A Demonstrative Computer Session Using ADINA- · PDF fileA Demonstrative Computer Session...
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Contents: Textbook: References: Topic 22 A Demonstrative Computer Session Using ADINA- Nonlinear Analysis • Use of ADINA for elastic-plastic analysis of a plate with a hole • Computer laboratory demonstration-Part II • Selection of solution parameters and input data preparation • Study of the effect of using different kinematic assumptions (small or large strains) in the finite element solution • Effect of a shaft in the plate hole, assuming frictionless contact • Effect of expanding shaft • Study and evaluation of solution results Appendix The use of the ADINA program is described and sample solutions are given in Bathe, K. J., "Finite Elements in CAD - and ADINA," Nuclear Engineering and Design, to appear. ADINA, ADINAT, ADINA-IN, and ADINA-PLOT Users Manuals, ADINA Verification Manual, and ADINA Theory and Modeling Guide, ADINA Engineering, Inc., Watertown, MA 02172, U.S.A.
Transcript of A Demonstrative Computer Session Using ADINA- · PDF fileA Demonstrative Computer Session...
Contents:
Textbook:
References:
Topic 22
A DemonstrativeComputer SessionUsing ADINA-Nonlinear Analysis
• Use of ADINA for elastic-plastic analysis of a plate witha hole
• Computer laboratory demonstration-Part II
• Selection of solution parameters and input datapreparation
• Study of the effect of using different kinematicassumptions (small or large strains) in the finite elementsolution
• Effect of a shaft in the plate hole, assuming frictionlesscontact
• Effect of expanding shaft
• Study and evaluation of solution results
Appendix
The use of the ADINA program is described and sample solutions aregiven in
Bathe, K. J., "Finite Elements in CAD - and ADINA," NuclearEngineering and Design, to appear.
ADINA, ADINAT, ADINA-IN, and ADINA-PLOT Users Manuals,ADINA Verification Manual, and ADINA Theory and Modeling Guide,ADINA Engineering, Inc., Watertown, MA 02172, U.S.A.
22-2 Computer Session Using ADINA - Nonlinear Analysis
References:(continued)
Proceedings of the ADINA Conferences, (K. J. Bathe, ed.)Computers & Structures
13, No. 5-6, 198117, No. 5-6, 198321, No. 1-2, 1985
The contact solution procedure used in the analysis of the plate withthe shaft is described in
Bathe, K. J., and A. Chaudhary, "A Solution Method for Planar andAxisymmetric Contact Problems," International Journal for Numerical Methods in Engineering, 21, 65-88, 1985.
Topic 'l\venty-two 22-3
A FINITE ELEMENTANALYSIS - NONLINEAR
SOLUTION• We continue to consider the plate
with a hole.
• A nonlinear analysis should only beperformed once a linear solution hasbeen obtained.The linear solution checks the finiteelement model and yields valuableinsight into what nonlinearities mightbe important.
Transparency22-1
Plate with hole: Schematic drawing
Transparency22-2
(Repeat 21-4)
plane stressconditions
r////J'///'/J'///71""'-""'We consider thisquarter of theplate anduse symmetryconditions
1 E = 207000 MPar-~---f-7"TTn7-rrT77777I v = 0.3
thickness = 0.01 m
0.01m-+--.../
0.1m
I.0.1m
.1
22-4 Computer Session Using ADINA - Nonlinear Analysis
Transparency22-3
(Repeat 21-25)
Finite element mesh to be generatedusing ADINA-IN:
• Mesh contains 64 elements,288 nodes.
eight-nodeisoparametricelement
Transparency22-4
• Some important considerations arenow
What material model to selectWhat displacement/strainassumption to makeWhat sequence of load application to chooseWhat nonlinear equation solutionstrategy and convergence criteriato select
• We use the ADINA system toanalyse the plate for its elastoplastic static response.
• We also investigate the effect onthe response when a shaft isplaced in the plate hole.
Some important observations:• The recommendations given in the
linear analysis are here also applicable (see previous lecture).
• For the nonlinear analysis we needto, in addition, be careful with the
- sequence and incrementalmagnitudes of load application
- choice of convergence tolerances
Topic Twenty-two 22·5
Transparency22-5
Transparency22-6
22-6 Computer Session Using ADINA - Nonlinear Analysis
Transparency22-7
Transparency22-8
Limit load calculations:
p
rTTTTl
o
LL..LLLJp
• Plate is elasto-plastic.
