while the Show option only applies to the Show column · The Review option is used to redefine the Quantity, Location and Display Type for the window.

• The Change option is used to access results from different analyses in a multidisciplinary design study (for example: an optimization study with modal and static analyses).

• Save & Load – Allows you to store and recall the current result windows definitions.• A summary of the result window parameters (Study, Analysis, Loadcase, Quantity,

Location, Display) is displayed for the window currently selected in the Edit column.

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Demonstrations

� Analyze a part for stresses.

� Create design study to run simultaneously with a thermal and static analysis.

� Create a model analysis.


In this demonstration, I will:• Review the basic steps for building a Pro/ENGINEER Wildfire model for analysis. • Analyze a roller mill bearing part for stresses. • De-feature a model.• Analyze a pan assembly for heat distribution and strength • Design a tuning fork for the musical note "G".


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Summary


� Describe the basic steps for building a Pro/ENGINEER Wildfire model for analysis.

� Set up and run a thermal analysis and a structural analysis, simultaneously.

� Set up and run a modal analysis and an optimization design study.

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Module 12: Running Sensitivity Studies







Mechanica• TBD

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© 2002 PTC

Lesson Activities: Day Four

Demos & Exercises

Lectures

Optimizing a Design

Pro/FICIENCYDaily

AssessmentsDesign Parameters

RunningSensitivity Studies

Setup a LocalSensitivity Study

Defining anOptimization Study

Review OptimizationStudy Results

RunningOptimization Studies


Defining andRunning Design

Studies

Setup a GlobalSensitivity Study


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© 2002 PTC

Objectives


� Describe the purpose of design parameters.

� Create design parameters and measures.

� Set up and run a local and global sensitivity studies.

� Review sensitivity plots.

OverviewSo far, you have learned how to model and analyze a part in Mechanica. In this lesson, you will learn the tools that enable you to determine how sensitive measures such as stress, displacement, and mass are to changes in model parameters. You will also learn in a later module how to optimize your model by setting goals and limits on measures, while varying model parameters.Sensitivity studies enable you to more fully understand the effects of varying the design parameters on your model. You can use these studies to determine how sensitive a particular quantity, such as von Mises stress, is to variations of a particular dimension parameter. Mechanica provides the following sensitivity capabilities:

• Global Sensitivity Studies• Local Sensitivity Studies

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Design Parameters

Design Parameters

� Parameterization of shape and properties of a model.

� Pro/ENGINEER Wildfire dimensions and parameters can be used as Design Parameters.

� Relations capture design intent.

Animate

� Regenerate at specified number of interval.

Review

� Regenerate at specified setting.

Design Parameters• Design Parameters are used to define what can change in a model when running Sensitivity

and Optimization Studies. • Design Parameters are used ONLY in Integrated Mode and Linked Mode. They allow the

parameterization of any Pro/ENGINEER Wildfire dimension (including section dimension) as well as the use Pro/ENGINEER Wildfire parameters. The following command sequence is used: Structure> Model>Idealizations> Dsgn Controls> Design Params.

• To accomplish the desired changes on the geometry in Integrated Mode, we need to do the following:

• Define a relation in Pro/ENGINEER Wildfire, relating “d8” to the length of the plate (trans_curve) Define a Design Parameter called “trans_curve”, assigning minimum and maximum values of 4 and 6 to that dimension.

• Define a Design Parameter on called “radius_change”, assigning minimum and maximum values of 0.5 and 1.5 to that dimension.

• When defining a design parameter, the Type (Dimension, Pro/ENGINEER Wildfire Parameter, Section Dimension) must be selected first, along with the feature dimension (click on Select).

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Design Parameters

Measures

� Additional probes in the model.� Quantity

� Component

� Spatial Evaluation● At a point● Maximum● Minimum

�Time/Freq Evaluation● At each step● Maximum● Minimum● At time

Displacement Magnitude at a

point

MeasuresIdentify Measures (default or user defined) to be used to control the optimization goal and limits (for example: minimize mass while keeping stress at a particular location below a given value).

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Global Sensitivity Studies

Global Sensitivity

� Select a base analysis.

� Choose a single parameter.

� Enter a range for the parameter.

� Repeat convergence.

