Nonlinearly Elastic Shell Models: A Formal Asymptotic Approach II. The Flexural Model

Abstract.

This paper is the sequel of Part I, in which the limiting displacement field of a thin shell when its thickness approaches zero is identified as the solution of a two‐dimensional nonlinear membrane shell model. When the geometry of the middle surface of the shell and the boundary conditions allow non‐zero “inextensional displacements”, the previous membrane limit model is not relevant. In this case, we show how to “update” the assumptions on the applied forces acting on the shell so that a limiting model can be derived by an asymptotic analysis. Furthermore, we identify this limit as the two‐dimensional nonlinear flexural shell model.