考虑几何非线性的三维连续体结构显式拓扑优化  

Explicit topology optimization of three-dimensional geometrically nonlinear structures

作　　者：郭云航 杜宗亮 刘畅 张维声 薛日野 郭一麟 唐山 郭旭 Yunhang Guo;Zongliang Du;Chang Liu;Weisheng Zhang;Riye Xue;Yilin Guo;Shan Tang;Xu Guo(State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116023,China;Ningbo Institute of Dalian University of Technology,Ningbo 315016,China;Xi’an Aerospace Propulsion Institute,Xi’an 710100,China)

机构地区：[1]不详

出　　处：《Acta Mechanica Sinica》2023年第12期86-103,共18页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11821202,12002073,and 12002077);the National Key Research and Development Plan(Grant No.2020YFB1709400);Liaoning Revitalization Talents Program(Grant Nos.XLYC2001003 and XLYC1907119);Dalian Talent Innovation Program(Grant No.2020RQ099);the Fundamental Research Funds for the Central Universities(Grant Nos.DUT20RC(3)020,DUT21RC(3)076,and DUT22QN238);111 Project(Grant No.B14013).

摘　　要：本文提出了一种考虑几何非线性的三维连续体结构显式拓扑优化方法.采用移动可变形孔洞(MMV)方法描述结构,具有设计变量少、可与CAD系统无缝集成的优点.此外,由于结构拓扑描述模型与有限元分析模型之间解耦,在有限元分析中可以直接删除孔洞区域的冗余自由度,从根本上解决有限变形拓扑优化因弱单元引起的收敛性问题,同时显著提高了有限元分析的计算效率.数值算例验证了该方法的有效性,结果表明:(1)无论单工况还是多工况载荷作用下,几何非线性对三维结构的最优拓扑构型均具有显著影响;(2)优化后的几何非线性结构可以充分利用大位移和小应变来降低结构柔顺度;(3)几何非线性拓扑优化应评估优化设计的临界失稳荷载,以保证结构服役的安全性.In this work,a three-dimensional explicit geometrically nonlinear topology optimization method is developed.Moving morphable voids(MMVs)are used to describe the optimized structures,which enjoy the advantages of fewer design variables and seamless integration with CAD system.Furthermore,attributing to the decoupling between the description of topology and finite element analysis,redundant degree of freedoms in the void regions are directly removed during mechanical analysis,and this could significantly alleviate the mesh distortion of weak elements and also improve the computational efficiency of finite element analysis in the finite deformation regime.Numerical examples verify the effectiveness of the developed method and reveal that:(1)the finite deformation has a significant influence on the optimal topology of the three-dimensional structures both for single and multiple load cases;(2)the optimized geometrically nonlinear structures may take advantage of large displacements and small strains for achieving a minimized end compliance;(3)the critical load factor should be evaluated to guarantee the validity of the optimized structures.

关 键 词：冗余自由度 几何非线性 无缝集成 拓扑优化 收敛性问题 有限变形 三维结构 柔顺度 

分 类 号：O3[理学—力学]