有理多项式技术有工程结构可靠度分析中的应用

给出了在相关空间中改进JC方法计算结构可靠指标的迭代格式,并采用有理多项式技术计算功能函数的偏导数,以模拟实际工程中常见的功能函数不能明确的可靠度计算问题。因此,功能函数无论是线性或非线性,显式或隐式,该方法都简单且适用。数值结果表明本文方法具有较好的效率和精度。     

A collocation reliability analysis method for probabilistic and fuzzy mixed variables

The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts.Existing methods are either computationally unaffordable or with limited application scope.Accordingly,a new technique for capturing the minimal and maximal point vectors instead of the extremum of the function is developed and thus a novel reliability analysis method for probabilistic and fuzzy mixed variables is proposed.The fuzziness propagation in the random reliability,which is the focus of the present study,is performed by the proposed method,in which the minimal and maximal point vectors of the structural random reliability with respect to fuzzy variables are calculated dimension by dimension based on the Chebyshev orthogonal polynomial approximation.First-Order,Second-Moment(FOSM)method which can be replaced by its counterparts is utilized to calculate the structural random reliability.Both the accuracy and efficiency of the proposed method are validated by numerical examples and engineering applications introduced in the paper.     

弹性约束平面预应力钢桁架系统可靠性分析

基于一次二阶矩法建立了平面索张拉预应力钢桁契任意单元失效模式的可靠性指标与验算点的迭代模型,并基于点估计法得到了整体结构失效概率的计算公式,其中任意单元随机内力统计特性一标准差则基于随机摄动理论确定,且考虑了任意弹性约束的影响．整体结构的基本随机参数包括折线索单元和桁架单元的截面面积（或综合刚度）、张拉钢索的预拉力、外荷载及约束刚度等．按照本文所建立的计算模型编制了相应的计算程序,对工程中常见的预应力钢桁架结构进行了分析,并对影响整体可靠性指标的有关参数进行了讨论,得到了有一定参考价值的结论．     

Reliability of elasto-plastic structure using finite element method

A solution of probabilistic FEM for elastic-plastic materials is presented based on the incremental theory of plasticity and a modified initial stress method. The formulations are deduced through a direct differentiation scheme. Partial differentiation of displacement, stress and the performance function can be iteratively performed with the computation of the mean values of displacement and stress. The presented method enjoys the efficiency of both the perturbation method and the finite difference method, but avoids the approximation during the partial differentiation calculation. In order to improve the efficiency, the adjoint vector method is introduced to calculate the differentiation of stress and displacement with respect to random variables. In addition, a time-saving computational method for reliability index of elastic-plastic materials is suggested based upon the advanced First Order Second Moment (FOSM) and by the usage of Taylor expansion for displacement. The suggested method is also applicable to 3-D cases. The project supported by the Research Grant Council of Hong Kong (HKUST 722196E, 6039197E), the National Natural Science Foundation of China(59809003) and the Foundation of University Key Teacher by the Chinese Ministry of Education     

基于FOSM法的预应力钢桁架系统可靠性分析

基于一次二阶矩法(FOSM)建立了索张拉预应力钢桁架任意单元失效模式可靠性指标的计算模型,并分别根据点估计法和窄界限法得到了整体结构失效概率的计算公式,随机内力统计特性-均值和标准差则根据随机摄动理论确定.该计算模型中的基本随机参数包括任意折线索单元和桁架单元的截面面积 (或综合刚度) 、张拉钢索的预拉力、外荷载及弹性约束刚度等.利用本文计算模型编写的计算程序对工程中普遍采用的结构形式进行了可靠性分析,并对影响结果的有关参数进行了讨论,为索张拉预应力钢结构整体可靠性设计奠定了一定的基础.分析表明,窄限法得到的整体可靠性指标与点估计法(PNET)所确定的基本一致, 这是因为本文计算模型中各失效模式间的相关系数较小之故.此外,随机变量的相关性对预应力钢结构不同阶段可靠性指标有不同的影响,其中加载阶段影响更大.