Introduction - Tennessee Technological University
Course inFEM – ANSYS ClassicIntroductionFEM – ANSYS ClassicComputational Mechanics, AAU, Esbjerg
Introduction Presentation– Anders Schmidt Kristensen– M.Sc. in Mechanical Eng. from AalborgUniversity in 1993– Ph.D. in Mechanical Eng. from AalborgUniversity in 1997– Consultant for PTC Denmark 1997-1998 –implementation of Pro/ENGINEER– 1998 to pt. Associate Prof. at AalborgUniversity EsbjergFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction2
Introduction The course is conducted the followingway:– 20-40 minutes lecture followed by 40-60minutes exercise (including a break)– Questions are allowed at any timeFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction3
References [ANSYS] ANSYS 10.0 Documentation (installed with ANSYS):––––––– Basic Analysis ProceduresAdvanced Analysis TechniquesModeling and Meshing GuideStructural Analysis GuideThermal Analysis GuideAPDL Programmer’s GuideANSYS Tutorials[Cook] Cook, R. D.; Concepts and applications of finite elementanalysis, John Wiley & Sons[Burnett] Burnett, D. S.; Finite element analysis: From concepts toapplication, Addison-Wesley[Kildegaard] Kildegaard, A.; Elasticitetsteori, Aalborg UniversitetFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction4
FEM - ANSYS Classic Lecture 1 - Introduction:––––– Lecture 2 - Preprocessor:––––– Boundary conditions/constraints/supportsLoadsMesh attributes, meshingSectionsLecture 4 – 2D plane models :––– Geometric modelingSpecification of Element type, Real Constants, Material, MeshFrame systemsTruss systemsElement tablesLecture 3 - Loads:–––– Introduction to FEMANSYS BasicsAnalysis phasesGeometric modelingThe first model: Beam model2D Plane Solid systemsGeometric modelingPostprocessingLecture 5 – Analysis types:–––Analysis typesModal analysisBuckling analysisFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction5
FEM - ANSYS Workbench/CAD Lecture 6 – 3D Solids:– 3D solid models– Booleans– Meshing issues Lecture 7 – 3D Modeling:– Operate– Import CAD– Advanced topics Lecture 8 – Analysis types:– Analysis types– Postprocessing– TimeHistProc Lecture 9 – Workbench basics:– Workbench basics– Geometric modeling Lecture 10 – Workbench analysis:– Workbench analysis typesFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction6
Overview CAD - Computer Aided Design– AutoCAD, Bentley MicroStation, CadKey CAD - Solid Modeling– Pro/ENGINEER, Inventor, IDEAS, CATIA, UGS, Solid Works FEM/FEA - Finite Element Method/Analysis– ANSYS, ABAQUS, Algor, Altair, MscNastran, Cosmos CAE - Computer Aided Engineering– Workbench, Design Space, Pro/Mechanica, CosmosWorks,Inventor/ANSYS BEM - Boundary Element MethodMesh-less systemsCFD - Computational Fluid Dynamics– ANSYS/Fluent, ANSYS/Flotran, ANSYS/CFX, CF-Design, Altair Multi-scale systemsOptimization – sizing, shape and topologyFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction7
Introduction to Finite Element Analysis What is Finite Element Analysis?AdvantagesDisadvantagesHow to avoid pitfallsHistoryFEM - ResourcesExamplesFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction8
What is Finite Element Analysis? The FEM is a computer-aidedmathematical technique for obtainingapproximate numerical solutions to theabstract equations of calculus that predictthe response of physical systemssubjected to external influences – [Burnett]FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction9
What is Finite Element Analysis?Each point have aninfinite number ofdeformation statevariables, i.e. degrees of freedom (dof)TransformationReal modelContinuumEach point have afinite number ofdeformation statevariables (u,v), i.e.degrees of freedomFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroductionAnalysis modelDiscrete10
What is Finite Element Analysis? Divide a continuum withinfinitely degrees offreedom in to finiteelements with a givennumber of degrees offreedom An element is geometricaldefined by a number ofnodes in which theelements are connected.The directions a node canmove in is termeddegrees of freedom (dof)FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction11
What is Finite Element Analysis? Following conditionsmust always be satisfied––––Equilibrium conditionsCompatibility conditionsConstitutive conditionsBoundary conditionsFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction12
What is Finite Element Analysis? Most FEA systems are displacementbased, i.e. an approximate displacementfield is establishedu(x,y) a1 a2 x a3 y Using a deformation based method yieldone unique kinematic determined systemto be determinedFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction13
What is Finite Element Analysis? The deformation method yield the FEMcharacteristic system of equations:Unknown displacement vector[K]{D} {R}Stiffness matrixLoad vector This system of equations is solved for {D} by,e.g. Gaussian elimination Note on matrix algebra is found hereFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction14