Radius

Vo

n M

ises

Str

ess

R = 3

R = 5

R = 4

R = 8

Global SensitivityGlobal sensitivity studies are used to generate a picture of how measures respond to changing a design parameter over a specified range (usually a large range, hence the name global). Global sensitivity studies provide the big picture and will be most useful in understanding the overall effect of a given parameter.Running a global sensitivity study helps you understand in detail how changes are affecting your part. You will then use this information to set up the optimization study. Normally you would run global sensitivity studies on all the parameters that survived the local sensitivity study, but in the interest of time, you will run global sensitivity studies for limited parameters. A global sensitivity study allows the user to obtain information on the way a particular quantity is affected by a parameter over a range of values. The following inputs are required to define a global sensitivity analysis:

• Study name: Mechanica will use this name to create the directory in which results are stored.

• Type: Select “Global Sensitivity” from the design study types available.• Description: Descriptions will save you time when retrieving old analysis files or performing

disk maintenance operations. • Base analysis: This is the analysis to be performed for each value of the parameter • Parameters: Select a single parameter from the list. Selecting several parameters removes

the ability to isolate the effect of one parameter on the quantity of interest. If several parameters are selected, they are incremented (from minimum to maximum) together.

• Range: Enter a range of values (Integrated Mode) or percentages (Independent mode) through which the parameter will vary.

• Number of intervals: This is the number of intervals (between the minimum and maximum value) for which you want to run the analysis.

• Repeat P-Loop convergence: When this option is selected, Mechanica performs the convergence algorithm at every value of the parameter. Otherwise, edge orders (p-levels) determined for the model at the initial parameter value are used.

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Global Sensitivity


� Choose a single parameter.

� Enter a range for the parameter.

� Repeat convergence?

� Determine which options are needed using shape-animate.

Global Sensitivity (cont.)• Element update options (Independent Mode only): The mesh has to adapt to changing

geometry. This can be done in two ways: • Smooth: When Smooth is selected, AutoGEM checks the validity of elements and

attempts to fix invalid elements by moving points, while retaining the original set of elements. Validity is defined by the AutoGEM settings limits (face angles, edge angles, etc.).

• Regenerate: if parameters impose geometric changes on the mesh that are “beyond repair” then new elements must be generated.

• Determining which option should be used can be done using Shape-Review and Shape-Animate.

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Local Sensitivity Studies

Local Sensitivity


� Select all the parameters to study.

� Enter settings for the parameters.

� Analysis conducted with all parameters at specified settings.

� Analysis conducted for each parameter at +1% from specified setting.

� Slopes are calculated in all directions.

Slope

� Slope of the global curve at the current variable setting

� Each variable changed separately

� Results are ONLY ACCURATE LOCALLY

Local Sensitivity Local Sensitivity Studies are used to calculate the sensitivity of your model's measures to perturbations (very slight changes) in parameters. Mechanica uses local sensitivity to perturb a dimension parameter by 1% to estimate the derivative of your measure with respect to the parameter. Thus, for a given location in parameter space, you may take a "snapshot" of the sensitivity of your model subject to all parameters. If parameter A induces a slope of your measure of 100, while parameter B induces a slope of your measure of 0.01, then you may postulate that changing the parameter A will have a bigger effect than working with parameter B. Therefore, you use local sensitivity to narrow your selection of dimension parameters to the most important ones. • Local Sensitivity design studies are used to find out which design variables have the

most influence on the design.• The process of a Local Sensitivity Analysis is defined below:

1. The base analysis is performed at the specified parameter settings.2. The analysis is then repeated with each parameter set a +/- 1% from its original

value while all other parameters remain unchanged (this is also known as a perturbation analysis). The 1% change is based on 1% of the difference between the minimum and maximum design variable settings. If the current value is set at the maximum of the range, the perturbation is set at 1% towards the minimum setting, otherwise the perturbation is set at 1% towards the maximum.

3. Sensitivity slopes are obtained by comparing results of steps 1 and 2. 4. Slopes are displayed graphically by extending the line in both directions. The

graphs can be compared in order to determine which design variables have the most influence. For E

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© 2002 PTC


Local Sensitivity


� Select all the parameters to study.

� Enter settings for the parameters.

Local Sensitivity (cont.)The following inputs are used to define a local sensitivity study:

• Study name: Mechanica will use this name to create the directory in which results will be stored.

