共查询到20条相似文献,搜索用时 31 毫秒
1.
S. Matysiak A. A. Evtushenko R. D. Kul'chitskii-Zhigailo 《Journal of Mathematical Sciences》2000,99(5):1569-1583
We propose a method of solution of problems of thermoelasticity for an inhomogeneous half-space. We assume that Poisson's
ratio of a material in the half-space is constant, and Young's modulus and the coefficients of linear thermal expansion and
thermal conduction vary exponentially with distance from the surface of the half-space. As an example, we consider the contact
problem on sliding an inhomogeneous body along the surface of a rigid base with regard for frictional heating.
I. Franko L'viv University, L'viv; Warsaw University, Warsaw. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya,
Vol. 41, No. 2, pp. 45–56, April–June, 1998. 相似文献
2.
An analytic solution of the boundary-value problem of heat conduction for a tribosystem that consists of a plane-parallel
layer sliding over the surface of a semiinfinite base with a constant velocity is obtained. For the materials of an aluminum–steel
friction pair, we investigate the evolution of temperature and its distribution in the layer and base along the normal to
the friction surface. 相似文献
3.
We consider the contact interaction of a stamp with rectilinear base and an elastic wedge. One of the wedge faces is fixed,
and the stamp edge touches the wedge vertex. Using the Wiener–Hopf method, we have obtained an exact solution of this problem.
We have also determined the stress distributions in the contact region and on the wedge fixed face as well as the displacements
of its free boundary. 相似文献
4.
The mechanical contact interaction of bodies with a thin composite coating is investigated with account of wear. The thermal
effects are not considered. The coating is modeled by a thin plate. Between the body and the coating is an interlayer, which
is modeled by a Winkler body with one modulus of subgrade reaction. Under the action of a rigid stamp on the coating, the
process of abrasive wear proceeds. The contact interaction of the coating with the base is described by using the model of
an intermediate layer. To determine the stress-strain state of the coating, equations of the generalized theory of plates
including the shear strains and the compression of normal are utilized. For the contact wear problem formulated, the basic
integral equation with a Fredholm-type kernel is derived, and its solution algorithm is proposed. Numerical results are presented.
__________
Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 319–330, May–June, 2006. 相似文献
5.
R. M. Martynyak B. S. Slobodyan V. M. Zelenyak 《Journal of Mathematical Sciences》2009,160(4):470-477
A model of contact between an elastic half space and a rigid base with a shallow surface rectangular hole is proposed. The
hole contains an incompressible liquid and gas. The liquid occupies the middle part of the hole and forms a capillary bridge
between the opposite surfaces. The remaining volume of the hole is filled with gas under a constant pressure. The liquid completely
wets the surfaces of the bodies. The pressure drop at the liquid–gas interface caused by the surface tension is defined by
the Laplace formula. The corresponding plane contact problem for the elastic half space is essentially nonlinear because the
pressure of the liquid and the length of the capillary in the contact-boundary conditions are not known in advance and depend
on the external load. The problem is reduced to a system of three equations (a singular integral equation for the function
of height of the hole and two transcendental equations for the length of the capillary and the height of the meniscus). An
analytic-numerical procedure for the solution of these equations is proposed. Dependences of the length of the capillary and
the pressure drop at the liquid–gas interface on the external load, volume of liquid, and its surface tension are analyzed.
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 150–156, January–March, 2008. 相似文献
6.
An asymptotic solution is constructed to the Signorini problem for a two-dimensional thin beam that is in possible contact
with two rigid supports. For the position of points where the beam leaves the base, an asymptotic formula is derived by analysis
of the boundary-layer phenomenon near these points. Bibliography: 13 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 43–60. 相似文献
7.
V. I. Ostryk 《Journal of Mathematical Sciences》2009,160(4):453-469
We consider the problem of contact interaction between a semiinfinite stamp with rectilinear base and an elastic strip with
one rigid side. Friction forces in the contact region are taken into account. These forces lead to the division of the contact
region into slipping and adhesion zones. With the use of the Wiener–Hopf method, a system of integral equations is reduced
to an infinite system of algebraic equations. The computational results of stresses and strains at the boundary and at inner
points of the elastic strip are presented.
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 138–149, January–March, 2008. 相似文献
8.
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. 相似文献
9.
We obtain an exact solution of the problem of the stress-strain state of an elastic piezoelectric half-space acted on by a
rigid elliptic die with a flat base. The axis of symmetry of the body coincides with the direction of the field of preliminary
polarization of the body. The solution is confined to the case of translational displacement of the die. We determine the
quantities that characterize the mechanical and electric fields that arise in the region of contact of the die with the half-space.
Bibliography: 7 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 40–52. 相似文献
10.
We consider the small mass asymptotics (Smoluchowski–Kramers approximation) for the Langevin equation with a variable friction
coefficient. The limit of the solution in the classical sense does not exist in this case. We study a modification of the
Smoluchowski–Kramers approximation. Some applications of the Smoluchowski–Kramers approximation to problems with fast oscillating
or discontinuous coefficients are considered. Bibliography: 15 titles. 相似文献
11.
We present a method for rational application of the deformation properties of a shell system with an elastic filler: design
of a shell with variable thickness while preserving the load-bearing ability of the system as a whole. For the equi-strength
shell thereby obtained we state and solve the mixed contact problem taking account of dry friction with nonmonotone loading,
making it possible to estimate the structural hysteresis in the system.
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 86–91. 相似文献
12.
