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**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

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**Outline Motivation Objectives**

Tension Field Theory for Predicting Wrinkling Thin-Shell Theory for Predicting Wrinkling Wrinkling Analyses Summary

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**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.

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**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

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**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

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

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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)

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**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.

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**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 s10

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**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)

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**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

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**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

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**Wrinkling Analyses Square Membrane Loaded in Tension**

Rectangular Membrane Loaded in Shear

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**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)

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**Wrinkling Results Wrinkled Region Experimental Results**

(Blandino, Johnston, et al) ABAQUS IMP Results 10,000 elements M3D3/M3D4 Membrane Elements

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**Rectangular Membrane Loaded in Shear (Wong and Pellegrino, 2002)**

380 mm d = 3 mm 128 mm Fixed Kapton foil: 25 mm thick

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**Wrinkling Results 3960 elements 5% initial random imperfections**

Out-of-plane Deflection

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**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

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