共查询到20条相似文献,搜索用时 15 毫秒
1.
Ladislav Ceniga 《Acta Mechanica Sinica》2010,26(5):695-709
This paper deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid continuum with uniaxial or triaxial anisotropy. The anisotropic solid continuum consists of anisotropic spherical particles periodically distributed in an anisotropic infinite matrix. The particles are or are not embedded in an anisotropic spherical envelope, and the infinite matrix is imaginarily divided into identical cubic cells with central particles. The thermal stresses are thus investigated within the cubic cell. This mulfi-particle-(envelope)-matrix system based on the cell model is applicable to two- and three-component materials of precipitate-matrix and precipitate-envelope-matrix types, respectively. Finally, an analysis of the determination of the thermal stresses in the multi-par- ticle-(envelope)-matrix system which consists of isotropic as well as uniaxial- and/or triaxial-anisotropic components is presented. Additionally, the thermal-stress induced elastic energy density for the anisotropic components is also derived. These analytical models which are valid for isotropic, anisotropic and isotropic-anisotropic multi-particle- (envelope)-matrix systems represent the determination of important material characteristics. This analytical determination includes: (1) the determination of a critical particle radius which defines a limit state regarding the crack initiation in an elastic, elastic-plastic and plastic components; (2) the determination of dimensions and a shape of a crack propagated in a ceramic components; (3) the determination of an energy barrier and micro-/macro-strengthening in a component; and (4) analytical-(experimental)-computational methods of the lifetime prediction. The determination of the thermal stresses in the anisotropic components presented in this paper can be used to determine these material characteristics of real two- and three-component materials with anisotropic components or with anisotropic and isotropic components. 相似文献
2.
A contact problem is studied for a prestressed elastic strip with an elastic reinforcement. The integral Fourier transform is used to construct an influence function for an infinite strip with one face fixed. A unit concentrated force is applied to the strip at an arbitrary angle. The contact problem on force transfer from a thin infinite stringer to the prestressed strip is solved. The problem is mathematically formulated as a system of integro-differential equations for the unknown contact stresses on the assumption that the beam bending model and the uniaxial stress model are valid for the stringer, which is subjected to both vertical and horizontal forces. This system is solved in a closed form using the integral Fourier transform. The contact stresses are expressed in terms of Fourier integrals in a quite simple form. The influence of the initial stresses on the contact stress distribution is analyzed, and effects of concentrated load are revealed 相似文献
3.
The contact problem for a prestressed elastic strip reinforced with equally spaced elastic plates is considered. The Fourier integral transform is used to construct an influence function of a unit concentrated force acting on the infinite elastic strip with one edge constrained. The transmission of forces from the thin elastic plates to the prestressed strip is analyzed. On the assumption that the beam bending model and the uniaxial stress model are valid for an elastic plate subjected to both vertical and horizontal forces, the problem is mathematically formulated as a system of integro-differential equations for unknown contact stresses. This system is reduced to an infinite system of algebraic equations solved by the reduction method. The effect of the initial stresses on the distribution of contact forces in the strip under tension and compression is studied 相似文献
4.
This paper represents a continuation of the author's previous work which deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid elastic continuum. This continuum consists of anisotropic spherical particles which are periodically distributed in an anisotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with central particles. This multi-particle–matrix system represents a model system which is applicable to two-component materials of the precipitate–matrix type. The thermal stresses, which originate due to different thermal expansion coefficients of components of the model system, are determined within the cubic cell. The analytical modelling results from fundamental equations of continuum mechanics for solid elastic continuum (Cauchy's, compatibility and equilibrium equations, Hooke's law). This paper presents suitable mathematical procedures which are applied to the fundamental equations. These mathematical procedures lead to such final formulae for the thermal stresses which are relatively simple in comparison with the final formulae presented in the author's previous work which are extremely extensive. Using these new final formulae, the numerical determination of the thermal stresses in real two-component materials with anisotropic components is not time-consuming. 相似文献
5.
T. S. Krasnopolskaya 《Meccanica》2006,41(3):299-310
This paper deals with vibrations of an infinite plate in contact with an acoustic medium where the plate is subjected to a
point excitation by an electric motor of limited power-supply. The whole system is divided into two “exciter - foundation”
and “foundation-plate-medium”. In the system “motor-foundation” three classes of steady state regimes are determined: stationary,
periodic and chaotic. The vibrations of the plate and the pressure in the acoustic fluid are described for each of these regimes
of excitation. For the first class they are periodic functions of time, for the second they are modulated periodic functions,
in general with an infinite number of carrying frequencies, the difference between which is constant. For the last class they
correspond to chaotic functions. In another mathematical model where the exciter stands directly on an infinite plate (without
foundation) it was shown that chaos might occur in the system due to the feedback influence of waves in the infinite hydro-elastic
subsystem in the regime of motor shaft rotation. In this case the process of rotation can be approximately described as a
solution of the fourth order nonlinear differential equation and may have the same three classes of steady state regimes as
the first model. That is the electric motor may generate periodic acoustic waves, modulated waves with an infinite number
of frequencies or chaotic acoustic waves in a fluid. 相似文献
6.
