Abstract
This paper describes a multi-objective free-form optimization method for designing shell structures under multiple loading conditions. Compliances for multiple loadings are used as the objective functionals. This vector objective functional is scalarized by the weighted method and minimized under a volume and the state equations constraints. This problem is formulated as the parameter-free shape optimization problem under the assumptions that the shell is varied in the normal direction to the surface and the thickness is constant, and the shape gradient function is theoretically derived. The free-form optimization method which was proposed by the author is used to determine the natural free-form shell, while minimizing the objective functional. The calculated result shows the effectiveness of the proposed solution for designing multi-objective free-form shell structures under multiple loading conditions.
