modeling & analysis of wrinkled membranes – an overview...cable network model zengineering...
TRANSCRIPT
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Modeling & Analysis of Wrinkled Modeling & Analysis of Wrinkled Membranes Membranes –– An OverviewAn Overview
B. Yang and H. DingUniversity of Southern California
M. Lou and H. FangJet Propulsion Laboratory
2001 FEMCI Workshop
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OutlineOutlineBackground
Literature Review
--- Existing membrane models and
membrane analysis tools
Open Issues
A New Modeling & Analysis Tool
Conclusions
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BackgroundBackground
Inflatable membrane sunshield
Telescope
The Next GenerationSpace Telescope
(NGST)
The Inflatable SyntheticAperture Radar (ISAR)
Membranes are a basic element of space Membranes are a basic element of space inflatables and gossamer spacecraftinflatables and gossamer spacecraft
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Wrinkling is a Critical Problem in Wrinkling is a Critical Problem in Design of Membrane StructuresDesign of Membrane Structures
Poor surface accuracy
Degraded performance
Significant effects on structural behaviors
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Motivation:Motivation: Urgent Need for Urgent Need for Wrinkling Analysis ToolsWrinkling Analysis Tools
Full-scale tests difficult
Gravity & aerodynamic effects
Optimal design
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Research ObjectivesResearch ObjectivesWrinkle formation and patterns
Static and dynamic behaviors of wrinkled membranes
Guidance for membrane design and wrinkling control
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OutlineOutlineBackground
Literature Review
Open Issues
A New Modeling & Analysis Tool
Conclusions
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1 0
2 0
Wrinkled StateWrinkled State
1 0
2 0
Slack StateSlack StateTaut StateTaut State
Three States of Thin MembranesThree States of Thin Membranes
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Tension Field TheoryTension Field Theory
•• Wrinkling occurs Wrinkling occurs when when σσ22 = 0= 0
•• Wrinkle orientation Wrinkle orientation follows follows σσ11 -- lineslines
(Wagner, 1929; Reissner, 1939)
1 0
2 0
Wrinkle line
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Modified Elasticity MatrixModified Elasticity Matrix{ } [ ]{ } { } { }DDσ ε σ ε= ⇒ =
• Stein-Hedgepeth Model (1961)Viable Poisson’s ratioViable Poisson’s ratioCannot model slack stateCannot model slack state
•• Miller & Hedgepeth (1985) Miller & Hedgepeth (1985) Equivalent elasticity matrixEquivalent elasticity matrix
Selection of matrices not uniqueSelection of matrices not uniqueMaterial homogeneity destroyed Material homogeneity destroyed Discontinuous among three statesDiscontinuous among three states
[ ] [ ] [ ], ort w sD D D D =
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Relaxed Energy DensityRelaxed Energy Density(Pipkin, 1986; Steigmann and Pipkin 1989)
•• No general algorithm available No general algorithm available for numerical analysesfor numerical analyses
{ } [ ]{ } { } [ ]{ }D Dσ ε σ ε= ⇒ =
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Cable Network ModelCable Network Model
Engineering model for dynamic analysis
--- NGST sunshield (Johnston & Lienard, 2001)
Prior knowledge of wrinkled patterns
needed
(Alder, Mikulas and Hedgepeth, 2000)
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Iterative Membrane Properties Iterative Membrane Properties (IMP) Method(IMP) Method
(Alder, Mikulas and Hedgepeth, 2000)
2D elastic elements in ABAQUS
Slack state modeled byMiller-Hedgepeth Model
which could lead to numerical problems
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BarBar--Networking ApproachNetworking Approach(Yang, Ding, Lou & Fang, 2001)(Yang, Ding, Lou & Fang, 2001)
Viable control parameter λλλλ
Convergent solutions by math programming
Wrinkle formation and patterns modeled
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OutOut--ofof--Plane DeformationPlane Deformation
Plate/shell elements
Operator singularity occurs as D shrinks =>=>numerical problems
Many elements needed to model wrinkle waves
Out-of-planedeformation
In-planedeformation
4 ( , , ) 0( , , ) 0
1
b
m
D w NL u v wNL u v w
D
∇ + ==
<<
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OutlineOutline
Background
Existing Membrane Models
Open Issues
A New Modeling & Analysis Tool
Conclusions
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UserUser--ProvidedProvidedWrinkleWrinkleModelModel
Use of Finite Element CodesUse of Finite Element Codes
BeginBegin YesYes2 0 ?σ ≥ EndEnd
NoNo
IterationIteration
2D ElasticityFE Solver
SoftwareSoftware--dependentdependentConvergence not sure Convergence not sure
ReRe --
calc
ulat
ion
calc
ulat
ion
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Problem with Modified Elasticity Matrix:Problem with Modified Elasticity Matrix:Energy NonEnergy Non--minimum minimum =>=> DivergenceDivergence
Convergence not guaranteedConvergence not guaranteed
{ } [ ]{ } 0TU Dε ε= >
{ } { }T DU ε ε =
•• Conventional elasticity theoryConventional elasticity theory
•• After modificationAfter modification
not surely pos. def.not surely pos. def.
pos. def.pos. def.
