动力响应约束下的结构拓扑优化设计  

Topology Optimization of Structures under Dynamic Response Constraints

作　　者：张桥[1] 张卫红[1] 朱继宏[1] 

机构地区：[1]西北工业大学现代设计与集成制造技术教育部重点实验室,西安710072

出　　处：《机械工程学报》2010年第15期45-51,共7页Journal of Mechanical Engineering

基　　金：国家自然科学基金委员会-中国工程物理研究院联合基金(10676028);国家自然科学基金(10925212);高等学校学科创新引智计划(B07050)资助项目

摘　　要：以动力响应为性能设计指标的结构拓扑优化设计技术在航空航天和汽车工业等领域具有重要的应用价值。研究白噪声激励力作用下以结构减重为设计目标、指定位置的均方响应为约束的拓扑优化设计问题。为了消除动力学设计中易出现的局部模态现象,通过在伪密度方法中引入有理近似材料属性模型,建立设计变量和材料属性以及设计函数之间的关系。优化过程采用频域分析方法求解系统均方响应。推导均方响应的灵敏度求解表达式,并利用单元的各阶应变能和动能公式简化系统圆频率和振型的灵敏度求解格式。采用凸线性近似对偶优化算法求解优化模型。列举的3个典型拓扑优化算例验证了所提出的方法的可行性、相对优势以及解决复杂问题的可靠性。Structural optimization subjected to dynamic responses constraints is of great importance in the aeronautical and automobile industries. Topology optimization problem with the weight reduction as the objective function and the mean square response of the specified locations on the structure as design constraints is studied under white-noise force excitation. In order to avoid the occurrence of localized mode, the pseudo-density based optimization method is established by means of the rational approximation of material properties, and the relationship between design variables and material properties as well as design functions is formulated. In the developed optimization procedure, the mean square response of the system is calculated by means of frequency domain analysis. The sensitivity analysis is formulated for the mean square response, and sensitivity analyses of the circular frequency and vibration mode are simplified according to the expressions of element kinematic energy and strain energy of each mode. The dual algorithm with convex linearity is used to solve the optimization problem. Three typical topology optimization examples are solved to demonstrate the validity and the advantage as well as the adaptability of the proposed optimization procedure in solving complicated problems.

关 键 词：动力响应 拓扑优化 有理近似材料属性模型 灵敏度求解 

分 类 号：O332[理学—一般力学与力学基础]