Perturbation-based successive approximate topology optimization for a displacement minimization problem

This paper discusses a new approach for displacement-based topology optimization of continuum. Topology optimization of continuum can be performed with the optimization of material distribution. This optimization problem will include a large number of design variables, and it may require a high computational cost, especially for computation of gradient components with respect to an objective function and determination of an appropriate updating increment. A conventional approximate optimization technique may not be effective for this problem because it is a very large-scale problem.From this viewpoint, a new optimization technique, which is based on a successive approximation algorithm, is proposed. The proposed method consists of two main processes: (1) a linear approximation for determination of an updating direction, and (2) a nonlinear approximation for determining a scale coefficient of the updating vector. The first approximation is performed using the perturbation-based finite element analysis, and the second approximation is performed using the Kriging Method.In order to investigate effectiveness of the proposed method, it is applied to some typical examples for topology optimization problem. From the numerical results, effectiveness and validity of the proposed method are discussed.