A density-and-strain-based K-clustering approach to microstructural topology optimization

Microstructural topology optimization (MTO) is the simultaneous optimization of macroscale topology and microscale structure. MTO holds the promise of enhancing product-performance beyond what is possible today. Furthermore, with the advent of additive manufacturing, the resulting multiscale structures can be fabricated with relative ease. There are however two significant challenges associated with MTO: (1) high computational cost, and (2) potential loss of microstructural connectivity. In this paper, a novel density-and-strain-based K-means clustering method is proposed to reduce the computational cost of MTO. Further, a rotational degree of freedom is introduced to fully utilize the anisotropic nature of microstructures. Finally, the connectivity issue is addressed through auxiliary finite element fields. The proposed concepts are illustrated through several numerical examples applied to two-dimensional single-load problems.