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1.
Hamdy M. Youssef Amnah H. Al-Harby 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(9):675-687
In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing
equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech
26(4):470–475 2005a, IMA J Appl Math, pp 1–8, 2005). 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 when the bounding plane of the cavity is subjected to thermal loading (thermal shock and
ramp-type heating). 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 and the ramping parameters. 相似文献
2.
《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
3.
Hamdy M. Youssef 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(11):1213-1224
In this work, a problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity thermally shocked
at its bounding surface and subjected to moving heat source with constant velocity has been solved. The governing equations
are taken in the context of two-temperature generalized thermoelasticity theory (Youssef model). The analytical solution with
direct approach in the Laplace transforms domain has been obtained. The derived analytical expressions have been computed
for specific situations. Numerical results for the dynamical and conductive temperatures, stress, strain, and displacement
are represented graphically with comparisons by one-temperature generalized thermoelasticity (Lord–Shulman model). 相似文献
4.
In this work, a general finite element model is proposed to analyze transient phenomena in thermoelastic 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 in IMA J. Appl. Math. 71(3):383–390, 2006). A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The medium is assumed initially quiescent. A finite element scheme is presented for the high accuracy numerical purpose. The numerical solutions of the non-dimensional governing partial differential equations of the problem have been shown graphically and some comparisons have been shown in figures to estimate the effect of the ramping parameter of heating and the parameter of two-temperature. 相似文献
5.
A model of the equations of a generalized thermoelasticity (GT) with relaxation times for a saturated porous medium is given
in this article. The formulation can be applied to the GT theories: Lord–Shulman theory, Green–Lindsay theory, and Coupled
theory for the porous medium. A two-dimensional thermoelastic problem that is subjected to a time-dependent thermal/mechanical
source is investigated with the model of the generalized porous thermoelasticity. By using the Laplace transform and the Fourier
transform technique, solutions for the displacement, temperature, pore pressure, and stresses are obtained with a semi-analytical
approach in the transform domain. Numerical results are also performed for portraying the nature of variations of the field
variables. In addition, comparisons are presented with the corresponding four theories. 相似文献
6.
A model for calculating the flow of a turbulent mixture of air and suspended liquid particles injected into the near-wall
region is developed within a unified approach of mechanics of heterogeneous media in the two-velocity and two-temperature
approximation of the Eulerian approach. The influence of droplet evaporation in the near-wall jet on heat transfer between
the two-phase gas-droplet flow and the wall is studied in the case of heat addition to the latter.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 5–17, January–February, 2006. 相似文献
7.
Ibrahim A. Abbas Abo-el-nour N. Abd-alla 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(4):283-293
Thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity are studied. The cavity surface
is subjected to ramp-type heating of its internal boundary, which is assumed to be traction free. Lord–Shulman and Green–Lindsay
models for the generalized thermoelasticity theories are selected since they allow for second-sound effects and reduce to
the classical model for an appropriate choice of the parameters. The temperature, radial displacement, radial stress, and
hoop stress distributions are computed numerically using the finite-element method (FEM). The results are presented graphically
for different values of the thermal relaxation times using the three different theories of generalized thermoelasticity. Excellent
agreement is found between the finite-element analysis and analytical and classical solutions. 相似文献
8.
R. Karmakar A. Sur M. Kanoria 《Journal of Applied Mechanics and Technical Physics》2016,57(4):652-665
The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord–Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord–Shulman and dual-phase-lag models. 相似文献
9.
H.M.YOUSSEF 《应用数学和力学(英文版)》2013,34(1):63-74
In this work,a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed.The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions.The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity.The inverse Laplace transforms are computed numerically,and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter. 相似文献
10.
The model of one-dimensional equations of the two-temperature generalized magneto-thermoelasticity theory with two relaxation
times in a perfect electric conducting medium is established. The state space approach developed in Ezzat (Can J. Phys. Rev.
86(11):1241–1250, 2008) is adopted for the solution of one-dimensional problems. The resulting formulation together with the Laplace transform techniques
are applied to a specific problem of a half-space subjected to thermal shock and traction-free surface. The inversion of the
Laplace transforms is carried out using a numerical approach. Some comparisons have been shown in figures to estimate the
effects of the temperature discrepancy and the applied magnetic field. 相似文献
11.
Ibrahim A. Abbas 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(1):41-50
In this paper, we constructed the equations of generalized magneto-thermoelasticity in a perfectly conducting medium. The
formulation is applied to generalizations, the Lord–Shulman theory with one relaxation time, and the Green–Lindsay theory
with two relaxation times, as well as to the coupled theory. The material of the cylinder is supposed to be nonhomogeneous
isotropic both mechanically and thermally. The problem has been solved numerically using a finite element method. Numerical
results for the temperature distribution, displacement, radial stress, and hoop stress are represented graphically. The results
indicate that the effects of nonhomogeneity, magnetic field, and thermal relaxation times are very pronounced. In the absence
of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and/or classical dynamical
thermoelasticity, respectively. Results carried out in this paper can be used to design various nonhomogeneous magneto-thermoelastic
elements under magnetothermal load to meet special engineering requirements.
An erratum to this article can be found at 相似文献
12.
The paper proposes computer algebra system (CAS) algorithms for computer-assisted derivation of the equations of motion for
systems of rigid bodies with holonomic and nonholonomic constraints that are linear with respect to the generalized velocities.
The main advantages of using the D’Alembert-Lagrange principle for the CSA-based derivation of the equations of motion for
nonholonomic systems of rigid bodies are demonstrated. Among them are universality, algorithmizability, computational efficiency,
and simplicity of deriving equations for holonomic and nonholonomic systems in terms of generalized coordinates or pseudo-velocities
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 106–115, September 2006. 相似文献
13.
