Sep 19, 2014

Interns:

Khaled

ElmekawyComputer Aided DesignLecture 1

Dr./ Ahmed Nagib Elmekawy Sep 19, 20181

Finite Element Analysis Overview

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Research and Development

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Mathematical Model

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Mathematical Model

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Mathematical Model

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Finite Element Analysis

The linear equation of motion for vibration is

𝑴 ሷ𝒙 + 𝑪 ሶ𝒙 + 𝑲 𝒙 = 𝑭

• 𝒙 , which is the displacement vector• ሷ𝒙 , which is the acceleration vector• 𝑴 , which is the Mass matrix• 𝑲 , which is the stiffness matrix• 𝑪 , which is the damping matrix• 𝑭 , which is the load vector

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Finite Element Softwares

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Finite Element Analysis

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Finite Element Analysis

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Finite Element Analysis

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Static Analysis

For a linear static structural analysis, the global displacement vector 𝒙 is solved for in the matrix equation below:

𝑲 𝒙 = 𝑭

Assumptions made for linear static structural analysis are: • 𝑲 , which is the global stiffness matrix, is constant – Linear elastic material behavior is assumed – Small deflection theory is used • 𝑭 , which is the global load vector, is statically applied – No time-varying forces are considered – No damping effects

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Axial Stress

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Beam under the action of two tensile forces

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Beam under the action of two tensile forces

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Torsion Stress

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Torsion Stress

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Torsion Stress

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Angle of Twist

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Torsion of a Shaft with Circular Cross-Section

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Torsion of a Shaft with Circular Cross-Section

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Torsion of a Beam with the Square Cross-Section

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Torsion of a Beam with the Square Cross-Section

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Bending Stress

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Bending Stress

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Bending a Cantilever Beam under a Concentrated Load

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Bending a Cantilever Beam under a Concentrated Load

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Bending Stress

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Bending Stress

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Bending Stress

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Bending Stress

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Bending Stress

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Bending Stress

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Bending Stress

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Bending of Curved beam

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Displacement Stress in x direction

Finite Element Analysis

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Finite Element Analysis

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Static Analysis

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Static Analysis

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Static Analysis

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Static Analysis

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Static Analysis

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Static Analysis

Linear vs Non Linear solveIn a linear analysis, the matrix equation [K]{x}={F} is solved in one iteration. That means the model stiffness does not change during solve : [K] is constant. A non linear solve allow stiffness changes and uses an iterative process to solve the problem. In a static structural analysis, ANSYS runs a non linear solve automatically when the model contains : - Non linear material laws : Plasticity, Creep, Gasket, Viscoelasticity … - Non linear contact : Frictionless, Rough, Frictional - Large deflection turned - Joints - Bolt pretension

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Modal AnalysisThe linear equation of motion for free, un-damped vibration is

𝑴 ሷ𝒙 + 𝑲 𝒙 = 𝟎Assume harmonic motion:

𝒙 = 𝝓 𝒊 sin 𝜔𝑖𝑡 + 𝜃𝑖ሷ𝒙 = −𝜔𝒊

𝟐 𝝓 𝒊 sin 𝜔𝑖𝑡 + 𝜃𝑖

Substituting 𝒙 and ሷ𝒙 𝐢n the governing equation gives an eigenvalue equation:

−𝜔𝒊𝟐 𝑴 + 𝑲 𝝓 𝒊 = 𝟎

where𝜔𝑖: Natural Frequencies𝝓 𝒊 : Mode Shapes

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Modal Analysis

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Modal Analysis

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Modal Analysis

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Modal Analysis

Assumptions for Modal Analysis• [K] and [M] are constant: – Linear elastic material behavior is assumed – Small deflection theory is used, and no nonlinearities included – [C] is not present, so damping is not included – {F} is not present, so no excitation of the structure is assumed – Mode shapes 𝝓 𝒊 are relative values, not absolute

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Modal AnalysisModal Results: • Because there is no excitation applied to the structure the mode shapes are relative values not actual ones. –Because a modal result is based on the model’s properties and not a particular input, we can interpret where the maximum or minimum results will occur for a particular mode shape but not the actual value.

