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.

中文翻译：

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一种用于结构拓扑优化的高效梯度投影方法

本文提出了一种有效的基于梯度投影的结构拓扑优化问题方法，其特征是非线性目标函数在由双边边界和单个线性等式约束定义的可行区域上最小化。利用约束类型的特殊性以及启发式工程经验来改进缩放方案、投影和搜索步骤。具体而言，利用梯度裁剪和特定条件下搜索方向的修正投影来提高所提出方法的效率。此外，还提出了一种解析解来近似该投影，而计算和内存成本可忽略不计。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。所提出的方法是在 MATLAB 中实现的，MATLAB 是开源的，用于教育用途。