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1.
Dynamic (Harmonic) Interfacial Stress Field in a Half-Plane Covered with a Prestretched Soft Layer 总被引:1,自引:0,他引:1
A half-plane covered with a prestretched layer is considered under the action of a periodic dynamic (harmonic) lineal load applied to the free surface of the layer. Within the framework of a piecewise homegeneous body model, with the use of equations of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the problem of stress state is formulated. It is assumed that the materials of the layer and half-plane are linearly elastic, homogeneous, and isotropic, and a plane strain state is considered. The corresponding boundary-value problems are solved analyticaly by employing the exponential Fourier transformations. Numerical results are obtained in the case where the elastic modulus of the half-plane material is greater than that of the layer material. It is established that, because of softening of the layer material, the stresses on the interplane increase mainly in the vicinity of the acting force and this increase has a local character. Moreover, it is established that the prestretching of the cover layer decreases the absolute values of these stresses. 相似文献
2.
Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic
waves in initially stressed bodies, the dynamical response of a system consisting of a prestressed covering layer and a prestressed
half-plane to a moving load applied to the free face of the covering layer is investigated. Two types (complete and incomplete)
of contact conditions on the interface are considered. The subsonic state is considered, and numerical results for the critical
speed of the moving load are presented. The influence of problem parameters on the critical speed is analyzed. In particular,
it is established that the prestressing of the covering layer and half-plane increases the critical speed.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 257–270, March–April, 2007. 相似文献
3.
We consider two dissimilar elastic half-planes bonded by a nonhomogeneous elastic layer in which there is one crack at the lower interface between the elastic layer and the lower half-plane and two cracks at the upper interface between the elastic layer and the upper half-plane. The stress intensity factors for these three cracks are solved for when tension is applied perpendicular to the interface cracks. The material properties of the bonding layer vary continuously between those of the lower half-plane and those of the upper half-plane. The differences in the crack surface displacements are expanded in a series of functions that are zero outside the cracks. The unknown coefficients in the series are solved by the Schmidt method so as to satisfy the conditions inside the cracks. The stress intensity factors are calculated numerically for selected crack configurations. 相似文献
4.
V. N. Tereshchenko 《Journal of Mathematical Sciences》1995,77(5):3458-3462
In this paper Green functions are constructed in analytic form for a deformable half-plane of a quasi-static problem of thermoelasticity
when the heat flow on the boundary x2=0 of the half-plane is zero. To construct the Green functions, certain integral representations are used whose kernels are
known Green functions of the corresponding problems of elasticity theory. The functions constructed make it possible to obtain
a wide class of new solutions of boundary-value problems of thermoelasticity, in particular solutions for a piecewise homogeneous
half-plane. Bibliography: 6 titles.
Translated fromObchyslyuwval’na ta Pryklandna Matematyka, No. 77, 1993, pp. 97–104. 相似文献
5.
Within the framework of a piecewise homogeneous body model, with the use of exact equations of the geometrically nonlinear
theory of viscoelastic bodies, the distribution of near-surface self-balanced normal stresses in a body consisting of a viscoelastic
half-plane, an elastic locally curved bond layer, and a viscoelastic covering layer is investigated. A method for solving
the problem considered by employing the Laplace and Fourier transformations is developed. Numerical results for the self-balanced
normal stresses caused by a local curving (imperfection) of an elastic bond layer upon tension and compression of the body
mentioned along the free face plane are presented and analyzed. The viscoelasticity of the materials is described by the Rabotnov
fractional-exponential operators. A macroscopic failure criterion is proposed, and the validity of this criterion is examined. 相似文献
6.
V. B. Andreev 《Computational Mathematics and Mathematical Physics》2017,57(12):1935-1972
In a half-plane, a homogeneous Dirichlet boundary value problem for an inhomogeneous singularly perturbed convection–diffusion equation with constant coefficients and convection directed orthogonally away from the boundary of the half-plane is considered. Assuming that the right-hand side of the equation belongs to the space Cλ, 0 < λ < 1, and the solution is bounded at infinity, an unimprovable estimate of the solution is obtained in a corresponding Hölder norm (anisotropic with respect to a small parameter). 相似文献
7.
