Highly Efficient Multi-resolution Topology Optimization Based on the Kriging-Interpolation Network

Topology optimization aims to search for the optimal material distribution with a prescribed volume fraction. Recently, to reduce the computational cost of finite element analysis, multi-resolution topology optimization (MTOP) has been proposed to decouple the finite elements and density elements. However, MTOP introduces new problems with checkerboard patterns and numerous design variables, which hinder its popularity. To overcome these problems of MTOP and significantly improve the computational efficiency, an efficient multi-resolution topology optimization method based on the Kriging-Interpolation network (MTOP-KIN) is proposed in this paper. In the proposed MTOP-KIN, a customized single-layer neural network (Kriging-Interpolation network) is designed to express the topology description function of the design domain, avoiding the checkerboard patterns without filtering techniques or higher-order elements and reducing the design space. Several two-dimensional and three-dimensional numerical examples of topology optimization problems with compliance minimization are studied to demonstrate the effectiveness of the proposed method. The results show that the proposed MTOP-KIN can obtain better optimization results than MTOP. Meanwhile, compared with MTOP, an acceleration of about 11 to 18 times can be achieved.