On a consistent finite-strain shell theory based on 3-D nonlinear elasticity

This paper presents a general finite-strain shell theory, which is consistent with the principle of stationary three-dimensional (3-D) potential energy. Based on 3-D nonlinear elasticity and by a series expansion about the bottom surface, we deduce a vector shell equation with three unknowns, which preserves the local force-balance structure. The key in developing this consistent theory lies in deriving exact recursion relations for the high-order expansion coefficients from the 3-D system. Appropriate 2-D boundary conditions and associated 2-D weak formulations are also proposed, including various practical cases on the edge. Then, to demonstrate its validity, axisymmetric deformations of spherical and circular cylindrical shells are investigated, and comparisons with the exact solutions are made. It is found that the present shell theory produces second-order correct results for the general dead-load case and internally pressurized case. The advantages of the present shell theory include consistency, high accuracy, incorporating both stretching and bending effects, no involvement of higher-order stress resultants and its applicability to general loadings.