不确定性简谐激励下连续体结构可靠性拓扑优化

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (6) : 11-18.

论文

王选1,2，时元昆1，陈翔1，龙凯3

作者信息 +

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

WANG Xuan1,2，SHI Yuankun1，CHEN Xiang1，LONG Kai2

Author information +

文章历史 +

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(Performance Measure Approach, PMA)实现结构可靠性分析，并基于移动渐进线方法(method of moving asymptotes, MMA)实现设计变量的更新。最后，通过三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。

Abstract

An effective reliability-based topology optimization method is proposed for the design problem of continuum structure considering the uncertainty of load amplitude and frequency of harmonic excitation. A reliability design optimization model of minimizing structural volume ratio under probabilistic reliability constraint is established, in which the limit state function is the sum of the amplitude squares of the degrees of freedom concerned. The analytic sensitivity formulations of limit state function with respect to design variables and random variables are derived using adjoint variable method. The Performance Measure Approach (PMA) is used to achieve reliability analysis, and the method of moving asymptotes (MMA) is used to update design variables. Finally, three numerical examples and Monte Carlo simulation are tested to verify the effectiveness and stability of the proposed method for the design problem of continuum structure under uncertain harmonic excitation. The influences of the uncertainty of amplitude and frequency of harmonic excitation, reliability index, and coefficient of variations on the optimization results are also discussed.

导出引用

王选1,2，时元昆1，陈翔1，龙凯3. 不确定性简谐激励下连续体结构可靠性拓扑优化[J]. 振动与冲击, 2024, 43(6): 11-18

WANG Xuan1,2，SHI Yuankun1，CHEN Xiang1，LONG Kai2. Reliability-based topology optimization of continuum structures under uncertain harmonic excitations[J]. Journal of Vibration and Shock, 2024, 43(6): 11-18

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