ANSYS Structural Analysis Guide-Chapter 7 Buckling Analysis b

3/6/2010METBD 450: Nonlinear Analyses, Part 1METBD 450 Lecture NotesNonlinear Analysis, Part 1Text: Building Better Products with FEA,by V. Adams & A. Askenazi, (Read pp. 425-448)Reference: ANSYS Structural Analysis GuideChapter 8: Nonlinear Structural AnalysisChapter 9: Contact"... most of the world is nonlinear."

"In many cases, simply understanding the effects of the nonlinearity can enable adesign engineer to make sound design decisions on linear results".When you start doing nonlinear analyses:move slowlyresearch your software's capabilitieshave a "coach"All problems could be run as nonlinear analyses, but is that necessary ?A nonlinear solution is a series of successive linear steps (iterations) along a path that is USE NONLINEAR ANALYSIS ?when the answer cannot be found in linear ear solutions require more datacan take more time to setup and solve (= more costly)Types of nonlinear behavior:yielding/plasticity (beyond Hooke's law:

 = E)changing contact or interferencelarge displacement, large rotation, large strain, stress stiffening (fishing pole, guitar string,drum head), sin()= and tan()=cturing processes (mold filling, forging, rolling, stamping, welding, coating)Beware: yield stress in the handbook is an estimated quantify, may vary around some meanand may be subject to experimental AT YOUR RESULTS: check for large displacement, penetration/interferenceSOLUTION APPROACHIterative solution: uses previous step results, to correct behavior and try again (/davej/…/lec_NL_1/4

3/6/2010METBD 450: Nonlinear Analyses, Part 1Raphson)Apply the loads GRADUALLY (incremental solution)In ANSYS, Load steps: user selected points which describe the load history (convenient tothe analyst).

In ANSYS, even though we are doing a static analysis, time is used simply as a counterduring the solution. If the analyst doesn't set the value for time, ANSYS increases time byone for each load step (i.e. time always increases during a solution).In ANSYS, Substeps: incremental solutions within a load step (for stability and accuracy);too small = long runs; too big = error or ANSYS, ramped loading (KBC,0) increases the load linearly from the previous step'slevel to the current load step's final value. The opposite of ramped loading is "stepped"loading (KBC,1).In ANSYS, Equilibrium iterations: solutions without increment in loading, just correction ofimbalance caused by nonlinear behavior. To establish a "stable" solution (equilibrium)before additional loading is l guidelines:The first load step should not cause yieldingTake small steps at an abrupt transition."Mildly" nonlinear problems can take larger stepsLET THE FEA PROGRAM ADJUST THE STEPPING PROCESS. Author: this may slowdown the run. Mr. J: better to get a solution with less of your time spent trying to controlit. ANSYS does a fairly good since ANSYS 5.5 the default setting for SOLCON = ON (automatic solution controls).

Based on the types of and severity of nonlinearities in your model, ANSYS sets many solutionoptions in a manner which is usually appropriate for success in on Controls makes automatic settings for:load incrementsautomatic adjustment of load increments during the solutionconvergence tolerancesconvergence enhancement "tools" (algorithms)reasonable limit on equilibrium iterationsactivates prediction of contact changes and onset of yieldingANSYS makes these settings based on years of experience in solving nonlinear analyses.

However, the analyst can override any of the automatic a nonlinear analysis, ANSYS writes a solution monitor text file (extension: mntr) whichyou can view to check on the progress of the cal Solution Tracking: during an interactive nonlinear analysis, ANSYS shows a graphof convergence norm values vs. /davej/…/lec_NL_2/4

