On a consistent shell theory based on finite elasticity

Abstract eng:
This paper presents a finite-strain shell theory, which is consistent with the principle of stationary three-dimensional (3-D) potential energy. Based on 3-D finite elasticity and by a series expansion, we deduce a vector shell equation with three unknowns. The success relies on deriving exact recursion relations for the expansion coefficients from the 3-D system. Appropriate 2-D boundary conditions and associated 2-D weak formulations are also proposed. As an example, the axisymmetric deformation of a spherical shell is considered, and the shell theory produces second-order correct results by comparison with the exact solution. The advantages of the present shell theory include consistency, high accuracy, without higher-order stress resultants and its applicability to general loadings.

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