Bending of clamped orthotropic rectangular plates: a variational symbolic solution

The Galerkin method is herein applied to the classical bending problem of a uniformly-loaded orthotropic rectangular plate with clamped edges, a problem for which, to our knowledge, no exact analytical solution in its general form exists. The tedious and error-prone computations inherent in such an approach are facilitated through the use of a computer algebra system; and several solutions, based on different approximations for the infinite series representing the assumed deflection function for the plate, are worked out, thereby extending previous work in the literature. The accuracy and convergence of the present formulation are assessed on the basis of solutions corresponding to the special case of material isotropy; and one such existing, manually-derived, result is shown to be incorrect.