考虑自重影响和屈曲约束的结构拓扑优化方法  

A structural topology optimization method considering self-weight influences and buckling constraints

作　　者：李方义[1,2] 卢志宏 易继军[1] 荣见华[1] 周泉 LI Fang-yi;LU Zhi-hong;YI Ji-jun;RONG Jian-hua;ZHOU Quan(School of Automobile and Mechanical Engineering,Changsha University of Science&Technology,Changsha 410114,China;Key Laboratory of Bridge Engineering Safety Control of Ministry of Education,Changsha University of Science&Technology,Changsha 410114,China;China Construction Fifth Engineering Division Corp.,Ltd.,Changsha 410004,China)

机构地区：[1]长沙理工大学汽车与机械工程学院,湖南长沙410114 [2]长沙理工大学桥梁工程安全控制教育部重点实验室,湖南长沙410114 [3]中国建筑工程集团第五工程局有限公司,湖南长沙410004

出　　处：《长沙理工大学学报（自然科学版）》2021年第3期97-104,共8页Journal of Changsha University of Science and Technology:Natural Science

基　　金：国家自然科学基金资助项目(11772070);湖南省自然科学基金资助项目(2019JJ40296);长沙理工大学桥梁工程安全控制教育部重点实验室开放基金资助项目(19KB06);长沙理工大学青年教师成长计划项目(2019QJCZ032);中国建筑第五工程局有限公司科研项目(3030402)。

摘　　要：为综合解决考虑自重影响和屈曲约束的结构拓扑优化问题,提出一种新的拓扑优化设计方法。首先,针对优化过程中低密度区域的伪屈曲模态问题和自重引起的寄生效应问题,同时为了减少计算量,提出了改进的材料惩罚模型,并引入伪屈曲模态的识别和删除措施。其次,为克服常规应力单元的应力刚化问题,采用混合应力单元对结构应力进行了精确评估。基于密度过滤及Heaviside三场映射方案,建立了目标函数为考虑自重影响的结构柔顺度最小、满足屈曲和体积主动约束的拓扑优化模型。利用伴随变量法对屈曲约束的灵敏度进行了推导,并采用移动渐近线(method of moving asymptotes,MMA)算法对模型进行了优化求解。最后,通过算例说明了本研究方法的正确性和可行性。In order to comprehensively solve the structural topology optimization problem considering the self-weight influences and buckling constraints,a new topology optimization design method was proposed.First,for the problems of pseudo-buckling modes and parasitic effects caused by self-weight of low-density areas during the optimization process,and aiming to reduce the calculation,an improved material penalty model was proposed,and measures for identifying and deleting pseudo-buckling modes were introduced.Then,in order to overcome the stress stiffening problem of the conventional stress elements,the mixed stress element was used to accurately evaluate the structural stress.Based on the density filtering and Heaviside three-field mapping scheme,a topology optimization model satisfying buckling constraints and volume active constraints was established,whose object function was that the structural compliance considering self-weight influences was minimal.The adjoint variable method was used to derive the sensitivity of the buckling constraints,and the method of moving asymptotes(MMA)algorithm was adopted to optimize the model.Finally,examples were given to illustrate the correctness and feasibility of the method proposed in this study.

关 键 词：拓扑优化 屈曲约束 自重 伪屈曲模态 材料惩罚模型 MMA算法 

分 类 号：TH122[机械工程—机械设计及理论]