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1.
I. I. Argatov 《International Applied Mechanics》2006,42(1):67-83
Consideration is given to the contact without friction among an arbitrary number of elliptic punches or punches in the form
of an elliptic paraboloid and an elastic half-space with Young's modulus as a power-law function of the distance from the
edge. Asymptotic models of contact interaction are designed assuming that the distance between punches is large compared with
their dimensions
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 78–96, January 2006. 相似文献
2.
N. A. Lavrov E. E. Pavlovskaya 《Journal of Applied Mechanics and Technical Physics》1999,40(6):1180-1186
The dynamic interaction (contact) between an elastic half-space and several smooth punches is studied. It is assumed that
the dimensions of the contact regions Ωi are much smaller than the distances between them and the scale of time of the process considered is comparable with the time
required for an elastic wave to travel from one region to another. An asymptotic approach to the solution of the problem is
proposed and the first two terms of the asymptotic representation of the displacement in the contact region and its neighborhood
are constructed.
Institute of Problems of Machine Science, Russian Academy of Sciences, St. Petersburg 199178. Translated from Prikladnaya
Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 204–210, November–December, 1999. 相似文献
3.
The paper establishes the relationship between the solutions of the static contact problems of elasticity (no friction) for
an isotropic half-plane and problems of electroelasticity for a transversely isotropic piezoelectric half-plane with the boundary
perpendicular to the polarization axis. This allows finding the contact characteristics in the electroelastic case from the
known elastic solution, without the need to solve the electroelastic problem. The contact problems of electroelasticity for
different types of wedge-shaped punches (flat punch with rounded one or two edges, half-parabolic punch, and a periodic system
of punches) are solved as examples
Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 55–70, November 2008. 相似文献
4.
We study a three-dimensional contact problem on the indentation of an elliptic punch into a face of a linearly elastic wedge.
The wedge is characterized by two parameters of elasticity and its edge is subjected to the action of an additional concentrated
force. The other face wedge is free from stresses. The problem is reduced to an integral equation for the contact pressure.
An asymptotic solution of this equation is obtained which is effective for a given contact region fairly remote from the edge.
Calculations are performed that allow one to evaluate the effect of a force applied outside the contact region on the contact
pressure distribution. The problem under study is a generalization of L. A. Galin’s problem on a force applied outside a circular
punch on an elastic half-space [1, 2]. In a special case of a wedge with an opening angle of 180° and zero contact ellipse
eccentricity, the obtained asymptotic relation coincides with the expansion of Galin’s exact solution in a series. Problems
of indentation of an elliptic punch into a spatial wedge with the face not loaded outside the contact region have been studied
previously. For example, the paper [3] dealt with the case of a known contact region (asymptotic method) and the paper [4]
considered the case of an unknown contact region (numerical method). The solution of Galin’s problem allowed the authors of
[2] to reduce the contact problem on the interaction of several punches applied to a half-space to a system of Fredholm integral
equations of the second kind (Andreikin-Panasyuk method). A topical direction in contact mechanics is the model of discrete
contact as well as related problems on the interaction of several punches [2, 5–8]. The interaction of several punches applied
to a face of a wedge can be treated in a similar manner and an asymptotic solution can be obtained for the case where a concentrated
force is applied at an arbitrary point of this face beyond the contact region rather than on the edge. 相似文献
5.
V. S. Kirilyuk 《International Applied Mechanics》2006,42(11):1256-1269
The paper establishes the relationship between the static contact problems of elasticity and electroelasticity (in the absence
of friction) for a transversely isotropic half-space whose surface is the isotropy plane. This makes it possible to avoid
solving the electroelastic problem by finding all the characteristics of electroelastic contact from known cases of purely
elastic interaction. Moreover, the electroelastic state of the half-space can be fully described using a known harmonic function,
which is a solution of the purely elastic problem. The approach is exemplified by solving contact problems of electroelasticity
for flat, elliptic, two circular, conical, and paraboloidal (circular and elliptic in plan) punches
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 69–84, November 2006. 相似文献
6.
In this paper we consider the problem of adhesive frictionless contact of an elastic half-space by an axi-symmetric punch.
