Robust multi-objective and multi-level optimization of complex mechanical structures

This paper presents a new approach to robust multi-objective and multi-level optimization of the design of complex mechanical structures. The optimization is at two levels: system and elements. At system-level, the robust multi-objective problem has four cost functions: on the one hand the minimization of the global mass and displacement at a fixed point of the mechanical structure, and on the other hand the maximization of both the robustness and the displacement of the mass. At element-level the robust multi-objective problem has two cost functions: minimization of the element mass and maximization of its robustness. A robust condensation technique, based on an enriched Karhunen–Loève condensation, is used for complex structures which require a large finite element model. In contrast to existing formulations, this new approach takes into account uncertainties in the design parameters at system-level and element-level. It also allows for the task sharing which is commonly used in structural engineering.