On Some Contact Problems for Bodies with Elastic Inclusions

Abstract

The paper deals with the contact problems of the theory of elasticity. The problems are reduced to Prandtl-type integral dif- ferential equations with a coecient at the singular operator which has higher-order zeros at the ends of the integration interval. In some concrete cases the solution is constructed eciently. Asymptotic rep- resentations are obtained. Investigation of the problem of stress concentration when contact be- tween dierent elastic media takes place remains one of the most topical tasks. Inclusions such as punches and cuts are stress concentrators and hence the study of the insuence of inclusions on the stress-strained state of solid deformable bodies, as well as the elaboration of methods allowing one to reduce stress concentration, are of great theoretical and practical importance. The problems of contact interaction between rigid inclusions of various geometrical forms and elastic bodies are considered in (1-5). In (6) some problems of contact interaction between a piecewise-homogeneous plane and a rigid inclusion, and also the anti-plane problem of an elastic half-space and problems of bending of plates with thin-shelled inclusions, are reduced to integral equations by means of the generalized method of integral transforms. As distinct from the previous papers, this paper deals with the problems of contact interaction between a thin elastic inclusion of varying rigidity and (a) an elastic half-space which is in the state of anti-plane deformation, and (b) an elastic piecewise-homogeneous plane.