Shape-topology Optimization for Designing Shell Structures

In this study, we propose a new approach for creating the optimal shape and topology of shell structures. 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 shells are used for shape and topology optimization, respectively. Compliance is minimized under both volume constraints for shape and topology optimization, and out-of-plane shape variation and fictitious density are used as the design variable. The optimum design problem is formulated as a distributed-parameter optimization problem, and the sensitivity functions for shape variation and density are theoretically derived. Both the optimal the optimal shape variation and density distribution are determined by using the H 1 gradient method, where the sensitivity functions are applied under the Robin condition to vary the shape and density. With the proposed method, the compliance is minimized, while maintaining smooth surface and the density distribution. The results show that the proposed simultaneous optimization method provides stiffer and lighter structures with less numerical instabilities. H. Nakayama and M. Shimoda 2