3/6/2010METBD 450: Nonlinear Analyses, Part 1method for correcting the stiffness matrix between solution iterations based on thenonlinear behavior a "tangent" modulus corresponding to the previous of Nonlinear BehaviorMaterial Nonlinearity: plasticitybased on a yield criteria (Tresca, vonMises, Mohr-Coulomb, Drucker-Prager)requires definition of a hardening rule if unloading/reversed loading occurs:isotropic hardening (no Bauschinger effect) compressive yield = tensile yieldkinematic hardening (w/ Bauschinger effect) tensile yielding changes the compressiveyieldBi-linear (two straight lines); elastic modulus, tangent modulus, meet at the yield pointMultilinear ( > two straight lines); enter the stress vs. strain points along the ature and strain rate can effect the material datatrue stress-strain vs. engineering stress-strain dataIn ANSYS 5.7: Preprocessor > Material Props > Material Models ... >click on the material number you want to add data todouble-click "Structural"double-click "Nonlinear"double-click "Inelastic"double-click on the hardening rule choice (e.g., Kinematic hardening),double-click on the data format (e.g., Bilinear)pick the appropriate stress-strain options (e.g., to account for stress relaxation withincreasing temperature)for each temperature, enter the yield stress and the tangent modulus"Exit" Material Models, once you have entered the data.

You can graph or list the nonlinear data that you defined in the material model tables fromthe ANSYS Utility Menu:

Plot > Data Tables ...List > Properties > Data Tables ...Geometric Nonlinearityaccounts for changes in stiffness that are not from material properties (things like largedeflection, large rotation, large strain, stress stiffening).In ANSYS, Solution > Analysis Options >Large Deformation Effects = ON (or NLGEOM,ON)Boundary NonlinearityCONTACT /davej/…/lec_NL_3/4

3/6/2010METBD 450: Nonlinear Analyses, Part 1you can specify "contact pairs," ANSYS: Contact wizard for elements TARGE169, 170and CONTA171, 172, 173, 174point-to surface contact, ANSYS: CONTAC48, 49point-to-point contact, ANSYS CONTAC12, 52slide line contact, ANSYS CONTAC26Contact can be difficult to set up. Often it is used "only when necessary". Use it "judiciously",but don't be afraid to use it !ANSYS contact models (element options, real constants, material properties):formulation: penalty method or penalty + LaGrange multiplierspredictions: for best performancespecialty: sticking, hook, initial interference, sliding with friction, bonded, and moreopen = no stiffness, closed = stiff spring (stiffness may default or may require userspecification)Guidelines for Target/Contact Surfaces:if a convex face will contact a flat or concave face, the flat or concave face should be thetarget one surface has a coarser mesh, it should be the target one surface is stiffer than the other, it should be the target one surface is higher-order and the other is lower-order, the lower-order surface shouldbe the target one surface is larger, it should be the ER FORCESLoads can vary in large displacement/large rotation analyses. Should the load follow the partas it bends or keep its original orientation ?In ANSYS, with large deformation effects ON, pressure loads follow the surface as it bends,while force loads keep their original vector /davej/…/lec_NL_4/4

1/5/2010METBD 450: Nonlinear Analyses, Part 2METBD 450 Lecture NotesNonlinear Analysis, Part 2Text: Building Better Products with FEA,by V. Adams & A. Askenazi, (Read pp. 449-475)Reference: ANSYS Structural Analysis GuideChapter 7: Buckling AnalysisOther types of Nonlinearity:

Hyperelasticityrubber or elastomersstrain-displacement is nonlinear even at small strainHooke's law is not used, strain energy densityMooney-Rivlin material constantsViscoplasticity and viscoelasticitymetal at high temperature and glass/plasticstime dependent plasticity (depends on the rate ofloading)Nonlinear transientcrash or impactproperties and boundary conditions may change overtimeimplicit (LS-DYNA) or explicit (ANSYS) time integrationmethods"convergence nightmare"Creeptime varying permanent strain due to stress andtemperaturematerial "relaxes" under long term /davej/…/lec_NL_1/5

