基于网格退化和重组技术的类桁架拓扑优化方法  

A truss-like topology optimization method based on a mesh degradation and recombination technology

作　　者：祁武超[1] 申笑莲 王猛[1] 田素梅[1] 赵维涛[1] QI Wu-chao;SHEN Xiao-lian;WANG Meng;TIAN Su-mei;ZHAO Wei-tao(Key Laboratory of Liaoning Province for Aircraft Composite Structural Analysis and Simulation,Shenyang Aerospace University,Shenyang 110136,China)

机构地区：[1]沈阳航空航天大学辽宁省飞行器复合材料结构分析与仿真重点实验室,沈阳110136

出　　处：《计算力学学报》2023年第4期522-531,共10页Chinese Journal of Computational Mechanics

基　　金：辽宁省自然科学基金(2019-ZD-0228);辽宁省教育厅系列项目(JYT2020029;JYT2020034)资助。

摘　　要：发展了一种基于有限元网格退化和重组技术的类桁架拓扑优化方法,可在不改变设计域包络的情况下(如维持流型、艺术外观和附加功能等)对结构进行减重。首先,分别对二维问题和三维问题发展相应的有限元网格退化算法,并在刚度等效的意义上对网格进行重组,建立了具有杆元拓扑特征的有限元模型。其次,以全局种子网格的长度尺寸和杆元横截面积为优化变量,构造了域内双层驱动拓扑优化问题,得到具有最优体分比的杆元拓扑结构。数值算例表明,所提方法可获得新型式的结构拓扑优化方案,并可将结构拓扑优化理论推向工程化应用。A truss-like topology optimization method for truss-like structures is developed based on a degradation and recombination technology of the finite element mesh.The method can reduce the weight of a structure without changing the design domain envelope(e.g.maintaining flow pattern,artistic appearance,additional functions,etc.).Firstly,finite element mesh degradation algorithms for two-dimensional and three-dimensional problems are proposed,respectively.And then the mesh is reorganized on the basis of stiffness equivalence.Thus,a finite element model with topological characteristics of bar elements is established.Secondly,taking lengths of the global seed grid and cross-sectional areas of the bar element as the optimization variables,a two-layer driven topology optimization problem in the domain is constructed to obtain the topological structure of bar element with optimal volume fraction ratio.Two numerical examples show that the proposed method can obtain a new structural topology optimization scheme,and can promote structural topology optimization theories for engineering applications.

关 键 词：有限元网格 退化和重组 类桁架 拓扑优化 

分 类 号：TU323.4[建筑科学—结构工程] O342[理学—固体力学]