共查询到20条相似文献,搜索用时 31 毫秒
1.
《International Journal of Solids and Structures》2007,44(5):1550-1562
In this paper, we will consider a half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory [Youssef, H., 2005a. The dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity, J. Appl. Math. Mech., 26(4), 4827; Youssef, H., 2005b. Theory of two-temperature generalized thermoelasticity, IMA J. Appl. Math., 1–8]. The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a half-space subjected to thermal shock and traction free. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature parameter. 相似文献
2.
The disturbance caused by the application of continuous mechanical source on the free surface of a homogeneous, isotropic
elastic half space in the context of the theory of generalized thermoelastic diffusion with one relaxation time parameter
is investigated in the Laplace-Fourier transform domain for a two dimensional problem using eigenvalue approach. The integral
transforms are inverted by using a numerical technique. The expressions for displacement components, stresses, temperature
field, concentration and chemical potential so obtained in the physical domain are computed numerically and illustrated graphically
at different times, for copper like material. As a special case the effect of diffusion on various expressions has also been
obtained analytically and depicted graphically. 相似文献
3.
The stress-concentration problem for an elastic transversely isotropic medium containing an arbitrarily oriented spheroidal inclusion (inhomogeneity) is solved. The stress state in the elastic space is represented as the superposition of the principal state and the perturbed state due to the inhomogeneity. The problem is solved using the equivalent-inclusion method, the triple Fourier transform in space variables, and the Fourier-transformed Green function for an infinite anisotropic medium. Double integrals over a finite domain are evaluated using the Gaussian quadrature formulas. In special cases, the results are compared with those obtained by other authors. The influence of the geometry and orientation of the inclusion and the elastic properties of the medium and inclusion on the stress concentration is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 33–40, February 2005. 相似文献
4.
求解饱和半空间上弹性圆板固结沉降的积分方程 总被引:1,自引:0,他引:1
本文采用解析方法分析了弹性圆板在饮和半空间上的固结沉降。考虑弹性圆板与饮和半空间的接触面上无摩擦力,且饱和半空间表面为全部透水的。运用Biot固结理论和积分方程技术,在Laplace变换域上建立了弹性圆板固结沉降的对偶积分方程,并化此对偶积分方程为第二类Fredholm积分方程。通过对其核函数的有效数值发得到第二类Fredholm积分方程的解,再利用Lapace反演技术获得弹性板在时间域中的固结沉 相似文献
5.
白冰 《应用数学和力学(英文版)》2006,27(11):1531-1539
An analytical method was derived for the thermal consolidation of layered, saturated porous half-space to variable thermal loading with time. In the coupled governing equations of linear thermoelastic media, the influences of thermo-osmosis effect and thermal filtration effect were introduced. Solutions in Laplace transform space were first obtained and then numerically inverted. The responses of a double-layered porous space subjected to exponential decaying thermal loading were studied. The influences of the differences between the properties of the two layers (e.g., the coefficient of thermal consolidation, elastic modulus) on thermal consolidation were discussed. The studies show that the coupling effects of displacement and stress fields on temperature field can be completely neglected, however, the thermo-osmosis effect has an obvious influence on thermal responses. 相似文献
6.
7.
V. S. Kirilyuk 《International Applied Mechanics》2005,41(8):895-903
The static-equilibrium problem for an elastic orthotropic space with an elliptic crack is solved. The stress state of the
space is represented as a superposition of the principal and perturbed states. To solve the problem, Willis' approach is used.
It is based on the Fourier transform in spatial variables, the Fourier-transformed Green function for anisotropic material,
and Cauchy's residue theorem. The contour integrals appearing during solution are evaluated using Gaussian quadratures. The
results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress
intensity factors is studied
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 72–81, August 2005. 相似文献
8.
V. S. Kirilyuk 《International Applied Mechanics》2005,41(3):302-308
The stress-concentration problem for an elastic orthotropic medium containing an ellipsoidal cavity is solved. The stress state in the elastic space is represented as a superposition of the principal state and the perturbed state due to the cavity. The equivalent-inclusion method, the triple Fourier transform in spatial variables, and the Fourier-transformed Green function for an infinite medium are used. Double integrals over a finite domain are evaluated using the Gaussian quadrature formulas. The results for particular cases are compared with those obtained by other authors. The influence of the geometry of the cavity and the elastic properties of the material on stress concentration is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 93–100, March 2005. 相似文献
9.
Propagation of discontinuities in electromagneto generalized thermoelasticity in cylindrical regions
In this work we study wave propagation for a problem of an infinitely long solid conducting circular cylinder whose lateral surface is traction free and subjected to known surrounding temperatures in the presence of a uniform magnetic field in the direction of the axis. The problem is in the context of generalized magneto-thermo-elasticity theory with one relaxation time. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Wave propagation in the elastic medium and in the free space, bounding it, is investigated. 相似文献
10.
V. S. Kirilyuk 《International Applied Mechanics》2005,41(4):358-366
The static-equilibrium problem for an elastic orthotropic space with an elliptical crack is solved. The stress state of the space is represented as a superposition of the principal and perturbed states. To solve the problem, Willis’s approach is used. It is based on the Fourier transform in spatial variables, the Fourier-transformed Green function for anisotropic material, and Cauchy’s residue theorem. The contour integrals appearing during solution are evaluated using Gaussian quadratures. The results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress intensity factors is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 20–29, April 2005. 相似文献
11.
