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1.
IntroductionStressconcentrationisoneimportantproblemofmechanicsresearchdomain .Inthemicropolarelasticitytheory ,itismoreabsorptive .Itiswell_knownthatthemicropolarelasticitytheoryusuallygivesalowcoefficientandchangesthestrangenessatthetipofthecrack .Thes… 相似文献
2.
An exact solution of the model Boltzmann equation with BGK (Bhatnagar-Gross-Krook) collision operator is obtained in the problem of strong evaporation (condensation) from a plane surface. The generalized eigenvectors of the corresponding characteristic equation are found. The existence and uniqueness of the expansion of the solution in eigenvectors of the continuous and discrete spectra are demonstrated. This expansion reduces to a vector Riemann-Hilbert boundary-value problem with matrix coefficient. An apparatus for the diagonalization and factorization of the boundary-value problem coefficient is developed. The matrix diagonalizing the problem coefficient has branch points in the complex plane which depend parametrically on the evaporation (condensation) rateu. The solution of the problem is investigated in terms ofu and the physical characteristics of the evaporation process are described.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 143–155, November–December, 1993. 相似文献
3.
Z. N. Dobrovol'skaya 《Fluid Dynamics》1976,11(1):73-76
The flow around a slender profile by an ideal gas flow at a constant, almost sonic, velocity at infinity is considered. The behavior of the perturbed stream in the domain upstream of the compression shocks sufficiently remote from the streamlined body is studied. The question is investigated of what conditions the solution in the hodograph plane satisfies when it corresponds to a flow without singularities on the limit characteristic in the physical flow plane. It is known that cases are possible when a regular solution in the hodograph plane loses its regularity property upon being mapped into the physical plane [1]. A regular flow on the limit characteristic can be continued analytically downstream into the supersonic domain between the limit characteristic and the shock. The requirement of analyticity of the streamlined profile is essential for realizability of the flow under consideration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 84–88, January–February, 1976.In conclusion, the author is grateful to O. S. Ryzhov for discussing the research. 相似文献
4.
We solve analytically the Eshelby’s problem in an anisotropic multiferroic bimaterial plane. The solution is based on the extended Stroh formalism of complex variables, and is valid for the inclusion of arbitrary shapes, described by a Laurent polynomial, a polygon, or the one bounded by a Jordan curve. Furthermore, the results in the corresponding half plane and full plane can be reduced directly from the bimaterial-plane solution. As such, the solution unifies the complex variable method and the Green’s function method, extending further to the multiferroic bimaterial plane of general anisotropy. The essential eigenfunctions are also identified by which the induced fields can be simply determined. Numerical results are presented to investigate the features of these eigenfunctions as well as the strain, electric and magnetic fields (components of the extended Eshelby tensor). Particularly, we present the values of these fields at the center of the N-side regular polygonal inclusion and also the average values of these fields over the inclusion area. The effect of the half-plane traction-free surface condition as well as the effect of various couplings on the induced fields is discussed in detail. For the N-side regular polygonal inclusion, it is found that, when the inclusion is in the full plane, both the center and average values of the Eshelby tensor are independent of the side number N, except for N = 4. We further show that the piezoelectric and piezomagnetic coupling coefficients could significantly affect the Eshelby tensor. These features should be useful in controlling the Eshelby tensor for the design of better multiferroic composites. Typical contours of the field quantities in and around the inclusion bounded by both straight and curved line segments in a multiferroic bimaterial plane are also presented. 相似文献
5.
6.
In this paper, an automated numerical simulation of the propagation of multiple cracks in a finite elastic plane by the distributed dislocation method is developed. Firstly, a solution to the problem of a two-dimensional finite elastic plane containing multiple straight cracks and kinked cracks is presented. A serial of distributed dislocations in an infinite plane are used to model all the cracks and the boundary of the finite plane. The mixed-mode stress intensity factors of all the cracks can be calculated by solving a system of singular integral equations with the Gauss–Chebyshev quadrature method. Based on the solution, the propagation of multiple cracks is modeled according to the maximum circumferential stress criterion and Paris' law. Several numerical examples are presented to show the accuracy and efficiency of this method for the simulation of multiple cracks in a 2D finite plane. 相似文献
7.
