桁架结构动力学拓扑优化设计解的存在性探讨  

Exploration of Existence of Optimal Solution for Truss Dynamical Topology Optimization

作　　者：徐斌[1] 吴克恭[1] 姜节胜[1] 

机构地区：[1]西北工业大学振动工程研究所,西安710072

出　　处：《机械科学与技术》2002年第4期575-578,共4页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目 ( 10 0 72 0 5 0 )资助

摘　　要：首先证明了桁架结构在拓扑构形不变的情况下 ,优化的关键约束—频率的极值的存在。然后进一步从两个方面给出了桁架结构动力学拓扑优化解存在的基本理论 :无固频约束时 ,设计变量连续且不考虑上限约束 ,则优化问题总是有解 ;考虑固频约束时 ,频率约束是是否有解的关键约束 ,并且改变结构拓扑形状可以改变解的存在性。文中算例说明所提理论是正确、合理和有效的。In this paper, under the condition of unchanged topology configuration of the truss, the theorem of the extremum existence of the natural frequency, which is the key constraint for the dynamic topology optimization, is demonstrated. Then the basic theory of solution existence for dynamic topology optimization of truss is clarfied from two aspects, when the design variables (section areas)are continuous and their bound are not imposed, if there is no frequency constraint, the optimal solution always exists for a given optimization problem and contrarily, when the frequency constraint is considered, the frequency will become the key constraint and also the existence of solution will be changed by the topology alteration. The numerical examples show that the proposed theory is correct and effective.

关 键 词：桁架 动力学 拓扑优化 固频极值 解 存在性 

分 类 号：TH113[机械工程—机械设计及理论] O327[理学—一般力学与力学基础]