JOURNAL OF SPACECRAFT AND ROCKETSVol. 39, No. 5, September–October 2002Corner Wrinkling of a Square MembraneDue to Symmetric Mech anical LoadsJoseph R. Blandino¤James Madison Unive rsity, Harrisonburg, Virginia 22 807John D. Johnston†NASA Goddard Spaceight Center, Greenbelt, Maryland 20771andUrmil K. Dharamsi‡James Madison Unive rsity, Harrisonburg, Virginia 22 807Thin- lm membrane structures are under consideration for use in many future gossamer spacecraft systems.Examples include sunshields for large-aperture telescopes, solar sails, and membrane optics. The d evelopment ofcapabilities for testing and analyzing pretensioned, thin- lm membrane structures is an important and challengingaspect of g ossamer spacecraft technologydevelopment.Results are presented from experimental and computationalstudies performed to characterize the wrinkling behavior of thin- lm membranes under mechanical loading. Thetest article is a 500-mm-square Kap ton®membrane subjected to symmetric corner loads. Data are presented forloads ranging from 0.49 to 4.91 N. The experimental results show that as the load increases the number of wrinklesincreases, while the wrinkle amplitude decreases. The computational model uses a  nite element implementationof Stein–Hedgepeth membrane wrinkling theory to predict the behavior of the membrane. Comparisons weremade with experimental results for the wrinkle angle and wrinkled region. There was reasonably good agreementbetween the measured wrinkle angle and the predicted directions of the major principle stresses. The shape of thewrinkled region predicted by the  nite element model matches that observed in the experiments; however, the sizeof the predicted region is smaller that that determined in the experiments.Nomenclatured= distance along diagonal cutE= modulus of elasticityKslack= stiffness matrix for slack el ementsKtaut= stiffness matrix for taut elementsKwrinkled= stiffness matrix for wrinkled elementsL= length of diagonal cutP= applied loadX,Y,Z= coordinates® = principle stress angleº = Poisson’s ratioIntroductionVERY large, ultraligh tweightor gossamer sp acecraft are an en-abling technol ogy for many future space missions. Thin- lmmembrane structures (including sunshields, solar sails, in atableantennas, and membra ne optics) are a common element in thesesystems. Because of to their unprecedentedsize and  exibility, go s-samer spacecraft systems wil l require advanced modeling and test-ing technologiesto support their development.The behaviorof thesestructurescan be highly nonlinearand challengingto model and test.Modeling and analysis techniques to predict nonlinear membran ebehavior such as wrinkling should be validated through comparisonwith test results. However, ground testing of ultralightweightstruc-tures is inherently dif cult due to the presence of gravity and the in-Received 13 July 2001; revision received 28 May 2002; accepted forpublication 28 May 2002. Copyrightc°2002 by the American Institute ofAeronautics and Astronautics, Inc. All rights reserved. Copies of this papermay be made for personal or internal use, on condition that the copier paythe $10.00 per-copy fee to the Copyright Clearance Cent er, Inc., 222 Rose-wood Drive, Danvers, MA 01923; include the code 0022-4650/02 $10.00 incorrespondence with the CCC.¤Assistant Professor, Integrated Science and Technology Prog ram, MSC4102; [email protected]. Member AIAA.†Aerospace Engineer, Mechanical Systems Analysis and SimulationBranch, Code 542, Next Generation Space Telescope Mechanical SystemsTeam; [email protected] AIAA.‡Undergraduate Research Assistant, Int egrated Science and TechnologyProgram, MSC 4102; [email protected]. uence of instrumentationmass on structuralbehavior,and new testmethods and noncontact instrumentation are needed. These needsare speci cally addressed through the study of analytical and exper-imental capabilities to predict the wrinkling behavio r of a simplethin- lm membrane structure.Previous StudiesWhen a thin- lm membrane is subjected to discrete tensilepreloads, localized buckling (or wrinklin g) often results. Wrinklesform because thin membranes have negligible bending stiffnessand cannot resist compressive loads.1The wrinkles serve to elimi-nate compressivestresses.The behavior of membrane structures hasbeen studied previous ly by numerousresearchers.A comprehensiveoverview of the modeling and analysis of membranes completedby Jenkins and Leona rd dis cusses many important contributionsto this  eld of research.2Finite element modeling techniques willbe utilized extensively to predict the behavior of future thin- lmmembrane structures due to the no nlinear nature of the problem.Typically, the capabilities of commercially available  nite elementcodes are inadequate to model all of the important aspects of mem-brane behavior. For example, modeling thin- lm membrane struc-tures using standard membrane elements is not advisable when themembranes experience signi cant wrinkling because the stress dis-tribution in the membrane s will not be represented properly. Ther eare several approaches available for modeling memb rane structuresthat account for the effects of wrinkles, including the cable net-work meth od and modi ed membrane element methods.3The ca-ble network method was developed spe ci cally for mod eling thedynamics of pretensioned, wrinkled membranes. The approach isbased on the established principle that load trans fer in wrinkledregions takes place along wrinkle lines. The membrane is meshedwith a network of cables (preloaded bar elements) that is mappedto the wrin kle pattern of the structure. This approach is useful fordetermining the out-of-plane structu ral dynamic characteristics ofpretensioned, wrinkled membrane structures; however, the methodis limited in that it requires prior knowledge of the wrinkle patterntocreate the cable network and does not account for in-plane shear orthermal effects. The cable network method has been previouslyused717718 BLANDINO, JOHNSTON, AND DHARAMSIto model the in atable sunshield in space and110th scale model NextGeneration Space Telescope (NGST) sunsh ield.4; 5A more accuraterepresentation of wrink led membrane structural behavior can beobtained by using standa rd membrane  nite elements in conjunc-tion with a no-compression membrane material model.3;6 ;7Theseapproaches start by developing a set of criteria by