JOURNAL OF SPACECRAFT AND ROCKETS Vol. 39, No. 5, September–October 2002 Corner Wrinkling of a Square Membrane Due to Symmetric Mechanical Loads Joseph R. Blandino ¤ James Madison University, Harrisonburg, Virginia 22807 John D. Johnston † NASA Goddard Spaceight Center, Greenbelt, Maryland 20771 and Urmil K. Dharamsi ‡ James Madison University, Harrisonburg, Virginia 22807 Thin-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 development of capabilities for testing and analyzing pretensioned, thin-lm membrane structures is an important and challenging aspect of gossamer spacecraft technologydevelopment.Results are presented from experimental and computational studies performed to characterize the wrinkling behavior of thin-lm membranes under mechanical loading. The test article is a 500-mm-square Kapton ® membrane subjected to symmetric corner loads. Data are presented for loads ranging from 0.49 to 4.91 N. The experimental results show that as the load increases the number of wrinkles increases, while the wrinkle amplitude decreases. The computational model uses a nite element implementation of Stein–Hedgepeth membrane wrinkling theory to predict the behavior of the membrane. Comparisons were made with experimental results for the wrinkle angle and wrinkled region. There was reasonably good agreement between the measured wrinkle angle and the predicted directions of the major principle stresses. The shape of the wrinkled region predicted by the nite element model matches that observed in the experiments; however, the size of the predicted region is smaller that that determined in the experiments. Nomenclature d = distance along diagonal cut E = modulus of elasticity K slack = stiffness matrix for slack elements K taut = stiffness matrix for taut elements K wrinkled = stiffness matrix for wrinkled elements L = length of diagonal cut P = applied load X , Y , Z = coordinates ® = principle stress angle º = Poisson’s ratio Introduction V ERY large, ultralightweightor gossamer spacecraft are an en- abling technology for many future space missions. Thin-lm membrane structures (including sunshields, solar sails, inatable antennas, and membrane optics) are a common element in these systems. Because of to their unprecedentedsize and exibility,gos- samer spacecraft systems will require advanced modeling and test- ing technologiesto supporttheirdevelopment.The behaviorof these structurescanbe highlynonlinearandchallengingto modelandtest. Modeling and analysis techniques to predict nonlinear membrane behaviorsuch as wrinklingshouldbe validatedthroughcomparison with 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 for publication 28 May 2002. Copyright c ° 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rose- wood Drive, Danvers, MA 01923; include the code 0022-4650/02 $10.00 in correspondence with the CCC. ¤ Assistant Professor, Integrated Science and Technology Program, MSC 4102; blandijx@jmu.edu.Member AIAA. † Aerospace Engineer, Mechanical Systems Analysis and Simulation Branch, Code 542, Next Generation Space Telescope Mechanical Systems Team; John.D.Johnston.1@gsfc.nasa.gov.Member AIAA. ‡ Undergraduate Research Assistant, Integrated Science and Technology Program, MSC 4102; dharamuk@jmu.edu. uence of instrumentationmass on structuralbehavior,and new test methods and noncontact instrumentation are needed. These needs are specically addressedthroughthe study of analyticaland exper- imental capabilities to predict the wrinkling behavior of a simple thin-lm membrane structure. Previous Studies When a thin-lm membrane is subjected to discrete tensile preloads, localized buckling (or wrinkling) often results. Wrinkles form because thin membranes have negligible bending stiffness and cannot resist compressive loads. 1 The wrinkles serve to elimi- natecompressivestresses.The behaviorof membrane structureshas beenstudiedpreviouslyby numerousresearchers.A comprehensive overview of the modeling and analysis of membranes completed by Jenkins and Leonard discusses many important contributions to this eld of research. 2 Finite element modeling techniques will be utilized extensively to predict the behavior of future thin-lm membrane structures due to the nonlinear nature of the problem. Typically, the capabilities of commercially available nite element codes 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 the membranes experiencesignicant wrinkling because the stress dis- tribution in the membranes will not be represented properly. There are several approachesavailable for modeling membrane structures that account for the effects of wrinkles, including the cable net- work method and modied membrane element methods. 3 The ca- ble network method was developed specically for modeling the dynamics of pretensioned, wrinkled membranes. The approach is based on the established principle that load transfer in wrinkled regions takes place along wrinkle lines. The membrane is meshed with a network of cables (preloaded bar elements) that is mapped to the wrinkle pattern of the structure. This approach is useful for determining the out-of-plane structural dynamic characteristics of pretensioned,wrinkled membrane structures; however, the method is limited in that it requirespriorknowledgeof the wrinklepatternto create the cable network and does not account for in-plane shear or thermaleffects.The cablenetworkmethodhas beenpreviouslyused 717