面向超材料微结构的离散变量拓扑优化设计  

Discrete variable topology optimization design for metamaterial microstructure

作　　者：刘宏亮 蒋亦煌[1] 梁缘 王培金 郝鹏 LIU Hongliang;JIANG Yihuang;LIANG Yuan;WANG Peijin;HAO Peng(Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation,College of Aerospace Engineering,Shenyang Aerospace University,Shenyang 110136,China;State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116023,China)

机构地区：[1]沈阳航空航天大学航空宇航学院,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 [2]大连理工大学工程力学系,工业装备结构分析国家重点实验室,大连116023

出　　处：《固体火箭技术》2023年第3期344-351,共8页Journal of Solid Rocket Technology

基　　金：国家自然科学基金(12002218);工业装备结构分析国家重点实验室开放基金(GZ22108)。

摘　　要：由周期性微结构组成的材料结构因其独特性质在飞行器结构设计中展现出良好的应用潜力。为了避免超材料微结构拓扑优化过程引入的中间密度所导致的灰度模糊设计结果,基于一种离散变量的拓扑优化方法,利用序列近似整数规划和正则松弛算法实现材料体积约束下的微结构拓扑优化设计。利用离散变量的特点首先给出了两种微结构的几何形状初始猜测,并根据这两种初始设计的构型分别进行了体积模量最大化和剪切模量最大化问题的求解。结果表明,微结构拓扑优化设计构型受初始设计和材料体积约束的影响较大,考虑不同的性能目标所获得的优化设计构型差异明显。数值算例展现了文中基于离散变量实现超材料微结构拓扑优化设计的可行性和有效性,避免了中间密度引起的灰度模糊问题,清晰的微结构拓扑构型提高了结构的可制造性。Because of its unique properties,the material structure composed of periodic microstructure shows good application potential in aircraft structure design.In order to avoid the gray and fuzzy design result caused by the intermediate density introduced in the process of topology optimization of metamaterial microstructure,based on a discrete variable topology optimization method,sequential approximate integer programming and regular relaxation algorithm was used to achieve the microstructure topology optimization design under material volume constraints.Using the characteristics of discrete variables,the initial geometric guesses of the two kinds of microstructure were given,and the bulk modulus maximization and shear modulus maximization problems were solved respectively according to the two initial designs.The results indicate that the microstructure topology optimization design configuration is greatly affected by the initial design and material volume constraints,and the optimal design configuration is obviously different considering different performance objectives.Numerical examples show feasibility and effectiveness of the topological optimization design of metamaterial microstructure based on discrete variables.The gray level ambiguity caused by intermediate density is avoided,and the structural manufacturability is improved by the clear topology of microstructure.

关 键 词：微结构设计 拓扑优化 离散变量 整数规划 

分 类 号：V414[航空宇航科学与技术—航空宇航推进理论与工程]