坡形加热下的二维广义磁热黏弹性问题研究

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.     

Two-temperature generalized thermoelasticity under ramp-type heating by finite element method

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.     

Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading

This paper presents the problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity, and the surface is assumed initially quiescent. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite time of rise of temperature, stress, displacement, and strain. The problem has been solved analytically using a direct approach. The derived analytical expressions have been computed for a specific situation. Numerical results for the temperature distribution, thermal stress, displacement, and strain are represented graphically. A comparison is made with the results predicted by the three theories.     

A two-dimensional thermoelasticity problem for a half space subjected to heat sources

The two-dimensional problem for a half space whose surface is traction free and subjected to the effects of heat sources is considered within the context of the theory of thermoelasticity with two relaxation times. Laplace and Fourier transform techniques are used. The solution in the transformed domain is obtained by using a direct approach. Numerical inversion of both transforms is carried out to obtain the temperature, stress and displacement distributions in the physical domain. Numerical results are represented graphically and discussed.     

The effect of rotation on generalized micropolar thermoelasticity for a half-space under five theories

A model of the equations of a two-dimensional problem in a micropolar thermoelastic medium for a half-space whose surface is free and subjected to an instantaneous thermal point source is studied. The entire elastic medium is rotating with a uniform angular velocity. The formulation is applied under five theories of the generalized thermoelasticity: Lord–Shulman with one relaxation time, Green–Lindsay with two relaxation times, Green–Naghdi theory (of type II) without energy dissipation and Chandrasekharaiah–Tzou theory with dual-phase-lag, as well as the coupled theory. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are illustrated graphically. Comparisons are made with the results predicted by the five theories in the presence and absence of rotation.     

Two-dimensional inverse problem of thermoelasticity for a medium with an elastic discontinuity

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 10, pp. 72–76, October, 1990.     

2-D problem of a Mode-I crack for a generalized thermoelasticity under Green-Naghdi theory

A general model of the equations of the generalized thermoelasticity for an infinite space weakened by a finite linear opening Mode-I crack is solved. The crack is subjected to prescribed temperature and stress distribution in the context of Green-Naghdi theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, the force stresses, the temperature and the couple stresses. Comparisons are made with the results predicted in the both type II, III of Green-Naghdi theory. It is found that a Mode-I crack has great effects on the distribution of field quantities with energy dissipation.     

State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem

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.     

Numerical solution to a nonlinear,one-dimensional problem of thermoelasticity with volume force and heat supply in a half-space

A numerical solution is presented for a nonlinear, one-dimensional boundary-value problem of thermoelasticity with variable volume force and heat supply in a half-space. The surface of the body is subjected to a given periodic displacement. The volume force and bulk heating simulate the effect of a beam of particles infiltrating the medium. No phase transition is considered and the domain of the solution excludes any shock wave formation. The basic equations are formulated in material coordinates, making them adequate for dealing with moving boundaries. The used numerical scheme reproduces correctly the process of coupled thermomechanical wave propagation. The presented figures display the process of propagation of the coupled nonlinear thermoelastic waves. They also show the effects of volume force and heat supply on the distributions of the mechanical displacements and temperature inside the medium. Moreover, the interplay between these two factors and the applied boundary disturbance is outlined. The presented solutions, however, is not meant to capture the expected process of shock formation at the breaking distance.     

State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source

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.     

A half-space problem in the theory of generalized thermoelastic diffusion

In this work we consider the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. Laplace transform techniques are used. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace transform based on Fourier expansion techniques.The temperature, displacement, stress and concentration as well as the chemical potential are obtained. Numerical computations are carried out and represented graphically.     

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

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.     

Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity

The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag(TPL), dual-phase-lag(DPL), Green-Naghdi-III(GNIII), Lord-Shulman(LS), and classical coupled(CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.     

A half-space saturated poro-elastic medium subjected to a moving point load

In this paper, an analytical solution for the dynamic response of a half-space porous medium subjected to a moving point load is derived. In the model, the displacements of the solid skeleton and the pore pressure are expressed in terms of two scalar potentials and one vectorial potential. Based on Biot’s theory, the frequency domain Holmholtz equations for the potentials are derived through the Fourier transformation with respect to time. The general solutions for the potentials are derived through the Fourier transformation with respect to the horizontal coordinates. Numerical results suggest that moving loads have very complicated effects on the dynamic response of the porous medium. Generally speaking, a moving load with a high speed will generate a larger response in the porous medium than a static or a lower speed load.