Shell theories as Gamma-limit of 3d nonlinear elasticity

Marta Lewicka University of Minnesota lewicka@math.umn.edu

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 Kármán theory for plates.</p>

<p>Work done in collaboration with M.G. Mora and M.R. Pakzad.</p>