On the derivation of constant-coefficient partial differential equations for elastic shells

Abstract

Here the problem of formulating a representative model problem of shell theory is considered. We study two ways to obtain a constant-coefficient expression for the strain energy density function of a linearly elastic shell. The first formulation has already been given in the context of the analysis of boundary layers in thin shells, while the other is introduced here. It appears that the essential difference between the formulations is that the constant-coefficient expressions for the strains given here depend on four geometric parameters instead of the two parameters of curvature needed by the earlier derivation. The source of this discrepancy is investigated and shown to be related to the properties of the metric tensors that are attainable by means of different parametrizations of a given surface.