What is Finite Element Analysis? Formulation techniques to determine thestiffness matrix [K]– Direct method– Variational methods, i.e. principle of stationarypotential energy– Weighted Residual methods, e.g. the GalerkinformulationFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction15
What is Finite Element Analysis? The unknown displacements (can be any fieldvariable, e.g. temperature) {D} {u1, v1, u2, v2 }T in the element nodes (nodal values) aredetermined fromv3Unknown displacement vectoru3[K]{D} {R}Stiffness matrixLoad vectoryDisplacement field variables:In 2D: (u,v)In 3D: (u,v,w)FEM – ANSYS ClassicComputational Mechanics, AAU, Esbjergndof 6v2v1u2u1Introductionx16
What is Finite Element Analysis? It is assumed that displacements within anelement can be interpolated from knownnodal valuesu2ui ?u N1 u1 N2 u2u1u2uiu1x1xix2FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergN1 (1 – x/L)N2 x/LIntroductionx1xix2Linear case17
What is Finite Element Analysis?The element stiffness matrix for a beam element with 2 nodes and2 dof at each node [Cook], see also note:ndof 4Found by the Direct MethodUnknown displacement vectorndof x 1-1[K]{D} {R} {D} [K] {R}Known stiffness matrixndof x ndofFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroductionKnown load vectorndof x 118
Advantages Irregular BoundariesGeneral LoadsDifferent MaterialsBoundary ConditionsVariable Element SizeEasy ModificationDynamicsNonlinear Problems (Geometric and/or Material)FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction19
DisadvantagesNB: Always document assumptions! An approximate solution An element dependent solution– Shape quality of elements affect the solution,e.g. poorly shaped elements (irregularshapes) reduce accuracy of the FE solution– Element density affect the solution, i.e. theelement size should be adjusted to capturegradients Example: plate with a circular hole Errors in input dataFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction20
Disadvantages[Cook]FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction21
Disadvantages[Cook]FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction22
How to avoid pitfalls Carry out:– Hand calculations (Navier, Airy,Timoshenko )– Norm based calculations (Euro-Code, EN,API )– Experiments (strain-gauge, accelerometer )– Evaluate the kinematic behaviour(deformations)FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction23
History A. Hrennikoff [1941] - Lattice of 1D barsMcHenry [1943] - Model 3D solidsR. Courant [1943] - Variational formLevy [1947, 1953] - Flexibility & StiffnessM. J. Turner [1953] - FEM computations on a wingBoeing [1950's] Engineer's at Boeing apply FEM to deltawings Argryis and Kelsey [1954] - Energy Prin. for MatrixMethods Turner, Clough, Martin and Topp [1956] - 2D elements R. W. Clough [1960] – Coins the term “Finite Elements”FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction24
History 1963 - Mathematical validity of methodestablished - applied to non-structural problems 1960's - First general purpose FEA codedeveloped 1970's - Non-linear solvers developed 1980's - Graphical pre-/postprocessors aredeveloped 1990's - FEM tools integrated in CAD softwareFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction25
FEM - Resources 000ADINANISAGT StrudlABAQUSPlaxisFEM – ANSYS ClassicComputational Mechanics, AAU, Esbjerg Matlab based:– CalFem– FemLab CAE products:– Pro/ENGINEER Pro/FEA Pro/MECHANICA– Cosmos/Works– Inventor/ANSYS– IDEAS ResourcesIntroduction26
Introduction to ANSYS What is ANSYSFacilities in ANSYSInterfacing with ANSYSCommon termsFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction27
What is ANSYS ANSYS finite element analysis software enablesengineers to perform the following tasks:– Build computer models or transfer CAD models ofstructures, products, components, or systems.– Apply operating loads or other design performanceconditions.– Study physical responses, such as stress levels,temperature distributions, or electromagnetic fields.– Optimize a design early in the development process toreduce production costs.– Do prototype testing in environments where it otherwisewould be undesirable or impossible (for example,biomedical applications).FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction28
Facilities in ANSYS Structural LinearStructural NonlinearStructural Contact/Common BoundariesStructural DynamicStructural BucklingThermal AnalysisCFD AnalysisElectromagnetic - Low FrequencyElectromagnetics - High FrequencyField and Coupled-Field AnalysisFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction29
Facilities in ANSYS Solvers– Iterative– Sparse– Frontal– Explicit Preprocessing Postprocessing General FeaturesFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction30
Facilities in ANSYS.ANSYS Commands referenceANSYS Element reference.Basic Analysis ProceduresAdvanced Analysis Techniques.Structural Analysis Guide.ANSYS TutorialsFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction31
Facilities in ANSYSDuring an analysis, you may want to modify or deletecommands entered since your last SAVE or RESUME. You can access the following fileoperations from the session editordialog:––––OK: Enters the series of operationsdisplayed in the window below. You willuse this option to input the commandstring after you have modified it.Save: Saves the command stringdisplayed in the window below to aseparate file. ANSYS names the fileJobnam000.cmds, with eachsubsequent save operationincrementing the filename by one digit.You can use the /INPUT command toreenter the saved file.Cancel: Dismisses this window andreturns to your analysis.Help: Displays the command referencefor the UNDO command.The Session Editor is available ininteractive (GUI) mode only.FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction32
Facilities in ANSYSFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction33
Interfacing with ANSYS Matlab, ExcelCAD – Pro/ENGINEERIGESLog-file editingApplication Programming Interface (API)FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction34
Interfacing with ANSYSFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction35
Common termsProcessorFunctionGUI PathCommandPREP7Build the model (geometry, materials, etc.)Main Menu Preprocessor/PREP7SOLUTIONApply loads and obtain the finite element solutionMain Menu Solution/SOLUPOST1Review results over the entire model at specific time pointsMain Menu General Postproc/POST1POST26Review results at specific points in the model as a function of timeMain Menu TimeHist Postpro/POST26OPTImprove an initial designMain Menu Design Opt/OPTPDSQuantify the effect of scatter and uncertainties associated with inputvariables of a finite element analysis on the results of the analysisMain Menu Prob Design/PDSAUX2Dump binary files in readable formUtility Menu File List Binary Files/AUX2Utility Menu List Files Binary FilesAUX12Calculate radiation view factors and generate a radiation matrix for athermal analysisMain Menu Radiation Matrix/AUX12AUX15Translate files from a CAD or FEA programUtility Menu File Import/AUX15RUNSTATPredict CPU time, wavefront requirements, etc. for an analysisMain Menu Run-Time Stats/RUNSTFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction36
Basics Launching of ANSYSGraphical User Interface (GUI)Menus, dialogs and toolbarsWorking areaPreferencesFiles used by ANSYSANSYS MenusANSYS File menuANSYS PlotCtrls menuUnitsUndoHintsFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction37
Analysis phases Build the model. Apply loads andobtain the solution. Review the results.FEM – ANSYS ClassicComputational Mechanics, AAU, on38
Analysis phasesElement Type – select appropiate element type to modelthe structural response/behaviour most accurately.Real Constants – properties depending on the elementtype, e.g. cross-sectional properties, area, area momentof inertiaMaterial Props – material properties, e.g. modulus ofelasticity E and Poisson’s ratio nSections – cross-section definitionModeling – define the geometry of the structure - “it isessential to make some modeling considerations inthis phase”Meshing – divide the geometry of the structure intoelements – “take care of element distribution/density”FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction39
Analysis phasesAnalysis Type – specify the character of the problemDefine Loads – apply loads to the element modelSolve – run the solution process, e.g. for linear staticsystems solve (Gaussian elimination) for the unknowndisplacements:The global stiffnessUnknown displacement vectorndof x 1-1matrix [K]:ndof total number ofnodes x numberdegrees of freedomper node[K]{D} {R} {D} [K] {R}Known globalstiffness matrixndof x ndofFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroductionKnown load vectorndof x 140
Geometric modelingCreate – geometrical entitiesOperate – perform Boolean operationsMove / Modify – move or modify geometrical entitiesCopy – copy geometrical entitiesDelete – geometrical entitiesUpdate Geom – update the geometry in relationto for example buckling analysisFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction41
Modeling - Create The hierarchy of modeling entities is as listedbelow:––––––FEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergElements (and Element Loads)Nodes (and Nodal Loads)Volumes (and Solid-Model Body Loads)Areas (and Solid-Model Surface Loads)Lines (and Solid-Model Line Loads)Keypoints (and Solid-Model Point Loads)Introduction42
Examples - content Example0100’s: Link and/or beam modelsExample0200’s: Plane 2D modelsExample0300’s: Solid 3D modelsExample0400’s: Vibration/dynamic modelsExample0600’s: Thermal modelsFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction43
The first modelFEM – ANSYS ClassicComputational Mechanics, AAU, EsbjergIntroduction44
Computational Mechanics, AAU, Esbjerg FEM – ANSYS Classic References [ANSYS] ANSYS 10.0 Documentation (installed with ANSYS): – Basic Analysis Procedures – Advanced Analysis Techniques – Modeling and Meshing Guide – Structural Analysis Guide – Thermal Analysis Guide – APDL Programmer’s Guide – ANSYS Tutorials
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