摘要
本文根据薄板弯曲问题的控制微分方程，应用加权残值法推导出四边简支矩形板沿中线受线分布载荷时的挠曲面方程，并用该方程进行实例计算，结果表明：该计算方法不仅能简便地得到这类问题的近似解，而且当试函数选择合适时，近似解的收敛速度是非常快的，当试函数取到７级近似时，近似表达式的结果已与精确解完全吻合。
On the basis of a controlled differential equation of bending plates, the approximate flexible equation of the rectangular hinge plates under uniform loads along the symmetry line is obtained by means of weighted residuals, The results of a practical example calculated there by show that the calculation can easily solve this kind of problems, and the calculated results can be rapidly converged to the correct value when the trial functions are properly set. The approximate expression resulting from the 7th trial functions corresponds to the theoretical value exactly.