We obtain integral equations that define the tractions and displacements normal to the surface of the half-space, as well
as the size of the contact regions, for the cases of circular and annular contact regions. The novelty of our approach resides
in the use of Betti’s reciprocity theorem to impose equilibrium, and of Abel transforms to either solve or substantially simplify
the resulting integral equations. Additionally, the radii that define the annular or circular contact region are defined as
local minimizers of the function obtained by evaluating the potential energy at the equilibrium solutions for each pair of
radii. With this approach, we rather easily recover Sneddon’s formulas (Sneddon, Int. J. Eng. Sci., 3(1):47–57, 1965) for circular contact regions. For the annular contact region, we obtain a new integral equation that defines the inverse
Abel transform of the surface normal displacement. We solve this equation numerically for two particular punches: a flat annular
punch, and a concave punch. 相似文献
7.
S. V. Stebnovskii 《Journal of Applied Mechanics and Technical Physics》1999,40(3):407-411
The evolution of the structure of a medium containing disperse elements (the drops in a weakly viscous fluid, rigid spheres
in glycerin, and air pores in a gel) is studied experimentally in the case where the gradient temperature and the concentration
fields are absent in the system, and the medium is isolated from the influence of an external force field (including gravity
forces). It is shown that these systems are nonequilibrium: if the initial distance between disperse particles is of the order
of their sizes, the particles approach until they come in contact (coagulation) irrespective of the scale of the system.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 53–58, May–June, 1999. 相似文献
8.
The contact problem of indentation of a pair of rigid punches with plane bases connected by an elastic beam into the boundary of an elastic half-plane is considered under the conditions of plane strain state. The external load is generated by lumped forces applied to the punches and a uniformly distributed normal load acting on the beam.It is assumed that the contact between the punch and the elastic half-plane can be described by L. A. Galin’s statement, i.e., it is assumed that the adhesion acts in the interior part of each of the contact regions and the tangential stresses obeying the Coulomb law act on their boundaries.With the symmetry taken into account, the problem is stated only for a single punch, and solving this problem is reduced to a system of four singular integral equations for the tangential and normal stresses in the adhesion region and the contact pressure in the sliding zones. The solution of the constitutive system together with three conditions of equilibrium of the system of punches connected by a beam is constructed by direct numerical integration by the method of mechanical quadratures.As a result of the numerical analysis, the contact stress distribution functions were constructed and the values of the sliding zones and the punch rotation angle were determined for various values of the geometric, elastic, and force characteristics. 相似文献
9.
A technique is developed to solve contact problems for annular punches interacting with a transversely isotropic layer. The contact problem for two heated annular punches interacting with a layer is solved. The formulas for the contact stresses under the punches are derived, and the effect of the shape of the punches on the magnitude and distribution of these stresses is analyzed 相似文献
10.
P. P. Krasnyuk 《International Applied Mechanics》2005,41(12):1357-1367
A mathematical formulation is given and a solution is found to the quasistatic contact problem of thermoelasticity for a rigid
heat-conducting punch moving over an elastic layer with fixed base. The interaction is accompanied by heating due to frictional
forces obeying Amonton’s law. The problem is reduced to a system of integral equations with time-varying limits of integration.
The structure of these equations depends on the type of thermal and physical conditions on the contact surface. An algorithm
is proposed for the numerical solution of this kind of equations. The variation in the contact pressure and contact area with
time is studied
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 35–46, December 2005. 相似文献
11.
I. B. Semenova 《Journal of Applied Mechanics and Technical Physics》1998,39(3):447-453
The velocity field in a neighborhood of the point of contact between the free and solid boundaries is studied numerically
for the problem of noncrucible zone melting in a two-dimensional model formulation. A distinct Prandtl boundary layer on the
solid boundary and a Marangoni boundary layer on the free boundary and high gradients of the longitudinal velocity along the
free boundary in the immediate vicinity of the “cold corner” are observed. It is found for the first time that with distance
from the solid boundary, the velocity curve has a maximum, which is not typical of the ordinary flow near the solid boundary.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 141–148, May–June, 1998. 相似文献
12.
