On boundary-discontinuous double Fourier series solution to a system of completely coupled P.D.E.'s

Abstract

A heretofore unavailable boundary-discontinuous double Fourier series based approach for solution to a system of completely coupled linear second-order partial differential equations with constant coefficients and subjected to general (completely coupled) boundary conditions is presented. This method facilitates the selection of the unknown Fourier coefficients, contributing to the complete solution and also takes into account the possible discontinuities of the assumed solution functions and/or their first derivatives at the boundaries. Dirichlet and Neumann types of boundary conditions can be treated as two special cases. The method is applied to obtain solutions of the hitherto unsolved class of problems, pertaining to arbitrarily laminated anisotropic (constant)-shear-flexible doubly-curved shells of rectangular planform, with arbitrary admissible boundary conditions and subjected to general transverse loading. Such specific cases of lamination as anti-symmetric angle-ply, symmetric angle-ply and general cross-ply, such particular case of loading as uniformly distributed transverse load and such specific case of geometry as a rectangular plate, can be obtained as special cases of the above. In addition, this method is shown to reproduce the available boundary-continuous solutions for unsymmetric cross-ply plates and doubly-curved shells with SS3 type simply-supported boundary conditions and anti-symmetric angle-ply plates with SS2 type simply-supported boundary conditions.