Hetényi's elastic quarter space problem revisited

Transform methods are used to solve the problem of an elastic quarter space subjected to tractions on its surface. The present analysis uses the reflection principle to formulate problem as the solution of unknown residual surface tractions. A Fourier transform is taken in the direction of the edge of the quarter space. The problem is thereby reduced to decouplable integral equations, which are similar to those for the elastic quarter plane. Field quantities are obtained by performing the appropriate inverse transforms and the present results are compared with those of Hetenyi for the normally loaded case. Additional results are given for the cases of tangential surface loading.