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

2

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

Chapter 16

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

16.6 練習題：橡膠密封墊分析 Exercise: Hyperelastic Planar Seal

3/50

4/50

16.1.1 What is a Nonlinear Structure

Displacements

Forces

Displacements

Forces

5/50

16.1.2 Causes of Nonlinearities

• Geometric Nonlinearity

• Material Nonlinearity

• Status Nonlinearity

6/50

Geometric Nonlinearity

Force

Displacement

Moment arm

Forces

Displacements

7/50

Material Nonlinearity

Strain Strain

Stress

Stress

Mild Steel Rubber

8/50

Status Nonlinearity

The contact area depends on the applied force

Force

9/50

16.1.3 Consequences of Nonlinearities

• Principle of superposition no longer applicable

10/50

11/50

16.2.1 Equations for a Nonlinear Structure

FDDK

D

K(D)F(D)

12/50

16.2.2 Incremental Method

FDDK

F

Error

Calculated Response

ActualResponse

1

2

3

D

13/50

16.2.3 Newton-Raphson Method

D = D4

F = F4

Actualresponse

1

23

4

D1 D2 D3

F1

F2

F3

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

15/50

16/50

D

F

Actualresponse

Do Do

17/50

16.3.2 Consistent Stiffness Matrix

• Tangent stiffness• Additional stiffness due to deformation

direction.

aσuinc KKKKK

18/50

16.3.3 Load Steps, Substeps, and Equilibrium Iterations

Substeps

Time

D = D4

F = F4

Actualrespons

e

1

23

4

D1 D2 D3

F1

F2

F3

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.

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.

21/50

16.3.6 Text Output Information

1

2

3

45

22/50

16.3.7 Graphical Output Information

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.

24/50

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

26/50

16.4.1 Analysis Type (ANTYPE)

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

27/50

16.4.2 Nonlinear Geometry (NLGEOM)

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

28/50

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

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

30/50

16.4.5 Automatic Time Stepping (AUTOTS)

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

31/50

0Time

Substeps

32/50

16.4.7 Output Controls (OUTRES)

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

OUTRES, Item, FREQ, Cname

33/50

16.4.8 Monitor File (MONTOR)

34/50

35/50

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

LNSRCH, Key

PRED, Sskey, --, Lskey

SSTIF, Key

PSTRES, Key

CUTCONTROL, Lab, VALUE, Option

TIMINT, Key, Lab

TINTP, GAMMA, ...NCNV, KSTOP, DLIM, ITLIM, ETLIM, CPLIM

36/50

16.5.1 Equation Solver (EQSLV)

• EQSLV lets you choose the algorithm solving the equations.

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

38/50

16.5.3 Number of Equilibrium Iterations (NEQIT)

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

39/50

16.5.4 Convergence Criteria (CNVTOL)

• CNVTOL overrides the default convergence criteria.

40/50

16.5.5 Newton-Raphson Option (NROPT)

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

41/50

16.5.6 Line Search (LNSRCH)

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

42/50

16.5.7 Predictor (PRED)

43/50

44/50

16.5.9 Stress Stiffening (SSTIF, PSTRES)

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

45/50

16.5.10 Cutback Control (CUTCONTROL)

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

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, ...

47/50

16.5.12 Stop Control (NCNV)

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

NCNV, KSTOP, DLIM, ITLIM, ETLIM, CPLIM

48/50

16.5.13 Terminating an Analysis

49/50

16.5.14 Restarting an Analysis

• An analysis terminated normally can be restarted.

50/50

16.6 Exercise: Hyperelastic Planar Seal