滑动最小二乘插值函数在板弯曲问题上的应用

APPLI CATIONS OF THE MOVING LEAST SQUARES INTERPOLANT IN PLATE BENDING PROBLEMS

利用滑动最小二乘插值函数作为加权残值法的试函数,分析了该试函数的拟合特性,对试函数中的基函数以及权函数的选取提出了建议;采用最小二乘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;利用该试函数对薄板的挠曲、中厚板的弯曲两个例子进行了数值计算,并与理论结果或其它数值结果进行对比,结果表明,该试函数适用于多种边值问题,且精度高.该法简化了选择试函数的过程,尤其适用于工程中的各种数值计算.

The moving least squares interpolant is used as a trial function in the method of Weighted Residuals. The fitting performance of the function is checked. The choices of the basis function and weight functions in the trial function are proposed. The coefficients in the trial function are obtained by point collocation method, and therefore the approx-imate solutions of the boundary value problems are obtained. Two examples (deflection of a square thin plate and bending of medium thick plate) are cal-culated by this method. After comparing with the theoretical results it indicates that this trial func-tion may be used to solve many boundary value problems and also exhibits a high accuracy. The procedure in selecting the trial function is simpli-fied by this method, which is especially suitable to numerical calculations in engineering.