基于应力约束的多相材料结构拓扑优化设计

计算机集成制造系统Vol.27No.1第27卷第1期

20211Computer Integrated Manufacturing Systems Jan.2021 DOI：10.13196/j.cims.2021.01.013

基于应力约束的多相材料结构拓扑优化设计

占金青，彭怡平，龙良明，刘敏+

（华东交通大学机电与车辆工程学院，江西南昌330013）

摘要：传统的固体各向同性材料惩罚模型(SIMP)难以准确描述多相材料结构应力约束拓扑优化问题，鉴于此，提出一种基于可分离应力插值模型的多相材料结构应力约束拓扑优化设计方法。利用可分离应力插值模型计算多相材料结构的刚度和应力，以结构的体积最小化作为目标函数，采用改进的P范数求解各相材料结构的最大应力，以各相材料结构的最大应力作为约束，建立多相材料的结构全局应力约束拓扑优化模型，利用设计变量过滤技术避免数值不稳定性现象，采用移动渐近线优化算法求解多相材料结构应力约束拓扑优化问题。数值算例结果表明，采用多相材料结构全局应力约束拓扑优化获得的结构更加合理，能够有效地避免应力集中现象*关键词：连续体结构；多相材料；拓扑优化;应力约束；可分离应力插值模型

中图分类号:TB21；TH122文献标识码:A

Topology optimization of multiple materials continuum structure with stress constraints

ZHAN Jinqing,PENG Yiping,LONG Liangming,LIUMin+

(School of Mechatronics and Vehicle Engineering,East China Jiaotong University,Nanchang330013,China) Abstract：The standard Solid Isotropic Material with Penalization(SIMP)model is impossible to accurately describe -he problem for-opology op-imiza-ion of mul iple ma-erials con inuum s-ruc-ure wi h s-ress cons-rain-s.A me-hod for-opologyop-imiza-ionofmul-iplema-erialsconinuums-ruc-urewihs-resscons-rain-susing-heseparables-ress in-erpolaion modelwasproposed.Theelemen-si f nessandelemen-s-ressformuliplema-erialss-ruc-urewascal-cula-ed wi h-he separable s-ress in-erpola ion scheme.The minimum volume of-he s-ruc-ure was developed as-he objecivefuncion，and-hemodifiedPnorm wasapplied-osolve-hemaximums-ressforeachphasema-erials-ruc--ure.The maximum s-ress for each ma-erial was used as-he cons-rain-，and-he model for-opology op imiza ion of mul-iplema-erialsconinuums-ruc-urewihglobals-resscons-rain-swases-ablished.Thefil-ering-echniquesofde-signvariableswereused-oavoid-hephenomenonofnumericalins-abiliy.Themovingasymp-oicopimizaionalgo-ri hm was applied-o solve-he op imiza ion problem.Numerical resul-s showed-ha--he s-ruc-ures ob-ained by-o-pologyopimizaionofmuliple ma-erials con inuum s-ruc-ure wi-hglobals-resscons-rain-s were morereasonable and-hes-ressconcen-ra-ioncouldbeavoidede f ec-ively.

Keywords：continuum structure；multiple materials；topology optimization；stress constraints；separable stress inter­polation model

收稿日期：2019-05-14；修订日期：2019-09-11*Received14May2019；accepted11Sep.2019.

基金项目：国家自然科学基金资助项目(51665011,51305136)；江西省自然科学基金资助项目(20202BAB204015,20202ACBL214013, 20192BAB216021)；广东省精密装备与制造技术重点实验室幵放基金资助项目(PEM201601) *Foundation items：Project supported bytheNationalNaturalScienceFoundation，China(No51665011，51305136)，theNaturalScienceFoundationofJiangxiProvince，China(No.20202BAB204015,20202ACBL214013,20192BAB216021),and the Open Foundation of Guangdong Provincial Key Labo-ra-oryofPrecisionEquipmen-and Manufac-uringTechnology，China(No.PEM201601)*