在地基上梁板分析中移动最小二乘插值函数加权残值法的应用

介绍了移动最小二乘插值函数的构造方法;以该函数作为加权残值法中的试函数,采用配点法求出试函数中的系数,进而得到边值问题的解;对Winkler地基上的非均匀梁和非规则板以及弹性半空间地基上的板进行了数值计算,并与理论结果、有限元法或其它数值方法进行了对比,采用总残值判断数值结果的准确度。结果表明,该试函数适用于多种边值问题,且精度较高。

THE APPLICATION OF WEIGHTED RESIDUALS WITH MOVED LEAST SQUARE INTERPOLATING FUNCTION TO ANALYSIS OF BEAMS AND PLATES ON ELASTIC FOUNDATION

A method to form the interpolating function by using the moved least square method is introduced. The function is used as the trial function of the weighted residual method. The coefficients in trial function can be gained by the point collocation method, then the solution of the boundary value problems is obtained. Non - uniform beams and irregular plates on Winkler foundation and plates on elastic half space foundation can be numerical calculated by the introduced method. Using the accuracy of numerical results determined by total residuals, it is compared with the theoretical results, solution of finite element method or other solutions. The final results are shown that the trial funtion is suitable to solve varied boundary value problems and with a higher accuracy.