Boundary discontinuous Fourier solution for plates and doubly curved panels using a higher order theory

Abstract

A new analytical solution to the problem of a finite-dimensional general cross-ply plates and doubly curved panels of rectangular planform is presented using a higher order shear deformation theory (HSDT). A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach, is used to solve the highly coupled linear partial differential equations, generated by the HSDT-based laminated shell analysis, with the SS1–SS3-mixed type simply supported boundary conditions prescribed at all four edges. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. The accuracy of the present solution is checked by studying the convergence characteristics of deflections and moments of an antisymmetric cross-ply shell and results are also compared with the finite element counterparts using commercially available software for distributed load. The primary aim of this study is to understand the effect of in-plane (or surface-parallel) boundary conditions, quantify this effect and provide benchmark comparisons and verifications of numerical results such as finite element, boundary element, etc. The effects of curvature, lamination, material property, thickness, and different types of loads as well as their interactions are also investigated in detail.