A hybrid topology optimization algorithm for static and vibrating shell structures

Structural designers are reconsidering traditional design procedures using structural optimization techniques. Although shape and sizing optimization techniques have facilitated a great improvement in the emergence of new optimum designs, they are still limited by the fact that a suitable topology must be assumed initially. In this paper a hybrid algorithm entitled constrained adaptive topology optimization, or CATO is introduced. The algorithm, based on an arti cial material model and an adaptive updating scheme, combines ideas from the mathematically rigorous homogenization (h) methods and the intuitive evolutionary (e) methods. The algorithm is applied to shell structures under static or free vibration situations. For the static situation, the objective is to produce the sti est structure subject to given loading conditions, boundary conditions and material properties. For the free vibration situation, the objective is to maximize or minimize a chosen frequency. In both cases, a constraint on the structural volume=mass is applied and the optimization process is achieved by redistributing the material through the shell structure. The e ciency of the proposed algorithm is illustrated through several numerical examples of shells under either static or free vibration situations