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.