I. I. Argatov 《Journal of Applied Mechanics and Technical Physics》2004,45(5):764-773
The linear contact problem for a system of small punches located periodically on a part of the boundary of an elastic foundation is studied. An averaged contact problem is derived using the Marchenko–Khruslov averaging theory. An asymptotic formula is obtained for the translational capacity of a smooth punch with a fine-grained flat base. 相似文献
13.
An approximate solution of an initial-boundary-value problem appropriate for the semiaxist>0 (t is time) is constructed for a system of integrodifferential equations which describes the waves excited in an initially stationary
unbounded heavy two-layer fluid by a vertically oscillating sphere located at a distance from the interface that is significantly
greater than its radius. The shape of the steady-state wave is found by passing to the limit as time increases indefinitely.
The wave resistance experienced by the sphere during the transient process and in the steady-state regime is studied as a
function of frequency.
Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–133, March–April,
1998. 相似文献
14.
Although a fundamental physical parameter, surface tension is difficult to measure. Common tensiometry inaccuracy comes from
failure to control air–liquid–solid contact conditions, or account for liquid meniscus geometry and buoyancy corrections.
This paper describes an in situ tensiometry technique, based on withdrawal of a thin-walled tube from the liquid interface,
that enforces a known air–liquid–solid contact condition. This technique can be pursued at any level of experimental hygiene.
Experimental results for filtered tap water, an alcohol–water solution, and a surfactant–water solution show that results
repeatable to three significant digits are obtained with modest effort for a variety of geometrical parameters.
Received: 7 October 1997/Accepted: 23 April 1998 相似文献
15.
Feimin Huang Jing Li Akitaka Matsumura 《Archive for Rational Mechanics and Analysis》2010,197(1):89-116
We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes
system for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for
the compressible Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is proved
that for the one-dimensional compressible Navier–Stokes system, the combination wave of a “viscous contact wave”, which corresponds
to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave
is suitably small. This result is proved by using elementary energy methods. 相似文献
16.
A dual-probe hot-film anemometry technique has been developed to measure multiple gas-bubble velocities corresponding to
different gas-bubble size groups in air–water flows. A data reduction scheme using wavelet analysis combined with a phase-detection
technique is used to discriminate the hot-film anemometer output signals into signals corresponding to different bubble size
groups. The phase and bubble size discrimination is based on the magnitude and time derivative of the signal, and the streamwise
length of the gas bubbles. A cross-correlation between the discriminated signals from the two probes yields an average time
difference of arrival of the gas bubbles at the two sensor locations. The velocities are estimated from the distance between
the sensors and the time difference of arrival. The mean bubble size is estimated from the chord length distribution. Measurements
performed in vertical-up air–water slug flow show the technique to be a viable method for obtaining bubble velocity and size
information. The velocity measurements from the hot-film anemometry are corroborated using a high-speed quantitative flow
visualization system.
Received: 22 December 1999/Accepted: 8 May 2001 相似文献
17.
N. I. Shishkin 《Journal of Applied Mechanics and Technical Physics》2007,48(2):145-152
The seismic energy transferred to an elastic half-space as a result of a contact explosion and a meteorite impact on a planet’s
surface is estimated. The seismic efficiency of the explosion and impact are evaluated as the ratio of the energy of the generated
seismic waves to the energy of explosion or the kinetic energy of the meteorite. In the case of contact explosions, this ratio
is in the range of 10−4–10−3. In the case of wide-scale impact effects, where the crater in the planet’s crust is produced in the gravitational regime,
a formula is derived that relates the seismic efficiency of an impact to its determining parameters.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 3–12, March–April, 2007. 相似文献
18.
