限界法克服连续体结构拓扑优化载荷病态问题  

Bound Formula Method for Overcoming Load Sickness Phenomenon of Continuum Topology Optimization

作　　者：俞燎宏 荣见华[2,3] YU Liao-hong;RONG Jian-hua(School of Physical Science and Technology,Yichun University,Jiangxi Yichun 336000,China;School of Automotive and Mechanical Engineering,Changsha University of Science and Technology,Hu1 nan Changsha 410076,China;Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle College of Hunan Province,Hu'nan Changsha 410076,China)

机构地区：[1]宜春学院物理科学与工程技术学院,江西宜春336000 [2]长沙理工大学汽车与机械工程学院,湖南长沙410076 [3]工程车辆轻量化与可靠性技术湖南省高校重点实验室,湖南长沙410076

出　　处：《机械设计与制造》2022年第6期139-144,共6页Machinery Design & Manufacture

基　　金：国家自然科学基金—面向智能制造的高性能集成结构构型设计方法与应用研究(11772070)。

摘　　要：在连续体结构拓扑优化中,当结构所承受的工况载荷幅值相差多个量级时,使用传统优化方法所得结果中可能存在载荷病态问题。为了解决载荷病态问题,提出了基于限界法的优化求解思路。首先,通过限界法将多目标优化问题转化为单目标优化问题,结合变体积约束限技术,建立新的等效近似优化模型;当同一工况内有载荷病态时,在优化模型中增加柔顺度小量变化约束。然后,基于Heaviside密度过滤,对目标函数和约束函数进行灵敏度计算,采用移动渐近线算法(MMA)优化求解。最后,通过二维和三维算例,验证了所提方法的可行性和有效性。与现有方法比,该方法可高效地获得0/1分布更清晰、性能更优的结构拓扑。Most of engineering structures work under multiple load cases,when the load values differ by several orders of magnitude,there may be load sickness phenomenon in the results obtained by traditional optimization methods. In order to solve the load sickness phenomenon,an optimization method based on the bound formula method is proposed. Firstly,original multi-objective optimization problem is transformed into a single objective optimization problem by a bound variable. Combined with the varied volume limit scheme,a new equivalent approximate optimization model is established.When there are both strong and sickness loads in the working condition,a small change of compliance constraint is added to the optimization model.Then,based on the Heaviside density filtering,the sensitivity of objective function and constraint function are calculated,and the method of moving asymptotes(MMA)algorithm is adopted to solve it. Finally,several two-dimensional and three-dimensional structural optimization examples are presented to demonstrate the feasibility and validity of the proposed method. An optimal topology with clearer 0/1distribution and better performance can be obtained by the proposed method than the existed methods.

关 键 词：拓扑优化 载荷病态 限界法 Heaviside过滤 MMA算法 

分 类 号：TH16[机械工程—机械制造及自动化] TH122