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Why to Study Finite Element Analysis!
That is, “Why to take 2.092/3”
Klaus-Jürgen Bathe
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Why You Need to Study Finite Element Analysis!
Klaus-Jürgen Bathe
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Analysis is the key to effective designeffective design
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• fluid flows (with or without heat transfer)
We perform analysis for:
• deformations and internal forces/stresses
• temperatures and heat transfer in solids
• fluid flows (with or without heat transfer)
• conjugate heat transfer (between solids
and fluids)
• etc...
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•
An effective designeffective design is one that:
• performs the required task efficiently
• is inexpensive in materials used
• is safe under extreme operatinis safe under extreme operating
conditions
• can be manufactured inexpensively
• is pleasing/attractive to the eye
• etc...
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AnalysisAnalysis means probing into,
modeling, simulating naturesimulating nature
Therefore, analysisanalysis gives us insight intogives us insight intothe world we live in,the world we live in, and this
Enriches Our life
Many great philosophers were analysts and engineers …
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AnalysisAnalysis is performed based upon the laws of mechanicsmechanics
Mechanics
Solid/structural mechanics
(Solid/structural dynamics)
Fluid mechanics
(Fluid dynamics)
Thermomechanics (Thermo
dynamics)
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Solution of
The process of analysis
Physical problem (given by a “design”)
Mechanical model
Improve model
Change of physical problem
Solution of mechanical
model
Interpretation of results
Refine analysis
Design improvement
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Analysis of helmet subjected to impact
New Helmet Designs
CAD models of MET bicycle helments removed due to copyright restrictions.
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Analysis of helmet impact
Laboratory Test
Head
ADINA Simulation Model
Helmet
Anvil
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Analysis of helmet subjected to impact
Comparison of computation with laboratory test results
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In engineering practice, analysis
is largely performed with the use of finite element computer programs (such as NASTRAN, ANSYS, ADINA, SIMULIA, etc…)
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desi n CAD ro rams Catia
These analysis programs are
interfaced with computer-aided design (CAD) programs Catia,g ( ) p g , SolidWorks, Pro/Engineer, NX,
etc.
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The process of modeling for analysis
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The process of modeling for analysis (continued)
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2-D solid
Hierarchical modelingHierarchical modeling
Means taking increasingly more complex models to simulate nature with increasing accuracy
Increasingly
more
Assumptions:Assumptions:
spring, rod, truss
beam, shaft
complex
models
2-D solid
plate
shell
fully three-dimensional
dynamic effects
nonlinear effects
naturenature
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CAD and Analysis
In CAD System
CAD solid model is established
In Analysis System
• Preparation of the
mathematical model
• Meshing and Solution
• Presentation of results
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CAD model of missile
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Finite Element Representation
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Pump
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Finite Element Representation
Number of equations 1,040,049
Pump
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Engine block - photo Courtesy of AB Volvo Penta. Used with permission
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Engine block - mesh Courtesy of AB Volvo Penta. Used with permission
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for a reasonable finite element- alwa s ivey g ,
A reliable and efficient finite element
discretization scheme should
- for a well-posed mathematical model
- always give, for a reasonable finite element mesh, a reasonable solution, and
- if the mesh is fine enough, an accurate solution should be obtained
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- and meshin usedg
Element Selection
We want elements that are reliable for any
- geometry
- boundary conditions
- and meshing used
The displacement method is not
reliable for
- plates and shells
- almost incompressible analysis
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Schematic solution results
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Example problem:
to show what can go wrong
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1 112.4 110.5 110.6
Smallest six frequencies (in Hz) of 16 element meshConsistent mass matrix is used
16el. model 16el. model 16x64 element model Mode
Use of 3x3 Use of 2x2 use of 3x3 Gauss number
Gauss integration Gauss integration integration
1 112.4 110.5 110.6
2 634.5 617.8 606.4
3 906.9 905.5 905.2
4 154 8 958.4 * 1441
5 2654 1528 2345
6 2691 2602 2664
*Spurious mode (phantom or ghost mode)
Ref: Finite Element Procedures (by K. J. Bathe), Prentice Hall, 1996
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Some analysis experiences
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analyses
Tremendous advances have taken place –
• mixed optimal elements have greatly
increased the efficiency and reliability of
analyses
• sparse direct solvers and algebraic
multigrid iterative solvers have lifted the
analysis possibilities to completely new levels
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– lar e civil en ineerin structures
In Industry: Two categories of analyses
• Analysis of problems for which test results are
scarce or non-existent
– large civil engineering structuresg g g
• Analysis of problems for which test results can
relatively easily be obtained
– mechanical / electrical engineering structures
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• Seismic anal sis of ma or brid esy j g
Examples of category 1 problems
• Analysis of offshore structures
• Seismic analysis of major bridges
– only "relatively small" components can be
tested
Reliable analysis procedures are crucial
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• Ref. I. Holand, "Lessons to be learned from
Sleipner platform
Recall the catastrophic failure in 1991 of the
Sleipner platform in the North Sea
• Ref. I. Holand, "Lessons to be learned from
the Sleipner accident"
Proceedings, NAFEMS World Congress '97, Stuttgart,
Germany, April 1997.
