摘要
为了提高结构优化的可行性和高效性,提出了一种基于子结构平均单元能量的结构动态特性优化方法。从建立优化模型出发,结合结构几何特性将整体结构划分为多个准设计变量子结构,对于桁架结构来说,将每根杆作为一个子结构,对于连续结构而言,多个单元作为一个子结构,再结合结构平均单元体积应变能及平均单元动能与结构动态响应贡献的关系,将平均单元体积应变能较大的结构单元作为尺寸应该变大的子结构,平均单元动能较大的结构单元作为单元尺寸应该变小的子结构,从而确定了设计变量的合理范围。推导了平均单元能量与结构动态响应的关系,构造了结构动态特性优化模型,调用基于梯度的优化器进行迭代寻优。以124杆桁架结构为例的三类优化模型进行优化分析,并与传统优化方法从优化结果和收敛性两方面进行比较,说明了文中方法的合理性和优越性。
In this article,aiming for a high standard of feasibility and efficiency,a optimization method of structural dynamic characteristics based on the average unit energy of the substructure is proposed. According to the geometric characteristics of the optimization model,the whole structure is divided into several quasi-substructures with design variables. For the truss structure,each rod is used as a substructure,while pluralities of the elements are considered as a substructure for a continuous structure.In combination with the relationship between the structure of the average unit’s volume-strain energy and kinetic energy on the one hand and the contribution of dynamic structural response on the other hand,the structural elements with larger volume-strain energy are regarded as the substructure which should be larger in size;the structural elements with larger kinetic energy are taken as the substructure which should be small in size. Thus,the reasonable range of design variables is identified. The relationship between the average unit energy and the dynamic structural response is derived,and the optimization model of structural dynamic characteristics is worked out. Finally,the iterative optimization is carried out by means of the optimizer based on the gradient. With the 124 bar-truss structure as the example,three optimization models are analyzed and optimized;the reasonableness and superiority of the proposed method are illustrated by comparing with its traditional counterpart from the perspectives of convergence and optimization results.
作者
毛虎平
高鹏飞
MAO Hu-ping;GAO Peng-fei(School of Mechanical and Power Engineering,North University of China,Taiyuan 030051)
出处
《机械设计》
CSCD
北大核心
2020年第2期59-67,共9页
Journal of Machine Design
基金
国家自然科学基金资助项目(51275489)
山西省自然科学基金资助项目(201701D121082).
关键词
平均单元能量
子结构
动态特性
结构优化
average unit energy
substructure
dynamic characteristics
structural optimization
