New Methods Of Stochastic Finite Element Based On Random Characteristic Analysis For Thin-Walled Box Girders

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.