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• Probabl due to the Slei ner accidenty p ,
Heidrun platform
• The world's largest of its kind (in 1997)
• Probably due to the Sleipner accident,
increased analysis attention was given to
critical components
– designers and analysts worked closely
together
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Accuracy - part of reality
Coarse Mesh Converged Mesh Reference Mesh
Correct surface stress prediction at critical locations is of vital importance for fatigue life determination
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Seismic analysis of major California bridges
• Damage from the 1989 and 1994 earthquakes
• Objective is to retrofit / strengthen the bridges
(including the famous San Francisco-Oakland
Bay Bridge)
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Photo by Luis Alberto Higgins.
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Photo by USGS.
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Examples of category 2 problems
• Metal forming, crash and crush analyses in
the automobile industries
• These types of problems can now be solved
much more reliably and efficiently than just a
few years ago
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Roof crush analysis
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Roof crush analysis
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Roof crush analysis
ADINA
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Roof crush analysis
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Material model:
slab – aluminum, elastic-plastic material
roll – rigid
Rolling
Multi-pass rolling
ADINA:
static, implicit analysis
slab – 2160 u/p (4-node) elements, plastic-multilinear material model
roll – 360 rigid contact segments
contact algorithms – constraint-function
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Rolling
multi pass rolling
Initial mesh
Final mesh
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Rolling
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Bumper reinforcement
bumper
reinforcement
(steel)
molding
(plastic)
Bumper cross-section
Image from the Open Clip Art Library.
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Bumper reinforcement
pad
upper binder
initial blank
deformed sheet
punch
lower binder
Stamping on a single action press,
“springs” provide constant holding force
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Bumper reinforcement
Material data:
steel, 1.8 mm
friction coefficient, µ = 0.125
ADINA
static, implicit analysis
2750 MITC elements, 4-nodes
plastic-multilinear material model
rigid-target contact
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Bumper reinforcement
Effective plastic strain distribution
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Bumper reinforcement
Final thickness distribution
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Fluid-flows fully-coupled with structural
interactions –
an increasingly important analysis area
• Full Navier-Stokes equations for incompressible or fully compressible flows
• Arbitrary Lagrangian-Eulerian formulation for the fluid
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Shock absorber
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Shock absorber
Assembly parts
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Shock absorber
Structural model
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Shock absorber
Fluid mesh
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Shock absorber
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Shock absorber
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e e on
Specular Radiation Model
Lens
Direct Filament Radiation
Specular
R fl cti
Transmission
& Absorption
Bulb
Reflector
Power Input
Reflection
Bulb Absorption &
Re-Radiation
Filament
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Lamp Internal Air Volume Mesh
• 200,000 Tet
Elements
• Smooth
Transitioning
• Localized Mesh
Refinement
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Lens Temperature
*>248.0°F
220.0
240.0
MeasuredPredicted
Max 206.1 Max206.1
*<100.0°F
100.0
120.0
140.0
160.0
180.0
200.0
220.0
Max
211
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Signal Housing Temperature
*>247.8°F
220.0
240.0
MeasuredPredicted
Max 256
Max 237.4 Max237.4
*<100.0°F
100.0
120.0
140.0
160.0
180.0
200.0
220.0
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Exhaust Manifold Mesh
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Detail showing mesh mismatch
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Plot of effective stress in the solid
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Plot of pressure in the fluid
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Fuel pump
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Fuel pump
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Blood flow through an artery
Solid mesh Fluid mesh
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Blood flow through an artery
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Blood flow through a stenotic artery
Image by the National Heart, Lung, and Blood Institute.
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Blood flow through a stenotic artery
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Analysis of an artificial lung
Artificial Lung
Courtesy of MC3. Used with permission.
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Blood
flow
inlet
Blood
flow
outlet
Fiber
bundle –
exchange
CO2 in
blood with
oxygen
Flow
separator
Particle
trace plot
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Analysis of an artificial lungParticle trace
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Radio-frequency tissue ablation
Electrode Lesion
Courtesy of Medtronic, Inc. Used with permission.
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Radio-frequency tissue ablation
Blood
Electrode
Catheter
Tissue
Symmetry
face
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Radio-frequency tissue ablation
Temperature variation during ablation cycle
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So, why study finite element analysis?
because -
You learn modern analysis techniques used widely in engineering practice and the sciences
You learn how to establish computational models of problems of solids and fluids, solve them on a laptop, and assess the accuracy of the results
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You capitalize on your knowledge of mechanics, reinforce your knowledge, and solve problems that can only be tackled numerically on the computer
Great knowledge in your “toolbox” whatever your goals!
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MIT OpenCourseWarehttp://ocw.mit.edu
2.092 / 2.093 Finite Element Analysis of Solids and Fluids I Fall 2009
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