Thermoelastic contact interaction of bodies in the presence of surface thermophysical irregularities

We study the thermoelastic contact interaction (in the absence of friction) of half-spaces under conditions of planar deformation in the presence of thin surface thermophysical irregularities that are taken into account by means of generalized conditions of thermal contact with one another. The problem is reduced to solving a system of singular integrodifferential equations with respect to the jumps of temperature and heat flow on the boundary of a section. We analyze the influence of a nonuniform thermal resistance distributed periodically along the surface or localized in one region of it on the distribution of temperature and stresses in the bodies and on their boundary. Four figures.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 23–28.     

Thermoelastic contact with Barber's heat exchange condition

We consider a nonlinear parabolic problem that models the evolution of a one-dimensional thermoelastic system that may come into contact with a rigid obstacle. The mathematical problem is reduced to solving a nonlocal heat equation with a nonlinear and nonlocal boundary condition. This boundary condition contains a heat-exchange coefficient that depends on the pressure when there is contact with the obstacle and on the size of the gap when there is no contact. We model the heat-exchange coefficient as both a single-valued function and as a measurable selection from a maximal monotone graph. Both of these models represent modified versions of so-called imperfect contact conditions found in the work of Barber. We show that strong solutions exist when the coefficient is taken to be a continuously differentiable function and that weak solutions exist when the coefficient is taken to be a measurable selection from a maximal monotone graph. The proofs of these results reveal an interesting interplay between the regularity of the initial condition and the behavior of the coefficient at infinity.     

Hertzian contact in the presence of a Mindlin force

The smooth axisymmetric contact between a rigid spherical punch and an isotropic elastic halfspace is perturbed by an internally applied Mindlin force which is located along the axis of symmetry. The paper presents certain closed form solutions to this unilateral contact problem.     

Green's contact functions for heat conduction of two half-spaces and half-planes with application to several boundary contact problems

Green's contact functions are constructed for two half-spaces and two half-planes for materials with different thermal conductivities. With the aid of these contact functions some bimetal problems are reduced to boundary integral equations along the outer boundary where only the boundary conditions are to be satisfied. The boundary integral operators are investigated in the plane case. They are Fredholm operators with index zero. The asymptotics of the density of the potentials, which depends on the material parameters and on the angles between the contact line and the outer boundary, is determined by the Mellin transform technique.     

Reflected-refracted and head sh waves formed on a thin layer that is in welded contact with two elastic half-spaces

The reflection and refraction of SH waves by an elastic layer sandwiched between two elastic half-spaces are studied by using the numerical simulation on the basis of contour integration in the complex plane of the horizontal component of the slowness vector. The propagation of body, channel, head, and screened body waves are simulated in time and spectral domains. The wave fields associated with the propagation in the layer have strong attenuation, provided that the wave length is smaller than the value of the thickness of the layer. The stationary wave field of such waves is of resonance nature. Moreover, the maximum of the modulus of the spectral function is shifted to higher frequences as the epicentric distance increases. Thus, the attenuation of such waves depends on spectral characteristics of a source-receiver system. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 225, 1997, pp. 91–120. Translated by T. N. Surkova.     

An illustration of sliding contact at any constant speed on highly elastic half-spaces

A rigid smooth indentor slides at a constant speed on a compressibleisotropic neo-Hookean half-space that is subjected to pre-stressaligned with the surface and sliding direction. A dynamic steady-slidingsituation of plane strain is treated as the superposition ofcontact-triggered infinitesimal deformations superposed uponfinite deformations due to pre-stress. The neo-Hookean materialbehaves for small strains as a linear elastic solid with Poisson'sratio 1 : 4. Exact solutions are presented for both deformationsand, for a range of acceptable pre-stress values, the infinitesimalcomponent exhibits the typical non-isotropy induced by pre-stress,and several critical speeds. In view of the unilateral constraintsof contact, these speeds serve to define the sliding speed rangesfor which physically acceptable solutions arise. A Rayleighspeed is the upper bound for subsonic sliding, and transonicsliding can occur only at a single speed. For the generic parabolicindentor, contact zone traction continuity is lost at the zoneleading edge for trans- and supersonic sliding. For pre-stresslevels that fall outside the acceptable range, either a negativePoisson effect occurs, or a Rayleigh speed does not exist andthe unilateral constraints cannot be satisfied for any subsonicsliding speed. Received 15 March 2000. Revised 22 November 2000.     

Collective two-photon processes in the presence of a thermal electromagnetic field

Institute of Applied Physics, Academy of Sciences of the Moldavian Republic. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 3, pp. 416–429, September, 1991.     

Thermoelastic contact during pressing of a heated elliptical cross-section die into a transversely isotropic piezoceramic half space

The three-dimensional thermoelastic contact as a nonplanar elliptical cross-section die is pressed into a transversely isotropic half space is examined under conditions such that the die has a previously specified temperature while the boundary of the half space outside the die is kept at zero temperature. Contact between the die and the half space is assumed to be ideal. The stressed state in the elastic medium is characterized by potential functions which are constructed explicity. Expressions are given for determining the translational displacement of points on the base of the stamp as well as the major half axis and eccentricity of the contact area. Some possible forms of boundary conditions for the electrical variables at the contact area are examined. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 37–53, 1999.     

