滑动最小二乘插值函数配点法

Point Collocation Method with Moving Least Square Interpolation

给出了利用滑动最小二乘法构造加权残值法中试函数的方法,对试函数中的基函数以及权函数的选取提出了建议;该试函数适用于任何定解问题,采用配点法求出试函数中的系数,进而可得到定解问题的近似解;利用该试函数对简支板的挠曲、悬臂梁的弯曲、以及中心具有小圆孔的大板的均匀拉伸等三个例子进行了数值计算,并与理论结果进行对比;同时还检验了该法的精度对结点数、配点数、以及结点影响半径的依赖情况,结果表明,该试函数适用于多种边值问题,且精度高。该法简化了选择试函数的过程,尤其适用于工程中的各种数值计算。

The process of using the moving least square method to constructing trial function which was used in the method of Weighted Residuals was presented. The choices of basis function and weight functions in trial function were proposed. The coefficients in trial function which were suited to any boundary value problems were obtained by point collocation method, and therefore the resolutions of the boundary value problems were obtained. Three examples (deflection of a square plate with simply supported edges loaded by uniformly force, displacements of a uniformly loaded higher cantilever beam, stresses of a square plate with a central hole subjected an uniform tensile load) were calculated by this method and the dependence of the accuracy on nodes, collocating points, and the influence radius of nodes were examined. After comparing with the theoretical results it indicated that this trial function is suited to solving many boundary value problems and also has a high accuracy. The procedure in selecting trial function is simplified by this method, which is especially adopted to the numerical calculations in technique Engineering.