板分析的滑动最小二乘插值函数残值法

利用滑动最小二乘插值数作为加权残值法中试函数，对试函数中的基函数的以及权函数的选取提出了建议；分析了形函数的特性；对试函数拟合原函数的效果进行了分析，进而提出了权函数及相应的影响半径的取值；采用最小二北配点法求解定解问题的近似解；利用该试函数对矩形薄板和L形板的弯曲进行了数值计算，并与理论结果和有限元数值结果进行对比，结果表明，该试函数适用于多种边值问题，且精度高。该法简化了选择试验的过程，尤其适用于工程中的各种数值计算。

Applications of Moving Least Squares Interpolant in Solving Bending Problems of Plate

The moving least squares interpolating function was used as trial function in the method of weighted residuals. The principle, which is used in the selection of the basis and weight function, is proposed. The performance of the shape function is analyzed. The fitting performance of the function was checked. The fitting effects of the trial function were examined also, and the weight function and its radius of influence were determined. The coefficients in trial function were obtained by least squares method with point collocation, and then the resolutions of the boundary value problems were obtained. Two examples ( deflection of a square thin plate and L shape plate ) were calculated by this method. Comparing with the theoretical result and FEM result, it indicated that this trial function was suited for solving many boundary value problems and also had a high accuracy. The procedure in selecting trial function is simplified by this method, which is especially adopted to numerical calculations in technique engineering.