State of stress and strain of plates with two equal openings in the presence of high-elastic deformation

The apparatus of the nonlinear theory of elasticity [1–3] is used to investigate the high-elastic deformation of a plate with two equal circular openings and a massive block with two cylindrical channels. Computer-calculated stress concentration factors are given for compressible and incompressible materials.Translated from Mekhanika Polimerov, No. 4, pp. 687–692, July–August, 1969.     

On a thermal stress problem for contacting half-spaces with inclusions of other material involving a new method for computing potentials and singular integrals

This paper deals with a thermal stress problem for contacting half-spaces of different materials having an inclusion of other material. With the aid of the contact tensor of two half spaces the problem is reduced to singular integral equations. Some new theorems on potentials with the contact tensor are used. Finally, a potential of the double layer with the contact tensor in the kernel and a singular integral operator, being the direct value of the potential, are calculated. For this a Kupradze method is applied, interpreting this potential as a solution of a contact problem of elastostatics. Some numerical experiments are communicated.     

The dynamics of a rigid body with a sharp edge in contact with an inclined surface in the presence of dry friction

In this paper we consider the dynamics of a rigid body with a sharp edge in contact with a rough plane. The body can move so that its contact point is fixed or slips or loses contact with the support. In this paper, the dynamics of the system is considered within three mechanical models which describe different regimes of motion. The boundaries of the domain of definition of each model are given, the possibility of transitions from one regime to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces are discussed.     

Thermoelastic instability of functionally graded coating with arbitrarily varying properties considering contact resistance and frictional heat

Using the homogeneous multi-layered model, this paper studies the thermoelastic instability (TEI) of the functionally graded material (FGM) coating with arbitrary varying properties considering the frictional heat and thermal contact resistance. A homogeneous half-plane slides on an FGM coated half-plane at the out-of-plane direction under a uniform pressure. The perturbation method and transfer matrix method are used to deduce the characteristic equation of the TEI problem, which is then solved to obtain the relationship between the critical sliding speed and critical heat flux. The effects of the gradient index and varying form of material properties of the FGM coating on the stability boundaries are examined. The results show that FGM coating can adjust the thermoelastic contact stability of sliding systems.     

Estimates for the Thermoelastic Properties of a Composite with Ellipsoidal Anisotropic Inclusions

Mechanics of Composite Materials - A mathematical model describing the thermoelastic characteristics of a composite reinforced by anisotropic ellipsoidal inclusions is proposed. The model is...     

Thermal creep of polyethylene in the presence of thermal cycling

The temperature-time dependence of Poisson's ratio and the volume relaxation of LDP is investigated in the case of uniaxial tension. It is established that at elevated temperatures and loads the material becomes denser and Poisson's ratio exceeds 0.5. It is shown that the (t) curves and the temperature dependence of the instantaneous Poisson's ratio are nonmonotonic, while the nature of the (t) relaxation changes qualitatively as a certain temperature region is entered and the stress is increased.Mekhanika Polimerov, Vol. 4, No. 3, pp. 421–427, 1968     

Thermoelastic stresses in a nonuniform orthotropic cylinder

The stress distribution in a cylinder with cooling nonuniform with respect to the circumferential coordinate is investigated. The nonuniformity of the mechanical properties of the material in this direction is taken into account. Numerical results obtained at values of the parameters characteristic of wound glass-reinforced products are discussed.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 3, pp. 560–563, May–June, 1975.     

Tight upper bounds for the discrepancy of half-spaces

We show that the discrepancy of anyn-point setP in the Euclideand-space with respect to half-spaces is bounded byC _d n ^1/2−1/2d , that is, a mapping χ:P→{−1,1} exists such that, for any half-space γ, γ, |Σ _p∈P⋂γ χ(p)|≤C _d n ^1/2-1/2d . In fact, the result holds for arbitrary set systems as long as theprimal shatter function isO(m ^d ). This matches known lower bounds, improving previous upper bounds by a factor. Part of this research was done at the Third Israeli Computational Geometry Workshop in Ramot and during a visit at Tel Aviv University in December 1993. Also supported in part by Charles University Grant No. 351 and Czech Republic Grant GAČR 201/93/2167.     

Investigation of normal waves in a porous layer surrounded by elastic half-spaces

The wave field and dispersion equations are found for a porous layer surrounded by two elastic half-spaces. The porous layer is described by the effective model of a medium in which elastic and fluid layers alternate. To investigate the normal waves, all real roots of dispersion equations are determined and their movements as the wave number increases are investigated. As a result, the dispersion curves of all normal waves are constructed and the dependence of normal waves on the parameters of the porous layer and elastic half-spaces is analyzed. Bibliography: 6 titles.     

The quasisteady contact problem of thermoelasticity for a two-layered cylinder under frictional heating and nonideal thermal contact

In this article we give an analytic solution of the polar-symmetric quasisteady thermoelastic contact problem for a two-layer hollow circular cylinder. The problem is solved taking account of frictional heat production and thermal resistance on the mutually tangent surfaces of the components of the cylinder. On the exterior boundary of the two-layer system we study the condition of Winkler elastic fixing. In the solution we apply the Laplace transform with respect to time. We carry out a numerical analysis whose results are shown as graphs. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 104–110.