FEA Traning09Sep2011

8/13/2019 FEA Traning09Sep2011

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Finite Element AnalysisIntroduction to

Praveen AhujaTechnical Manager - CAE

HCL Technologies , Bangalore



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What This Presentation Covers

• Introduction to Different Numerical Method • Introduction to FEM - Concept & Philosophy

• Need & Advantages of Finite Element Analysis

• Practical Application of FEA

• Different Professional FEA Tools/Software

• Steps involved in any Finite Element Analysis – Best Practices Approach

Introduction to “Finite Element Analysis”



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Objective of this Session

By the End of this session, You will be able to :

Understand and apply the Concept of FEM / FEA on Actual practical

day-to-day / complex problems

Understand Different Type of Analysis covered in FEA

Prepare a suitable FE model for a given problem

Know the Behavior of different type of FE Elements used , Concept of FE

Mesh , Loads and Boundary Condition

Step by Step approach followed in any Finite Element Analysis




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Introduction to FEA

Methods to Solve Any Engineering Problem

Analytical Method Numerical Method Experimental MethodClassical Approach

100% Accurate Results

Applicable only for Simple problems like

Cantilever , simply supported beams and

Cylinders etc..

Complete in itself

Mathematical Approach

Approximate, Assumptions Made

Applicable to real life complicated problems

Results can not be believed blindly and

must be verified by experimental methods

and Hand Calculations.

Actual Measurement

Time Consuming , Needs expensive setup

Applicable only if physical prototype is

available

Results can not be believed blindly and

Minimum 2 or more prototypes must be

tested.

Although applicable to simple shaped

geometries only , Analytical methods areconsidered as Closed form solutions i.e.

100% Accurate

Finite Element Method: Linear , Nonlinear ,

Buckling , Thermal, Dynamics & Fatigueanalysis

Boundary Element Method: Acoustics /NVH analysis

Finite Volume Method: CFD

(Computational Fluid Dynamics) &

Computational Electromagnetic

Finite Difference Method: Thermal & Fluid

Flow analysis (in combination with FVM)

-Strain Gauge

- Photo elasticity- Vibration measurement (accelerometers)

- Sensors for Temp & pressure etc… - Fatigue test




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Cantilever Beam Deflection

Analytical Approach – An example

Cantilever Beam Deflection – Analytical Approach

Analytical Approach

provides VeryAccurate Solution




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Analytical Approach – An example

If analytical approach isaccurate then why arethey not used for solvingReal life problems ??

Any Guesses ??

For a simple cantilever Beam, Governing equation is readily available , but this type of equations are not

available for real life complex problems

Basic Beam Bending equation is based upon many assumptions such as Small deflection , isotropic material ,

C/S of the beam remains plane and perpendicular to neural axis etc…

Answer:




Numerical Method (FEA Approach)

How does Numerical Method solve the same Cantilever problem ??

Finite Element Analysis Approach:•Component / Structure is modeled using discrete

building blocks called Elements (structure/component is

dicretize into smaller finite number of blocks called elements)

•Each element has exact equation that describe howit respond to certain load.

•The sum of response of all the elements in themodel gives the total response of the component.

•The Elements have finite number of unknowns (DOF

and loads) , hence the name “Finite Elements”




Different Numerical Methods

Finite Element Method (FEM) :Very Popular Method based upon discretization of component into Finite number of blocks (elements)

Applications : Linear, Nonlinear, Thermal, Dynamics , Buckling and Fatigue Analysis

Boundary Element Method (BEM) :It’s a very powerful and efficient technique to solve acoustics and NVH problems

Just like Finite Element Method, it also requires Nodes and Elements but as the name suggest, it considers only

the outer boundary of the domain

Finite Volume Method (FVM) : All Computational Fluid Dynamics (CFD) soft wares are based upon FVM.

Unit Volume is considered in Finite Volume Method (similar to Elements in Finite Element Method)

Variable properties at nodes are Pressure , Velocity , Area , Mass etc.

It is based on Navier – Stoke equations ( Mass ,Momentum and Energy Conservation equations)

Finite Difference Method (FDM) :Finite Element and Finite Difference share many common things.

In general, Finite difference Method is described as a way to solve difference equation.It uses Taylor’s series to convert differential equation into algebraic equation. Higher order terms neglected.

Is it possible to use all the above listed methods (FEA ,BEM , FVM, FDM)to solve same problem (say Cantilever problem)?Answer : YES ! But the difference is in Accuracy achieved , programming ease and timerequired to obtain the solution




Are FEA and FEM different ?

Finite Element Analysis (FEA) and Finite Element Method (FEM) both areone & the same.

FEA is a method/process based upon FEM

Term “FEA” is more popular in industries while “FEM” at Educationcenters




Why Finite Element Method ?

FEA is the most widely applied computer simulation method in Engineering.

It is very closely integrated with CAD/CAM applications.

It is very well proven , tested and validated method for simulating any complex

practical scenario in the area of Structural ,Thermal ,Vibration etc..




