Asymptotic generalization of Reissner–Mindlin theory: accurate three-dimensional recovery for composite shells Original Research Article

A rigorous and systematic dimensional reduction of a shell-like structure is undertaken. It starts with geometrically nonlinear, three-dimensional (3-D), anisotropic elasticity theory and takes advantage of small parameters associated with the geometry. This reduction is carried out using the variational asymptotic method and splits the 3-D problem into a linear, one-dimensional (1-D), through-the-thickness analysis and a nonlinear, two-dimensional (2-D), shell analysis. The 2-D equations are put into the form of a nonlinear Reissner–Mindlin shell theory, details of which are dealt with in a separate paper. The focus of this paper is on the through-the-thickness analysis, which is solved by a 1-D finite element method and which provides two useful pieces of information: a generalized 2-D constitutive law for the shell equations, and a set of recovery relations that can be used to express the 3-D field variables through the thickness in terms of 2-D shell variables calculated in the shell analysis. The resulting analysis can be incorporated into standard Reissner–Mindlin shell finite element codes. Numerical results are compared with the exact solution, and the excellent agreement validates the fidelity of this modeling approach.