中文摘要：

纽曼—蒙特卡洛法可以改进普通蒙特卡洛法计算效率低的缺点,但需要完善多变量随机场的结构随机抽样分析技术。为了研究箱形梁在荷载、材料同时具有随机特性时的剪力滞效应,结合箱形梁剪力滞效应分析的一维离散有限元法,利用基于多变量随机场抽样的纽曼—蒙特卡洛法,计算具有随机材料特性的箱形梁在随机外荷载下响应量的统计特征数字。研究结果表明,多变量随机场抽样的固定搭配法能够保持不同随机量之间固有的互不相关性;利用纽曼级数建立的随机荷载下结构随机响应量的迭代计算格式,能有效避免在大样本重复计算过程中刚度矩阵的反复求逆运算,提高蒙特卡洛法的计算效率;箱形梁的剪力滞效应与箱梁的随机性密切相关,忽略剪力滞效应或忽略随机因素的作用,都将给工程结构计算和设计埋下安全隐患。

英文摘要：

Neumann expansion is usually employed to improve the efficiency of Monte Carlo simulation（MCS）,while further research is required for stochastic analysis of structures with multivariate random field.In order to investigate the shear lag effect on the box girder with the uncertainty of material and loading,the first two moments of the response of box-girders by means of the Neumann Monte Carlo Simulation（NMCS） technique based on the one-dimension discrete finite element method and the regular collocation method.The results show that the regular collocation method is able to keep the irrelevancy among the random variables and applicable for sampling of multiple random quantities.The iteration procedures presented for the stochastic analysis of structures with the uncertainty of material and loading using Neumann series and MCS can avoid repeated calculation of the inverse stiffness matrices so that the algorithm efficiency is greatly improved,and it reduces the consumption of computer time and memory.The shear lag effect on box girders is closely related with the randomness of the box girders,and ignoring the shear lag effect or the randomness in the calculation and design of engineering structures will undermine the safety of the structures.