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.

本文针对结构拓扑优化问题提出了一种基于梯度投影的有效方法，该方法的特征是非线性目标函数，该函数在双边边界和单个线性相等约束定义的可行区域内被最小化。利用约束类型的专业知识和启发式工程经验来改进缩放方案，投影和搜索步骤。详细地，在特定条件下利用梯度裁剪和搜索方向的修改投影来提高所提出方法的效率。此外，提出了一种解析解决方案，可以用可忽略的计算和存储成本来近似该投影。此外，大大简化了搜索步骤的计算。基准问题，包括MBB，力逆变器机构和3D悬臂梁用于验证该方法的有效性。所提出的方法在MATLAB中实现，该MATLAB是开源的，用于教育用途。