Direct Variational Method of Analysis for Elliptic Paraboloidal Shells of Translation

Abstract

<p> The Rayleigh-Ritz method of Trial Function has been adopted to solve problems of translational shells under uniform external pressure. The basic energetical expressions have been written in terms of direct tensor notation. The stress-strain displacement relations are given in linear sense. Three different kinds of boundary conditions --- all four edges fixed, one pair of edges fixed and another pair of edges simply supported, and all four edges simply supported --- have been analysed. The stress and moment resultants at different points of the shell have been computed by means of IBM 7040, and are plotted into curves and figures to show their variations. The convergence of the displacement function uz is roughly verified. Certain comparison with other established results have been made. The results obtained by the present approach are satisfactory, at least from an engineering point of view.</p>