• Type: Select “Local Sensitivity” from the design study types available .• Description: These descriptions are used for keeping track of analysis performed.

These will save you time when retrieving old analysis files or performing disk maintenance operations.

• Base analysis: This is the analysis to be performed for different values of the parameters considered in sensitivity study.

• Parameters: Select parameters to be compared in terms of their impact on the quantity of interest (for example: Sensitivity of Maximum von Mises stress to changes in radius, trans_curve).

• Setting: Enter a value (about which the local sensitivity analysis is to be performed.• Element update options (Independent Mode only): See discussion in section on

“Global Sensitivity” .

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Standard Design Study

� Allows running several analyses under one study.

� A Standard study with parameters provides a way to run differentanalyses with a particular setting of the parameter values.

Design StudyA standard design study can be used to run a base analysis at specific parameter values. This allows the user to run consequential scenarios without modifying actual part dimensions. The following inputs are used to define a standard design study:

• Study name: Mechanica will use this name to create the directory in which results will be stored.

• Type: Select “Standard” from the design study types available.• Description: These descriptions are used for keeping track of analysis performed. These will

save you time when retrieving old analysis files or performing disk maintenance operations.• Base analysis: Select one or more analysis to be performed with the particular set of

parameters.• Parameters: Select parameters to be used.• Settings: Specify values for parameters.

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Demonstrations

� Setup a stress analysis using the belt clip.

� Setup a local and global sensitivity study for the belt clip.

� Create design parameters for the PCB assembly.

� Create and run local and global sensitivity studies for the PCB assembly.


In this demonstration, I will:• Setup a stress analysis using the belt clip.• Setup a local and global sensitivity study for the belt clip.• Create design parameters for the PCB assembly.• Create and run local and global sensitivity studies for the PCB assembly.


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Summary


� Describe the purpose of design parameters.

� Create design parameters and measures.

� Set up and run a local and global sensitivity studies.

� Review sensitivity plots.

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Module 13: Running Optimization Studies







Mechanica• TBD

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© 2002 PTC

Lesson Activities: Day Four

Demos & Exercises

Lectures

Optimizing a Design

Pro/FICIENCYDaily

AssessmentsDesign Parameters

RunningSensitivity Studies

Setup a LocalSensitivity Study

Defining anOptimization Study

Review OptimizationStudy Results

RunningOptimization Studies


Defining andRunning Design

Studies

Setup a GlobalSensitivity Study


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© 2002 PTC

Objectives


� Setup and run optimization studies.

� View optimized models.

Overview

Running OptimizationsAn optimization study adjusts one or more parameters to best achieve a specified goal or to test feasibility of a design, while respecting specified limits.To create an optimization study, you define the following components:

• Goal – You select a measure to minimize or maximize as the study's goal.• Limits – You define limits on one or more measures that Mechanica cannot violate

during the optimization.• Parameters – You select one or more design parameters you want Mechanica to adjust

to achieve the goal. You will also define a range and initial value for each parameter.The goal and limits are each optional, but you must have at least one goal or one limit.Mechanica adjusts the model's parameters in a series of iterations through which it tries to move closer to the goal while satisfying any limits. If you have no goal, Mechanica simply tries to satisfy your limits. An optimization with no goal is sometimes called a feasibility study. If you do not define a goal, you must define limits. Without a goal, Mechanica searches for the first feasible design that satisfies the limits you define.When defining a goal and limits, you can select measures associated with different analysis types. You can set up an optimization that would perform any of Mechanica's analysis types except motion and contact. For example, you could optimize the clip for stress, displacement, natural frequencies (modes), and temperature simultaneously.

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© 2002 PTC


Optimization Study

� Set a single goal.

� Set limits on measures.

� Select the base analysis.

� Select the parameters to study. � Enter range and initial settings for the parameters.

� Use global results to choose the starting points.

� Use the results of global studies to reduce the list of parameters.

� Set OPTIMIZATION percentage (this is not convergence percentage).

� Set Repeat Convergence.

Running Optimizations (cont.)

