Three-dimensional solution of concentrated forces in semi-infinite coating materials

The spatial analytical solution of concentrated forces in semi-infinite coating materials has been deduced by adopting the image point technology. The explicit fundamental solution is given in the series of the displacement functions corresponding to each image point. The displacement functions corresponding to the higher order image points can be determined from those to the lower ones by the recurrence formula presented in this paper. Numerical analysis by means of the finite element method has been carried out to verify the theoretical results. It is found that the accurate enough theoretical solution can be obtained by only taking the displacement functions corresponding to the first several image points into account.