论文部分内容阅读
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 Design Optimization Based on Dynamic Response for Performance Topology optimization design technology has important application value in the fields of aerospace and automobile industry. Under the action of white noise excitation force, the structural weight reduction is the design goal and the mean square response of the specified location is constrained topological optimization design problem. In order to eliminate the local modal phenomena easily appearing in dynamic design, the relationship between design variables and material properties and design functions is established by introducing rational approximate material property model in pseudo-density method. The optimization process uses the frequency domain analysis method to solve the system mean square response. The sensitivity expression of the mean square response is derived, and the sensitivity of the circular frequency and mode shape of the system is simplified by using the strain energy and the kinetic energy formula of the unit. Solving Optimization Model by Using Convex Linear Approximation Duality Optimization Algorithm. Three typical topological optimization examples are given to verify the feasibility, relative advantages and reliability of the proposed method.