We consider the class of invariant solutions which can describe only vortex flows (curl P 0, P is the generalized momentum) and show that they contain solutions corresponding to flows from a plane or cylindrical emitter with a linear voltage drop across it (direct heating) in the temperature-limited regime*. The solution is obtained in analytic form for emission from a plane in a uniform magnetic field perpendicular to the flow plane. It also (for=0) defines a plane magnetron in the T-regime. The solution of the problem for a cylindrical emitter reduces to considering equations describing a cylindrical diode or magnetron in the T-regime, where the shape of the collector is given by the potential distribution curve for these cases. We can extend the results to a relativistic beam if restrictions are imposed on its relative dimensions which permit us to ignore the magnetic self-field. Brillouin type flows (including irrotational ones) are studied in which particles move without intersecting the equipotential surfaces along three-dimensional spirals on the surface of cones. An analytic solution is given for relativistic Brillouin flow in a conical diode when strict allowance is mede for the magnetic self-field. 相似文献
8.
9.
Non-local theory solution for in-plane shear of through crack 总被引:5,自引:0,他引:5
A non-local theory of elasticity is applied to obtain the plane strain stress and displacement field for a through crack under in-plane shear by using Schmidt's method. Unlike the classical elasticity solution, a lattice parameter enters into the problem that make the stresses finite at crack tip. Both the angular variations of the circumferential stress and strain energy density function are examined to associate their stationary value with locations of possible fracture initiation. The former criterion predicted a crack initiation angle of 54° from the plane of shear for the non-local solution as compared with about 75° for the classical elasticity solution. The latter criterion based on energy density yields a crack initiation angle of 80° for a Poisson's ratio of 0.28. This is much closer to the value that is predicted by the classical crack tips solution of elasticity. 相似文献
10.
Yu. N. Podil'chuk 《International Applied Mechanics》1999,35(8):804-811
An explicit solution of the static problem of electroelasticity is obtained for a transversally isotropic medium that contains
bilateral hyperbolic tunnel cavities. It is assumed that the plane of isotropy of the medium coincides with the plane of symmetry
of the medium, and also that the surfaces of the cavities are free of mechanical forces and that the normal component of the
electric induction vector is equal to zero on the cavities. A uniform tensile force and difference in the electric potentials
are specified at a sufficient distance from the cavities in a direction perpendicular to the plane of isotropy of the medium.
A solution of the corresponding problem for a piezoceramic medium containing external bilateral rectilinear cracks is obtained
as a special case.
S. P. Timoshenko Institute of Mechanics. National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika,
Vol. 35, No. 8, pp. 54–60, August, 1999. 相似文献
11.
《International Journal of Solids and Structures》2002,39(4):943-957
Schwarz–Neumann's alternating technique is applied to singularity problems in an anisotropic `trimaterial', which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. Linear elastic materials under general plane deformations are assumed, in which the plane of deformation is perpendicular to the two parallel interface planes.It is well known that if the solution is known for singularities in a homogeneous anisotropic medium, the solution for the same singularities in an anisotropic bimaterial can be constructed by the method of analytic continuation. It is shown here that the solution for singularities in a homogeneous medium may also be used as a base of the solution for the same singularities in a trimaterial. The alternating technique is applied to derive the trimaterial solution in a series form, whose convergence is guaranteed. The solution procedure is universal in the sense that no specific information about the singularity is needed. The energetic forces exerted on a dislocation due to interfaces are also evaluated from the trimaterial solution. The trimaterial solution studied here can be applied to a variety of problems, e.g. a bimaterial (including a half-plane problem), a finite thin film on semi-infinite substrate, and a finite strip of thin film, etc. Some examples are presented to verify the usefulness of the obtained solutions. 相似文献
12.