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Need to Model Slack StateNeed to Model Slack State
•• Physically, many membrane Physically, many membrane structures have slack regionsstructures have slack regions
•• Numerically, slack state is a Numerically, slack state is a necessary transition in solution necessary transition in solution processprocess
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Need to Know Wrinkle FormationNeed to Know Wrinkle Formation
Wrinkle patterns dependent upon loading path
Optimal design
Surface control by boundary loads
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Five Stages of Wrinkling ProcessFive Stages of Wrinkling Process
SS00
UndeformedUndeformedSSWW
WrinkledWrinkledSSFF
Fully stretchedFully stretchedSSPP
PostPost--stretchingstretchingSSDD
DamagedDamaged
GAP:GAP: No modeling & analysis tools covering No modeling & analysis tools covering wrinkling process wrinkling process fromfrom SSww to Sto SFF to Sto SPP
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State of the ArtState of the Art
Cable Network
Model
FEM with Modified Elasticity
Matrix
Bar-Networking Approach
Desired Modeling &
Analysis Tool
Guaranteed Convergence
Yes
Not sure
Yes
Yes Modeling of Slack State
No
Yes ####
Yes
Yes Wrinkle Formation
No PS
Partially WS
Partially,W FS S
Fully, ,W F PS S S
Wrinkle Waves
No
No
No
Yes Dependent on FE Solver
Yes
Yes
No
No
# # Miller-Hedgepeth Model could lead to numerical problems
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OutlineOutlineBackgroundLiterature ReviewOpening IssuesA New Modeling & Analysis ToolConclusions
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New Modeling & Analysis ToolNew Modeling & Analysis Tool
{ } [ ]{ }1 2( , )Dσ λ λ ε=
TwoTwo--viableviable--parameter parameter membrane modelmembrane model
1 2
1 2
1 2
taut: 0wrinkled: 0, 0slack: 0, 0
λ λλ λ
λ λ
= == >
> >
Parametric FE Parametric FE formulationformulation
1 2,e
Solution via nonlinear Solution via nonlinear math programmingmath programming
{ }( ) { } 0Γ λ ⋅ λ =
No iteration of No iteration of membrane stressesmembrane stresses
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Uniqueness and CapabilitiesUniqueness and Capabilities
Complete description of wrinkling processComplete description of wrinkling process
Convergent solution methodConvergent solution method
Determination of outDetermination of out--ofof--plane deformationplane deformation
Modeling of Modeling of multimulti--layered and/or composite layered and/or composite membranes, thermal effects, curved membranes, thermal effects, curved membrane surfaces, ……membrane surfaces, ……
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Why Convergence GuaranteedWhy Convergence Guaranteed
Iteration BasedIteration Based New ToolNew Tool
Numerical SolutionNumerical SolutionWrinkle SolutionWrinkle Solution
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New:New: Prediction of Prediction of OutOut--ofof--Plane DeformationPlane Deformation
4 ( , , ) 0( , , ) 0
b
m
D w NL u v wNL u v w
∇ + ==
[ ] [ ]( ){ } { }( ) ( )m bK K U Pλ λ+ =
Shell/plate Shell/plate modelmodel
NewNewmembranemembrane
modelmodel
viable parametersviable parameters
NonlinearNonlinearoptimizationoptimization
problemproblem{ }( ) { } 0λ λΓ ⋅ = SolutionSolution
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Taut: blankTaut: blank
Wrinkled:Wrinkled:Slack: Slack:
Example 1: Existence of slack elementsExample 1: Existence of slack elements
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Example 2: Wrinkle EvolutionExample 2: Wrinkle Evolution
pp fixed at 0.01; fixed at 0.01; τ τ variedvaried from 0from 0
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Example 2Example 2
0.04τ = 0.06τ =
0.08τ = 0.10τ = 0.115τ =
Evolution of Wrinkle LinesEvolution of Wrinkle Lines
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Preliminary ExperimentPreliminary Experiment
3 mil aluminizedKapton membrane
800 mm x 800 mm
Loading at corners
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Simulated ResultSimulated Result
7 lbs7 lbs
17 lbs17 lbs
Point APoint A
Slackregion
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Comparison (at Point A)Comparison (at Point A)
NumericalNumericalExperimentalExperimental
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ConclusionsConclusionsWrinkling analysis by FEM with modified elasticity matrix is software-dependent, and needs convergence proof
The Cable Network Model is good for post-stretching stage (SP) if wrinkle patterns are known
No tools are available to predict out-of-plane deformation and wrinkle waves
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Issues to Resolve Issues to Resolve In Future Wrinkling AnalysisIn Future Wrinkling Analysis
Guaranteed convergence
Complete description of wrinkling process
Out-of-plane deformation and wrinkle waves
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Recommendation:Recommendation:The twoThe two--viableviable--parameter model parameter model with nonlinear math programming with nonlinear math programming scheme is a promising tool for scheme is a promising tool for wrinkling analysis and optimal wrinkling analysis and optimal design of gossamer spacecraftdesign of gossamer spacecraft
{ }( ) { } 0λ λΓ ⋅ =
{ } [ ]{ }1 2( , )Dσ λ λ ε=
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THE ENDTHE END