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Transcript of FEA Traning09Sep2011
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Finite Element AnalysisIntroduction to
Praveen AhujaTechnical Manager - CAE
HCL Technologies , Bangalore
8/13/2019 FEA Traning09Sep2011
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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
Introduction to “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
Introduction to “Finite Element Analysis”
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Cantilever Beam Deflection
Analytical Approach – An example
Cantilever Beam Deflection – Analytical Approach
Analytical Approach
provides VeryAccurate Solution
Introduction to “Finite Element Analysis”
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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:
Introduction to “Finite Element Analysis”
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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”
Introduction to “Finite Element Analysis”
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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
Introduction to “Finite Element Analysis”
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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
Introduction to “Finite Element Analysis”
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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..
Introduction to “Finite Element Analysis”
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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….
Introduction to “Finite Element Analysis”
I d i “Fi i El A l i ”
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Practical Applications of FEA
• Aerospace Domain
• Automotive Domain
Introduction to “Finite Element Analysis”
I t d ti t “Fi it El t A l i ”
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Practical Applications of FEA
• Hi-Tech /Electronics
• Medical Devices
Introduction to “Finite Element Analysis”
I t d ti t “Fi it El t A l i ”
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and many more ….
Practical Applications of FEAIntroduction to “Finite Element Analysis”
Introduction to “Finite Element Analysis”
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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.
Introduction to “Finite Element Analysis”
Introduction to “Finite Element Analysis”
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Available Commercial FEA Tools/Software Packages
Introduction to Finite Element Analysis
Introduction to “Finite Element Analysis”
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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?
Introduction to Finite Element Analysis
Introduction to “Finite Element Analysis”
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Another Example :
FEM Philosophy : DiscretizationIntroduction to Finite Element Analysis
Introduction to “Finite Element Analysis”
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Concept of Discretization (Meshing)
Physical System FE Model
Introduction to Finite Element Analysis
Introduction to “Finite Element Analysis”
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Concept of Discretization (Meshing)
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”
Introduction to Finite Element Analysis
Introduction to “Finite Element Analysis”
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Concept of Discretization (Meshing)Introduction to Finite Element Analysis
Introduction to “Finite Element Analysis”
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Concept of Discretization (Meshing)
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
Introduction to Finite Element Analysis
Introduction to “Finite Element Analysis”
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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
Introduction to “Finite Element Analysis”
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Stiffness Matrix Derivation - using a Spring Element:y
Introduction to “Finite Element Analysis”
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Different Type of Elements
Linear - 1st Order
Element
Quadratic 2nd
Order Element
HexahedralElement
QuadrilateralElement
TriangularElement
2D
3D
Introduction to “Finite Element Analysis”
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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 !)
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