CVGMT: Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity

Submitted Paper
(2008)

Authors: Marta Lewicka - Maria Giovanna Mora - Mohammad Reza Pakzad
Keywords: shell theories, nonlinear elasticity, Gamma-convergence, dimension reduction
Abstract: We discuss the limiting behavior (using the notion of Gamma-limit) of the three-dimensional nonlinear elasticity for thin shells around an arbitrary smooth two-dimensional surface. In particular, under the assumption that the elastic energy of deformations scales like h⁴ (where h is the thickness of a shell), we derive a limiting theory which is a generalization of the von Kármán theory for plates.

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