Simultaneous shape and topology optimization for multi-objective design of a multi-layered shell

This paper describes a new approach for creating the optimal shape and topology of a multi-layered shell considering multi-objective design. By implementing topology optimization in the variable design domain which is optimized by shape optimization at every iteration, the optimal topology and shape is simultaneously determined. The free-form optimization method and the SIMP method for multi-layered shells are applied to shape and topology optimization, respectively. The compliance vector minimization problem is formulated and its sensitivity functions for shape and density variations are theoretically derived. Both the optimal shape and density variations are determined by using the H1 gradient method, where the sensitivity functions are applied to vary the shape and density. The results show that the proposed simultaneous optimization method provides stiffer and lighter structures with less numerical instabilities while maintaining smooth surface and density distribution.