A stress analysis method for multilayer compound cylinders under steady state thermal and force loading is developed utilizing complex potentials in series form. An optimization to determine the thickness of the cylindrical layers is formulated based on this analysis method. Stress and thickness constraints are considered in this formulation. A generalized steepest descent method was applied to solve the problem, where a numerical derivative calculation was used.
A single layer problem for a thermal load is used to check the validity of the solution method with existing one in the literature. A three layer cylinder with a concentrated force is taken as the second example to check the solution with that obtained by a commercial program, ANSYS. The results agreed well with each other. The present method is much efficient in time as expected due to its specialization for axisymmetric geometry problems. A spent fuel shipping cask is then modeled using this three layer model including nonaxisymmetric thermal and uniform pressure loading. This model is used as an examplary optimization problem. It has shown the applicability of the optimal design formulation, by obtaining proper sizes under given loads.
