Theoretical Solution for Concentrated Force on the Free Surface of a Coating Material. 2nd Report. Three Dimensional Solution for a Normal Force.

Abstract

The three dimensional theoretical solution of a normal concentrated forces on the free surface of a coating material is deduced 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 spatial axisymmetric problems. It is found that all the stress functions corresponding to the mirror points, which satisfy the continuous conditions at the interface and the free boundary conditions at the free surface, can be deduced from the fundamental solution of a concentrated normal force on the free surface of a semi-infinite homogeneous solid. It is also found that only the stress functions corresponding to the first few mirror points have an influence on the accuracy of the theoretical solution. It is also found that the effect of material combination cannot be expressed by Dunders' parameters only. The stress field can be described by using Dunders' parameters together with the additional parameter.