The paper addresses a plane problem for an infinite plane consisting of two different piezoceramic half-planes with an interfacial
crack with smooth contact zones and subjected to the uniformly distributed electromechanical loading applied at infinity.
Methods of complex-variable theory are used to reduce the problem to a Dirichlet-Riemann mixed homogeneous boundary-value
problem. Its solution is found in closed form. A system with one crack that has one or two contact zones is calculated. Expressions
for stresses, electric-flux density, and displacement discontinuities at the interface are written. Equations for the determination
of the length of the contact zones and expressions for the stress intensity factors at the crack tips are derived
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 66–74, March 2008. 相似文献
7.
A. N. Guz’ 《International Applied Mechanics》1998,34(12):1175-1186
This paper studies the brittle fracture of materials with initial stresses when the stresses act only along the cracks. Dynamic
problems for moving cracks are considered when the plane crack infinite in one direction moves with constant velocity. General
formulas are presented for compressible and incompressible elastic bodies with an arbitrary structure of elastic potentials.
The stresses and displacements are presented as analytical functions of complex variables. Some general relationships may
be used in order to obtain exact information on the singularity order of the crack tip for dynamical problems under consideration
in the general formulation.
Translated from Prikladnaya Mechanika, Vol. 34, No. 12, pp. 3–15, December, 1998. 相似文献
8.
Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks.
Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack
planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described
by the Bartenev–Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading
conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed
Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 3–18, February 2009. 相似文献
9.
This paper presents an analysis of the steady-state thermal stresses and displacements in an infinite elastic medium containing
two or more parallel coaxial circular cracks. A “perturbation” technique is employed to reduce the problem of finding the
temperature and the induced stresses to integral equations of Fredholm type which may be solved by numerical means or iterations.
Two types of prescribed thermal conditions are considered. The first is concerned with a uniform flow of heat disturbed by
insulated cracks and the second deals with stress-free cracks whose surfaces are exposed to identical amounts of heat. The
details of the analysis are illustrated by considering the case of two cracks symmetrically located about the mid plane of
the solid. When the cracks are of equal radii, iterative solutions of the governing integral equations are derived and used
to determine expressions for the stress-intensity factors (opening and edge-sliding modes), displacements of crack surfaces
and other quantities of physical interest which are valid for widely spaced cracks. 相似文献
10.
Summary This paper deals with interaction problems of elliptical and ellipsoidal inclusions under bending, using singular integral
equations of the body force method. The problems are formulated as a system of singular integral equations with Cauchy-type
or logarithmic-type singularities, where unknown functions are densities of body forces distributed in the x,y and r,θ,z directions in infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy
the boundary conditions along the elliptical and the ellipsoidal boundaries, the unknown functions are approximated by a linear
combination of fundamental density functions and polynomials. The present method is found to yield the exact solutions for
a single elliptical or spherical inclusion under a bending stress field. It yields rapidly converging numerical results for
interface stresses in the interaction of inclusions.
Received 9 September 1999; accepted for publication 15 January 2000 相似文献
11.
A method is proposed to study the stress concentration around a shallow spheroidal crack in an infinite elastic body. The
stress concentration is due to the diffraction of a low-frequency plane longitudinal wave by the crack. The direction of wave
propagation is established in which the combined concentration of mode I and mode II stresses is maximum
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 70–77, January 2006. 相似文献
12.
Ladislav Ceniga 《Meccanica》2010,45(1):73-77
The paper deals with an analytical model of thermal stresses acting in an particle-matrix system represented by one isotropic
spherical particle embedded in a triaxial-anisotropic infinite matrix, or by one triaxial-anisotropic spherical particle embedded
in an isotropic infinite matrix. The thermal stresses originate during a cooling process as a consequence of the difference
in thermal expansion coefficients between a matrix and a particle. 相似文献
13.
S. Itou 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(1):53-62
Summary Transient stresses around two parallel cracks in an infinite elastic medium are investigated in the present paper. The shape
of the cracks is assumed to be square. Incoming shock stress waves impinge upon the two cracks normal to tzheir surfaces.
