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Chapter 16非線性分析的收斂性探討 Convergence of Nonlinear Analysis 2/50Contents16.1何謂非線性分析？ What Are Nonlinear Analyses? 16.2解題方法 Solution Methods 16.3收斂性控制的一些重要觀念 Important Concepts for Convergence Controls 16.4收斂性控制的基本參數 Basic Solution Options 16.5收斂性控制的進階參數 Advanced Solution Options 16.6練習題：橡膠密封墊分析 Exercise: Hyperelastic Planar Seal 3/50第16.1節何謂非線性分析？What Are Nonlinear Analyses? 4/5016.1.1 What is a Nonlinear StructureDisplacementsForcesDisplacementsForces5/5016.1.2 Causes of Nonlinearities Geometric Nonlinearity Material Nonlinearity Status Nonlinearity6/50Geometric NonlinearityForceDisplacementMoment armForcesDisplacements7/50Material NonlinearityStrainStrainStressStressMild SteelRubber8/50Status NonlinearityThe contact area depends on the applied forceForce9/5016.1.3 Consequences of Nonlinearities Principle of superposition no longer applicable Solution may depend on loading history10/50第16.2節解題方法Solution Methods 11/5016.2.1 Equations for a Nonlinear Structure FDDKDK(D)F(D)12/5016.2.2 Incremental Method FDDKFErrorCalculated ResponseActualResponse123D13/5016.2.3 Newton-Raphson MethodD = D4F = F4Actualresponse1234D1D2D3F1F2F314/5016.2.4 Convergence Criteria in ANSYSD = D4F = F4Actualresponse1234D1D2D3F1F2F3maxmax 005.0 05.0FFDD15/50第16.3節收斂性控制的一些重要觀念Important Concepts for Convergence Controls 16/5016.3.1 Radius of ConvergenceDFActualresponseDoDoRadius of convergence17/5016.3.2 Consistent Stiffness Matrix Tangent stiffness Additional stiffness due to deformation (geometric change) Additional stiffness due to stress stiffening Additional stiffness due to change of loading direction.auincKKKKK18/5016.3.3 Load Steps, Substeps, and Equilibrium IterationsSubstepsTimeLoadLoad step 2Load step 1D = D4F = F4Actualresponse1234D1D2D3F1F2F319/5016.3.4 Concepts of Time The ends of load steps or substeps can be identified by time. For dynamic problem, time is used as a real-world clock. For static problem, time is used as a counter.20/5016.3.5 Automatic Time Stepping For nonlinear problem, the user-input t is used as initial incremental time. ANSYS adjusts t automatically according to the convergence behavior of the solution.21/5016.3.6 Text Output Information1234522/5016.3.7 Graphical Output Information23/5016.3.8 Automatic Nonlinear Solution Control SOLCONTROL command can be used to activate automatic nonlinear solution control algorithm. The default is ON.24/50第16.4節收斂性控制的基本參數Basic Solution Options 25/50Basic Solution Options01020304050607080910SOLCONTROL, KeyANTYPE, AntypeNLGEOM, KeyTIME, TIMENSUBST, NSBSTP, NSBMX, NSBMN, CarryDELTIM, DTIME, DTMIN, DTMAX, CarryAUTOTS, KeyKBC, KEYOUTRES, Item, FREQ, CnameMONITOR, VAR, Node, Lab 26/5016.4.1 Analysis Type (ANTYPE) For nonlinear analysis, only two analysis types applicable: STATIC and TRANS.27/5016.4.2 Nonlinear Geometry (NLGEOM) NLGEOM turns ON/OFF the effects of geometric nonlinearity.28/5016.4.3 Load Step Time (TIME) TIME specifies the time at the end of the following load step.29/5016.4.4 Number of Substeps (NSUBST, DELTIM) NSUBST specifies number of substeps for the following load step. DELTIM specifies time for each substep for the following load step. The two commands are equivalent, i.e.,NSUBSTDELTIMTIMENSUBST, NSBSTP, NSBMX, NSBMN, CarryDELTIM, DTIME, DTMIN, DTMAX, Carry30/5016.4.5 Automatic Time Stepping (AUTOTS) AUTOTS turns ON/OFF the functions of auto time stepping.31/5016.4.6 Ramped/Stepped Loading (KBC)0TimeLoadStepped loadSubsteps32/5016.4.7 Output Controls (OUTRES) OUTRES controls the amount of data stored in Jobname.RST.OUTRES, Item, FREQ, Cname33/5016.4.8 Monitor File (MONTOR)34/50第16.5節收斂性控制的進階參數Advanced Solution Options 35/50Advanced Solution Options01020304050607080910111213EQSLV, Lab, TOLER, MULTSOLCONTROL, Key1, Key2NEQIT, NEQITCNVTOL, Lab, VALUE, TOLER, NORM, MINREFNROPT, Option, AdptkyLNSRCH, KeyPRED, Sskey, -, LskeySSTIF, KeyPSTRES, KeyCUTCONTROL, Lab, VALUE, OptionTIMINT, Key, LabTINTP, GAMMA, .NCNV, KSTOP, DLIM, ITLIM, ETLIM, CPLIM 36/5016.5.1 Equation Solver (EQSLV) EQSLV lets you choose the algorithm solving the equations.37/5016.5.2 Time Step Prediction Based on Contact Status (SOLCONTROL) The second key of SOLCONTROL command is to ask ANSYS to adjust time steps according to contact status.SOLCONTROL, Key1, Key238/5016.5.3 Number of Equilibrium Iterations (NEQIT) NEQIT specifies the number of iterations beyond which ANSYS would start another “attempt”. 39/5016.5.4 Convergence Criteria (CNVTOL) CNVTOL overrides the default convergence criteria. 40/5016.5.5 Newton-Raphson Option (NROPT)(a) Full Method(b) Modified Method(c) Initial MethodNROPT, Option, Adptky41/5016.5.6 Line Search (LNSRCH) LNSRCH turns ON/OFF the “line search” algorithm in ANSYS. 42/5016.5.7 Predictor (PRED)43/5016.5.8 Adaptive Descent (NROPT)NROPT, Option, Adptky44/5016.5.9 Stress Stiffening (SSTIF, PSTRES) SSTIF/PSTRES turns ON/OFF the computation of stress stiffness (Ks) and storing on file. 45/5016.5.10 Cutback Control (CUTCONTROL) CUTCONTROL specifies the conditions in which ANSYS would decrease time step during auto time stepping. 46/5016.5.11 Time Integration Effects (TIMINT, TINTP) TIMINT turns ON/OFF transient effects. The parameter GAMMA of TINTP command can be used to introduce a “numerical damping”. TIMINT, Key, LabTINTP, GAMMA, .47/5016.5.12 Stop Control (NCNV) NCNV specifies the stop (failure) conditions of the computation.NCNV, KSTOP, DLIM, ITLIM, ETLIM, CPLIM 48/5016.5.13 Terminating an Analysis49/5016.5.14 Restarting an Analysis An analysis terminated normally can be restarted.50/5016.6 Exercise: Hyperelastic Planar Seal
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