Feodor M. Borodich Boris A. Galanov 《Journal of the mechanics and physics of solids》2002,50(11):2441-2461
Self-similar problems of contact for non-convex punches are considered. The non-convexity of the punch shapes introduces differences from the traditional self-similar contact problems when punch profiles are convex and their shapes are described by homogeneous functions. First, three-dimensional Hertz type contact problems are considered for non-convex punches whose shapes are described by parametric-homogeneous functions. Examples of such functions are numerous including both fractal Weierstrass type functions and smooth log-periodic sine functions. It is shown that the region of contact in the problems is discrete and the solutions obey a non-classical self-similar law. Then the solution to a particular case of the contact problem for an isotropic linear elastic half-space when the surface roughness is described by a log-periodic function, is studied numerically, i.e. the contact problem for rough punches is studied as a Hertz type contact problem without employing additional assumptions of the multi-asperity approach. To obtain the solution, the method of non-linear boundary integral equations is developed. The problem is solved only on the fundamental domain for the parameter of self-similarity because solutions for other values of the parameter can be obtained by renormalization of this solution. It is shown that the problem has some features of chaotic systems, namely the global character of the solution is independent of fine distinctions between parametric-homogeneous functions describing roughness, while the stress field of the problem is sensitive to small perturbations of the punch shape. 相似文献
19.
In this work, the authors study the influence of noise on the dynamics of base-excited elastic cantilever structures at the
macroscale and microscale by using experimental, numerical, and analytical means. The macroscale system is a base excited
cantilever structure whose tip experiences nonlinear interaction forces. These interaction forces are constructed to be similar
in form to tip interaction forces in tapping mode atomic force microscopy (AFM). The macroscale system is used to study nonlinear
phenomena and apply the associated findings to the chosen AFM application. In the macroscale experiments, the tip of the cantilever
structure experiences long-range attractive and short-range repulsive forces. There is a small magnet attached to the tip,
and this magnet is attracted by another one mounted to a high-resolution translatory stage. The magnet fixed to the stage
is covered by a compliant material that is periodically impacted by the cantilever’s tip. Building on their earlier work,
wherein the authors showed that period-doubling bifurcations associated with near-grazing impacts occur during off-resonance
base excitations of macroscale and microscale cantilevers, in the present work, the authors focus on studying the influence
of Gaussian white noise when it is included as an addition to a deterministic base excitation input. The repulsive forces
are modeled as Derjaguin–Muller–Toporov (DMT) contact forces in both the macroscale and microscale systems, and the attractive
forces are modeled as van der Waals attractive forces in the microscale system and magnetic attractive forces in the macroscale
system. A reduced-order model, based on a single mode approximation is used to numerically study the response for a combined
deterministic and random base excitation. It is experimentally and numerically found that the addition of white Gaussian noise
to a harmonic base excitation facilitates contact between the tip and the sample, when there was previously no contact with
only the harmonic input, and results in a response that is nominally close to a period-doubled orbit. The qualitative change
observed with the addition of noise is associated with near-grazing impacts between the tip and the sample. The numerical
and experimental results further motivate the formulation of a general analytical framework, in which the Fokker–Planck equation
is derived for the cantilever-impactor system. After making a set of approximations, the moment evolution equations are derived
from the Fokker–Planck equation and numerically solved. The resulting findings support the experimental results and demonstrate
that noise can be added to the input to facilitate contact between the cantilever’s tip and the surface, when there was previously
no contact with only a harmonic input. The effects of Gaussian white noise are numerically studied for a tapping mode AFM
application, and it is shown that contact between the tip and the sample can be realized by adding noise of an appropriate
level to a harmonic excitation. 相似文献
20.
An Argon droplet in contact with a Platinum surface was simulated by molecular dynamics method. Argon molecules were modeled
with modified Lennard-Jones potential function and the Platinum surface was represented by three layers of molecules. The
system temperature is fixed at saturation temperature from 72 to 108 K. An Argon droplet in contact with a Platinum surface
is also simulated, at different solid–fluid combinations
) \left( {{\frac{{\varepsilon_{sf} }}{\varepsilon }}} \right) (at fixed s(sf = 0.9s \sigma_{sf} = 0.9\sigma ) from 0.4 to 0.8, and at a temperature of 84 K. It is concluded that the contact angle decreases by increasing system temperature
and increases when solid–fluid interaction energy parameter decreases. When the temperature is high enough, the contact angle
drops to zero. 相似文献