In this paper we study a dynamic unilateral contact problem with friction for a cracked viscoelastic body. The viscoelastic model is characterized by Kelvin–Voigt's law and a nonlocal friction law is investigated here. The existence of a solution to the problem is obtained by using a penalty method. Several estimates are obtained on the solution to the penalized problem, which enable us to pass to the limit by using compactness results. To cite this article: M. Cocou, G. Scarella, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
13.
M.V. Abramovich Ye. M. KolosovaM.I. Chebakov 《Journal of Applied Mathematics and Mechanics》2014,78(2):181-186
The plane contact problem of elasticity theory on the interaction when there are friction forces in the contact area of an absolutely rigid cylinder (punch) with an internal surface of a cylindrical base, consisting of two circular cylindrical layers rigidly connected to one another and with an elastic space, is considered. The layers and space have different elastic constants. A vertical force and a counterclockwise torque, act on the punch, and the punch – base system is in a state of limiting equilibrium,. An exact integral equation of the first kind with a kernel represented in an explicit analytical form, is obtained for the first time for this problem using analytical calculation programs. The main properties of the kernel of the integral equation are investigated, and it is shown that the numerator and denominator of the kernel symbols can be represented in the form of polynomials in products of the powers of the moduli of the displacement of the layers and the half-space. A solution of the integral equation is constructed by the direct collocation method, which enables the solution of the problem to be obtained for practically any values of the initial parameters. The contact stress distributions, the dimensions of the contact area, the interconnection between the punch displacement and the forces and torques acting on it are calculated as a function of the geometrical and mechanical parameters of the layers and the space. The results of the calculations in special cases are compared with previously known results. 相似文献
14.
Marius Cocou Mathieu Schryve Michel Raous 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,94(3):721-743
The aim of this paper is to study an interaction law coupling recoverable adhesion, friction and unilateral contact between
two viscoelastic bodies of Kelvin–Voigt type. A dynamic contact problem with adhesion and nonlocal friction is considered
and its variational formulation is written as the coupling between an implicit variational inequality and a parabolic variational
inequality describing the evolution of the intensity of adhesion. The existence and approximation of variational solutions
are analysed, based on a penalty method, some abstract results and compactness properties. Finally, some numerical examples
are presented. 相似文献
15.
We consider an axisymmetric problem of heat conduction taking account of frictional heating in a conetorus pair that models
the functioning of a conical support. The bodies are pressed together and are rotating about a common axis. Heat is generated
in the region of contact of the bodies due to frictional forces. Outside the region of contact there is heat exchange with
the surrounding medium. The thermal contact between the two bodies is nonideal.
The problem is reduced to a system of integral equations whose solution is constructed by the method of successive approximations.
We give the results of numerical studies of the temperature distribution and heat flows from the geometric and thermophysical
parameters of the body.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 19–27. 相似文献
16.
I. S. Skorodyns'kyi 《Journal of Mathematical Sciences》2002,109(1):1243-1250
We develop a constructive iterative algorithm for solution of a quasivariational system that describes the quasistatic unilateral thermal contact interaction of two anisotropic thermoelastic bodies. For the generalized linear dissipative mechanism of interphase slippage and a nonideal thermal contact in the region of real interaction, this algorithm considers heat generation due to friction in the presence of an adhesive layer. We establish the sufficient conditions for the algorithm to be valid and its convergence rate in the norms of the corresponding functional spaces. 相似文献
17.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(12):1253-1258
The existence result in linear elasticity obtained for the quasistatic problem of unilateral contact with regularized Coulomb friction is extented to a local friction problem. After discretizing the implicit variational inequality with respect to time, we have to solve a sequence of variational inequalities similar to the one of the static problem. If the friction coefficient is small enough, we show the existence of the incremental solution. We construct a suitable sequence of functions converging towards a quasistatic solution of the problem. 相似文献
18.
R. M. Martynyak 《Journal of Mathematical Sciences》2000,99(5):1607-1615
We investigate the instability of thermoelastic interaction between elastic and rigid half-spaces through a liquid interlayer
under the conditions of heat transfer across the interfaces. Due to the small thickness of the liquid layer, its influence
on the temperature field is taken into account by the thermal resistance of the contact between the bodies, which depends
on the normal displacement of the boundary of the elastic body. The pressure inside the liquid is equal to the external pressure
applied to the bodies. We determined the critical value of the external heat flow for which the instability becomes possible
in such a system and studied the dependence of this value on the parameters of the elastic half-space, the thickness of the
liquid layer, and its thermal conduction.
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya,
Vol. 41, No. 2, pp. 76–82, April–June, 1998. 相似文献
19.
Based on the generalized Timoshenko-type shell theory, a numerical-analytical procedure for determining contact stresses from
the interaction between a cylindrical composite shell and rigid bandings is proposed. Specific cases of loading and contact
interaction (ideal contact through an adhesive interlayer) are considered. The contact problems are reduced to the solution
of a Fredholm integral equation of the second-kind. A calculation analysis is performed.
Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 109–120, January–February, 2000. 相似文献
20.
An explicit static thermoelastic solution is constructed for an infinite transversely isotropic body containing a thermally
insulating parabolic crack in the plane of isotropy. The surface of the crack is free of stress. A uniform thermal flux is
incident on the crack perpendicular to its surface. Formulas are obtained for the stress intensity factors near the tip of
the crack.
Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev; Catholic University, Portugal. Translated from Teoreticheskaya
i Prikladnaya Mekhanika, No. 30, pp. 54–66, 1999. 相似文献