Elasto-plastic analysis:
Material properties (steel)(T
740 -I--
(T
(MPa)~
ET = 2070 MPa, isotropic hardening
E = 207000 MPa, v = 0.3
e• This is an idealization, probably
inaccurate for large strain conditions(e > 2%).
Load history:
650+---------++
Topic 1\venty·two 22·7
Transparency22-9
Load(MPa)
13 14 time
• Load is increased 50 MPa per load step.
• Load is released in one load step.
USER-SUPPLIED
MATERHlL 1 PLASTIC E=207000 NU=0.3 ET=2070 YIELD=740MATERIAL 1 PLASTIC E=207000 NU=0.3 ET=2070 YIELD=740DELETE EQUILIBRIUM-ITERATIONSDELETE EQUILIBRIUM-ITERATIONSADINAADINA
ADINADemonstration
22-1Input data
22-8 Computer Session Using ADINA - Nonlinear Analysis
Transparency22-10
(Repeat 21-25)
Finite element mesh to be generatedusing ADINA-IN:
• Mesh contains 64 elements,288 nodes.
eight-nodeisoparametricelement
Transparency22-11
Load history:
650-+-------~+
Load(MPa)
o~-------+-+---
o 13 14 time
• Load is increased 50 MPa per load step.
• Load is released in one load step.
• The BFGS method is employed for each load step.
Convergence criteria:
Energy:
d1!(i)T [t+~tB _ t+~tE(i-1)] < =
dU(1)T[t+~tR _ tF] - ETOl 0.001
Force:Ilt+~tR _ t+~tF(i-1)112 < _
RNORM - RTOl - 0.01
(RNORM = 100 MPa x 0.05 m x 0.01 m)~~~
nominal width thicknessappliedload
Topic Twenty-two 22-9
Transparency22-12
ADINADemonstration
22-2Plot of plasticityin plate with hole
22·10 Computer Session Using ADINA - Nonlinear Analysis
Transparency22-13
Stress vector output: Example
integrationpoint ~
/ maximum principal stress/ .....-" (tensile)
-s-- minimum principal stress(compressive)
ADINADemonstration
22-3Close-up of stress
vectors around hole
The length of the line is proportionalto the magnitude of the stress.
ORIQ:tNAL _ BSCALE '987. A
Finite element mesh to be generatedusing ADINA-IN:
• Mesh contains 64 elements,288 nodes.
Topic 1\venty-two 22-11
Transparency22-14
(Repeat 21-25)
eight-nodeisoparametricelement
M.N.O. Materially-Nonlinear-Only analysis
T.L. Total Lagrangianformulation
U.L. Updated Lagrangianformulation
Transparency22-15
22-12 Computer Session Using ADINA - Nonlinear Analysis
Transparency22-16
(Repeat 21-25)
Finite element mesh to be generatedusing ADINA-IN:
• Mesh contains 64 elements,288 nodes.
ADINADemonstration
22-4Elasto-plastic load
displacement response
I•
III
I..
eight-nodeisoparametricelement
100 MPa
rTTTTlPlate with shaft:
plate, /E = 207000 MPav=0.3thickness = 0.01 mplane stress
conditions
long shaft,E = 207000 MPa
b v =0.3~ thickness=0.05 m
_~ plane strain., conditions
Topic Twenty-two 22-13
Transparency22-17
LLLLLJ100 MPa
• The shaft is initially flush with the hole.
• We assume no friction between the shaft andthe hole.
Detail of shaft:
shaft .J(collapsed 8-node
elements)
Transparency22-18
22-14 Computer Session Using ADINA - Nonlinear Analysis
Transparency22-19
ADINADemonstration
22-5Deformed mesh
Solution procedure: Full Newtoniterations withoutline searches
Convergence criteria:
Energy: ETOL = 0.001
Force: RTOL = 0.01 , RNORM = 0.05 N
Incremental contact force:
IILiB(i-1) -: LiB(i-2)112 < =IILiR(,-1)112 - RCTOL 0.05
DEFORMED _ DSCALE 18641TU1E 1.888 DtlAX .388
Plate with expanding shaft:
Topic Twenty-two 22-15
Elasto-plasticplate ~
100 MPa
rTTTn/Shaft
./
~100 MPa
Transparency22-20
• The shaft now uniformly expands.
ADINADemonstration
22-6Close-up of
deformations atcontact
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Resource: Finite Element Procedures for Solids and Structures Klaus-Jürgen Bathe
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