A Variational Method of Solution for Problems in Plane Elasticity

Abstract

A variational method of solution is considered which has a practical application to problems in classical plane elasticity with very general boundary contours and in the presence of mixed boundary conditions, edge reinforcements and multiple connectivity. Appreciable simplifications ensue from the fact that the solution is reduced to a consideration of two successive variational principles each associated with Laplace's equation. Special attention is given to the irregular behaviour which generally occurs at corner points and at points where the boundary conditions are discontinuous and which has caused difficulties in other methods. In the example, numerical values are obtained for a finite rectangular plate which is encastré along one edge and loaded by uniform tension along the opposite edge. The boundary conditions are mixed and infinite stresses occur at the extremities of the encastré edge.