2. Chapter_01_Intro CAE & FEM

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CHAPTER 01

Introduction

Part 1 : CAE

Part 2 : FEM

Part 3 : FEM Application

MAH 2012


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Part 1:

Introduction to CAE


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Part 1: CAE

What is CAE??

Stress analysis of a beam Fluid flow around an F1 car using a

CFD software


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Part 1: CAE

CAE is

Computer Aided Engineering

Use of computer software to aid engineering tasks :-

- Design Analysis

- Material Analysis

- Process Simulation

CAE examples :-

- CAD (Computer Aided Design) Autocad, Solidworks

- CFD (Computational Fluid Dynamics) Fluent, Ansys

- FSI (Fluid Structure Interaction ) Adina-FSI

- FEM (Finite Element Method) Algor, Nastran Patran


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Part 1: CAE

Why is CAE important?

Predict possible design problems

-try and error is not acceptable for designs that concern

safety e.g. stadium, high rise buildings

-reduce cost by reducing error, reducing scrap material,

shorter manufacturing time

Simulate conditions that are impossible to achieve

experimentally

-extreme conditions can be simulated using CAE

- e.g. high velocity high temperature wind tunnel were not

available in the past; no possible way to test aerospace plane

except CFD


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Part 1: CAE

What are major CAE components?

Computational Fluid Dynamics

- Thermal and fluid flow analysis

Computer Aided Design- Drafting and tooling design

Finite Element Analysis

- Stress & Strain analysis


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Part 1: CAE

Application of CAE in industries

STRUCTURE AND BUILDING : Stress analysis of a building


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Part 1: CAE


MANUFACTURING : Plastic foam flow analysis for plastic molding


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Part 1: CAE


POWERPLANT: Heat flow simulation of a heat exchanger


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Part 1: CAE


AEROSPACE : Pressure simulation of space shuttle


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Part 2:

Introduction to FEM


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Part 2: FEM

What is FEM?

Finite Element Method

most common method used in Finite Element Analysis (FEA)

numerical method for solving engineering and physics problems

- usually, engineering problems are described by differential equations,

or by integral expressions

- FEM formulates these differential equations and integral expressions

into numerical solutions


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Part 2: FEM

Mathematical solution:

consider this object with thickness t

thickness constant; two dimensional problem

for mathematical solution, we consider the

red dots differential equation, and we have

to consider each dot on the whole area ofthe object

the dot of the size dxdy is considered

infinitesimal (very very very small), so if we

consider these elements, the number will be

infinite

so, it is impossible for a human to calculate

all these solutions!


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Part 2: FEM

FEM solution:

substitute the red dots with larger elements

the new elements are not of the size dxdy,

so they are not infinite, they are finite

the blue dots with the number 1,2,3 are

called nodes

the triangle made by the dots is the element

that is why this method is called Finite

Element Method

the values that have to be calculated for this

method are only the node values and thevalues between nodes are then

approximated

. node and element

. basic idea of FEM


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Part 2: FEM

Comparison ofFEM and Mathematical solution

1. compare the elongation and stress of a tapered cylinder

when pulled by a load

2. understand that the solution of FEM is just the

approximation of the real solution

3. understand methods to improve the accuracy of FEM

approximation


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Part 2: FEM

Comparison ofFEM and Mathematical solution

Compare the elongation of a tapered cylinder when pulled by load F

(a) Tapered cylinder

element 1

(b). Tapered cylinder modeled

with 4 elements

element 3

element 2

element 4


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Part 2: FEM

- slight difference betweenexact and four elementssolutions

- the modeled solution can

be improved if the numberof elements increased

- modeled solution is justan approximation of the

exact solution

graph of the elongation of the tapered cylinder


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Part 2: FEM

Conclusion from the comparison:

I. understand that the solution of FEM is just the

approximation of the real solution

II. understand methods to improve the accuracy of FEM

approximation

III. the example given is just a simple problem; FEM is

usually used for much more complicated structures and

problems

IV. for most cases, the exact solutions are not needed, theestimations are sufficient


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Part 3:

Application of FEM


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Part 3: Application of FEM

General procedure of FEM:

1. Pre-processing

2. Solution

3. Post-processing


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1. Pre-processing

Define the geometric domain of the problem.

Define the element type(s) to be used.

Define the material properties of the elements.

Define the geometric properties of the elements (length, area)

Define the element connectivity (mesh the model)

Define the physical constraints (boundary condition)

Define the loadings.


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2. Solution (done by FEM software)

Assemble algebra equations in matrix form.

Compute unknown values of the primary field variable(s).

Compute additional, derived variables.


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3. Post-processing

Sort element stresses in order of magnitude.

Check equilibrium.

Calculate factors of safety.

Plot deformed structural shape.

Animate dynamic model behavior.

Produce color-coded temperature plots.


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Advantages of FEM:

FEM is capable of modeling and analyzing:

- irregular (complex) geometries

- general loading

- different material properties

- various BCs

- various element types and sizes

- nonlinear and dynamics

- easy modification


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Examples of FEM application:

Architecture : Stress analysis of a building

Fluid Mechanics : Fluid flow inside a house

Automotive : Thermal flow inside an engine, car crash simulation

Manufacturing : Plastic mold flow simulation

Aeronautical : Flow of air around an airplane


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End

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2. Chapter_01_Intro CAE & FEM