OVERVIEW OF FINITE ELEMENT METHOD - Universiti ...taminmn/SME 3033 Finite Element Method...OVERVIEW...

OVERVIEW OF FEM

SME3033 - INTRODUCTION TO FINITE ELEMENT METHOD

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OVERVIEW OF FINITE ELEMENT METHOD

OVERVIEW OF FEM


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COMPUTER-AIDED ENGINEERING (CAE)

The use of computers to analyze and simulate the

function (structural, motion, etc.) of mechanical,

electronic or electromechanical systems.

• Computer-Aided Design (CAD)

- Drafting

- Solid modeling

- Animation & visualization

- Dimensioning & tolerancing

• Engineering Analyses

- Analytical & numerical methods

OVERVIEW OF FEM


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FINITE ELEMENT METHOD (FEM)

A numerical analysis technique for obtaining

approximate solutions to a wide variety of

engineering problems.

The basic premise of the method is that a

solution region can be analytically modeled or

approximated by replacing it with an

assemblage of discrete elements.

OVERVIEW OF FEM


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Steps in solving a continuum problem by FEM

Select the solution domain

Select the solution region for analysis.

Discretize the continuum

Divide the solution region into finite number of elements,

connected to each other at specified points / nodes.

Select interpolation functions

Choose the type of interpolation function to represent the

variation of the field variables over the element.

Derive element characteristic matrices and vectors

Employ direct, variational, weighted residual or energy

balance approach.

[k](e) {}(e) = {f}(e)

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Steps … (Continued)

Assemble the element characteristic matrices and vectors

Combine the element matrix equations and form the matrix

equations expressing the behavior of the entire solution region /

system.

Modify the system equations to account for the boundary conditions

of the problem.

Solve the system equations

Solve the set of simultaneous equations to obtain the unknown

nodal values of the field variables.

Make additional computations, if desired

Use the resulting nodal values to calculate other important

parameters.

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Select the solution domain

Discretize the continuum

Choose inerpolation functions

Derive element characteristic

matrices and vectors

Assemble element

characteristic matrices and

vectors

Solve the system equations

Make additional

computations, if desired

Draw the model geometry

Mesh the model geometry

Select element type

(The FEA software was written to do this)

Input material properties

(The computer will assemble it)

Input specified load and boundary conditions

(The compiler will solve it)

Request for output

Post-process the result file

FE procedures: FE software user steps:

OVERVIEW OF FEM


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Draw the model geometry

Mesh the model geometry

Select element type

[20-node Hexahedral elements]

Input material properties

[Elastic modulus, Poisson’s ratio]

Input specified load and BC

[Pin loading, displacement rate,

zero displacement at lower pin]

Request for output

[Displacement, strain and stress

components]

Post-process the result file

EXAMPLE: Stresses in a C(T) specimen

OVERVIEW OF FEM


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EXAMPLE: Stresses in a C(T) specimen

Check for obvious mistakes/errors

Extract useful information

Explain the physics/ mechanics

OVERVIEW OF FEM


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MODELING CAPABILITIES – Microelectronic device reliability

MT1

TC1

TD1

0.00

0.02

0.04

0.06

0.08

0.10

0 1 2 3 4 5

N

εin

-40

125

183

25

Re-flow

T

Time

- Prediction of spatial distribution of physical parameters

- Prediction of damage evolution characteristics

Silicon Die

Substrate

Heat sink

Motherboard PCB

Solder jointsSolder

mask

OVERVIEW OF FEM


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MODELING CAPABILITIES – Fatigue life of compressor components

- Identify critical locations at early stage of design

OVERVIEW OF FEM


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Epoxy

Silica Filler

SiO2-filled epoxy

Single Maxwell model

for viscoelasticity

)()( 0 tGt

dt

dt

)(

Gdt

d

Gdt

d

1

20% SiO2-Filled Epoxy

E

CTE

0

1000

2000

3000

4000

-50 0 50 100 150 200 250

T (°C)

E (

MP

a)

0

40

80

120

160

Se

ca

nt

CT

E (

pp

m/°

C)

Silica-Filled

Epoxy

(Ref)

Epoxy

1

10

100

1000

10000

1.0E-07 1.0E-04 1.0E-01 1.0E+02 1.0E+05

Reduce Time

Sh

ea

r R

ela

xati

on

Mo

du

lus,

G (

MP

a)

MODELING CAPABILITIES – Prediction of composite behavior

OVERVIEW OF FEM


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• 14 layers [0/45/90/-45/45/-45/02]s

• Layer thickness = 0.3571 mm

Al Comp-0º Comp-90º

E E11 E22

70 GPa 44.74 GPa 12.46 GPa

)L(6

EI3

xwx

y

w

MODELING CAPABILITIES – Deflection of composite laminates beam

OVERVIEW OF FEM


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MODELING CAPABILITIES – Deformation of composite panel

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0 250 500 750 1000

Path length (mm)

Def

lect

ion

(m

m)

Single orientation

Mixed orientation Uni-directional

[0/45/90/-45/45/-45/02]SYM

OVERVIEW OF FEM


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14F.S. Silva, Engineering Failure Analysis 13 (2006) 480-492

MODELING CAPABILITIES – Failure investigation

OVERVIEW OF FEM


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FINITE DIFFERENCE VERSUS FINITE ELEMENT METHOD

Finite element method:

envisions the solution region as built up of many small

interconnected sub-regions or elements.

gives a piecewise approximation to the governing equations.

Finite difference scheme:

envisions the solution region as an array of grid points.

gives a pointwise approximation to the governing equations.

OVERVIEW OF FEM


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FINITE DIFFERENCE

Finite difference scheme:

envisions the solution region as an array of grid points.

gives a pointwise approximation to the governing equations.

0

22

0

2

101112

2

211101

2

2

2

2

y

TTT

x

TTT

y

T

x

T

For node (1,1):

OVERVIEW OF FINITE ELEMENT METHOD - Universiti ...taminmn/SME 3033 Finite Element Method...OVERVIEW...

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