Orthotropic rectangular plates under in-plane loading part 1: closed-form solutions for stresses

Abstract

Exact closed-form expressions for the three stress components in orthotropic rectangular plates, subjected to in-plane loadings, are presented. The problem is treated as one of plane-stress, and solutions are provided for the general case of orthotropy (whether material or geometry-based). Use is made of the symbolic manipulator ALTRAN for solving the systems of equations implicit in the analytical approach adopted. The latter employs Fourier series for which the convergence aspect is addressed. On the basis of the ensuing solutions, stress distributions within generally orthotropic rectangular plates may be obtained using minimum computational effort. Typical applications will be dealt with in a suceeding article which will illustrate the use of the present technique.