1/5/2010METBD 450: Nonlinear Analyses, Part 2Nonlinear Bucklingto find behavior after buckling or secondary states ofstabilityrequires eccentricity/imperfection of the FEA modelMetal Forminglarge strainforging, stamping, cold heading, rollingmay need a program that re-meshes during theanalysisLINEAR BUCKLING ANALYSIS (Eigenvalue Buckling)to determine the lack of stability in a structure due tocompressive loadpredicts the theoretical buckling strength of an ideal elasticstructureis often unconservativereports the critical load factorshows the buckled mode shape = the shape of the part asit bucklesConsider buckling when:there are high compressive loads in your systemthe structure appears long and slenderwhen the structure is thin-walledANSYS LINEAR BUCKLING PROCEDURE:Solve the linear, static analysis of a structureInclude the calculation of the stress stiffness matrixPSTRES,ON from Solution > Analysis OptionsFollow with an "Eigenvalue Buckling" analysis (the .emat /davej/…/lec_NL_2/5

1/5/2010METBD 450: Nonlinear Analyses, Part files from the previous static solution are required for thisanalysis)Select the Eigenvalue extraction method (usually: Subspace)and the number of modes to extract from Solution > AnalysisOptionsThe solution gives the critical load factor and you canpostprocess to see both the buckled mode shape and thecritical load EAR BUCKLING ANALYSISeccentric loading or geometry / imperfection is requiredis more accurate then linear buckling solutionsrequires gradual loading to find the point of instabilitycan model "post-buckling" response of a structureANSYS NONLINEAR BUCKLING PROCEDURE:(OPTIONAL) CLEAR the Options of previous analyses onthe same model, see Solution > Reset Options ...2.

Solve the linear, static analysis of a structure3.

Include large deformation effects

NLGEOM,ON fromSolution > Analysis Options4.

Use Output Controls to insure data other than the LastStep is available for postprocessing (use ALL SUBSTEPS,if possible)5.

Use gradual (ramped) loading and automatic time steppingfrom Solution > Time/Frequenc > Time and Substeps6.

Control convergence behavior for number of equilibriumiteration, convergence criteria, etc. under Solution >Nonlinear ...7.

Difficult problems (or analysis of post-buckling) may require1.

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1/5/2010METBD 450: Nonlinear Analyses, Part 2use of the "Arc Length" convergence enhancement tool fora successful EAR RESULTS DATAmore results info to deal withoutput of intermediate load steps and substepsyou can limit the output data (to save disk space):in initial debugging runs, try storing only thedisplacement results for large modelsif convergence is a problem, storing every solution canhelp you find problemsMethodologyUse small, simple test models to debug newfeatures/elementsrun a linear solution first:to debug boundary conditionsto evaluate mesh qualityAdd each nonlinearity after you have control of the previousoneadd each nonlinearity from easiest to hardest degree ofdifficulty:large deflection effectscontactplasticityWHAT TO DO WHEN IT WON'T CONVERGEcheck the solution output and error log file for messagesapply the load in more, smaller substepsallow more equilibrium iterationstry alternative material models (bilinear vs. multilinear,/davej/…/lec_NL_4/5

1/5/2010METBD 450: Nonlinear Analyses, Part 2different hardening rules, etc.)inspect the mesh in high stress regions for poor elementshapesre-evaluate you choice of loads (get rid of point loads,overconstrained edges)look at the last good solution for any irregularitiesre-check element options (and material properties, and realconstants, and load values, and dimensions)experiment with convergence enhancement tools in thecodedeactivate one or more of the nonlinear conditions to findthe problem(rarely) loosen the convergence criteria - to find theproblem - then tighten it up againRESTARTING a SolutionWhen a job stops due to failure to converge, you can adjustsolution parameters (substep size, convergence criteria, no. ofequilibrium iterations) and "restart" the analysis from where itstopped.

Sometimes, this can help you get past a difficult loadincrement.A restarted analysis will continue to write results on the sameresults file, as good solutions are completed. Some of the filesfrom the prior run must be available for the restart /davej/…/lec_NL_5/5