Neumann展开Monte Carlo随机无网格点插值法

用Neumann展开Monte Carlo随机无网格点插值法(NMC-SMPIM)进行随机结构分析。在随机无网格点插值法(stochastic meshless point interpolation method，SMPIM)中，所求解问题的域由分布的节点表示；并且利用具有Delta函数性质的多项式进行节点插值，为此，很容易类似有限元法一样处理本质边界条件。同时利用Neumann展开法，建立随机结构分析的Neumann展开Monte Carlo随机无网格点插值法。数值实例表明，Neumann展开Monte Carlo随机无网格点插值法适用于材料变异系数大和要求精度高的随机结构分析。

NEUMANN EXPANSION MONTE CARLO STOCHASTIC MESHLESS POINT INTERPOLATION METHOD

The stochastic structure has been analyzed by Neumann expansion Monte Carlo stochastic meshless point interpolation method(NMC-SMPIM). In the stochastic meshless point interpolation method (SMPIM), the problem domain is represented by properly scattered points. A technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points, so the essential boundary conditions can be implemented with ease as the finite element method. By the Neumann expansion method, a Neumann expansion Monte Carlo stochastic meshless point interpolation method in probabilistic structural analysis is constructed. Numerical example shows that Neumann expansion Monte Carlo stochastic meshless point interpolation method can be applied in probabilistic structural analysis with the large variance coefficient and the high accuracy.