不确定性简谐激励下连续体结构可靠性拓扑优化  

Reliability-based topology optimization of continuum structures under uncertain harmonic excitations

作　　者：王选 时元昆 陈翔 龙凯[3] WANG Xuan;SHI Yuankun;CHEN Xiang;LONG Kai(College of Civil Engineering,Hefei University of Technology,Hefei 230009,China;School of Mechanical Engineering,Tianjin University,Tianjin 300072,China;State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources,North China Electric Power University,Beijing 102206,China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009 [2]天津大学机械工程学院,天津300072 [3]华北电力大学新能源电力系统国家重点实验室,北京102206

出　　处：《振动与冲击》2024年第6期11-18,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(12202129);中央高校科研业务费(JZ2022HGTB0291);中国博士后科学基金(2022M712358)。

摘　　要：针对不确定性简谐激励下连续体结构设计问题,提出了一种有效的考虑载荷振幅和频率不确定性的谐响应可靠性拓扑优化方法。建立了概率可靠性约束下结构体积比最小化的可靠性设计优化模型,其中极限状态函数定义为所关注自由度振幅平方和。利用伴随变量法推导了极限状态函数关于设计变量和随机变量的解析灵敏度列式,采用功能度量法实现结构可靠性分析,并基于移动渐进线方法实现设计变量的更新。最后,通过3个数值算例及蒙特卡罗仿真,验证了所提方法对不确定性简谐激励下连续体结构设计问题的有效性和稳定性,并讨论了简谐激励的振幅大小和频率不确定性、可靠度指标及变异系数对优化结果的影响。An effective reliability-based topology optimization method was proposed for the design of continuum structures considering the uncertainty of the load amplitude and frequency of harmonic excitation.A reliability design optimization model of minimizing the structural volume ratio under probabilistic reliability constraint was established,in which the limit state function was defined as the sum of the amplitude squares of the degrees of freedom concerned.The analytic sensitivity formulations of limit state functions with respect to design variables and random variables were derived using the adjoint variable method.The performance measure approach(PMA)was used to achieve the reliability analysis,and the method of moving asymptotes was used to update design variables.Finally,three numerical examples and Monte Carlo simulation were tested to verify the effectiveness and stability of the proposed method for the design of continuum structure under uncertain harmonic excitations.The influences of the uncertainty of amplitude and frequency of harmonic excitation,reliability index,and coefficient of variations on the optimization results were also discussed.

关 键 词：拓扑优化 简谐激励 不确定性 可靠性拓扑优化 谐响应分析 

分 类 号：TH122[机械工程—机械设计及理论]