连续体结构及其支撑位置协同优化设计方法  

HYBRID OPTIMIZATION METHOD OF CONTINUUM STRUCTURE AND ITS SUPPORTING LOCATIONS

作　　者：胡天男 丁晓红[1] HU TianNan;DING XiaoHong(Institute of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学机械工程学院,上海200093

出　　处：《机械强度》2021年第3期629-635,共7页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(51975380)资助。

摘　　要：在工程问题中,结构支撑位置和结构材料分布具有相关性,同时优化结构拓扑形态及其支撑位置,可在一定的材料和支撑件个数的条件下,最大限度提高结构力学性能。通过引入独立的支撑单元,以连续变量描述支撑位置,提出一种连续体结构及其支撑位置协同优化设计方法。建立考虑结构刚度和结构平均特征值的多目标优化设计数学模型,并采用决定因子确定多目标优化的最优解,以受横向载荷作用的简支受弯薄板和简支弯扭薄板为例进行优化设计及分析,结果表明,协同优化设计结果的结构拓扑形态清晰,支撑位置明确,能同时有效优化结构的支撑位置和结构拓扑形态。相对于给定边界条件的标准拓扑优化设计,两算例中的静动态性能分别提升30%和88%以上,在满足约束条件的同时,能以更少的支撑个数,显著提升结构的静动态性能。In engineering problems,there is interaction between the layout of supporting locations and the distribution of structural material. Thus,simultaneously optimizing the topology of the structure and its supporting locations under a certain limit of material and supports is an effective approach to improve the mechanical properties of the structure. In this paper,supporting locations are described by continuous variables with the introduction of the independent supporting elements,then a hybrid optimization method of continuum structure and its supporting locations is proposed. The mathematical models of multi-objective optimization are established considering both the structural stiffness and the mean eigenvalue of the structure. The optimal solution of multi-objective optimization is determined by a certain decision factor. A simply supported plate under bending and bending-torsion loading conditions are optimized by the proposed hybrid optimization method. The results show that the distribution of material and supporting locations is clear,and the layout of supporting locations and the topology of structure can be effectively optimized at the same time. Compared with the design results from the standard topology optimization with given supporting conditions,the static and dynamic performances of the two examples are improved more than 30% and 88%,respectively. It is found that the proposed design method can satisfy the constraints,and remarkably improve the static and dynamic performance of the structure with a smaller number of supporters.

关 键 词：连续体结构 支撑位置 协同优化 SIMP 

分 类 号：TH11[机械工程—机械设计及理论]