THREE DIMENSIONAL THEORETICAL SOLUTION OF A TANGENTIAL FORCE ON THE SURFACE OF TWO COATING MATERIALS WITH THE SAME THICKNESS

Based on the Papkovitch's general solution of spatial elasticity and the fundamental solution of a semi-infinite body subject to a tangential concentrated force, the theoretical solution of a tangential force acting at the free surface of two bonded dissimilar coating materials with the same thickness has been derived by utilizing mirror point method and the Dirichlet uniqueness principle. The solution is expressed by the displacement functions defined under the local coordinate systems whose origins are placed at their mirror points individually. There are infinite mirror points because of repeating imaging of the load point through the free surface and the interfaces, but the last numerical analysis indicates that we can get enough accurate solution by taking the first several mirror points into account, which proves the correctness of the theoretical deduction and shows that only the displacement functions corresponding to the first several mirror points have an effect on the accuracy of the solution. The theoretical solution can also be used as the Green Function to deal with more complicated problems.