考虑几何非线性的多相多孔结构拓扑优化设计  

Topology optimization design of multiphase porous structures considering geometric nonlinearity

作　　者：周焕林[1] 郭鑫 王选 方立雪 龙凯[3] ZHOU Huan-lin;GUO Xin;WANG Xuan;FANG Li-xue;LONG Kai(College of Civil Engineering,Hefei University of Technology,Hefei 230009,China;School of Mechanical Engineering,Tianjin University,Tianjin 300072,China;State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources,North China Electric Power University,Beijing 102206,China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009 [2]天津大学机械工程学院,天津300072 [3]华北电力大学新能源电力系统国家重点实验室,北京102206

出　　处：《吉林大学学报（工学版）》2024年第10期2754-2763,共10页Journal of Jilin University:Engineering and Technology Edition

基　　金：国家自然科学基金项目(12202129);中央高校科研业务费项目(JZ2022HGTB0291);中国博士后科学基金项目(2022M712358)。

摘　　要：本文基于固体各向同性材料惩罚(solid lsotropic material with penalization,SIMP)插值模型提出一种考虑几何非线性效应的多相多孔结构拓扑优化设计方法。通过控制不同材料相的局部体积分数来形成多相多孔结构,利用p-范数将多个局部体积约束聚合为一个全局约束函数,以减少优化问题中的约束个数。采用附加超弹性技术避免几何大变形下的网格畸变问题。最后两个优化算例验证了本文方法的有效性,结果表明:本文方法可以实现不同材料相之间的合理分布,考虑几何非线性效应的多相多孔结构的位移、应力均更小。相比于单材料,考虑多相材料的多孔结构具有更好的性能。A topology optimization method of multiphase porous structures considering geometric nonlinearity effects is proposed based on SIMP interpolation model.The multi-phase porous structure is formed by controlling the local volume fraction of different material phases.To reduce the number of constraints in the optimization problem,the p-norm is used to aggregate multiple local volume constraints into a global constraint function.The additional hyperelastic technique is used to avoid mesh distortion under large geometric deformation.Finally,two optimization examples are presented to verify the effectiveness of the proposed method.The optimization results show that the proposed method can achieve reasonable distribution among different material phases,and the displacement and stress of the porous structures considering the nonlinear effect are smaller.Compared with the single material structure,the porous structures composed of multi-materials has better mechanical properties.

关 键 词：机械工程 多孔结构 几何非线性 拓扑优化 局部体积约束 多相材料 

分 类 号：O342[理学—固体力学]