Tie-jun Liu Yue-sheng Wang Yong-ming Xing 《International Journal of Solids and Structures》2012,49(10):1283-1293
In this paper, the fretting contact problem for two elastic solids with graded coatings is investigated. We assume a conventional axisymmetric Hertzian contact takes place between two elastic solids under the action of the normal pressure. The application of the torque produces an annulus of slip. It is assumed that the surface shear traction within the contact area is limited by Coulomb’s friction law and the torsion angel was produced within the central adhesion zone as a rigid body. The linear multi-layer model is used to model the functionally graded coating with arbitrarily varying shear modulus. This model divides the coating into a series of sub-layers with the elastic modulus varying linearly in each sub-layer and continuous on the sub-interfaces. By using the transfer matrix method and Hankel integral transform technique, this problem is formulated as the solution of the Cauchy singular integral equations. The contact tractions are calculated by solving the equations numerically. The results show that the appropriate gradual variation of the shear modulus can significantly alter the contact tractions. Therefore, graded coatings may have potential applications in improving the resistance to fretting contact damage at the contact surfaces. 相似文献
12.
The present paper is concerned with the investigation of disturbances in'a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically. 相似文献
13.
应用弹性接触理论及Fourier变换,考虑接触域的粘着及微小滑状态,对具有弹性层的两圆筒间夹入弹性薄膜的非对称回转接触问题进行了0研究,讨论了接触宽度,弹性层厚度及摩擦系数等对弹性薄膜传送速度和圆筒公称圆周速度之比的影响。 相似文献
14.
The problem of determining the nonstationary wave field of an elastic truncated cone with nonzero dead weight is formulated
in terms of wave functions. The Laplace transform with respect to time and an integral transform with respect to time polar
angle are used to reduce the problem to a one-dimensional vector problem in the transform domain. The transforms of the wave
functions are expanded into series in inverse powers of the Laplace transform parameter, which makes it possible to study
the wave process at the initial instants of interaction. A method is proposed to solve the problem for an elastic cone doubly
truncated by spherical surfaces 相似文献
15.
V. D. Kubenko 《Mechanics of Solids》2011,46(2):256-265
The problem of unsteady deformation of an elastic half-plane is considered whose surface is impacted, at an initial instant,
by a blunt-nosed rigid body, which generates diverging unsteady elastic waves and deforms the medium. The corresponding initial-boundary-value
problem is formulated whose solution is constructed for the early stage of the interaction. The integral Laplace transform
in the time variable and the integral Fourier transform in the one of the spatial variables are used. The solution of the
problem is obtained in terms of the transforms and a formal solution is constructed in terms of the original functions. For
a body with a fixed contact region, an analytical expression of the normal stress at an arbitrary point of the half-plane
as a function of time is obtained. For a body shaped as an obtuse-angled wedge, analytical expressions of the normal stress
and displacement at an arbitrary point at the symmetry axis of the problem are obtained. Calculations are performed and used
to analyze the characteristic features of the wave processes in the medium as functions of time, the surface distance, and
the mechanical properties of the material. 相似文献
16.
Santwana Mukhopadhyay Roushan Kumar 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(8):869-881
The present work is attempted to formulate the state-space approach to the problems of thermoelastic interactions with energy
dissipation on the basis of the theory of generalized thermoelasticity type-III, recently developed by Green and Naghdi. The
formulation is then applied to solve a boundary value problem of an isotropic elastic half space with its plane boundary subjected
to two different types of boundary conditions: (1) sudden increase in temperature and zero stress and (2) sudden increase
in load and zero temperature change. Integral transform method is applied to obtain the solution of the problem. The short
time approximated solutions for the field variables have been constructed analytically for both the cases. The problem is
illustrated with the help of different graphs of numerical values of the field variables. 相似文献
17.
《International Journal of Solids and Structures》2006,43(18-19):5779-5798
A multi-layered model for frictionless contact analysis of functionally graded materials (FGMs) with arbitrarily varying elastic modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be linear function while the Poisson’s ratio is assumed to be a constant. With the model, the frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Fourier integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. 相似文献
18.
We consider a plane problem of propagation of unsteady waves in a plane layer of constant thickness filled with a homogeneous
linearly elastic isotropic medium in the absence of mass forces and with zero initial conditions. We assume that, on one of
the layer boundaries, the normal stresses are given in the form of the Dirac delta function, the tangential stresses are zero,
and the second boundary is rigidly fixed. The problem is solved by using the Laplace transform with respect to time and the
Fourier transform with respect to the longitudinal coordinate. The normal displacements at an arbitrary point are obtained
in the form of finite sums. 相似文献
19.
坡形加热下的二维广义磁热黏弹性问题研究 总被引:1,自引:1,他引:0
运用具有一个热松弛时间的广义热黏弹性理论,研究了处于均布磁场中的二维磁热黏弹
性问题. 运用Laplace变换(对时间变量)和Fourier变换(对于一个空间变量),得到了变
换域内场量的精确表达式,并把结果应用到表面受到坡形加热的半空间问题. 应用
数值逆变换得到了时间-空间域内场量的解,对丙烯酸塑料
给出场量的响应图. 并把运用广义热黏弹性理论所得的结果与传统热黏弹性理
论及热弹性理论下的结果进行了比较. 相似文献
20.
《International Journal of Solids and Structures》2005,42(14):4192-4203
The paper deals with the thermo-elastic interactions due to distributed periodically varying heat sources in a homogeneous, isotropic, unbounded elastic medium in the context of the theory of thermo-elasticity without energy dissipation. Closed form solutions for displacement, temperature, stress and strain are derived by using Laplace transform on time and then Fourier transform on space. It reveals that the interactions consist of two coupled modified dilatational and thermal waves modified by finite thermal wave speed and thermo-elastic coupling traveling with finite speeds and without attenuation. The results are compared with previous results derived by using other generalized thermo-elasticity theories. Numerical results for a hypothetical material are presented. 相似文献