FULLY NONLINEAR MODELING AND ANALYSIS OF PRECISION MEMBRANES

Abstract

International Journal of Computational Engineering ScienceVol. 04, No. 01, pp. 19-65 (2003) No AccessFULLY NONLINEAR MODELING AND ANALYSIS OF PRECISION MEMBRANESP. FRANK PAI and LEYLAND G. YOUNGP. FRANK PAIDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA Search for more papers by this author and LEYLAND G. YOUNGDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA Search for more papers by this author https://doi.org/10.1142/S1465876303000788Cited by:4 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractHigh precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODEs) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODEs, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.Keywords:Nonlinear membrane theorynumerically exact analysis References M. Salama , M. Lou and H. Fang , Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference ( 2000 ) . Google Scholar M. S. Smith , R. S. Schallenkamp and L. G. Seely , AIAA International Balloon Technology Conference . Google Scholar D. Gorinevsky , T. Hyde and C. Cabuz , Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference ( 2001 ) . Google Scholar V. Firt , Statics, Formfinding and Dynamics of Air-Supported Membrane Structures ( Martinus Nijhoff Publishers , Boston , 1983 ) . Google Scholar A. L. 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Kolsti and Donald L. Kunz1 Jan 2013 | International Journal of Solids and Structures, Vol. 50, No. 2Numerical and experimental dynamic characteristics of thin-film membranesLeyland G. Young, Suresh Ramanathan, Jiazhu Hu and P. Frank Pai1 May 2005 | International Journal of Solids and Structures, Vol. 42, No. 9-10Modeling, Analysis and Testing of some Deployable/Inflatable StructuresPerngjin Pai and Leyland Young26 June 2012 Recommended Vol. 04, No. 01 Metrics History Received 26 August 2002 Accepted 4 November 2002 KeywordsNonlinear membrane theorynumerically exact analysisPDF download