A meshless moving morphable component-based method for structural topology optimization without weak material

Traditional topology optimization methods often introduce weak artificial material to mimic voids to avoid the singularity of the global stiffness matrix and carry out topology optimization with a fixed finite element (FE) mesh. This treatment, however, may not only increase the computational cost for structural analysis but also lead to unfavorable numerical instabilities, especially when large deformations and dynamic/buckling behaviors are involved. In the present work, a new meshless moving morphable component-based method (ML-MMC), which structural analysis is carried out only on the solid region occupied by components, is proposed. In this approach, the coupling of discrete components is achieved through the adaptively constructed influence domain of the meshless shape function. Therefore, the singularity problem of the stiffness matrix can be naturally avoided without introducing weak artificial material. Compared with traditional methods, the number of degrees of freedoms (DOFs) can be reduced substantially under this treatment. The effectiveness of the proposed approach is also illustrated by some representative examples.