基于显式拓扑优化方法的多孔结构基频最大化设计  

Fundamental frequency maximization design of porous structures using explicit topology optimization method

作　　者：王选 时元昆 陈翔 阎琨 无 WANG Xuan;SHI Yuankun;CHEN Xiang;YAN Kun;无(School of Mechanical Engineering,Tianjin University,Tianjin 300072,China;Department of Engineering Mechanics,Hefei University of Technology,Hefei 230009,China;State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology,Dalian 116024,China;School of Mechanical Engineering,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]天津大学机械工程学院,天津300072 [2]合肥工业大学土木与水利工程学院,合肥230009 [3]大连理工大学工业装备结构分析优化与CAE软件全国重点试验室,辽宁大连116024 [4]合肥工业大学机械工程学院,合肥230009

出　　处：《振动与冲击》2025年第8期124-132,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(12202129);中央高校科研业务费(JZ2022HGTB0291);中国博士后科学基金(2022M712358);工业装备结构分析优化与CAE软件全国重点试验室开放基金(GZ23105)。

摘　　要：多孔结构以其独特的性能,已成为解决动力学设计挑战的有效方案之一。为了改善多孔结构的动力学性能,针对无阻尼自由振动下的多孔结构基频最大化设计问题,提出了一种基于移动变形杆件方法的显式拓扑优化方法。该方法通过优化杆件的几何变量来实现多孔结构的建模与优化。将杆件映射到背景网格上的密度场,避免杆件移动过程中重新划分网格的繁琐任务。建立了体积比约束下的一阶特征值最大化的多孔结构动力学拓扑优化模型。详细推导了特征值目标函数关于几何设计变量的解析灵敏度列式,采用移动渐近线方法更新几何设计变量,实现多孔结构的优化设计。最后,通过三个数值算例验证了所提方法的有效性和稳定性,并讨论了尺寸控制和体积比约束对优化结果的影响。Porous structures have become one of the solutions to address the challenges in dynamic design due to their unique properties and broad application prospects.In order to achieve excellent dynamic performance in porous structure design,an explicit topology optimization method based on the moving deformable bars approach was proposed to maximize the fundamental frequency of undamped free vibration of porous structures.The modeling and optimization of porous structures were realized by optimizing the geometric variables of these moving bars.The bars were mapped to a density field on a background grid to avoid the cumbersome task of grid redivision during the bar movement.A dynamic topology optimization model of maximizing the first eigenvalue for porous structures under volume ratio constraint was established.The analytical sensitivity of the eigenvalue objective function with respect to geometric design variables was derived in detail,and the geometric design variables were updated using the method of moving asymptotes to achieve the optimization design of porous structures.Finally,the effectiveness and stability of the proposed method were verified through three numerical examples,and the influence of size control and volume ratio constraint on the optimization results was also discussed.

关 键 词：拓扑优化 多孔结构 频率优化 动力学优化 

分 类 号：O327[理学—一般力学与力学基础]