基于浮动投影方法的三维非线性结构拓扑优化研究  

Topology optimization of three-dimensional nonlinear structures based on floating projection method

作　　者：张映博 李家春[1] 陈跃威 邹中妃 王永涛[4] ZHANG Yingbo;LI Jiachun;CHEN Yuewei;ZOU Zhongfei;WANG Yongtao(School of Mechanical Engineering,Guizhou University,Guiyang 550025,China;School of Mechanical Engineering,Zhejiang University,Hangzhou 310058,China;School of Mechanical Engineering,Guizhou Institute of Technology,Guiyang 550003,China;Guizhou Institute of Water Resources Research,Guiyang 550002,China)

机构地区：[1]贵州大学机械工程学院,贵州贵阳550025 [2]浙江大学机械工程学院,浙江杭州310058 [3]贵州理工学院机械工程学院,贵州贵阳550003 [4]贵州省水利科学研究院,贵州贵阳550002

出　　处：《机电工程》2024年第10期1776-1783,共8页Journal of Mechanical & Electrical Engineering

基　　金：国家水利部重大科技项目(2022056);贵州省科技计划项目(2022196);贵州省科技创新基地建设项目(2023010)。

摘　　要：针对三维非线性拓扑优化设计时的单元畸变现象与刚度准则选取问题,以涉及几何与材料非线性的超弹性结构为研究对象,对三维非线性结构拓扑优化进行了研究。首先,将物理场变量与Mooney-Rivlin模型线性相乘以表征设计域的超弹性,并提出了一种用于线性插值方案的改进附加超弹性技术,通过将Yeoh超弹性材料加入到低刚度区域,缓解了单元畸变现象;然后,基于三场密度模型,构造了三维超弹性结构拓扑优化的数学列式,在该框架下,比较了最小化末端柔度和最大化平衡势能两种刚度准则,推导了相应的灵敏度表达式,并采用浮动投影方法施加了设计变量的0/1约束;最后,采用两个数值算例对该方法的有效性进行了验证。研究结果表明:大变形情况下,不同目标函数的优化结果在拓扑构型和结构响应方面具有显著差异,但与线性设计相比,其均具有更优的力学性能。Aiming at the problems of element distortion and stiffness criteria selection in topology optimization design of three-dimensional nonlinear structures,the hyperelastic structure involving geometric and material nonlinearities was taking as the research object,and topology optimization of three-dimensional nonlinear structures was investigated.Firstly,the physical variables were linearly multiplied with the Mooney-Rivlin model to characterize the hyperelasticity of the design domain,and a modified additive hyperelasticity technique for linear interpolation scheme was proposed,it added the Yeoh hyperelastic material into low-stiffness regions to alleviate the element distortion.Then,the mathematical formula for topology optimization of three-dimensional hyperelastic structures was constructed based on the three-field density model.Under this framework,two stiffness criteria,i.e.,minimizing the end compliance and maximizing the total equilibrium potential energy,were compared,and the corresponding sensitivity expressions were derived.The floating projection method was adopted to impose the 0/1 constraint of design variables.Finally,the effectiveness of the proposed method was validated by two numerical examples.The research results demonstrate that their optimized results have significant differences in terms of topological configuration and structural response under large deformations,but all of them have better mechanical behaviors than the linear design.

关 键 词：三维结构 超弹性结构变形分析 非线性效应 刚度准则 浮动投影方法 Mooney-Rivlin模型 

分 类 号：TH122[机械工程—机械设计及理论] TB115[理学—数学]