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Chapter 16

Chapter 16. 非線性分析的收斂性探討 Convergence of Nonlinear Analysis . Contents. 16.1 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

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Chapter 16

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  1. Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis

  2. Contents 16.1 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. 第16.1節 何謂非線性分析？ What Are Nonlinear Analyses?

  4. Forces Forces Displacements Displacements 16.1.1 What is a Nonlinear Structure

  5. 16.1.2 Causes of Nonlinearities • Geometric Nonlinearity • Material Nonlinearity • Status Nonlinearity

  6. Forces Displacements Displacement Moment arm Force Geometric Nonlinearity

  7. Stress Stress Mild Steel Rubber Strain Strain Material Nonlinearity

  8. Force The contact area depends on the applied force Status Nonlinearity

  9. 16.1.3 Consequences of Nonlinearities • Principle of superposition no longer applicable • Solution may depend on loading history

  10. 第16.2節 解題方法 Solution Methods

  11. K(D) F(D) D 16.2.1 Equations for a Nonlinear Structure

  12. Error 3 F 2 Calculated Response 1 Actual Response D 16.2.2 Incremental Method

  13. Actual response F = F4 4 F3 3 F2 2 F1 1 D2 D1 D3 D = D4 16.2.3 Newton-Raphson Method

  14. Actual response F = F4 4 F3 3 F2 2 F1 1 D2 D1 D3 D = D4 16.2.4 Convergence Criteria in ANSYS

  15. 第16.3節 收斂性控制的一些重要觀念 Important Concepts for Convergence Controls

  16. Radius of convergence F Actual response Do Do D 16.3.1 Radius of Convergence

  17. 16.3.2 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.

  18. Actual response Load step 2 F = F4 4 F3 3 Load step 1 Load F2 2 F1 1 Substeps D2 D1 Time D3 D = D4 16.3.3 Load Steps, Substeps, and Equilibrium Iterations

  19. 16.3.4 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. 16.3.5 Automatic Time Stepping • For nonlinear problem, the user-input Dt is used as initial incremental time. • ANSYS adjusts Dt automatically according to the convergence behavior of the solution.

  21. 16.3.6 Text Output Information 1 2 3 4 5

  22. 16.3.7 Graphical Output Information

  23. 16.3.8 Automatic Nonlinear Solution Control • SOLCONTROL command can be used to activate automatic nonlinear solution control algorithm. • The default is ON.

  24. 第16.4節 收斂性控制的基本參數 Basic Solution Options

  25. Basic Solution Options

  26. 16.4.1 Analysis Type (ANTYPE) • For nonlinear analysis, only two analysis types applicable: STATIC and TRANS.

  27. 16.4.2 Nonlinear Geometry (NLGEOM) • NLGEOM turns ON/OFF the effects of geometric nonlinearity.

  28. 16.4.3 Load Step Time (TIME) • TIME specifies the time at the end of the following load step.

  29. 16.4.4 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.,

  30. 16.4.5 Automatic Time Stepping (AUTOTS) • AUTOTS turns ON/OFF the functions of auto time stepping.

  31. Load Stepped load Substeps Time 0 16.4.6 Ramped/Stepped Loading (KBC)

  32. 16.4.7 Output Controls (OUTRES) • OUTRES controls the amount of data stored in Jobname.RST.

  33. 16.4.8 Monitor File (MONTOR)

  34. 第16.5節 收斂性控制的進階參數 Advanced Solution Options

  35. Advanced Solution Options

  36. 16.5.1 Equation Solver (EQSLV) • EQSLV lets you choose the algorithm solving the equations.

  37. 16.5.2 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.

  38. 16.5.3 Number of Equilibrium Iterations (NEQIT) • NEQIT specifies the number of iterations beyond which ANSYS would start another “attempt”.

  39. 16.5.4 Convergence Criteria (CNVTOL) • CNVTOL overrides the default convergence criteria.

  40. 16.5.5 Newton-Raphson Option (NROPT) (b) Modified Method (c) Initial Method (a) Full Method

  41. 16.5.6 Line Search (LNSRCH) • LNSRCH turns ON/OFF the “line search” algorithm in ANSYS.

  42. 16.5.7 Predictor (PRED)

  43. 16.5.8 Adaptive Descent (NROPT)

  44. 16.5.9 Stress Stiffening (SSTIF, PSTRES) • SSTIF/PSTRES turns ON/OFF the computation of stress stiffness (Ks) and storing on file.

  45. 16.5.10 Cutback Control (CUTCONTROL) • CUTCONTROL specifies the conditions in which ANSYS would decrease time step during auto time stepping.

  46. 16.5.11 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”.

  47. 16.5.12 Stop Control (NCNV) • NCNV specifies the stop (failure) conditions of the computation.

  48. 16.5.13 Terminating an Analysis

  49. 16.5.14 Restarting an Analysis • An analysis terminated normally can be restarted.

  50. 16.6 Exercise: Hyperelastic Planar Seal

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