V. I. Shalaev 《Fluid Dynamics》1993,28(6):770-777
The singularities in the three-dimensional laminar boundary layer on a cone at incidence are studied. It is shown that these singularities are formed in the outer part of the boundary layer and described by linear equations whose solutions are obtained in analytic form. The known results for the plane of symmetry are classified on this basis. Two solutions of the non-self-similar problem are found, one of which has a singularity at zero incidence and in the sink plane. The second branch goes over continuously into the solution for axisymmetric flow. However, as the angle of attack increases, in the sink plane a singularity is formed and all the self-similar solutions existing here lose their meaning. Starting from the critical angle of attack, the flow in the vicinity of the sink plane is no longer described by the boundary layer equations, so that the results can be used to construct an adequate physical model.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 25–33, November–December, 1993. 相似文献
13.
A solution of an initial-boundary-value problem for a system of integrodifferential equations which describes the plane waves
excited in an initially stationary heavy two-layer ideal fluid by a cylinder moving at an angle to the horizontal is investigated.
The homogeneous fluid fractions of different densities are assumed to be separated by an evolving fluid interface (horizontal
plane, if the liquid is at rest). An approximate solution of two problems for the waves excited by a cylinder moving with
a constant acceleration and an oscillating cylinder is constructed analytically.
Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–152, July–August,
1998. 相似文献
14.
L. D. Akulenko D. V. Georgievskii D. M. Klimov S. A. Kumakshev S. V. Nesterov 《International Applied Mechanics》2006,42(4):375-406
A review is given to and comprehensive numerical-analytic study is carried out of the problem of steady Bingham viscoplastic
flow in a plane confuser. The solution is constructed in the first approximation with the yield stress as a small parameter
and the solution of the Jeffery-Hamel problem (steady radial motion of an incompressible viscous material in a plane confuser)
as the zero-order approximation. The numerical analysis is based on the modified accelerated-convergence method proposed earlier
by the authors. The bifurcations of the deformation pattern occurring when the parameters reach some critical values are discussed
and commented on. The asymptotic boundaries of the rigid zones that appear at infinity upon perturbation of the yield stress
are determined
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 3–45, April 2006. 相似文献
15.
Yu. L. Yakimov 《Fluid Dynamics》1990,25(4):555-565
It is proposed to consider plane or axisymmetric incompressible flows when at a certain point in space a finite source of momentum is instantaneously created. This type of flow is characterized by the continuous setting in motion of new volumes of fluid with a simultaneous decrease in velocity. It is usual to associate this diffusional process with viscosity [1]. Here it is shown, that such processes can be described within the framework of an ideal fluid. The main concern is to prove the existence of four-parameter plane ideal-fluid flow. The method of constructing the solution is based on the conformal transformation of the dimensionless variable, so that from the relatively simple self-similar solution the unknown flow can be obtained. It is shown that this method can be applied to other problems. The results obtained are compared with the well-known [2] solution of the linearized dipole diffusion problem for the plane motion of a viscous fluid and with certain generalizations of that solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 73–83, July–August, 1990.The author is grateful to A. A. Barmin and A. G. Kulikovskii for useful discussions. 相似文献
16.
Radiation and scattering from bodies of revolution 总被引:1,自引:0,他引:1
The problem of electromagnetic radiation and scattering from perfectly conducting bodies of revolution of arbitrary shape is considered. The mathematical formulation is an integro-differential equation, obtained from the potential integrals plus boundary conditions at the body. A solution is effected by the method of moments, and the results are expressed in terms of generalized network parameters. The expansion functions chosen for the solution are harmonic in ø (azimuth angle) and subsectional in t (contour length variable). Because of rotational symmetry, the solution becomes a Fourier series in ø, each term of which is uncoupled to every other term.Illustrative computations are given for radiation from apertures and plane wave scattering from bodies of revolution. The impedance elements, currents, radiation patterns, and scattering patterns for a conducting sphere are computed both from the general solution and from the classical eigenfunction solution. The agreement obtained serves to check the general solution. Similar computations for a cone-sphere illustrate the application of the general solution to problems not solvable by classical methods. 相似文献
17.
