关键词: 固体力学, 局部正交无网格伽辽金法, 移动最小二乘, 局部正交基函数, 摄动法

Abstract:

A pertubation stochastic local orthogonal elementfree Galerkin method was proposed based on the study of the local orthogonal elementfree Galerkin method and the second order pertubation method. The proposed method needs only the node information instead of the connection of the nodes to form elements. It is not necessary that the discrete point of the stochastic field coincides with the discrete node and without restraint by the element. It can guarantee the attributes of the orthogonal basis function without need of matrix reversal, and its derivatives have general and simple expressions, being convenient to program. The essential boundary conditions are imposed by the penalty function method which does not increase the quantity of unknown variables, converges fast. A case example on analysis of a static mechanical problem for a structure with stochastic parameters showed that the proposed method is correct and effective, providing a new method for solving the stochastic response problem of the structure.

Key words: solid mechanics, local orthogonal elementfree Galerkin method, moving leastsquares, local orthogonal basis function, perturbation method