Mixed Contact Problems in Plane Elasticity

Abstract

The paper is concerned with the contact problem of the isotropic elastic plane with a simply connected elastic inclusion of different material in the frame of elastostatics. The contact curve is dissected into 9 pairwise disjoint curve systems, at which 9 different contact conditions are prescribed. Some regularity concepts are defined (so-called *-regularity, $ϵ$*-regularity and $ϵ$-regularity), which imply certain restrictions for the contact data, for instance certain compatibility conditions. Using Green formulas, the problem of uniqueness is studied and, in certain cases, some necessary conditions are given. By the aid of elastic potential of single layer, a system of integral equations is obtained, containing two arbitrary constants on the right-hand side. The solution $\Phi$ to be determined is subjected to an additional integral relation. By application of a suitable differential operator ${\Omega }_p$, a system, of singular integral equations with discontinuous coefficients is obtained. The dimension of the linear space ker ${\Omega }_p$ is calculated. In a following note in this journal, the investigation of the contact problem will be continued by detailed study of the singular integral equation system.