Contact Problems for Cylindrical Stamps and Elastic Bodies with Initial (Residual) Stresses

The chapter is devoted to contact problems of a cylindrical punch with prestressed bodies without consideration of friction. It highlights the problems concerning rigid or elastic ring-shaped punches on a half-space with initial stresses, problems for prestressed cylindrical punch and elastic layer, and the problem with two prestressed half-spaces with elastic cylindrical punches with initial stresses. The results are expressed in the general form for the theory of large initial deformations and two options for the theory of small initial deformations under the arbitrary form of an elastic potential. Many fundamental results are used to study the problem, such as Hankel’s transformations, dual integral equations, orthogonal polynomials, and other contact mechanics methods of linearized elasticity theory.