A. O. Rodnikov B. A. Samokish 《Computational Mathematics and Mathematical Physics》2009,49(12):2117-2134
In the numerical solution of the diffraction problem for an acoustic plane wave in a half-plane with a cut, boundary conditions
that are equivalent to the radiation conditions at infinity are set in a neighborhood of the points of the cut. Joining the
physical boundary conditions on the cut, a closing set of equations of order 4N, where N is the number of grid points on the cut, is obtained. The so-called Green’s grid function for the half-plane is used, which
makes it possible to pass from one grid layer to another one for the solution satisfying certain conditions at infinity. 相似文献
8.
The dynamic response of a system consisting of an initially stressed covering layer and an initially stressed half-plane to a moving time-harmonic load is investigated within the scope of the piecewise-homogeneous body model utilizing three-dimensional linearized wave propagation theory in the initially stressed body. It is assumed that the material of the layer and half-plane is orthotropic. It is also assumed that the velocity of the line-located time harmonic moving load which acts on the covering layer is constant. The investigations were carried out were for the plane-strain state under subsonic velocity of the moving load for two types of contact conditions, namely: complete and incomplete. An algorithm is developed for the determination of the values of the moving load’s critical velocity. For various values of the problem parameters the numerical results were presented and discussed. 相似文献
9.
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. 相似文献
10.
《Journal of Applied Mathematics and Mechanics》2006,70(5):796-803
For the problem of the diffusion of a discontinuity of the shear stress at the boundary of a half-plane, which is a special case of the general problem of the diffusion of a vortex layer, the classes of media and types of assignment of boundary conditions for which self-similar solutions exist are discussed. For a viscoplastic medium in a half-plane the problem reduces to the problem in a layer of time-variable thickness, the solution of which does not possess the property of analyticity. The long-term asymptotic of this problem are investigated. In the case where, at an accessible boundary, it is possible simultaneously to measure both the shear stress and the horizontal velocity, an algorithm is proposed for finding a quantity that is difficult to measure, A namely, the thickness of the zone of viscoplastic flow. 相似文献
11.
The diffraction problem for a plane wave on a half-plane covered by thin layer with an interface is solved by the difference
method. The system of difference equations is derived from the variational principle. A boundary solution at infinity must
be imposed; this is a radiation condition, which is used in the form of the limit absorption principle. The arising infinite
system of difference equations is reduced to a finite part of the boundary (the interface) by using the technique of so-called
interior boundary conditions in the sense of Ryaben’kii. The real conditions are found by the Fourier method with respect
to one spatial variable in the form of Fourier or Laurent series in the corresponding variable, which converge either inside,
outside, or on the unit circle. Above the upper boundary of the layer, all unknowns are eliminated by using the so-called
grid Green function, that is, the resolving function for the half-plane satisfying the radiation condition at infinity. For
the unknowns on the upper boundary of the layer, an equation in terms of a function of a complex variable of Wiener-Hopf type
is obtained, which is solved by factorization. Factorization is performed numerically: the logarithm of the function is expanded
in a bi-infinite series, which is replaced by a discrete Fourier series. The closing system in a neighborhood of the interface
has order proportional to the number of points on the interface. Solving this system yields all of the required characteristics
of the solution. 相似文献
12.
Within the frame work of the three-dimensional linearized theory of stability of deformable bodies (TLTSDB), the near-surface
buckling instability of a system consisting of a half-plane (substrate), a viscoelastic bond layer, and an elastic covering
layer is suggested. The equations of the TLTSDB are obtained from the three-dimensional geometrically non linear equations
of viscoelasticity theory by using the boundary-form perturbation technique. By employing the Laplace transform, a method
for solving the problem is developed. It is supposed that the covering layer has an insignificant initial imperfection. The
stability of the system is considered lost if the imperfection starts to increase and grows indefinitely. Numerical results
for the critical compressive force and the critical time are presented.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 517–530, July–August, 2006. 相似文献
13.