The mixed boundary value equations with respect to stresses and displacements are reduced to two sets of dual integral equations
in the Laplace transform domain using the Fourier transform technique. These equations are solved by expanding the differences
in the crack surface displacements in a double series of a function that is equal to zero outside the cracks. Unknown coefficients
in the series are calculated using the Schmidt method. Stress intensity factors defined in the Laplace transform domain are
inverted numerically to the physical space. Numerical calculations are carried out for transient dynamic stress intensity
factors under the assumption that the shape of the upper crack is identical to that of the lower crack.
Received 2 February 2000; accepted for publication 10 May 2000 相似文献
14.
V. P. Ryabchenko 《Journal of Applied Mechanics and Technical Physics》2008,49(2):267-276
This paper considers a two-dimensional linear unsteady problem of rigid-stamp indentation on an elastic layer of finite thickness
lying on the surface of a compressible fluid of infinite depth. The Lamé equations holds for the elastic layer, and the wave
equation for the fluid velocity potential. Using the Laplace and Fourier transforms, the problem is reduced to determining
the contact stresses under the stamp from the solution of an integral equation of the first kind, whose kernel has a logarithmic
singularity. An asymptotic solution of the problem is constructed for large times of interaction.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 131–142, March–April, 2008. 相似文献
15.
A wedge subjected to tractions in proportion tor
n
(n≥0), is considered. The stresses in the solutions of the classical theory of elasticity become infinite when the angle of the
wedge is ρ or 2ρ. The paradox has been resolved by Dempsey[4] and T.C.T. Ting[5] whenn=0. The purpose of this paper is to resolve the paradox whenn>0. 相似文献
16.
Summary An analysis of a two dimensional oscillatory flow past an infinite porous plate with contant suction is carried out on taking
into account the couple stresses. Here the free stream velocity oscillates about a nonzero constant mean. Approximate solutions
are derived to coupled linear equations, and the expressions for the mean velocity, the transient velocity, the mean skinfriction,
the amplitude and the phase of skin-friction are obtained. The solutions are followed by discussion. the effects of variations
of α(νr/ν), β(Iν/γ) and λ, the frequency are graphically represented and physically interpreted. It is observed that the reverse
type of flow does not occur in the presence of the couple stresses.
Sommario In questo lavoro è svolta un'analisi di un flusso oscillatorio bidimensionale sopra una piastra porosa, infinita, con aspirazione costante, tenendo conto delle coppie di sforzo. La velocità della corrente libera oscilla attorno ad un valore medio costante diverso da zero. Si deducono le soluzioni approssimate per le equazioni lineari accoppiate e si ottengono le espressioni per la velocità media, la velocità transitoria, l'attrito superficiale, l'ampiezza e la fase. Si discutono le soluzioni. Si rappresentano graficamente e si interpretano fisicamente gli effetti delle variazioni di α(νr/ν), β(Iν/γ) e λ. Si osserva che in presenza delle coppie di sforzo nel fluido non si ha il tipo inverso di flusso.相似文献
17.
Yu. M. Volchkov L. A. Dergileva 《Journal of Applied Mechanics and Technical Physics》2007,48(3):450-459
Shell equations are constructed in orthogonal curvilinear coordinates using approximations of stresses and displacements by
Legendre polynomials. The order of the constructed system of differential equations is independent of whether stresses and
displacements or their combination are specified on the shell surfaces, which provides the correct formulation of the surface
conditions in terms of both displacements and stresses. This allows the system of differential equations of laminated shells
to be constructed using matching conditions for displacements and stresses on the contact surfaces.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 179–190, May–June, 2007. 相似文献
18.
The heat transfer through an infinite flat plate is studied when the temperatures of the two free streams surrounding it are
varying harmonically with time and out of phase, with a delay period τd. The configuration is a simplified model for the heat transfer through the separating wall in the isochoric counter-current
heat exchanger. The results show that apart from the τd effect, the perturbation parameters depend mainly on the cavity passing frequency f. At the thick plate solution, the combined passing frequency–delay time influences are significant only when the dimensionless
frequency is smaller than 10. Within this range τd affects seriously not only the temperature perturbation amplitudes (which determine the thermal stresses) but also the heat
fluxes and the accumulated energy ones. When f ≥ 10, the plate behaves as two separate semi-infinite slabs. Heat penetration delays greater than one cavity passing period
may be possible. 相似文献
19.
T. V. Dobrodzii 《Nonlinear Oscillations》2010,13(2):161-171
Explicit estimates are obtained for the closeness of trajectories of exact and averaged systems. We show that an optimal control
of an averaged system is ε-optimal for an exact system both on asymptotically finite (of order 1/ε) time intervals and on infinite time intervals. 相似文献