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Modal Analysis

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Modal Analysis

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Modal Analysis

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Modal Analysis

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Modal Analysis

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Modal Analysis

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Modal Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Dynamic Analysis

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Fluid-Structure Interaction

Solid Mechanics-Structural Analysis Fluid Dynamics

Solved by Finite Element Analysis Computational Fluid Dynamics (CFD)

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Recent Computational Methodology

Finite Element Analysis Computational Fluid Dynamics (CFD)

CommercialSoftware

Ansys Mechanical, Abaqus Ansys Fluent, Ansys CFX, Open-foam

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Recent Computational Methodology

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Recent Computational Methodology

Fluid-Structure Interaction

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Recent Computational Methodology

1 way FSI vs Two way FSI

Fluid-Structure Interaction

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Fluid Structure Interaction

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CFD Analysis Overview

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Lecture Theme:

All CFD simulations follow the same key stages. This lecture will explain how togo from the original planning stage to analyzing the end results

Learning Aims:

You will learn:• The basics of what CFD is and how it works• The different steps involved in a successful CFD project

Learning Objectives:

When you begin your own CFD project, you will know what each of the stepsrequires and be able to plan accordingly

Introduction

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Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

What is CFD?

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Computational Fluid Dynamics (CFD) is the science of predicting fluid flow, heat andmass transfer, chemical reactions, and related phenomena.

To predict these phenomena, CFD solves equations for conservation of mass,momentum, energy etc..

CFD can provide detailed information onthe fluid flow behavior:• Distribution of pressure, velocity, temperature,

etc.

• Forces like Lift, Drag.. (external flows, Aero, Auto..)• Distribution of multiple phases (gas-liquid, gas-

solid..)• Species composition (reactions, combustion,

• Much morepollutants..)

CFD is used in all stages of theengineering process:

• Conceptual studies of new designs

• Detailed product development

• Optimization

• Troubleshooting

• Redesign

CFD analysis complements testing and experimentation by reducingtotal effort and cost required for experimentation and data acquisition

Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

CFD Applications

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Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

CFD Applications

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Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

CFD Applications

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Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

CFD Applications

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Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

How Does CFD Work?

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ANSYS CFD solvers are based on the finite volume method• Domain is discretized into a finite set of control volumes

• General conservation (transport) equations for mass, momentum, energy,species, etc. are solved on this set of control volumes

Unsteady Convection Diffusion Generation

• Partial differential equations are discretized into a system of algebraic equations

• All algebraic equations are then solved numerically to render the solution field

ControlVolume*

EquationContinuity

X momentumY momentumZ momentum

Energy

1

uvwh

Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

Step 1. Define Your Modeling Goals

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• What results are you looking for (i.e. pressure drop, mass flow rate),and how will they be used?

• What are your modeling options?• What simplifying assumptions can you make (i.e. symmetry, periodicity)?

• What simplifying assumptions do you have to make?

• What physical models will need to be included in your analysis

• What degree of accuracy is required?

• How quickly do you need the results?

• Is CFD an appropriate tool?

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Step 2. Identify the Domain You Will Model

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• How will you isolate a piece ofthe complete physical system?

• Where will the computational domainbegin and end?

− Do you have boundary condition information atthese boundaries?

− Can the boundary condition types accommodatethat information?

− Can you extend the domain to a point wherereasonable data exists?

• Can it be simplified or approximated asa 2D or axi-symmetric problem?

Domain of Interest asPart of a LargerSystem (not modeled)

Domain of interestisolated and meshedfor CFD simulation.

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Step 3. Create a Solid Model of the Domain

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• How will you obtain a model of the fluid region?− Make use of existing CAD models?− Extract the fluid region from a solid part?− Create from scratch?

• Can you simplify the geometry?− Remove unnecessary features that would complicate meshing;fillets, bolts…Ϳ?

− Make use of symmetry or periodicity?• Are both the flow and boundary conditions symmetric /

periodic?

• Do you need to split the model so that boundaryconditions or domains can be created?

Original CAD Part

ExtractedFluid Region

Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

Step 4. Design and Create the Mesh

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• What degree of mesh resolution is required in each region ofthe domain?

