Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity
Marta Lewicka, Maria Giovanna Mora, Mohammad Reza Pakzad · ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE · 2010
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 4 , h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Kármán theory for plates.