Haibing Wang 《Applicable analysis》2013,92(4):831-854
We consider the acoustic wave scattering by an impenetrable obstacle embedded in a multilayered background medium, which is modelled by a linear system constituted by the Helmholtz equations with different wave numbers and the transmission conditions across the interfaces. The aim of this article is to construct an efficient computing scheme for the scattered waves for this complex scattering process, with a rigorous mathematical analysis. First, we construct a set of functions by a series of coupled transmission problems, which are proven to be well-defined. Then, the solution to our complex scattering in each layer is decomposed as the summation in terms of these functions, which are essentially the contributions from two interfaces enclosing this layer. These contributions physically correspond to the scattered fields for simple scattering problems, which do not involve the multiple scattering and are coupled via the boundary conditions. Finally, we propose an iteration scheme to compute the wave field in each layer decoupling the multiple scattering effects, with the advantage that only the solvers for the well-known transmission problems and an obstacle scattering problem in a homogeneous background medium are applied. The convergence property of this iteration scheme is proven. 相似文献
14.
Petter Brändén 《Advances in Mathematics》2007,216(1):302-320
A polynomial f is said to have the half-plane property if there is an open half-plane H⊂C, whose boundary contains the origin, such that f is non-zero whenever all the variables are in H. This paper answers several open questions relating multivariate polynomials with the half-plane property to matroid theory.
- (1)
- We prove that the support of a multivariate polynomial with the half-plane property is a jump system. This answers an open question posed by Choe, Oxley, Sokal and Wagner and generalizes their recent result claiming that the same is true whenever the polynomial is also homogeneous.
- (2)
- We prove that a multivariate multi-affine polynomial f∈R[z1,…,zn] has the half-plane property (with respect to the upper half-plane) if and only if
15.
Arman Melkumyan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):330-349
The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium
is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation”
[15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means
of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion
between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield
structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details.
The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly.
Numerical analysis is presented. 相似文献
16.
D. V. Valovik Yu. G. Smirnov 《Computational Mathematics and Mathematical Physics》2008,48(12):2217-2225
TM electromagnetic waves propagating through a nonlinear homogeneous isotropic unmagnetized dielectric layer located between two homogeneous isotropic half-spaces are studied. The nonlinearity in the layer obeys the Kerr law. The problem is reduced to a system of nonlinear ordinary differential equations. A dispersion relation for the propagation constants is derived. The results are compared with those in the case of a linear layer. 相似文献
17.
Propagation of SH‐wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi‐infinite media 下载免费PDF全文
Santimoy Kundu Santanu Manna Shishir Gupta 《Mathematical Methods in the Applied Sciences》2015,38(9):1926-1936
The paper presents a study of propagation of shear wave (SH‐wave) in an orthotropic elastic medium under initial stress sandwiched by a homogeneous semi‐infinite medium and an inhomogeneous half‐space. The technique of separation of variables has been adopted to get the analytical solutions for the dispersion relation in a closed form. The propagation of SH‐waves is influenced by inhomogeneity parameters and initial stress parameter. Velocities of SH‐waves are calculated numerically for different cases. As a special case when the intermediate layer and half‐space are homogeneous, computed frequency equation coincides with general equation of Love wave. To study the effect of inhomogeneity parameters and initial stress parameter, we have plotted the velocity of SH‐wave in several figures and observed that the velocity of wave decreases with the increases of non‐dimensional wave number. It can be found that the phase velocity decreases with the increase of inhomogeneity parameters. We observed that the velocity of SH‐wave decreases with the increases of initial stress parameter in both homogeneous and inhomogeneous media. GUI has been developed by using MATLAB to generalize the effect of the parameters discussed. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
18.
We study the boundary value problem for the Kadomtsev–Petviashvili equation on the half-plane y > 0 with a homogeneous condition along the boundary. We show that the problem can be efficiently solved using the dressing method. We present explicit solutions for particular cases of the boundary value problem. 相似文献
19.
与经典有限阶整函数的Hadamard因子分解定理和半平面中属于Hardy空间的解析函数的内外函数的因子分解类似,对右半平面中有限阶ρ解析函数f,可以分解为三个解析函数G,eQ和eg的乘积GeQeg,其中G是一个加权Blaschke乘积,Q是一个次数不超过ρ的多项式以及eg是一个加权外函数,log|G|,ReQ和Reg-log|f|在右半平面的边界恒为零. 相似文献
20.
A. P. Soldatov 《Differential Equations》2016,52(6):798-812
We consider a mixed problem of plane isotropic elasticity in a half-plane in which the displacement vector and the normal component of the stress tensor are alternately specified on successive intervals of the real axis. We derive a closed-form expression for the solution of this problem, which is similar to the well-known Keldysh–Sedov formula for the half-plane. 相似文献