We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
23/2008
Shell Theories Arising as low Energy $\Gamma$-Limit of 3D Nonlinear Elasticity
Marta Lewicka, Maria Giovanna Mora and Mohammed Reza Pakzad
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 $h^4$, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Kármán theory for plates.
