1. STRUCTURAL WRINKLING PREDICTIONS FOR MEMBRANE SPACE STRUCTURES
David W. Sleight, Alexander Tessler, and John T. Wang Analytical and Computational Methods Branch
NASA Langley Research Center
Hampton, VA
FEMCI Workshop 2002
Innovative FEM Solutions to Challenging Problems
May 22-23, 2002

2. Outline Motivation Objectives
Tension Field Theory for Predicting Wrinkling
Thin-Shell Theory for Predicting Wrinkling
Wrinkling Analyses
Summary

3. Motivation Future space missions enabled by large Gossamer systems
Understanding and predicting the behavior of membrane structures is essential for design and assessment of their performance
Membrane Optics
Sunshield
Solar Sail
Structural behavior, particularly wrinkling behavior, is highly
nonlinear and difficult to predict.

4. Types of Wrinkles Structural Wrinkles Material Wrinkles
Permanent deformations
Creases
Result from manufacturing or packaging
Temporary deformations
Localized buckling
Result from loading or boundary conditions
Change load paths within a membrane structure
Material wrinkles are permanent out-of-plane deformations resulting from manufacturing or packaging processes. Material wrinkles remain after loading is removed.
Structural wrinkles are temporary out-of-plane deformations caused by localized buckling of the thin film due to compressive loads.
They depend upon the combination of applied loads and boundary conditions
Structural wrinkles change load paths within a membrane structure, keeping compressive stresses from forming

5. Problems Due to Structural Wrinkling
Degraded performance
Affect maneuverability and stability
Poor surface accuracy
NGST Test
Wrinkles Give a 3-D Aspect to a 2-D Structure, a Cause for Concern with Structures Like the NGST Sunshield.
Wrinkles Can Change Structural Responses to Out-of-Plane Loads, Important when Designing Structures such as Solar Sails.
Solar Sail
Inflatable Antenna

6. 10 m, 2 Quadrant Solar Sail in LaRC 16m Vacuum Chamber

7. Objectives
Develop effective and robust FEA capabilities to predict structural wrinkles in membrane space structures
Predict surface distribution of structural wrinkles using:
Membrane analysis
Shell analysis (with out-of-plane deformations)

8. Tension Field Theory for Predicting Wrinkling
Originated by Wagner (1929) and Reissner (1938)
Membranes have negligible bending stiffness and cannot sustain compressive stresses
Wrinkles are treated as infinitesimally close to one another
Out-of-plane deformations of wrinkles cannot be determined
Tension field Theory (TFT) has been implemented by
varying linear elastic material properties
introducing a wrinkle strain
formulating a ‘relaxed’ strain energy density
Wrinkling occurs when a compressive stress develops.
Troughs and Crests of Wrinkles run Parallel to Major Principal Stress Axis
Wrinkles only transmit load in direction of the troughs and crests.

9. Stein-Hedgepeth Theory (SHT) - 1961
Membrane cannot carry compressive stress
Two types of regions:
Taut
Wrinkled
Effects of wrinkling are accounted for using a variable Poisson’s ratio that permits “over-contraction” in the direction of minor principal stresses
Wrinkles are aligned with the major principal stress axis
A generalized modification of the previous membrane wrinkling theory
Wrinkles form in straight lines along direction of major principal stresses - load transfer in the wrinkled region is along these lines
Closed-form solutions
s2=0
Wrinkle line
s10

10. Iterative Membrane Property (IMP) Method (Miller and Hedgepeth, 1982)
FE implementation of the SHT
Geometrically nonlinear analysis
Wrinkle criteria based on element stress/strain states
Taut: s2 > 0 (isotropic material)
Wrinkled: 1 > 0 & s2 ≤ 0 (orthotropic material)
Slack: 1 < 0 (zero stiffness material)
Finite element implementation into ABAQUS
Adler-Mikulas (2000)

11. Thin-Shell Theory for Predicting Wrinkling
Membrane theory cannot predict the amplitude and shape of wrinkles
Shell theory includes both membrane and bending flexibilities
enables post-buckling response
can predict amplitude and shape of wrinkles
Geometrically nonlinear analysis is necessary to predict the structural behavior

12. Thin-Shell Wrinkling Analyses Using ABAQUS
Geometrically nonlinear FE analysis
Using reduced integration thin-shell element (S4R5)
Imperfections are added to initial geometry
mode shapes from buckling analysis
random imperfections
Employ ABAQUS with STABILIZE parameter to automatically add damping for preventing unstable and singular solutions
for accuracy, use lowest possible value for which convergence can be achieved

13. Wrinkling Analyses Square Membrane Loaded in Tension
Rectangular Membrane Loaded in Shear

14. Square Membrane Loaded in Tension (Blandino, Johnston, et al, 2002)
Applied Load
Applied Load
Kapton membrane: 2.54 x 10-2 mm thick
Applied Loads: 2.45 N (Isothermal)

15. Wrinkling Results Wrinkled Region Experimental Results
(Blandino, Johnston, et al)
ABAQUS IMP Results
10,000 elements
M3D3/M3D4 Membrane Elements

16. Rectangular Membrane Loaded in Shear (Wong and Pellegrino, 2002)
380 mm
d = 3 mm
128 mm
Fixed
Kapton foil: 25 mm thick

17. Wrinkling Results 3960 elements 5% initial random imperfections
Out-of-plane Deflection

18. Summary Future space missions enabled by Gossamer structures
Effective and robust analysis tools required
Structural wrinkles constitute a major concern
Affect surface topology and behavior/performance
FEA analyses using ABAQUS to predict structural wrinkling
Membrane analyses with IMP method
Thin-shell geometrically nonlinear analyses