− Can you predict regions of high gradients?• The mesh must resolve geometric features of interest and capture gradients

of concern, e.g. velocity, pressure, temperature gradients

− Will you use adaption to add resolution?

• What type of mesh is most appropriate?− How complex is the geometry?− Can you use a quad/hex mesh or is a tri/tet or hybrid mesh suitable?− Are non-conformal interfaces needed?

• Do you have sufficient computer resources?− How many cells/nodes are required?− How many physical models will be used?

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Step 5. Set Up the Solver

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• For a given problem, you will need to:

− Define material properties• Fluid

• Solid

• Mixture

− Select appropriate physical models• Turbulence, combustion, multiphase, etc.

− Prescribe operating conditions

− Prescribe boundary conditions at all boundary zones

− Provide initial values or a previous solution

− Set up solver controls

− Set up convergence monitors

Introduction CFD Approach Pre-Processing Solution

For complex problems solving a simplifiedor 2D problem will provide valuableexperience with the models and solversettings for your problem in a shortamount of time

Post-Processing Summary

Step 6. Compute the Solution• The discretized conservation equations are solved

iteratively until convergence• Convergence is reached when:− Changes in solution variables from one iteration to the

next are negligible

• Residuals provide a mechanism to helpmonitor this trend

− Overall property conservation is achieved•Imbalances measure global conservation

− Quantities of interest (e.g. drag, pressure drop) have reachedsteady values•Monitor points track quantities of interest

• The accuracy of a converged solution is dependentupon:

− Appropriateness and accuracy of physical models− Assumptions made− Mesh resolution and independence− Numerical errors

A converged and mesh-independentsolution on a well-posed problemwill provide useful engineeringresults!

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Step 7. Examine the Results

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• Examine the results to review solution andextract useful data

− Visualization Tools can be used to answer suchquestions as:

• What is the overall flow pattern?

• Is there separation?

• Where do shocks, shear layers, etc. form?

• Are key flow features being resolved?

− Numerical Reporting Tools can be used to calculatequantitative results:

• Forces and Moments

• Average heat transfer coefficients

• Surface and Volume integrated quantities

• Flux Balances

Examine results to ensure correct physical behavior andconservation of mass energy and other conservedquantities. High residuals may be caused by just a fewpoor quality cells.

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Step 8. Consider Revisions to the Model

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• Are the physical models appropriate?− Is the flow turbulent?− Is the flow unsteady?− Are there compressibility effects?− Are there 3D effects?

• Are the boundary conditions correct?− Is the computational domain large enough?− Are boundary conditions appropriate?− Are boundary values reasonable?

• Is the mesh adequate?− Does the solution change significantly with a refined mesh, or

is the solution mesh independent?− Does the mesh resolution of the geometry need to beimproved?− Does the model contain poor quality cells?

High residuals may be caused by justa few poor quality cells

Introduction CFD Approach Pre-Processing Solution Post-Processing Summary

Use CFD with Other Tools to Maximize its Effect

Prototype Testing Manufacturing

9.U

pd

ate

Mo

del

1. Define goals2. Identify domain

Pre-Processing

Problem Identification

3.4.5.6.

GeometryMesh PhysicsSolver Settings

7. Compute solution

Solve

8. Examine results

Post Processing

MeshCAD Geometry

Thermal Profile on Windshield

Final Optimized Design

Automated Optimization ofWindshield Defroster withANSYS DesignXplorer

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Summary and Conclusions

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• Summary:− All CFD simulations (in all mainstream CFD software products) areapproached using the steps just described

− Remember to first think about what the aims of the simulation areprior to creating the geometry and mesh

− Make sure the appropriate physical models are applied in the solver,and that the simulation is fully converged (more in a later lecture)

− Scrutinize the results, you may need to rework some of the earliersteps in light of the flow field obtained

1. Define Your ModelingGoals

2. Identify the Domain YouWill Model

3. Create a GeometricModel of the Domain

4. Design and Create theMesh

5. Set Up the Solver Settings6. Compute the Solution7. Examine the Results8. Consider Revisions to the

Model

Introduction CFD Approach Pre-Processing Solution Post-Processing Summary