An efficient gradient projection method for structural topology optimization. (November 2020) - Zeng, Zhi; Ma, Fulei
Highlights: A novel and efficient method is proposed which greatly improves the efficiency of the gradient projection method with neglectable loss of accuracy for structural topology optimization. An analytical approximation is provided to calculate projection onto the feasible region with negligible computation and memory costs. The proposed method is implemented in MATLAB and open-sourced for educational usage. Abstract: This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a single linear equality constraint. The specialty of the constraints type, as well as heuristic engineering experiences are exploited to improve the scaling scheme, projection, and searching step. In detail, gradient clipping and a modified projection of searching direction under certain condition are utilized to facilitate the efficiency of the proposed method. Besides, an analytical solution is proposed to approximate this projection with negligible computation and memory costs. Furthermore, the calculation of searching steps is largely simplified. Benchmark problems, including the MBB, the force inverter mechanism, and the 3D cantilever beam are used to validate the effectiveness of the method. The proposed method is implemented in MATLAB which is open-sourced for educational usage.