Additional components:• Base Analysis: Select the analysis to be performed. Note that optimizations can be

performed on several analyses of the same part (for example: modal, static and thermal).• Range and Initial setting: This defines the size of the solution space Mechanica will be

working with. For best results, we want to limit this solution space (for example: only use the necessary range for each parameter). The initial setting for each parameter is also important. Use results from global sensitivity studies to determine where to start your analysis. Note that initial conditions will greatly influence the runtime.

• Optimization convergence: This is the tolerance percentage used to determine if the goal/limits have been reached. This is not to be confused with the base analysis convergence percentage which will dictate when to terminate the p-pass algorithm.

• Max Iterations: If Mechanica can not converge to an optimum set of parameters, the optimizer algorithm will stop after 20 iterations. This usually points to a problem with the way the optimization study has been defined (Incompatible goal and limits, too many parameters, too large a solution space or poor initial values). Setting the “Max Iteration” value to a larger number will not solve these problems. Only when you consider that the optimizer is on the right track and wish to push it further, should that number be changed.

• Element Update Options and Repeat Convergence. See discussion on “Global Sensitivity Analysis”.

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© 2002 PTC


Optimization Process� Run local sensitivity study at initial setting.

� Checks local slopes.

� Guess on new position.

� Recalculate.

� Repeat until convergence is satisfied.

Start pointMeasure

Goal

Parameter 1

Limits

Parameter 2

Optimization Process• This is a schematic representation of how an Optimization study works. The analogy used

is that of a blind bug or blind-folded skier on top of a mountain.• Consider the surface generated by the variation of a particular measure (say stress) as a

function of 2 parameters (say hole diameter and thickness). This is the solution space. Note that limits have precedence over the optimization goal (in the example at hand, there is not much use for a very light but flimsy part).

• The goal is to get to the bottom of the hill. The problem is that we do not know what that surface looks like. We will therefore proceed with the following method: 1. Test the local slopes to see which way is down. We will perform a local sensitivity study

for each parameter and then decide in which direction we want to increment these parameters.

2. Once limits are satisfied, we can guess a new position based on the information obtained from sensitivity studies.

3. We now perform the base analysis at these parameter settings (Standard Study) and extract all necessary values of measures used to evaluate if our optimization goal or limits have been reached. If neither our goal or the maximum number of iterations has been reached, then iterate to step (1) above.

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© 2002 PTC

Demonstrations

� Setup and run an optimization study for a belt clip.

� View the optimized belt clip.

� Define and run an optimization study for the CPU assembly.


In this demonstration, I will:• Create an optimization study and run it.• View the results and check the optimized model.


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Module 14: Applying Mechanica Analysis Concepts







Mechanica• TBD

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© 2002 PTC

Lesson Activities: Day Five

Demos & Exercises

Lectures

Structure andThermal Analyses

Applying MechanicaAnalysis Concepts

Duration• Lecture: TBD mins• Demos (TBD): TBD mins• Labs (TBD): TBD hours• Total: 6 hours 30 mins

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© 2002 PTC

Objectives


� Create spot-welding connections.

� Create setup contact connections surfaces and setup contact analysis.

� Create a time dependent loads and setup a transient thermal analysis.

� Create a large deformation analysis.

� Create a dynamic time analysis.

� Create a dynamic frequency analysis.

OverviewThis module will provide design studies in varying degrees of difficulty. You can choose a design study that reflects your area of interest. Design studies cover the following topics:

• Static.• Thermal.• Contact.• Large deformations.• Vibrations.

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© 2002 PTC

Demonstrations

Examples

� Apply Mechanica analysis concepts to various Structure and Thermal designs.

�Spot Weld Analysis● Creating spot welds.

�Contact Analysis ● Defining contact regions and measures.● Defining a static analysis with contact regions.● Specifying load increments.

�Transient Thermal Analysis ● Defining time dependent boundary condition.

�Large Deformation Analysis

�Dynamic Time Analysis ● Defining measures.

�Dynamic Frequency Analysis

Demonstration (TBD minutes)

In this demonstration, I will:• Various Structure and Thermal Analyses.

You will have the opportunity to work on several real life models of your choosing.

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© 2002 PTC

Summary


� Create spot-welding connections.

� Create setup contact connections surfaces and setup contact analysis.

� Create a time dependent loads and setup a transient thermal analysis.

� Create a large deformation analysis.

� Create a dynamic time analysis.

� Create a dynamic frequency analysis.

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