lecture-intro to fea

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330:155g Finite ElementAnalysis

Nageswara Rao Posinasetti

2January 16, 2008 Rao, P.N.

1. Introduction

Finite element analysis is a computer-based numerical technique that is used tosolve stress analysis, heat transfer, fluidflow and other types of engineeringproblems.

Real power is in its ability to solveproblems that do not fit any standardformula.


Before FEA

Tested till failure before the availability of

FEM.


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Before FEA

Problems are simplified using certain

approximations before the availability ofFEM.


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X


X


X


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X1 2 3 4 5

12

34


1. Introduction

It involves partitioning of a structure into afinite number of elements Divide and Conquer

Elements are connected to one another atthe corner points These corner points are called nodes or nodal

points

Each element is a simple geometric shape Triangle, Quadrilateral, etc.



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1. Introduction

In order to completely define a finite

element model Nodal points

Elements

Loads

Supports

Element related data


1. Introduction

FEA program formulates the equations forsolutions

A nodal point can have upto 6 degrees of freedom

3 translational (x, y, z) and 3 rotational

An equilibrium equation for each degree of freedom

Equations are solved for displacement at eachnodal point

Displacements are then used to evaluate thestresses


1. Introduction

For the model to accurately represent the

physical part, the number of elementsshould be large.

Type of element should be correctlychosen

Boundary conditions should be correctly

applied.


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X1 2 3 4 5

12

34


X1 2 3 4 5 6 7 8 9 10 11 12 13 14


1. Introduction

Process of data preparation is tedious and

long.

It is called pre-processing

Results obtained are also voluminous

It is called post-processing


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Steps in finite element analysisprocess

Pre-processing

Define the model

Discretize the part defining nodal points andelements

Define element properties, material propertiessuch as density, modulus elasticity, etc.

Specify the boundary conditions

Specify the loads



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Preprocessor

Modelling of the geometry

Generating the finite element mesh by making asuitable approximation to the geometry

Calculates the nodes and elemental properties

Allows for the specification of the supportcondition and loading conditions for theindividual element positions.

Allows the material properties to be specified.




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Analysis

Formulates the equations that describe

each elements stiffness and assembles allof the equations so that they form a set ofsimultaneous equations

Solves the system of equations for thedisplacement at each nodal point

Uses the nodal point displacements tosolve for stress within each element


Results

Results generated from the analysis arevoluminous depending upon the number ofelements considered.

For proper understanding one has to gothrough all the data tables.


Postprocessor

Post processing involves the ability to go

through a large amount of data generatedduring the solving process and convert it

into an easily understood form for thedesign purpose.


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1.2 Library of Element Types

Depending upon the part geometry and

the type of analysis required a number ofdifferent types of elements are available inFEA


2-node linear3-node quadratic

3-node linear 6-node quadratic 4 -n od e li ne ar 8- no de q ua dr at ic

4-node linear 10-node quadratic

a) one dimensional

b) Two dimensional

c) Three dimensional

Triangular Quadrilateral

Tetrahedral



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1.3 Advantages of using FEA

Irregular shaped parts

Parts made from different materialsIrregularly placed loads

Large number of supports

Provides results throughout the part (allpoints)

Easy to change the model


Why Use FEA?Provides a non-destructivemeans of testing products.

Faster prototyping for what

if scenarios.

Design optimization.

Speed up time to market byshortening the design cycle.

Courtesy Algor Inc,Pittsburgh



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Best Practices

FEA requires engineering judgment.

In the best case, you should know theapproximate answer before you begin.

Proper selection of elements, materials,loads, constraints and analysis parameterscomes from experience.



Best Practices

Understand that the computer modelnever matches reality (its only anapproximation).

The surest route to failure in FEA is tounderestimate the complexity of the

technology.



Aerospace Industry

Orbital Technologies Corporation The above illustration shows how engineers

analyzed a Biomass Production System toconduct biotechnology plant research.

FEA in Different Industries



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Automotive Industry

Danly Engineering Services, Division of Enprotech

Mechanical Services, Inc.