Analytical solutions for the plane Couette flow and the plane Poiseuille flow of the one-mode Giesekus fluid without any retardation time have been obtained by considering the domain of definition for each of the two branch solutions which arise due to the presence of the quadratic stress terms in the constitutive equations. For each fixed value of the mobility parametera, the limiting value of the Weissenberg number for the upper branch solution, i.e., the physically realistic solution is determined in terms of the corresponding dimensionless shear stress for the plane Couette flow and in terms of the corresponding dimensionless pressure gradient for the plane Poiseuille flow. In the case of the plane Couette flow, it is shown that fora falling in the range 0a1/2 only the physically realistic solution exists while for 1/2<a 1 a nonphysical solution coexists with the realistic one. In the case of the plane Poiseuille flow, it is shown that the non-physical solution cannot even exist around the center plane of the channel, and the effects of the mobility parameter and the dimensionless pressure gradient on the flow variables are investigated. Possible extensions of the present approach to other steady simple shear flows with and without the introduction of the retardation time are also discussed. 相似文献
18.
Lifeng Ma 《International Journal of Solids and Structures》2010,47(22-23):3214-3220
In this paper, the transformation toughening problem is addressed in the framework of plane strain. The fundamental solution for a transformed strain nucleus located in an infinite plane is derived first. With this solution, the transformed inclusion problems are formulated by a Green’s function method, and the interaction of a crack tip with a single transformation source is found. On the basis of this solution, the fundamental formulations for toughening arising from martensitic and ferroelastic transformation are formulated also using the Green’s function method. Finally, some examples are provided to demonstrate the validity and relevance of the fundamental formulations proposed in the paper. 相似文献
19.
V. P. Zhitnikov O. R. Zinnatullilna S. S. Porechnyi N. M. Sherykhalina 《Journal of Applied Mechanics and Technical Physics》2009,50(4):617-627
Numerical solution of the Hele-Shaw problem reduces to solution of three boundary-value problems of determining analytic functions
of a complex variable in each time step: conformal mapping of the range of the parametric variable to the physical plane,
the Dirichlet problems for determining the electric-field strength, and the Riemann-Hilbert problem for calculating partial
time derivatives of the coordinates of points of the interelectrode space (the images of the points on the boundary of the
parametric plane are fixed). Unlike in the two-dimensional problem, the electric-field strength is determined using integral
transformations of an analytic function. Approximation by spline function is performed, and more accurate and steady (than
the well-known ones) general solution algorithms for the nonstationary axisymmetric problems are described. Results of a numerical
study of the formation of stationary and self-similar configurations are presented.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 87–99, July–August, 2009. 相似文献
20.
A cylindrical analog of trochoidal gerstner waves 总被引:1,自引:0,他引:1
N. A. Inogamov 《Fluid Dynamics》1985,20(5):791-796
This paper investigates isobaric motions for which the values of the pressure are conserved in fluid particles. In it, a new analytic exact particular solution of nonlinear multidimensional hydrodynamic equations is obtained; it describes a trochoidal wave in cylindrical geometry. It is also proved that trochoidal waves in cylindrical and plane geometry exhaust the class of nonlinear isobaric motions. Here and below by a wave in plane geometry we mean a wave in a uniform gravitational field which is characterized by the wave vector k. It is obvious that waves in both plane and cylindrical geometry are two-dimensional motions, since the fluid particles in motion are fixed in the plane and the motions in parallel planes are the same. The trochoidal wave in cylindrical geometry is of interest, since it describes a nonlinear wave on the surface of a cavity in a rotating fluid, a situation which is frequently encountered in applications.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–150, September–October, 1985. 相似文献