Optimal Axially Loaded Membrane Shells

The optimization problem consists in searching the shape and the thickness distribution of membrane shells, made of isotropic material. The optimization problem studies the shell of revolution for the case of pure axial force. For this purpose, the section of shell with the normal to the symmetrical axis end planes is considered. The problem consists in the optimizing the stiffness of the shell, assuming its mass to be constraint. The unknown variables are the radius of the shell and the thickness. The closed-form solutions of the optimization problem are stated. For verification, the codes for a finite-element program are presented.