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

50
Chapter 16 非非非非非非非非非非非 Convergence of Nonlinear Analysis
  • date post

    20-Dec-2015
  • Category

    Documents

  • view

    278
  • download

    2

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

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

Chapter 16

非線性分析的收斂性探討 Convergence of Nonlinear Analysis

Page 2: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

2/50

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

Page 3: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

3/50

第 16.1 節

何謂非線性分析?What Are Nonlinear Analyses?

Page 4: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

4/50

16.1.1 What is a Nonlinear Structure

Displacements

Forces

Displacements

Forces

Page 5: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

5/50

16.1.2 Causes of Nonlinearities

• Geometric Nonlinearity

• Material Nonlinearity

• Status Nonlinearity

Page 6: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

6/50

Geometric Nonlinearity

Force

Displacement

Moment arm

Forces

Displacements

Page 7: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

7/50

Material Nonlinearity

Strain Strain

Stress

Stress

Mild Steel Rubber

Page 8: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

8/50

Status Nonlinearity

The contact area depends on the applied force

Force

Page 9: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

9/50

16.1.3 Consequences of Nonlinearities

• Principle of superposition no longer applicable

• Solution may depend on loading history

Page 10: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

10/50

第 16.2 節

解題方法Solution Methods

Page 11: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

11/50

16.2.1 Equations for a Nonlinear Structure

FDDK

D

K(D)F(D)

Page 12: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

12/50

16.2.2 Incremental Method

FDDK

F

Error

Calculated Response

ActualResponse

1

2

3

D

Page 13: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

13/50

16.2.3 Newton-Raphson Method

D = D4

F = F4

Actualresponse

1

23

4

D1 D2 D3

F1

F2

F3

Page 14: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

14/50

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

Page 15: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

15/50

第 16.3 節

收斂性控制的一些重要觀念Important Concepts for Convergence Controls

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

16/50

16.3.1 Radius of Convergence

D

F

Actualresponse

Do Do

Radius of convergence

Page 17: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

17/50

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

Page 18: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

18/50

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

Page 19: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

19/50

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.

Page 20: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

20/50

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.

Page 21: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

21/50

16.3.6 Text Output Information

1

2

3

45

Page 22: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

22/50

16.3.7 Graphical Output Information

Page 23: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

23/50

16.3.8 Automatic Nonlinear Solution Control

• SOLCONTROL command can be used to activate automatic nonlinear solution control algorithm.

• The default is ON.

Page 24: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

24/50

第 16.4 節

收斂性控制的基本參數Basic Solution Options

Page 25: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

25/50

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

Page 26: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

26/50

16.4.1 Analysis Type (ANTYPE)

• For nonlinear analysis, only two analysis types applicable: STATIC and TRANS.

Page 27: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

27/50

16.4.2 Nonlinear Geometry (NLGEOM)

• NLGEOM turns ON/OFF the effects of geometric nonlinearity.

Page 28: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

28/50

16.4.3 Load Step Time (TIME)

• TIME specifies the time at the end of the following load step.

Page 29: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

29/50

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

Page 30: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

30/50

16.4.5 Automatic Time Stepping (AUTOTS)

• AUTOTS turns ON/OFF the functions of auto time stepping.

Page 31: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

31/50

16.4.6 Ramped/Stepped Loading (KBC)

0Time

Load

Stepped load

Substeps

Page 32: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

32/50

16.4.7 Output Controls (OUTRES)

• OUTRES controls the amount of data stored in Jobname.RST.

OUTRES, Item, FREQ, Cname

Page 33: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

33/50

16.4.8 Monitor File (MONTOR)

Page 34: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

34/50

第 16.5 節

收斂性控制的進階參數Advanced Solution Options

Page 35: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

35/50

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

Page 36: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

36/50

16.5.1 Equation Solver (EQSLV)

• EQSLV lets you choose the algorithm solving the equations.

Page 37: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

37/50

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

Page 38: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

38/50

16.5.3 Number of Equilibrium Iterations (NEQIT)

• NEQIT specifies the number of iterations beyond which ANSYS would start another “attempt”.

Page 39: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

39/50

16.5.4 Convergence Criteria (CNVTOL)

• CNVTOL overrides the default convergence criteria.

Page 40: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

40/50

16.5.5 Newton-Raphson Option (NROPT)

(a) Full Method (b) Modified Method (c) Initial Method

NROPT, Option,, Adptky

Page 41: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

41/50

16.5.6 Line Search (LNSRCH)

• LNSRCH turns ON/OFF the “line search” algorithm in ANSYS.

Page 42: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

42/50

16.5.7 Predictor (PRED)

Page 43: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

43/50

16.5.8 Adaptive Descent (NROPT)

NROPT, Option,, Adptky

Page 44: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

44/50

16.5.9 Stress Stiffening (SSTIF, PSTRES)

• SSTIF/PSTRES turns ON/OFF the computation of stress stiffness (K) and storing on file.

Page 45: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

45/50

16.5.10 Cutback Control (CUTCONTROL)

• CUTCONTROL specifies the conditions in which ANSYS would decrease time step during auto time stepping.

Page 46: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

46/50

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, ...

Page 47: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

47/50

16.5.12 Stop Control (NCNV)

• NCNV specifies the stop (failure) conditions of the computation.

NCNV, KSTOP, DLIM, ITLIM, ETLIM, CPLIM

Page 48: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

48/50

16.5.13 Terminating an Analysis

Page 49: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

49/50

16.5.14 Restarting an Analysis

• An analysis terminated normally can be restarted.

Page 50: Chapter 16 非線性分析的收斂性探討 Convergence of Nonlinear Analysis.

50/50

16.6 Exercise: Hyperelastic Planar Seal