Topology optimization using material-field series expansion and Kriging-based algorithm: An effective non-gradient method

Topology optimization is now a very effective and important tool for designing the layouts of various structural and multidisciplinary problems, but most existing methods require information about the sensitivity of the performance function with respect to an enormous number of design variables. This paper presents an efficient non-gradient approach to the topology optimization of structures when no information is available about design sensitivity. Based on the material-field series expansion (MFSE), the problem of topology optimization is constructed as a constrained minimization model with the series expansion coefficients as the design variables, thereby involving a considerable reduction of design variables. The Kriging-based optimization algorithm incorporating two infill criteria is used to solve the optimization problem. A special strategy of (i) using a self-adjusting design domain and (ii) remodeling the surrogate function is proposed to improve the searching efficiency of the Kriging-based algorithm. Several examples are given in the form of linear, nonlinear, and fluid topology optimization problems to demonstrate the effectiveness and applicability of the proposed Kriging-based MFSE method.