基于辛格插值模式的连续体结构拓扑优化研究  

Continuum structure topology optimization based on Singer interpolation model

作　　者：李玉刚 杨林[1] LI Yu-gang;YANG Lin(Guizhou Equipment Manufacturing Vocational College,Guiyang 550025,China;School of Mechanical Engineering,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州装备制造职业学院,贵州贵阳550025 [2]贵州大学机械工程学院,贵州贵阳550025

出　　处：《机电工程》2023年第1期136-143,共8页Journal of Mechanical & Electrical Engineering

基　　金：贵州省科技支撑计划项目(黔科合支撑2022);贵州装备制造职业学院科研资助项目(ZBKY2020-001)。

摘　　要：传统变密度拓扑优化求解方法存在单向惩罚特性缺陷,为了有效弥补传统变密度法的缺陷,对惩罚函数法进行了研究,提出了一种基于辛格插值模式的连续体结构拓扑优化新方法。首先,基于现有惩罚函数特性,提出了一种更加合理的中间单元处理策略;然后,采用辛格函数,构造了一种新的、更加合理的、且具有双向促进特性的材料特性插值模式,并建立了基于辛格插值模式的连续体结构拓扑优化模型;最后,利用移动渐进算法,并结合算例,验证了连续体结构拓扑优化新方法对于二维及三维设计域拓扑优化的有效性。研究结果表明:该连续体结构拓扑优化新方法在不采用过滤技术的情况下,既可消除数值不稳定现象,又可得到具有清晰边界的拓扑结构;与第二类辛格插值法和SIMP插值法相比,只对敏度进行辛格插值的第一类辛格插值法更加敏捷,可得到更小的目标函数值;对于三维设计域拓扑优化,采用连续体结构拓扑优化新方法所得结构拓扑可靠、清晰,且不失真。The traditional variable density topology optimization method has the defect of one-way penalty.In order to effectively make up for the defect of the traditional variable density method,the penalty function method was studied,and a new topology optimization method of continuum structure based on Singer interpolation mode was proposed.Firstly,based on the existing penalty function characteristics,a more reasonable strategy for handling intermediate elements was proposed.Then,a new and more reasonable interpolation model of material properties with bi-directional promotion characteristics was constructed by using the Singer function,and based on the Singer interpolation model,the mathematical model of continuum structure topology optimization was established.Finally,the effectiveness and feasibility of the new method for topology optimization in 2D and 3D design domains were verified by several typical example s optimization with the moving asymptotic algorithm.The research results indicate that without using filtering technology,the new method can not only reduce numerical instability effectively,but also obtain the final topological structure with clear boundaries.Comparing with the second type of Singer interpolation method and the solid isotropic microstructures with penalization(SIMP)interpolation method,the first type of Singer interpolation method,which interpolates only the sensitivity,is more agile,and smaller objective function values can be obtained;the topology of structure obtained by the new method for topology optimization in 3D design domain is reliable,clear and undistorted.

关 键 词：变密度拓扑优化求解方法 惩罚函数法 辛格函数 移动渐进算法 双向促进 

分 类 号：TH122[机械工程—机械设计及理论] TB115[理学—数学]