Inserted: 4 mar 2008
Last Updated: 13 sep 2010
Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci.
We discuss the limiting behavior (using the notion of Gamma-limit) of the three-dimensional nonlinear elasticity for thin shells around an arbitrary smooth two-dimensional 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 Kármán theory for plates.
Keywords: Gamma-convergence, dimension reduction, nonlinear elasticity, shell theories