考虑空间变异性的框架结构可靠度分析方法

空间变异性是结构参数的固有属性，对于工程结构的随机响应和可靠度分析具有重要影响。结合随机场离散的局部平均理论和随机响应分析的摄动随机有限元法，提出一种考虑参数空间变异性的平面框架结构可靠度分析方法，并定量分析了参数空间变异性对结构可靠度的影响规律。首先，考虑随机因素的空间变异性，采用二维线性随机场离散的局部平均理论将平面框架结构的连续随机场离散为一组随机变量，并通过理论推导建立了随机场局部平均间协方差矩阵的二重积分表达式；然后，采用摄动随机有限元法分析结构随机响应及其对基本随机变量的梯度向量，并利用可靠度分析的梯度优化法计算结构可靠指标，从而提出了一种考虑参数空间变异性的平面框架结构可靠度分析方法。分析表明，该方法具有较高的计算精度和计算效率；随机场离散的局部平均理论对相关结构类型不敏感；随着随机场相关偏度和变异性的增大，框架结构的可靠指标逐渐减小，说明结构参数的空间变异性对结构可靠度的影响不容忽视。

Reliability analysis method of frame structures considering spatial variability

Spatial variability is an inherent property of parameters,which has an important influence on the stochastic response and reliability of engineering structures.In this paper,a reliability method for planar frame structures considering spatial variability of parameters was proposed based on the local average theory and the perturbation stochastic finite element method (PSFEM).Meanwhile,the influence rule of spatial variability of parameters on structural reliability was quantitatively analyzed.Considering the spatial variability of random factors,the continuous random field was discretized into a group of random variables by using the local average theory of two-dimensional linear random field discretization,while the double integral expression of local average covariance matrix of the random field was established by theoretical derivation.Then the stochastic structural response and its gradient vector to the basic random variables were analyzed by using the PSFEM,and a reliability method for planar frame structures considering spatial variability of parameters was proposed by calculating the structural reliability index utilizing the gradient optimization method of reliability analysis.Analysis results show that the method proposed in this paper has high accuracy and efficiency.Moreover,the local average theory of random field discretization is insensitive to the correlation function types,and the reliability index of the structure decreases gradually with the increase of the skewness and variability,which shows that the influence of spatial variability of parameters on structural reliability cannot be ignored.