Topology Optimization Method for Microscale Structures Described with Integral Nonlocal Theory

The integration of additive manufacturing and topology optimization makes it possible to fabricate complex configurations, especially for microscale structures, which can guarantee the realization of high-performance structural designs. However, topology results often contain microstructures (several multicellular scales) similar to the characteristic length of local macrostructures, leading to errors in structural performance analysis based on classical theories. Therefore, it is necessary to consider the size effect in topology optimization. In this paper, we establish a novel topology optimization model utilizing the integral nonlocal theory to account for the size effect. The approach consists of an integral constitutive model that incorporates a kernel function, enabling the description of stress at a specific point in relation to strain in a distant field. Topology optimization structures based on nonlocal theory are presented for some benchmark examples, and the results are compared with those based on classical medium theory. The material layout exhibits significant differences between the two approaches, highlighting the necessity of topology optimization based on nonlocal theory and the effectiveness of the proposed method.