板材自由表面受法向集中力时的理论解

基于三维轴对称弹性理论，利用镜像点方法，给出了无限板表面受法向集中力作用的显式理论解．该解可用作格林函数，来求解分布力的问题．由于板的两个表面的反复映射，载荷点的镜像点有无穷多个，严密解是以固定在各镜像点的局部坐标系下的位移函数的和的形式给出的，但只需考虑前几个镜像点，就可获得足够精确的解．关于各镜像点的位移函数，是以递推形式给出的，易于计算机编程。

THEORETICAL SOLUTION FOR AN INFINITE PLATE WITH A NORMAL FORCE ON THE SURFACE

Based on the theory of spatial axisymmetrical elasticity, the theoretical solution for a infinite plate with a normal force acting at the free surface has been deduced in detail, by introducing infinite images reflected by the two free surface. This fundamental solution has been given in the form of Love's displacement functions, which are defined in the local coordinate systems with their origins placed at each mirror point. It is found that the displacement functions corresponding to the images of higher order can be determined from that to lower order ones, and only the displacement functions corresponding to the first several images are needed to get solutions with enough accuracy. This solution can be used as the Green function to deal with many complicated problems. Moreover, it is easy to implement the theoretical solution in numerical calculation prograrn, since it is given in a recurrence form.