Abstract
The three dimensional theoretical solution of a concentrated tangential force on the free surface of a coating material is deduced in detail, by introducing the infinite mirror points of the load point, and applying the Dirichlet's uniqueness theorem. The deduction is based on the basic equations of the Papokovitch's formula for three dimensional elastic problems. It is found all the harmonic stress functions corresponding to the infinite mirror points, which satisfy the continuous interface conditions and the free boundary conditions, can be deduced from the fundamental solution of a concentrated shear force at the free surface of a half infinite homogeneous solid. It is also found that only the stress functions corresponded to the first several mirror points can give the accurate enough solution, by comparing with the finite element analysis results. It is also found that the effect of material constants is quite complicate, and can not be described by only two Dunders' parameter. This theoretical solution can also be applied to any bonding dissimilar material with free surface parallel to its interface.
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