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基于安定分析和概率密度演化理论的 杆系结构整体可靠度分析
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Global Reliability Assessment of Framed Structures Based on Shakedown Analysis and Probability Density Evolution Method
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    摘要:

    经典体系可靠度仅涉及量值保持不变的随机静力荷载,对于随机变值静力荷载作用下的工程结构将给出不合理的评估结果,低估了结构面临的风险.鉴于此,基于安定理论提出了杆系结构在变值静力荷载作用下以安定状态作为极限状态的整体可靠度分析方法.首先,建议了具有单一功能函数的极限状态方程,并引入了两类计算功能函数的实用方法;进而,在概率密度演化理论的基础上,推导了功能函数的广义密度演化方程,并引入Dirac δ序列算法获得了其近似解;然后,对功能函数的概率密度进行一维积分即可得到结构整体可靠度;最后,通过多个算例验证了本文建议方法.结果表明:1) 建议方法有较好的精度和计算效率;2) 建议方法所得整体可靠度能更合理地评估变值静力荷载作用下结构的安全性.

    Abstract:

    The classical system reliability theory only involves random static load with constant value,which cannot provide reasonable estimation for the structure under random static load with variable value,and underestimates the risk of the structure. In view of this,a global reliability evaluation method for framed structures under static load with variable value is proposed,which is based on the shakedown theory with the shakedown state defined as the limit state. Firstly,a single performance function is proposed,and two implementations for calculating the performance function are introduced;Secondly,based on the probability density evolution method (PDEM),a generalized density evolution equation of the performance function is derived,and its approximate solution is obtained by introducing Dirac δ sequence algorithm,and then the global reliability of the structure can be obtained by the one-dimensional integral of the probability density of performance function. Finally,several examples are investigated to verify the proposed method. The results show that: 1) the proposed method is of high accuracy and efficiency;2) The global reliability obtained by the proposed method can evaluate the safety of the structure under static load with variable value more rationally.

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祖云飞,李正良,范文亮,刘蜀宇.基于安定分析和概率密度演化理论的 杆系结构整体可靠度分析[J].湖南大学学报:自然科学版,2020,47(3):106~114

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  • 在线发布日期: 2020-03-17
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