Shell Theories Arising as low Energy Γ-Limit of 3D Nonlinear Elasticity

Marta Lewicka, Maria Giovanna Mora, and Mohammed Reza Pakzad

Contact the author: Please use for correspondence this email.
Submission date: 06. Mar. 2008
Pages: 38
Bibtex
Download full preprint: PDF (385 kB), PS ziped (320 kB)

Abstract:
We discuss the limiting behavior (using the notion of -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 being the thickness of a shell, we derive a limiting theory which is a generalization of the von Kármán theory for plates.