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亢战 罗阳军. 基于凸模型的结构非概率可靠性优化[J]. 力学学报, 2006, 38(6): 807-815. DOI: 10.6052/0459-1879-2006-6-2005-629
引用本文: 亢战 罗阳军. 基于凸模型的结构非概率可靠性优化[J]. 力学学报, 2006, 38(6): 807-815. DOI: 10.6052/0459-1879-2006-6-2005-629
Zhan Kang, Yangjun Luo. On structural optimization for non-probabilistic reliability based on convex models[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(6): 807-815. DOI: 10.6052/0459-1879-2006-6-2005-629
Citation: Zhan Kang, Yangjun Luo. On structural optimization for non-probabilistic reliability based on convex models[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(6): 807-815. DOI: 10.6052/0459-1879-2006-6-2005-629

基于凸模型的结构非概率可靠性优化

On structural optimization for non-probabilistic reliability based on convex models

  • 摘要: 基于不确定性的凸模型描述,研究考虑非概率可靠性指标约束的结构优化问题. 该优化模型是一个内层优化为极小极大问题的嵌套优化模型. 为了有效地求解该模型,提出了一种基于目标性能的优化方法,通过寻找目标性能点来判断约束的满足情况,从而避免直接计算以极小极大(min-max)问题定义的非概率可靠性指标. 提出的数值方法可处理材料、几何及载荷等不确定性参数,并且目标性能值的灵敏度计算公式简便,算法稳定. 数值算例验证了所提出方法的正确性,也表明算法比文献中已有方法更为有效。

     

    Abstract: This paper discusses the setting and numerical solution ofthe non-probabilistic reliability-based structural optimization problem.Based on the convex model description for parameter scatters, the optimaldesign of non-deterministic structures is formulated as a nestedoptimization problem, in which the inner loop concerns a Min-max problem forevaluation of the reliability index. A performance measure-based method isproposed, where the feasibility of a design is determined throughminimization of the performance function value within the parameter domain.The expensive computation of the non-probabilistic reliability index, asneeded in the conventional approach, is thus avoided. The proposed approachis applicable to structural optimization problems accounting for deviationsof material properties, geometrical dimensions and loading conditions.Moreover, the design sensitivity of the minimum performance function valuecan be readily evaluated. Numerical examples show the validity andefficiency of the present method.

     

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