Concurrent Optimization of Structures and Anisotropic Materials for Mechanical Cloaking

This paper studies the concurrent optimization of structural topologies and material properties for mechanical cloaking problems, in which the macrostructures, microstructures, and novel spatially-varying microstructure orientations of the cloaking devices are simultaneously considered and form a multiscale topology optimization problem. In this work, we (1) propose a new element-based objective function for mechanical cloaking; (2) establish generic mathematical formulations to model the multiscale optimization problem, including a novel mathematical relation between the original objective function and material microstructures, and implement the formulated optimization problem via an extended moving iso-surface threshold (MIST) method; (3) investigate the concurrent optimization of the macrostructure and material microstructures and orientations; (4) propose a novel analytical method derived for fully anisotropic materials to compute the optimal material orientations. Benchmark numerical examples are investigated to validate the proposed method. The present numerical results show that the proposed method can improve the cloaking performance by up to 26.25% compared with the literature.