摄动随机局部正交无网格伽辽金法

通过研究局部正交无网格伽辽金法和二阶摄动技术,构造了摄动随机局部正交无网格伽辽金法。该方法只需节点信息,不需将节点连成单元,随机场离散点与离散节点无需重合,不受单元制约。因此,结构离散随机变量个数的增加不会增加求解方程的个数,并保留使用正交基函数本解时的优点,避免了矩阵求逆,且导数具有通式,简洁明了,易于编程实现。采用罚函数法施加本质边界条件,不会增加未知量个数,收敛速度快。对含随机参数结构静力学问题进行了分析,算例证明了该方法的正确性与高效性,为解决结构随机响应问题提供了一种新方法。

Perturbation stochastic local orthogonal element-free Galerkin method

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.