The above illustration shows how engineers analyzed a

power press with additional cutouts.Courtesy Algor Inc,

Pittsburgh



Biomedical Industry

Ophthalmic Consultants of Boston and theTufts University School of Medicine

The above illustration shows stresses on an eye as itunderwent a 30saccadic eye movement. This was

modeled to help understand why retinal detachments occur.Courtesy Algor Inc,Pittsburgh



Power/Utility Industry

Cronulla Sewage Treatment Plant

The above illustration shows how engineers modeled a pipingsystem to verify that the number of bellows could safely bereduced by using lightweight, spiral-wound stainless steel. Thisallowed them to keep a $90 million sewage treatment plantupgrade on budget.



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1.4 Historical Development

Concept first appeared in 1956

Name Finite Element is used in 1960 byClough

1970s large programs running inmainframe computers

1980s moved to personal computers andwidespread use


CAD to FEA

There are many approaches for integratingCAD systems to FEA


CAD System

Geometricmodeller

Pre-Processor

CADGeometry

FE Mesh

FullFEM model

FEAnalysis

FE Pre-Processor

FE PostProcessor

Inventor to Algor


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Geometric

modellerFE

Analysis

FE Pre-

Processor

FE Post

Processor

Integrated FEA System, e.g. Algor


Design problem

Select a round bar to be constructed from an AISI 1020cold-drawn steel to support the 300-pound ball. Assumea safety factor of 2, and determine the deflection for thesize selected

Yield stress = 61,000 psi


Design problem

Cantilever beam

Max bending moment = 300 x 36

= 10,800 in-lb

Stress in the beam, S = M/ZS = 10,800 x 32 / ( d3)

Allowable stress = 61,000 / 2 = 30,500 psi

Equating the above two, and solving

d = 1.533 in = 1.625 in (preferred size)

Deflection = -FL3/ (3EI) = 0.455 in


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Problem using FEA

Start with 2 in dia; Max stress = 13,751 lower thanthe allowable 30,500 psi


Problem using FEA (contd..)

Next try 1.5 in dia; Max stress = 32,599 higherthan the allowable 30,500 psi



Next try 1.625 in dia; Max stress = 25,635 lowerthan the allowable 30,500 psi - Acceptable


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For 1.625 in dia; Max displacement = 0.47 inCompare this to analytical solution of 0.455 in, a3% error


Analytical Problem Solving Process

Establish clearly defined goal

Compile and qualify the inputs

Solve the problem with the mostappropriate means

Verify and document the results


What is the goal of the Analysis?

The decisions to be made

How important is the exact solution to theproblem? This will help in identifying the precision of the

inputs to the problem.

What information from the analysis willhelp in taking the engineering decision When can you stop analyzing?

Which shortcuts are allowed?


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Common Misconceptions

Meshing is everything Current preprocessor are efficient and generally give

good meshes. But that is not the end since it is onlyan input.

Boundary conditions and forces are added by theuser. The accuracy of the results depend to a greatextent on them.

FEA replaces testing Depends on the confidence in the analytical methods

used.

There is no guarantee that the results are accurate.



Finite element analysis is easy

Dont underestimate the complexity of theproblem.

Dont jump to conclusions too quickly.

Some little experiments may be required togauge the forces and reactions in the part.

Interpreting the results is also an importanttask.



Finite element analysis is hard

It is estimated that 20% creativity and 80%hard work and patience.

Learned through more practice

Learning the interface equals learning FEA


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Questions orComments?


Exercises

Define the terms: nodal point, element and degree of freedom

What does the term discretization mean in the finite elementmethod?

List three different material properties that must be defined for each

of the element.

Explain why the computer is necessary in the use of the finiteelement method.

Explain why computer graphic techniques are used during the postprocessing phase of a finite element analysis. What is the alternative

to using these graphical displays?

What advantage would a company derive by performing a finiteelement analysis of an existing part, which can be strain gauged and

tested in a lab?

lecture-intro to fea

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