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

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

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Lewicka, Marta

Mora, Maria Giovanna

Pakzad, Mohammad Reza

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2008-10-02

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Abstract

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.

Keywords

shell theories

nonlinear elasticity

\Gamma-convergence

calculus of variations

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Lewicka, Marta; Mora, Maria Giovanna; Pakzad, Mohammad Reza. (2008). Shell theories arising as low energy \Gamma-limit of 3d nonlinear elasticity. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/43833.

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