Application of FEM in Engineering

• Mechanical / Aerospace / Civil Engineering / Automobile Engineering

• Structural Analysis ( Static / Dynamic , Linear / Non-Linear )

• Thermal Analysis ( Steady State / Transient )

• Electromagnetic Analysis

• Geomechanics

• Biomechanics

• etc….


I d i “Fi i El A l i ”



Practical Applications of FEA

• Aerospace Domain

• Automotive Domain


I t d ti t “Fi it El t A l i ”



Practical Applications of FEA

• Hi-Tech /Electronics

• Medical Devices


I t d ti t “Fi it El t A l i ”



and many more ….

Practical Applications of FEAIntroduction to “Finite Element Analysis”




Advantages of FEA

• Visualization

• Design Cycle time

• No. of Prototypes

• Testing

• Design Optimization

FEA Computer Simulation allows multiple “What-if” scenariosto be studied quickly and effectively.





Available Commercial FEA Tools/Software Packages

Introduction to Finite Element Analysis




FEM Philosophy …in layman terms

The Philosophy of FEA can be explained with a small example such as “Measuring the Perimeter of a Circle”

If one need to evaluate the perimeter of a circle without using the conventional

formula (2*pi*r), FEA approach is analogous to Dividing the circle into a number of

segments and joining the points using Straight lines

Since it is very easy to measure the length of straight line. Measure the length of

one line and multiply it by No. of lines to get the perimeter.

Approximate results….isn’t it ?

What if we want to achieve moreaccurate result?





Another Example :

FEM Philosophy : DiscretizationIntroduction to Finite Element Analysis




Concept of Discretization (Meshing)

Physical System FE Model






Concept of FEM is all about Discretization (Meshing) i.e. Dividing abig structure/component into small discrete Blocks (Nodes andElement concept)

But why do we do this Meshing ???

No. of Points = ∞

DoF per point = 6

Total No of Equations to be solved

=∞ * 6 = ∞

No. of Points = 8

DoF per point = 6

Total No of Equations to be solved

=8 * 6 = 48

From Infinite to Finite…Hence theTerm “Finite Element Method”





Concept of Discretization (Meshing)Introduction to Finite Element Analysis





Parameters deciding the “Quality” of Mesh : • Aspect ratio

• Skew / Warpage

• Element internal Angles

• and more…

Bad Quality FEA

Good Quality FEA

Better the Mesh Quality , Better the Accuracy





Concept of “Shape Function”

FEA solves for DOF values only at nodes.

An element Shape Function is a

mathematical function that allows values of

a DOF from the nodes to be mapped to

points within the element.

Thus, the element shape function gives the

“shape” of the results within the element.

How well each assumed element shape

function matches the true behavior directlyaffects the accuracy of the solution (see

next slide)

FE Model

Solution

y




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Concept of “Shape Function”

Fine Meshing and/or Higher order element yield more accurate results

y




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Stiffness Matrix Derivation - using a Spring Element:y




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Different Type of Elements

Linear - 1st Order

Element

Quadratic 2nd

Order Element

HexahedralElement

QuadrilateralElement

TriangularElement

2D

3D




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Types of Boundary Conditions, Loads & Results

Boundary Conditions :

– Fixed Boundary Conditions (U , ROT etc.. = 0)

– Prescribed Displacements (U , ROT , Temp etc.. ≠ 0)

Loads:

– Point /Concentrated Load (Force) – Surface Load (Pressure , Flux etc..)

– Body Load (Temp , Inertia g etc..)

Results: – Displacement and Rotations

– Reaction Forces

– Stresses /Strains (Equivalent Von Mises , Directional & Principal )

– Temperature etc..




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Steps involved in FEA

Understanding the Problem (Thermal , Structural, Dynamic etc)

Element Selection (Solid , Shell , Beams etc)

Deciding the Boundary Conditions (Constraints , Connections etc..)

Load Application (Point , Surface , Body loads etc..)

Solution (Solver , Sub step / Time step , Nonlinearity etc)

In-Depth study & interpretation of Analysis Results (Sanity Checks)

Post processing of Results (Deflection , Stress , Strain etc..)

Report Preparation

Observation and Conclusion from the Analysis (MoS Calcs, Design ok)

Suggestion and Recommendation for Design Changes, if required.

PreProcessing

Solution

PostProcessing




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Basics for Static Structural & Dynamic Analysis

The Basics for Static Structural and

Dynamic Analysis are derived from thewell know General Equation of Motion:

For Static Structural Analysis Case:(Ignoring First two time dependent terms)

For Dynamic Analysis Case:

Assume free vibrations and ignore damping:[M ]{Ü} + [K] {U}= 0

Assume harmonic motion:

{U}= {U0 } sint

[K]- 2 [M ]){U}= {0}For non-trivial solutions | [K]- 2 [M] | must

vanish :

[K]- 2 [M] = 0Hence

= √ K/M ( Fundamental Natural Frequency Equation)




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Finite Element Analysis – At a Glance

Best Practice Approach




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Best Practices Approach

Plan your analysis Analysis type (Static/Dynamic, Linear/Non-Linear etc..)

