Nonlinear analysis and optimization of shallow shells of variable thickness

Abstract

This paper is concerned with the nonlinear bending, stability and optimal design of revolution shallow shells with variable thickness. The problems are investigated by means of a modified iterative method proposed earlier by the author. Solutions for nonlinear bending and stability problems of revolution shallow shells with variable thickness, such as spherical and conical shells, are presented. Deflections and critical loads for stability are calculated and the numerical results are plotted and given in tabular forms. It is shown that the equation determining the maximum deflection and the load coincides with the cusp catastrophe manifold. The optimal design of plates and shells, in which the volume is minimized or the critical load of shells is maximized, is investigated. When the volume of the shell and the arch height of the shell are given, the variable thickness parameter can be solved. In addition, this paper also gives the constraint optimization of nonlinear bending of circular plates.