zbMATH — the first resource for mathematics

Nonlinearly elastic shell models: A formal asymptotic approach. II: The flexural model. (English) Zbl 0906.73042
Summary: This paper is the sequel of Part I [see the foregoing entry], 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.

74K15 Membranes
74B20 Nonlinear elasticity
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI