Application of the Green's function method to thin elastic polygonal plates

Abstract

Recently, the Green's function method has been applied successfully to problems of plane elasticity, using influence functions of some finite basic domain of simple geometrical shape, which contains the given one as a subdomain. The result of this formulation is a pair of integral equations, which have to be defined only along that part of the boundary not coinciding with the border of the basic domain. A rather general formulation for the solution of bending of plates of arbitrary convex planform and loading is presented, where, for the sake of brevity, plates of polygonal shape are considered. The polygonal plate is embedded in a rectangular domain, thereby applying coincidence of boundaries as far as possible. Those boundary conditions in the actual problem, which are not already satisfied, lead to a pair of coupled integral equations for a density function vector with components to be interpreted as line loads and moments distributed in the basic domain along the actual boundary. Thus, the kernel is the corresponding Green's matrix. Hence, having solved the integral equations, deflections and stresses in the actual problem are explicitly known. Solution of the integral equations is generally achieved by a numerical procedure. The method is tested in example problems by considering a trapezoidal plate under various boundary conditions.