Planar elastic problem for an orthotropic plane with a slit under edge contact conditions of the type of viscous friction

A system of hypersingular equations for the title problem is constructed. Qualitative properties of the solution of this system are discussed. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 195–197, July–August, 1999.     

Solution of a contact problem for a plate with a deformable insert

Contact problems with friction are solved for a rectangular plate with a circular hole into which a ring plate (insert) is placed with a small clearance. Two versions of contact boundary conditions are formulated. According to the proposed approximate formulation of the problem, the boundary conditions in both versions are satisfied not at the actual contact points but at specified pairs of points. Therefore, it is sufficient to determine attachment, slip, contact, and contact-free regions on just one of the contacting contours. The finite-element method and the Boussinesq principle are used to solve the problem. One of the versions of boundary conditions, compared to the other, gives smaller values for the strain energies of the plate and insert, the stress-concentration coefficient, and the lengths of attachment and contact regions. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 216–226, September–October, 1999.     

Solution of a contact problem for a prestressed layer and punch

Conclusions On the basis of the analysis of the analytical solution and of the numerical computations, we can draw the following conclusions.the initial stresses in the layer affect significantly the distribution law of the contact stresses and displacements in the layer and in the cylinder (Figs. 1–5). This influence is noted in the cylinder for the sections <1 (Figs. 1, 2) and in the domain of the contact of the punch and the layer (Figs. 3–5).The initial stresses affect in an essential manner the character of the distribution of u₃, and depend on the quantity .For h>15, for the determination of the stress-strain state in the punch and in the layer, with a sufficient accuracy for engineering applications, one can use the solution for the semispace. Thus in this paper one obtains the analytic and graphical dependences, reflecting the influence of the initial stresses on the stress-strain state of the elastic punchlayer system with initial stresses. This influence is essential (Fig. 1–5) for both compressible and incompressible bodies and has to be taken into account at the calculations of machine components and constructions.Hmelnickii Institute of Light Industrial Technology, Translated from Prikladnaya Mekhanika, Vol. 23, No. 3, pp. 14–22, March 1987.     

Solution of the plane Hertz problem

The paper considers the problem of onesided frictionless compression of plane elastic bodies that are initially in contact with each other at a point. The first terms of an asymptotic solution of the problem are constructed by the method of joined asymptotic expansions. Determination of the approach of the bodies as a function of the pressing force reduces to calculating socalled of local compliance. The problems of contact of an elastic ring and elastic circular disks with punches and an elastic disk compressed between two elastic strips are considered. An asymptotic model for the quasistatic collision of plane elastic bodies is proposed.     

Nonstationary plane contact problem in theory of elasticity for conformal cylindrical surfaces

A numerical–analytical approach is described to investigate the process of impact interaction between a long smooth rigid body and the surface of a circular cylindrical cavity in elastic space. A non-stationary mixed initial boundary value problem is formulated with a priori unknown boundaries moving with variable velocity. The problem is solved using the methods of the theory of integral transforms, expansion of desired variables into a Fourier series, and the quadrature method to reduce the problem to solving a system of linear algebraic equations at each time step. Some concrete numerical computations are presented.The cylindrical body mass and radius impact on the proile of the transient process of contact interaction has been analysed.     

Stress intensity factor in a contact problem for a plane crack under an antiplane shear wave

The frictional contact interaction of the finite edges of a plane crack under the action of a normally incident harmonic shear wave that produces antiplane deformation is studied. The influence of the forces of contact interaction on the stress intensity factor is analyzed Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 115–119, September 2007.     

A receding contact problem for an anisotropic elastic medium consisting of a layer and a half plane

This paper considers a frictionless receding contact problem between an anisotropic elastic layer and an anisotropic elastic half plane, when the two bodies are pressed together by means of a rigid circular stamp. The problem is reduced to a system of singular integral equations in which the contact stresses and lengths are the unknown functions. Numerical results for the contact stresses and the contact lengths are given by depending on various fibre orientations.