基于模板的子结构多分辨率拓扑优化  

Substructuring multi-resolution topology optimization with template

作　　者：黄孟成 霍文栋 刘畅 杨东生[4] 黄佳 杜宗亮 郭旭[1,2,3] HUANG Mengcheng;HUO Wendong;LIU Chang;YANG Dongsheng;HUANG Jia;DU Zongliang;GUO Xu(State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116023,Liaoning,China;International Research Center for Computational Mechanics,Dalian University of Technology,Dalian 116023,Liaoning,China;Ningbo Institute of Dalian University of Technology,Ningbo 315016,Zhejiang,China;China Academy of Launch Vehicle Technology,Beijing 100076,China;Beijing Institute of Structure and Environment Engineering,Beijing 100076,China)

机构地区：[1]大连理工大学,工业装备结构分析国家重点实验室,工程力学系,辽宁大连116023 [2]大连理工大学,国际计算力学研究中心,辽宁大连116023 [3]大连理工大学宁波研究院,浙江宁波315016 [4]中国运载火箭技术研究院,北京100076 [5]北京强度环境研究所,北京100076

出　　处：《力学进展》2021年第4期901-909,共9页Advances in Mechanics

基　　金：国家自然科学基金(11821202,11732004,12002073,12002077);国家重点研发计划(2020YFB1709401,2016YFB0201601);大连理工大学科研启动项目(DUT20RC(3)020);博士后科学基金(2020T130078,2020M680944)的支持

摘　　要：多分辨率拓扑优化(multi-resolution topology optimization,MTOP)方法将有限元网格和密度网格解耦,采用较粗的网格(超单元)进行有限元分析,从而大大降低了拓扑优化过程中的结构分析成本.但MTOP方法每次迭代都需要根据超单元内的平均密度计算有限元单刚,不仅精度不够且在过滤半径较小的情况容易出现棋盘格现象和QR模式.为解决相应问题,本文将超单元视为子结构,通过静态凝聚得到超单元刚度阵,并进一步根据拓扑优化过程中子结构的密度分布特征组建了其模板库,从而省去了超单元单刚的重复计算,显著提高了MTOP方法的分析精度,有效抑制了数值不稳定现象.In the multi-resolution topology optimization(MTOP) method, by decoupling the finite element mesh and discretization of density field, the finite element analysis is carried out with a coarser mesh(i.e., super-elements), and the computational cost is thus greatly reduced in the process of topology optimization. However, the elemental stiffness matrix is calculated each iteration using the average density of super-elements, and this treatment is actually not only inaccurate but also leads to the checkerboard phenomenon and QR patterns when the filter radius is relatively small. In order to alleviate such issues, the super-element is treated as a substructure and the corresponding elemental stiffness matrix is obtained using static condensation. Furthermore, a template library is developed for the substructure based on its density distribution during the topology optimization process. By this means, the elemental stiffness matrix is not required to be calculated repeatedly, the accuracy of the MTOP method is improved significantly and the checkerboard patterns are effectively inhibited as well.

关 键 词：多分辨率拓扑优化 子结构 模板 

分 类 号：O302[理学—力学]