弹性半空间上的薄扁壳基础

本文应用椭园型偏微分方程中的位势理论，把定义弹性半空间内任一点由表面分布压力所产生沉陷值的Ｂｏｕｓｓｉｎｅｓｑ积分，分别考虑为单层和双层位势之和。利用在超过边界时，单层位势有弱间断及双层位势有强间断的性质，得到用偏导数表达的Ｂｏｕｓｓｉｎｅｓｑ积分的逆变换公式，从而便于求出问题的解析解。它是将刚性压头产生的沉陷与扁壳弹性弯曲产生的沉陷相迭加而得到弹性半空间内及其表面任一点的总沉陷值。数值算例证明本文的理论计算结果可信。

THIN SHALLOW SHELL FOUNDATION ON ELASTIC HALF-SPACE

in this paper, the potential theory for partial differential equations of elliptic type is applied to define the Boussinesq integrals, which express the vertical settlement at any point in the elastic half space, as the combination of two integrals, one corresponding to a single layer potential and the other a double layer potential, with kernels being expressed in terms of the contacting pressure intensity. The single layer potential has weak discontinuity. and the double layer potential has strong discontinuity as they go through the boundary surface. Using these discontinuity phenomena, we get the inverse transformation formulae either taking the shallow shell as a rigid body or as an elastic thin shallow shell. This enables us in a very easy way to get the analytical solutions of the problem. One example is given to illustrate our approach to obtain the analytical solutions. Numerical result are presented to show the rationality of the solution.