论文标题
结构拓扑优化的有效梯度投影方法
An Efficient Gradient Projection Method for Structural Topology Optimization
论文作者
论文摘要
本文提出了一种有效的基于梯度投影的方法，用于结构拓扑优化问题，其特征在于非线性目标函数，该方法是在双边界限和单个线性平等约束下定义的可行区域中最小化的。利用约束类型的专长以及启发式工程经验，以改善缩放方案，投影和搜索步骤。详细说明，在某些条件下的梯度剪辑和修改的搜索方向投影被利用来促进所提出的方法的效率。此外，还提出了一种分析解决方案，以近似可忽略的计算和记忆成本。此外，搜索步骤的计算在很大程度上被简化了。基准问题，包括MBB，力逆变器机制和3D悬臂梁来验证该方法的有效性。提出的方法是在MATLAB中实施的，该方法是开源的，用于教育用法。
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.
