Abstract
Membrane theory may be regarded as a special case of the Cosserat theory of elastic surfaces, or, alternatively, derived from three-dimensional elasticity theory via asymptotic or variational methods. Here we obtain membrane theory directly from the local equations and boundary conditions of the three-dimensional theory.
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References
Healey, T.J., Rosakis, P.: Unbounded branches of classical injective solutions to the forced displacement problem in nonlinear elastostatics. J. Elast. 49, 65–78 (1997)
Ciarlet, P.G.: An introduction to differential geometry with applications to elasticity. J. Elast. 78–79, 3–201 (2005)
Le Dret, H., Raoult, A.: The membrane shell model in nonlinear elasticity: a variational asymptotic derivation. J. Nonlinear Sci. 6, 59–84 (1996)
Steigmann, D.J.: Thin-plate theory for large elastic deformations. Int. J. Non-linear Mech. 42, 233–240 (2007)
Hilgers, M.G., Pipkin, A.C.: Bending energy of highly elastic membranes II. Q. Appl. Math. 54, 307–316 (1996)
Steigmann, D.J.: Applications of polyconvexity and strong ellipticity to nonlinear elasticity and elastic plate theory. In: CISM Course on Applications of Poly-, Quasi-, and Rank-One Convexity in Applied Mechanics, Udine, Italy, September 24–28, 2007 (to appear)
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Steigmann, D.J. A Concise Derivation of Membrane Theory from Three-Dimensional Nonlinear Elasticity. J Elasticity 97, 97–101 (2009). https://doi.org/10.1007/s10659-009-9209-1
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DOI: https://doi.org/10.1007/s10659-009-9209-1