Material Details (isotropic/orthotropic , Constant/Temp dependent)

Choice of Elements and Meshing (2D/3D , Hex / Tet)

Results Evaluation (Detailed Post processing)

Verification (Sanity Checks , Test data match)




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Plan your analysis

• What are the design objectives?

– What do you need to know?

– Why are you doing FEA?

• What is the design criteria?

– What engineering criteria will be used to

evaluate the design?




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• What are you trying to find out?• How much of the structure needs to be

modeled?

• What are the boundary conditions and loads?

• Do you need to know stresses, displacements,frequency, buckling or temperature?

• Get ballpark figures through hand-calculationsor test data, so you have an idea of how thestructure will behave and what numbers arereasonable.

Plan your analysis




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Type of analysis

• Is it static or dynamic?

– Are the loads applied gradually, or quickly?

– Vibrations? Seismic?

• Linear or nonlinear?

– Are there large deflections?

– Nonlinear materials?

– Contact?




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Is it really static?

• Static analysis assumes that inertial and

damping effects are negligible

• You can use time-dependency of loads as

a way to choose between static and

dynamic analysis.

– If the loading is constant over a relatively long

period of time, choose a static analysis.




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Changing Status - Contact Nonlinearities

Yield Point y

Elastic Plastic

Unloading

Material Non-linearity - Plasticity

Geometric Non-linearity – Large Deflection

Nonlinearities in System




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Materials

• Material properties used will be approximate!

• Is the material homogenous (the same

throughout)?

• Is it isotropic, orthotropic or anisotropic?• Is temperature dependence important to the

analysis?

• Is there rate or time dependence?

• Are composites used?




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Material Information

• For linear isotropic material, need modulus of

elasticity and Poisson’s ratio for a static analysis

• Need density for inertial loads

• For thermal analysis, need thermal conductivity• Also need Coefficient of Thermal Expansion for

thermal stress

• Need elastic plastic data for nonlinear materials




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Material Data Sources

• Testing: – Datapoint Labs:

http://www.datapointlabs.com/

– Axel Products: http://www.axelproducts.com/• Online:

– Matweb: http://www.matweb.com

– Material Data Network:http://matdata.net/index.jsp




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Linear or Nonlinear?

If no stress-strain data is given, the program will assume the analysis is

linear, and will use Young’s Modulus even if the part yields. This gives

erroneous results when the loads cause the model to exceed yield.

Actual stress

“Linear” stress




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Units

• Many general purpose FEA codes allow the userto enter a consistent unit set

• Make sure forces, displacements, material

properties have same units – these determine

the units of the results.




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Consistent Unit Systems

Mass unit kg kg lbf-s2/in slug

Length unit m mm in ft

Time unit s s s s

Gravity const. 9.807 9807 386 32.2

Force unit N mN lbf lbf

Pressure/Modulus of Elasticity Pa kPa psi psf

Density Unit kg/m3 kg/mm3 lbf-s2/in4 slug/ft3

Mod. Elasticity Steel 0.2E12 0.2E9 30E6 4.32E9

Mod. Elasticity Concrete 30E9 30000 4.5E6 648E6

Density of Steel 7860 7.86E-6 7.5e-4 15.2

Density of Concrete 2380 2.38E-6 2.2e-4 4.61




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Symmetry

• Types of symmetry: – Axisymmetry

– Rotational

– Planar or reflective – Repetitive or translational




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Symmetry, Interrupted

• Sometimes a small detail

interrupts symmetry

• Can ignore it, or treat it as

symmetric – best to do a

small test case if unsure




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Choice of elements

• 2D vs 3D vs line

– 2D elements are spatially

3D, but in the model they

are geometrically 2D

• Element Order: linear,

quadratic, polynomial

• Specialized elements?

(composites, concrete,

acoustics, coupled field)

• Geometric dimensionality--

how the geometry is




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Evaluating Results

• Stress criteria (Recall – SoM Theory of Failures)

• Factor of safety

• Is stress greater than yield?

• Don’t assume the results are correct! • Are the displacements in the expected range?

• Compare to tests or theory, when possible

• Does the displaced shape make sense?• Check reactions against applied loads




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Results Verification

• Use deformed animation to check loads and

look for cracks in model

• Combined load behavior is sometimes difficult to

predict – consider separating each load into itsown load case to check




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Document Everything!

• Detail all decisions made• Explain simplifications

• Detail loads and supports

• Document material data• Document test data

• Document as much results data as possible

– List reaction forces – Stresses

– Displacements




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Sanity Check: Peer Review

Having a fellow engineer review your analysis can help you catchproblems in the model.

Can be informal, one-on-one, or a formal review, with a teamlooking over the analysis.

Either way, it's better to be embarrassed in front of yourcolleagues, than in front of your customer! (Garbage in ..GarbageOut !)

FEA Traning09Sep2011

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