比例-积分-微分控制算法求解结构拓扑优化问题  

Proportional-integral-differential Control Method on Solving Structural Topology Optimization Problems

作　　者：王文玥 赵清海[1,2] 张洪信[2] 张铁柱[2] 袁林 李信卿 王新亮 WANG Wenyue;ZHAO Qinghai;ZHANG Hongxin;ZHANG Tiezhu;YUAN Lin;LI Xinqing;WANG Xinliang(Mechanical and Electrical College,Qingdao University,Qingdao 266071,Shandong,China;National and Local Union Engineering Research Center of Electric Vehicle Intelligent Power Integration Technology,Qingdao University,Qingdao 266071,Shandong,China;Kama Automobile Company,Weifang 262700,Shandong,China)

机构地区：[1]青岛大学机电工程学院,山东青岛266071 [2]青岛大学电动汽车智能化动力集成技术国家地方联合工程研究中心,山东青岛266071 [3]山东凯马汽车制造有限公司,山东潍坊262700

出　　处：《机械科学与技术》2021年第2期223-229,共7页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目(51705268);中国博士后科学基金面上项目(2017M612191)。

摘　　要：拓扑优化具有设计变量多、目标性能与约束条件为设计变量的非线性、非单调隐式函数的特征,计算效率值得商榷。因此探索高效稳定的求解方法是结构拓扑优化的核心问题。提出一种基于PID控制算法的拓扑优化求解方法,采用固体各向同性微结构材料惩罚模型(SIMP)方法建立单工况条件下质量约束条件下结构柔度最小化拓扑优化模型,推导出基于PID法的设计变量迭代格式,引入基于Helmholtz偏微分方程的过滤方式抑制出现的数值不稳定问题,并将所提方法扩展到两类多工况结构拓扑优化问题,通过与优化准则法(Optimality criteria,OC)和移动渐近线法(Method of moving asymptotes,MMA)进行数值结果比较可知,PID控制方法具有设置简便、高效求解、收敛稳定且无需梯度信息的优点。Under the inherent characteristics of nonlinear and non-monotonic implicit function with tremendous design variables,the corresponding computational efficiency of topology optimization must be considered.Therefore,the kernel question is to explore efficient and stable solution strategy.The solution methodology based on the proportional-integral-differential(PID)control algorithm is proposed,under the solid isotropic microstructures material penalty(SIMP)model.The structural compliance minimization topology optimization model under the condition of single working condition is established.The iterative format of the design variables of PID algorithm is illustrated,and the filter method of Helmholtz partial differential equation is introduced to suppress the numerical instability problem.Then the proposed method is extended to the multi-loading condition topology optimization problems.Through the comparison of the optimization criteria method(OC)and the moving asymptote method(MMA),the numerical results demonstrated that the PID method exhibits the property of easy implementation,efficient solution,stable convergence and non-gradient information.

关 键 词：拓扑优化 PID控制 SIMP模型 非梯度 

分 类 号：TH122[机械工程—机械设计及理论]