The plane stress problem for rectangular regions treated using functions related to beam flexure

Abstract

A Ritz variational approach using a stress function formulation is presented for the solution of the plane stress problem for rectangular regions. The formal analogy between the stress function formulation of the plane stress problem and the out-of-plane plate bending problem is extended to include all four types of simple boundary conditions, leading to the use of products of ordinary and/or degenerated beam vibration functions for the terms in the Ritz series. This approach is particularly advantageous if the researcher is interested in both the in-plane and out-of-plane behavior of plates, when algebraic and computational savings are achieved. Two specific plane stress problems of practical significance are considered and numerical results and comparisons are made, illustrating the applicability and accuracy of the approach.