Static analysis of doubly curved film-substrate shells with thickness-dependent material properties

Based on Reissner’s mixed variational theorem (RMVT), we develop a weak-form formulation of finite doubly curved layer (FDCL) methods for the static analysis of simply-supported, multilayered functionally graded material (FGM) doubly curved shells (DCSs) under mechanical loads. This formulation is used to examine the spatial distributions of interlaminar stress and displacement components induced in a pressure-loaded FGM film-substrate DCS, and these solutions are compared with those obtained by using the principle of virtual displacements. The material properties of the multilayered (or film-substrate) shell are thickness-dependent, and the effective material properties of the FGM layer are estimated using the rule of mixtures and Mori–Tanaka scheme. The trigonometric functions and Lagrange polynomials are used to interpolate the in-surface and thickness variations of the primary variables of each individual layer, respectively. The orders used to expand the primary variables through the thickness direction are taken to be the same as one another, which are linear, quadratic and cubic variations. The accuracy and convergence rate of these RMVT-based FDCL methods are validated by comparing their solutions with the exact three-dimensional and accurate two-dimensional solutions available in the literature.