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.

增材制造和拓扑优化的集成使得制造复杂的配置成为可能，特别是对于微尺度结构，可以保证高性能结构设计的实现。然而，拓扑结果往往包含与局部宏观结构特征长度相似的微观结构（多个多细胞尺度），导致基于经典理论的结构性能分析存在误差。因此，在拓扑优化中需要考虑尺寸效应。在本文中，我们利用积分非局部理论建立了一种新颖的拓扑优化模型来考虑尺寸效应。该方法由一个积分本构模型组成，该模型包含一个核函数，能够描述特定点处的应力与远场应变的关系。针对一些基准示例，提出了基于非局部理论的拓扑优化结构，并将结果与​​基于经典介质理论的结果进行了比较。两种方法之间的材料布局表现出显着差异，凸显了基于非局部理论的拓扑优化的必要性以及所提方法的有效性。