Contact problems of the theory of elasticity with friction and adhesion

An exact closed solution of the plane contact problem for a semi-infinite stamp is constructed for the case when the free boundary of the half-plane is under a load (problem 1), or for an analytic solution, to any prescribed accuracy, of the problem of a finite stamp impressed into an elastic half-plane under the action of a central vertical forceP (problem 2), or under the action of the above force P, a horizontal force T and a pair of forces with moment M (problem 3). In all three cases the region of contact consists of a zone of adhesion and fraction, and the stamp has a plane profile.