【作者】 刘萍；

【导师】 杨绿峰；

【作者基本信息】 广西大学 ， 结构工程， 2008， 硕士

【摘要】 随机性是工程结构的固有特性,因而考虑实际工程中的随机性,对工程进行随机分析具有十分重要的现实意义。本论文研究了基于随机场Karhunen-Loève级数蒙特卡罗有限元法(KLSMCFEM)以及简缩基随机有限元法(RBSFEM);并将上述方法、理论应用于薄壁箱型梁的剪力滞效应和弯曲问题中。首先研究了随机场离散的局部平均法和Karhunen-Loève级数展开法。并针对特殊的随机场协方差函数形式,给出了特征值与特征函数的解析表达式;对于普通的随机场协方差函数,进一步讨论了特征值问题的Galerkin数值解法。基于随机场的Karhunen-Loève正交级数展开理论,结合蒙特卡罗有限元法(MCFEM)研究建立了基于随机场Karhunen-Loève级数的蒙特卡罗有限元法(KLSMCFEM)。在随机场Karhunen-Loève级数正交展开理论的基础上,利用预处理的随机Krylov子空间基向量,将结构位移随机响应过程展开为随机简缩基向量展开式,研究建立了简缩基随机有限元法(RBSFEM),导出了结构响应量的统计特征值的计算公式。并用于分析随机参数大变异问题。鉴于薄壁箱梁是桥梁工程通常采用的一种结构形式,在弯曲荷载下箱梁的剪力滞效应是桥梁发生损伤甚至破坏的重要原因之一,本文研究了箱梁在剪力滞效应下的随机挠曲,结合一维离散有限元方法,提出了考虑剪力滞效应的薄壁箱梁随机分析的新型随机有限元法,包括薄壁箱梁随机特性分析的KLSMCFEM法和RBSFEM法。更多还原

【Abstract】 Randomness is the natural characteristics of engineering structure, in the normal traditional determinate finite element method these stochastic factors are neglected originally, which cannot reflect the practical situation of engineering structure accurately, sometimes we will underestimate response severely. Therefore, it is especially important and has reality significance to develop stochastic analysis of engineering structure. This dissertation focuses on the new methods of stochastic finite element based on the Karhunen-Loève expansion for the random field. For example, stochastic finite element method based on Monte Carlo and stochastic finite element method based on stochastic reduced basis (RBSFEM).First, this dissertation focuses on the discretization of random fields which are based on the local average theory and Karhunen-Loève expansion. According to special form of convariance function, we provide the analytic expression of eigenvalues and eigenfunctions. According to normal form of convariance function, we further discuss the numerical solution of eigenvalues and eigenfunctions, such as Galerkin method.Second, the Karhunen-Loeve series based Monte-Carlo finite element method (KLSMCFEM) is proposed for stochastic analysis of structures for the first time. The Karhunen-Loeve series based the solution process is approximated using basis vectors spanning the preconditioned stochastic Krylov subspace(RBSFEM) is proposed for stochastic analysis of structures. Therefore, the stochastic response in the form of stochastic reduce basis can be used to generate statistical moments and probability distributions. The new methods of stochastic finite element can provide results of comparable or better accuracy particularly for large-scale problems with many random variables.Third, thin-walled box girder is a structure form that is used in bridge engineering frequently, the shear lag effect of the box girder under Bending Load is one of the important reasons of that bridge damage and even destroy. Combing the one-dimensional stochastic finite element method with the shear lag effect of the box girder theory under Bending Load, The new methods of stochastic finite element based on the shear lag effect of the box girder is proposed, including KLSMCFEM and RBSFEM. This confirms the applicability and superiority of the new methods of stochastic finite element based on the Karhunen-Loève expansion for the random field.更多还原