On the Strains of the Surface Layer on a Rigid Body due to a Statical Force applied to the Surface (2nd Paper)

Abstract

In this paper, the functional forms of applied statical force are of non-axial -symmetry at z=0, _??_=-F₂(r) cos mθ sin mθ (m=any integer not equal to zero.) in cylindrical coordinates.
At the boundary of two materials the components of displacement u_z, u_r, u_θ limit to zero.
Under these conditions the normal displacement u_z is expre_??_sed in the following integral with some approximation, where H is the thickness of the surface layer and, where p and q are certain constants.
If the force expressed by is applied, we get the following solutions:- and etc.
The first terms of these solutions are the solutions which have been introduced in the case of semi-infinite elastic body, and the other terms are correction terms due to the boundary.
If we put λ=μ p=5/9, q=4/9 are obtained and at the limits of H→o, displacements becomes clearly zero.