Problem Of Contact Interaction Research Articles

On Some Contact Problems for Bodies with Elastic Inclusions

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.

Contact Problems for Elastic Bodies With Initial Stresses: Focus on Ukrainian Research

In the present review article general results concerning problems of contact interaction (contact problems) of pre-stressed bodies with rigid, and elastic punches (facings) are presented. The modern classification of investigations on contact problems for bodies with initial stresses is based on two approaches. The first approach is applicable to bodies with a specific type of elastic potential. The second approach is developed in parallel with the first one. It describes investigations on contact problems for pre-stressed bodies with an arbitrary structure of an elastic potential in a general form for compressible and incompressible materials. In the last case, investigations were carried out in a common form for the theory of large (finite) initial strains and various variants of the theory of small initial strains. The formulation of the problems is given, and methods of solving planar and spatial contact problems for bodies with initial stresses are developed. Procedures of the theory of complex variables and methods of Riemann-Hilbert are used. For planar problems, the authors introduce planar potentials of the linearized static and dynamic problems for elastic compressible and incompressible bodies with initial stresses. In the case of spatial contact problems, various procedures are used: general solutions of spatial static problems for elastic bodies with initial stresses, methods of harmonic potential theory, integral transformations, and integral equations using numerical methods of investigation. The essential numerical results in the form of graphs and tables are presented. These give the quantitative and qualitative analysis of the influence of initial stresses on the main characteristics of contact problems. This review contains 98 references.

Elastic contact of two cylinders

We study the axially-symmetric problem of contact of two long elastic cylinders one of which is placed into the other under the action of a load varying along the axis. It is shown that if the loaded area is small as compared to the length of the cylinders, then there exist regions of separation, which should be taken into account. The comparison of solutions obtained by taking into account and by neglecting these regions demonstrates that they indeed can be neglected in computing contact stresses (with accuracy sufficient for practical purposes). In addition, we pose and solve a problem of contact interaction of a long elastic cylindrical band with a cylinder placed inside it. For this system, we study the cases of fixed and unknown contact area.

Mathematical modeling of wear-resistance processes of bodies with coatings

We study a mathematical formulation of problems of contact interaction of coated bodies when the material is worn. We state the physical relations that connect the intensity of wear with the characteristic physical quantities. For the case of a half-plane with a thin elastic coating the problem is reduced to singular integro-differential equations whose solution is obtained in the class of orthogonal polynomials. We give estimates of the influence of the characteristics of the coating and the base on the wear process. One figure, two tables.

On a class of elasticity theory problems with non-classical boundary conditions

A contact problem of interaction between a massive body containing a cavity and elastic shell reinforcements of these cavities is considered. It is replaced by some other just for a massive body with non-classical boundary conditions on the cavity boundaries that asymptotically describe the interaction in the original contact problem exactly. Error estimates are constructed for such a replacement in the norm L 2.

On the formulation of the contact problem of elastic plasticity

A differential and a variational formulation of the problem of contact interaction between an elastic-plastic body and a rigid support are examined. Equations of the theory of plastic flow with Isotropic hardening, which is a particular modification of the Il'yushin theory of elastic-plastic processes /1, 2/, are taken as governing relationships. A proof is presented of the existence and uniqueness of the generalized solution. To simplify the description the problem is considered in a Cartesian rectangular system of coordinates.

The dependence of the friction coefficient on the crystal structure of solids: Physical principles

The problem of contact interaction of pairs of the same pure metals with differing crystal structures was studied. The probability of formation of adhesive bonds, the formation of the true contact area and its dependence on the hardness of the metals and the atomic shearing force in the slip plane were investigated. Formulae were derived to calculate the friction coefficient and hardness of metals of various crystal structures in a wide temperature range from 0 K up to temperatures close to the melting point.

Application of the method of forces to the solution of problems of contact interaction of nodes in structures

Application of the method of forces to the solution of problems of contact interaction of nodes in structures