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Chapter 16
非線性分析的收斂性探討 Convergence of Nonlinear Analysis
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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
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第 16.1 節
何謂非線性分析？What Are Nonlinear Analyses?
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16.1.1 What is a Nonlinear Structure
Displacements
Forces
Displacements
Forces
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16.1.2 Causes of Nonlinearities
• Geometric Nonlinearity
• Material Nonlinearity
• Status Nonlinearity
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Geometric Nonlinearity
Force
Displacement
Moment arm
Forces
Displacements
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Material Nonlinearity
Strain Strain
Stress
Stress
Mild Steel Rubber
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Status Nonlinearity
The contact area depends on the applied force
Force
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16.1.3 Consequences of Nonlinearities
• Principle of superposition no longer applicable
• Solution may depend on loading history
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第 16.2 節
解題方法Solution Methods
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16.2.1 Equations for a Nonlinear Structure
FDDK
D
K(D)F(D)
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16.2.2 Incremental Method
FDDK
F
Error
Calculated Response
ActualResponse
1
2
3
D
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16.2.3 Newton-Raphson Method
D = D4
F = F4
Actualresponse
1
23
4
D1 D2 D3
F1
F2
F3
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16.2.4 Convergence Criteria in ANSYS
D = D4
F = F4
Actualrespons
e
1
23
4
D1 D2 D3
F1
F2
F3
max
max
005.0
05.0
FF
DD
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第 16.3 節
收斂性控制的一些重要觀念Important Concepts for Convergence Controls
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16.3.1 Radius of Convergence
D
F
Actualresponse
Do Do
Radius of convergence
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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.
aσuinc KKKKK
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16.3.3 Load Steps, Substeps, and Equilibrium Iterations
Substeps
Time
Load
Load step 2
Load step 1
D = D4
F = F4
Actualrespons
e
1
23
4
D1 D2 D3
F1
F2
F3
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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.
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16.3.5 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.
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16.3.6 Text Output Information
1
2
3
45
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16.3.7 Graphical Output Information
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16.3.8 Automatic Nonlinear Solution Control
• SOLCONTROL command can be used to activate automatic nonlinear solution control algorithm.
• The default is ON.
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第 16.4 節
收斂性控制的基本參數Basic Solution Options
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Basic Solution Options
01
02
03
04
05
06
07
08
09
10
SOLCONTROL, Key
ANTYPE, Antype
NLGEOM, Key
TIME, TIME
NSUBST, NSBSTP, NSBMX, NSBMN, Carry
DELTIM, DTIME, DTMIN, DTMAX, Carry
AUTOTS, Key
KBC, KEY
OUTRES, Item, FREQ, Cname
MONITOR, VAR, Node, Lab
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16.4.1 Analysis Type (ANTYPE)
• For nonlinear analysis, only two analysis types applicable: STATIC and TRANS.
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16.4.2 Nonlinear Geometry (NLGEOM)
• NLGEOM turns ON/OFF the effects of geometric nonlinearity.
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16.4.3 Load Step Time (TIME)
• TIME specifies the time at the end of the following load step.
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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.,
NSUBSTDELTIMTIME
NSUBST, NSBSTP, NSBMX, NSBMN, Carry
DELTIM, DTIME, DTMIN, DTMAX, Carry
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16.4.5 Automatic Time Stepping (AUTOTS)
• AUTOTS turns ON/OFF the functions of auto time stepping.
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16.4.6 Ramped/Stepped Loading (KBC)
0Time
Load
Stepped load
Substeps
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16.4.7 Output Controls (OUTRES)
• OUTRES controls the amount of data stored in Jobname.RST.
OUTRES, Item, FREQ, Cname
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16.4.8 Monitor File (MONTOR)
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第 16.5 節
收斂性控制的進階參數Advanced Solution Options
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Advanced Solution Options01
02
03
04
05
06
07
08
09
10
11
12
13
EQSLV, Lab, TOLER, MULT
SOLCONTROL, Key1, Key2
NEQIT, NEQIT
CNVTOL, Lab, VALUE, TOLER, NORM, MINREF
NROPT, Option,, Adptky
LNSRCH, Key
PRED, Sskey, --, Lskey
SSTIF, Key
PSTRES, Key
CUTCONTROL, Lab, VALUE, Option
TIMINT, Key, Lab
TINTP, GAMMA, ...NCNV, KSTOP, DLIM, ITLIM, ETLIM, CPLIM
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16.5.1 Equation Solver (EQSLV)
• EQSLV lets you choose the algorithm solving the equations.
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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.
SOLCONTROL, Key1, Key2
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16.5.3 Number of Equilibrium Iterations (NEQIT)
• NEQIT specifies the number of iterations beyond which ANSYS would start another “attempt”.
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16.5.4 Convergence Criteria (CNVTOL)
• CNVTOL overrides the default convergence criteria.
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16.5.5 Newton-Raphson Option (NROPT)
(a) Full Method (b) Modified Method (c) Initial Method
NROPT, Option,, Adptky
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16.5.6 Line Search (LNSRCH)
• LNSRCH turns ON/OFF the “line search” algorithm in ANSYS.
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16.5.7 Predictor (PRED)
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16.5.8 Adaptive Descent (NROPT)
NROPT, Option,, Adptky
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16.5.9 Stress Stiffening (SSTIF, PSTRES)
• SSTIF/PSTRES turns ON/OFF the computation of stress stiffness (K) and storing on file.
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16.5.10 Cutback Control (CUTCONTROL)
• CUTCONTROL specifies the conditions in which ANSYS would decrease time step during auto time stepping.
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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”.
TIMINT, Key, Lab
TINTP, GAMMA, ...
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16.5.12 Stop Control (NCNV)
• NCNV specifies the stop (failure) conditions of the computation.
NCNV, KSTOP, DLIM, ITLIM, ETLIM, CPLIM
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16.5.13 Terminating an Analysis
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16.5.14 Restarting an Analysis
• An analysis terminated normally can be restarted.
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16.6 Exercise: Hyperelastic Planar Seal
