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Shell theories arising as low energy $$\Gamma$$-limit of 3d nonlinear elasticity. (English) Zbl 1425.74298
Summary: 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 $$h^4, h$$ being the thickness of a shell, we derive a limiting theory which is a generalization of the von Kármán theory for plates.

##### MSC:
 74K25 Shells 74B20 Nonlinear elasticity
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