基于PnP-ADMM的离散体结构拓扑优化

The Discrete Structural Topology Optimization Method Based on PnP-ADMM

基于PnP-ADMM算法框架,提出了一种基于PnP-ADMM框架的离散变拓扑优化改进算法,旨在求解柔度更小的最优解。通过将PnP-ADMM框架推导目标函数和各约束的对应离散子变量的迭代式,采用敏度过滤的方法消除棋盘格,同时,应用移动限制策略逼近目标约束下的最优结构布局。通过MBB梁和悬臂梁算例实验,该方法计算得到的结构柔度与DVTOPCRA算法相比有明显下降,验证了该方法的可行性和有效性,为求解离散体结构最小化柔度提供了一种新的方法。

Based on the PnP-ADMM algorithm framework,an improved discrete topology optimization algorithm is proposed.The aim is to obtain a globally optimal solution with reduced flexibility.By deriving the objective function and iterative equations of corresponding discrete sub-variables within the PnP-ADMM framework,a sensitivity filtering method is employed to eliminate the checkerboard pattern.Additionally,a moving restriction strategy is applied to approximate the optimal structural layout under target constraints.Through experimental examples of MBB beams and cantilever beams,the proposed method demonstrates a significant decrease in structural flexibility compared to DVTOPCRA algorithm,validating the feasibility and effectiveness of this approach.It provides a new method for minimizing flexibility in discrete structural topology optimization.