Unformatted text preview: Why to Study Finite Element Analysis!
That is, "Why to take 2.092/3" KlausJrgen Bathe Why You Need to Study Finite Element Analysis!
KlausJrgen Bathe Analysis is the key to effective design 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... An effective design is one that: performs the required task efficiently is inexpensive in materials used is safe under extreme operatin operating conditions can be manufactured inexpensively is pleasing/attractive to the eye etc... Analysis means probing into, modeling, simulating nature
Therefore, analysis gives us insight into the world we live in, and this Enriches Our life Many great philosophers were analysts and engineers ... Analysis is performed based upon the laws of mechanics Mechanics Solid/structural mechanics (Solid/structural dynamics) Fluid mechanics (Fluid dynamics) Thermo mechanics (Thermo dynamics) The process of analysis
Physical problem (given by a "design") Mechanical model
Solution of mechanical model
Interpretation of results
Design improvement Refine analysis Change of physical problem Improve model Analysis of helmet subjected to impact CAD models of MET bicycle helments removed due to copyright restrictions. New Helmet Designs Analysis of helmet impact Laboratory Test
Head ADINA Simulation Model Helmet Anvil Analysis of helmet subjected to impact Comparison of computation with laboratory test results In engineering practice, analysis is largely performed with the use of finite element computer programs (such as NASTRAN, ANSYS, ADINA, SIMULIA, etc...) These analysis programs are interfaced with computeraided design (CAD) programs Catia, design (CAD) programs Catia, SolidWorks, Pro/Engineer, NX, etc. The process of modeling for analysis The process of modeling for analysis
(continued) Hierarchical modeling
Means taking increasingly more complex models to simulate nature with increasing accuracy
Increasingly more complex models Assumptions: spring, rod, truss beam, shaft 2D solid plate shell fully threedimensional dynamic effects nonlinear effects nature 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 CAD model of missile Finite Element Representation Pump Finite Element Representation
Number of equations 1,040,049 Pump Engine block  photo
Courtesy of AB Volvo Penta. Used with permission Engine block  mesh
Courtesy of AB Volvo Penta. Used with permission A reliable and efficient finite element discretization scheme should
 for a wellposed mathematical model
 always give, always give, for a reasonable finite element mesh, a reasonable solution, and  if the mesh is fine enough, an accurate solution should be obtained Element Selection
We want elements that are reliable for any  geometry  boundary conditions  and meshing used meshing The displacement method is not reliable for  plates and shells  almost incompressible analysis Schematic solution results Example problem: to show what can go wrong Smallest six frequencies (in Hz) of 16 element mesh Consistent mass matrix is used Mode number
1 16el. model Use of 3x3
112.4 16el. model Use of 2x 2
110.5 16x64 element model use of 3x3 Gauss integration
110.6 Gauss integration Gauss integration 634.5 906.9 1548 2654 2691 617.8 905.5 958.4 * 1528 2602 2 3 4 5 6 606.4 905.2 1441 2345 2664 *Spurious mode (phantom or ghost mode)
Ref: Finite Element Procedures (by K. J. Bathe), Prentice Hall, 1996 Some analysis experiences 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 In Industry: Two categories of analyses Analysis of problems for which test results are scarce or nonexistent large civil engineering structures large engineering Analysis of problems for which test results can relatively easily be obtained mechanical / electrical engineering structures Examples of category 1 problems Analysis of offshore structures Seismic analysis of major bridges analysis major bridges only "relatively small" components can be tested Reliable analysis procedures are crucial 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. Heidrun platform The world's largest of its kind (in 1997) Probably due to the Sleipner accident, Probably Sleipner accident, increased analysis attention was given to critical components designers and analysts worked closely together 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 Seismic analysis of major California bridges Damage from the 1989 and 1994 earthquakes Objective is to retrofit / strengthen the bridges (including the famous San FranciscoOakland Bay Bridge) Photo by Luis Alberto Higgins. Photo by USGS. 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 Roof crush analysis Roof crush analysis Roof crush analysis
ADINA Roof crush analysis Rolling
Multipass rolling Material model:
slab aluminum, elasticplastic material roll rigid ADINA:
static, implicit analysis slab 2160 u/p (4node) elements, plasticmultilinear material model roll 360 rigid contact segments contact algorithms constraintfunction Rolling
multi pass rolling Initial mesh Final mesh Rolling Bumper reinforcement bumper Image from the Open Clip Art Library. molding (plastic) reinforcement (steel) Bumper crosssection Bumper reinforcement
upper binder pad initial blank deformed sheet lower binder punch Stamping on a single action press, "springs" provide constant holding force Bumper reinforcement
Material data:
steel, 1.8 mm friction coefficient, = 0.125 ADINA
static, implicit analysis 2750 MITC elements, 4nodes plasticmultilinear material model rigidtarget contact Bumper reinforcement Effective plastic strain distribution Bumper reinforcement Final thickness distribution Fluidflows fullycoupled with structural interactions an increasingly important analysis area Full NavierStokes equations for incompressible or fully compressible flows Arbitrary LagrangianEulerian formulation for the fluid Shock absorber Shock absorber Assembly parts Shock absorber Structural model Shock absorber Fluid mesh Shock absorber Shock absorber Specular Radiation Model
Direct Filament Radiation Transmission & Absorption Specular Reflection Reflection Power Input Reflector Bulb
Filament Lens Bulb Absorption & ReRadiation Lamp Internal Air Volume Mesh 200,000 Tet Elements Smooth Transitioning Localized Mesh Refinement Lens Temperature
Predicted
*>248.0F 240.0 220.0 200.0 180.0 160.0 Measured Max 211 140.0 120.0 100.0 *<100.0F Max 206.1 Signal Housing Temperature
Predicted
*>247.8F Measured
240.0 220.0 200.0 180.0 160.0 140.0 120.0 100.0 *<100.0F
Max 237.4 Max 256 Exhaust Manifold Mesh Detail showing mesh mismatch Plot of effective stress in the solid Plot of pressure in the fluid Fuel pump Fuel pump Blood flow through an artery
Fluid mesh Solid mesh Blood flow through an artery Blood flow through a stenotic artery Image by the National Heart, Lung, and Blood Institute. Blood flow through a stenotic artery Analysis of an artificial lung Artificial Lung
Courtesy of MC3. Used with permission. Blood flow inlet Blood flow outlet Flow separator Fiber bundle exchange CO2 in blood with oxygen Particle trace plot Analysis of an artificial lung Particle trace Radiofrequency tissue ablation Electrode Lesion Courtesy of Medtronic, Inc. Used with permission. Radiofrequency tissue ablation
Catheter Blood
Electrode Tissue
Symmetry face Radiofrequency tissue ablation Temperature variation during ablation cycle 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 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! MIT OpenCourseWare http://ocw.mit.edu 2.092 / 2.093 Finite Element Analysis of Solids and Fluids I
Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. ...
View
Full Document
 Fall '09
 KlausJürgenBathe
 Fluid Dynamics, Deformation, Finite Element Analysis, Computational fluid dynamics

Click to edit the document details