N. M. Borodachev 《International Applied Mechanics》2006,42(8):849-878
New representations of the stress tensor in the linear theory of elasticity and thermoelasticity are proposed. These representations
satisfy the equilibrium equations and the strain compatibility equation. The stress tensor is expressed in terms of a harmonic
tensor or a harmonic vector. The second boundary-value problem for an elastic half-space and an elastic layer is solved as
an example
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 3–35, August 2006. 相似文献
14.
A dynamic boundary-value problem of coupled thermoelasticity for a finite cylinder with mixed boundary conditions is solved.
The problem is reduced to a system of four singular integral equations solved by the mechanical-quadrature method. A numerical
experiment is conducted to obtain amplitude-frequency characteristics for finite cylinders with different cross sections.
The effect of thermoelastic coupling on stress distribution is assessed
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 86–95, October 2006. 相似文献
15.
We present the theory of space–time elasticity and demonstrate that it is the extended reversible thermodynamics and gives the coupled model of thermoelasticity and heat conductivity and involves traditional thermoelasticity. We formulate the generally covariant variational model’s dynamic thermoelasticity and heat conductivity in which the basic kinematic and static variables are unified tensor objects (subject, matter). Variation statement defines the whole set of the initial-boundary problems for the 4D vector governing equation (Euler equation), the spatial projections of which define motion equations and the time projection gives the heat conductivity equation. We show that space–time elasticity directly implies the Fourier and the Maxwell–Cattaneo laws of heat conduction. However, space–time elasticity is richer than classical thermoelasticity, and it advocates its own equations of motion for coupled thermoelasticity. Moreover, we establish that the Maxwell–Cattaneo law and Fourier law can be defined for the reversible processes as compatibility equations without introducing dissipation. We argue that the present framework of space–time elasticity should prove adequate to describe the thermoelastic phenomena at low temperatures for interpreting the results of molecular simulations of heat conduction in solids and for the optimal heat and stress management in the microelectronic components and the thermoelectric devices. 相似文献
16.
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation
matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima–Shizuta stability
condition formulated in Umeda et al. (Jpn J Appl Math 1:435–457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249–275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition.
However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko
system and the Euler–Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is
weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375–413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647–667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001–1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima–Shizuta condition,
and to analyze the weak dissipative structure for general systems with non-symmetric relaxation. 相似文献
17.
S. M. Shugrin 《Journal of Applied Mechanics and Technical Physics》1998,39(3):411-420
A model is developed for a thermodynamically locally-nonequilibrium two-temperature two-velocity bubble medium. The mathematical
model is formulated in two stages. In the first stage, a quasiequilibrium model is deduced from the variational principle.
In the second stage, locally non-equilibrium exchange terms are introduced into the equations obtained. From the general model
thus formulated, one can obtain simpler equations (equations of the theories of long or short waves, etc.) using asymptotic
and other methods.
Deceased.
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. 100–110, May–June, 1998. 相似文献
18.
The goal of this article is to derive new estimates for the cost of observability of heat equations. We have developed a new
method allowing one to show that when the corresponding wave equation is observable, the heat equation is also observable.
This method allows one to describe the explicit dependence of the observability constant on the geometry of the problem (the
domain in which the heat process evolves and the observation subdomain). We show that our estimate is sharp in some cases,
particularly in one space dimension and in the multi-dimensional radially symmetric case. Our result extends those in Fattorini
and Russell (Arch Rational Mech Anal 43:272–292, 1971) to the multi-dimensional setting and improves those available in the literature, namely those by Miller (J Differ Equ 204(1):202–226,
2004; SIAM J Control Optim 45(2):762–772, 2006; Atti Accad Naz Lincei Cl Sci Fis Mat Natur Rend Lincei (9) Mat Appl 17(4):351–366, 2006) and Tenenbaum and Tucsnak (J Differ Equ 243(1):70–100, 2007). Our approach is based on an explicit representation formula of some solutions of the wave equation in terms of those of
the heat equation, in contrast to the standard application of transmutation methods, which uses a reverse representation of
the heat solution in terms of the wave one. We shall also explain how our approach applies and yields some new estimates on
the cost of observability in the particular case of the unit square observed from one side. We will also comment on the applications
of our techniques to controllability properties of heat-type equations. 相似文献
19.
Alexander Vatulyan Sergey Nesterov Rostislav Nedin 《Continuum Mechanics and Thermodynamics》2020,32(4):1173-1186
In present research, we investigate dynamic coupled thermoelasticity problem for a “coating-substrate” system. We present a number of models of thermoelastic deformation of the “coating-substrate” system with thermomechanical characteristics which may vary both continuously and discontinuously. To solve these problems, we use the variational principle of coupled thermoelasticity in the Laplace transforms space and hypotheses on a distribution of temperature and displacements transforms. The transforms inversion is realized according to the Durbin method. The calculations were carried out based on both proposed simplified models and FEM. 相似文献
20.
Duvan Henao 《Journal of Elasticity》2009,94(1):55-68
We prove that energy minimizers for nonlinear elasticity in which cavitation is allowed only at a finite number of prescribed
flaw points can be obtained, in the limit as ε→0, by introducing micro-voids of radius ε in the domain at the prescribed locations and minimizing the energy without allowing for cavitation. This extends the result
by Sivaloganathan, Spector, and Tilakraj (SIAM J. Appl. Math. 66:736–757, 2006) to the case of multiple cavities, and constitutes a first step towards the numerical simulation of cavitation (in the nonradially-symmetric
case).
相似文献