Single Fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of colinear compression. Part 1: Closed-form solution and convergence study

Abstract

This paper considers certain types of classical plane-stress problems, concentrating on their solutions by means of the simple, although usually approximate, single Fourier series technique. While this approach is well known, no systematic studies based on it seem to have been carried out in the past. Such a study is presently undertaken with reference to the problem of a colinearly compressed rectangular plate so as to reach some conclusions regarding (ordinary) convergence rates for stresses, as well as to investigate possible ways of improving convergence. In addition, a truly closed-form solution for the single Fourier series technique is given (thus bypassing the need to repeatedly solve systems of equations) which encompasses completely arbitrary normal and/or shear loading along two opposite edges. In a follow-up paper (Tahan et al., Thin Walled Structures 17(1) (1993)), the present findings will be used to conduct an investigation of the stress distribution in a plate subject to colinear compression .