We discuss the limiting behavior (using the notion of \Gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting
theory which is a generalization of the von Karman theory for plates.
Lewicka, Marta; Mora, Maria Giovanna; Pakzad, Mohammad Reza.
Shell theories arising as low energy \Gamma-limit of 3d nonlinear elasticity.
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