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

Details Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity

2008-03-04

arxiv.org/abs/0803.0358v1

Mathematics

Functional Analysis

36 pages, 1 figure

Scientific paper

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 h^4 (where h is the thickness of a shell), we derive a limiting theory
which is a generalization of the von K\'arm\'an theory for plates.

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