Minimum weight axisymmetric shell structures

The membrane approximation was used to determine the shapes and thickness distributions for axisymmetric shell structures that can support specified loads with minimum material. A Lagrange multiplier technique was employed. It resulted in Euler field equations and associated boundary conditions for the optimum shells. It also generated expressions for the multipliers directly in terms of the shell geometry. Specific solutions were obtained for the cases where the prescribed forces were uniform pressure, uniform vertical load and the weight of the shell itself. Both the Mises and the Tresca yield condition were used, and the optimum shells were shown to be in a state of yielding everywhere. The optimum shells, however, differed in general from equal strength shells which also satisfied yielding everywhere.