Two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to moving heat source

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).     

Generalized thermoelastic infinite transversely isotropic body with a cylindrical cavity due to moving heat source and harmonically varying heat

In this paper, the induced temperature, displacement, and stress fields in an infinite transversely isotropic unbounded medium with cylindrical cavity due to a moving heat source and harmonically varying heat are investigated. This problem is solved in the context of the linear theory of generalized thermoelasticity with dual phase lag model. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique the inversion of Laplace transform is done numerically. The numerical estimates of the displacement, temperature and stress are obtained and presented graphically. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and thermoelasticity without energy dissipation can extracted as special cases. Some comparisons have been shown in figures to present the effect of the heat source, dual phase lags parameters and the angular frequency of thermal vibration on all the studied fields.     

Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity

Introduction Thetheoryofgeneralizedthermoelasticitywithonerelaxationtimebasedonamodified Fourier’slawofheatconductionwasdevelopedbyLordandShulman[1].Thistheoryallowsfor theso_calledsecond_soundeffectsinsolids,hencethermaldisturbancespropagatewithfinite wavespeeds. Themathematicalmodelofthegeneralizedthermoelasticitytheoryisofacomplicatednature thathindersthepossibilityofderivingananalyticalsolution.Mostattemptsdealingwiththese equationsarebasedoneithershort_timesolution[2-4]. Modernstructur…     

物性与温度相关材料广义热弹性模型及渐近分析

计及材料物性与温度的相关性,基于Clausius不等式和L-S广义热弹性理论,通过对自由能公式的高阶展开,构建了具有变物性特征的广义耦合热弹性动力学模型。推导了各向同性材料表面受热冲击问题的线性化控制方程组,利用热冲击的瞬时特征,借助于Laplace正、逆变换技术及其极限性质,给出了变物性条件下一维热冲击问题的温度场、位移场和应力场的渐近表达式。通过算例,得到了热冲击作用下各物理场的分布规律以及材料物性与温度相关性对于热弹性响应的影响规律。结果表明：材料物性与温度相关性对于各物理场的阶跃位置、阶跃间隔以及阶跃峰值均产生影响,但值得注意的是,相比于位移场和应力场的显著影响,其对温度场的影响效果并不明显。     

A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source

This paper deals with a two dimensional problem for a transversely isotropic thick plate having heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in Laplace–Fourier transform domain by applying Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of Laplace transform is done by using a method based on Fourier Series expansion technique. Numerical computations have been done for magnesium (Mg) and the results are presented graphically. The results for an isotropic material (Cu) have been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg).     

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

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.     

Generalized magneto-thermoelasticity in a nonhomogeneous isotropic hollow cylinder using the finite element method

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     

Generalized thermoelastic functionally graded solid with a periodically varying heat source

This paper deals with the problem of thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of the linear theory of generalized thermoelasticity without energy dissipation (TEWOED). The governing equations of generalized thermoelasticity without energy dissipation (GN model type II) for a functionally graded materials (FGM) (i.e. material with spatially varying material properties)are established. The governing equations are expressed in Laplace–Fourier double transform domain and solved in that domain. Now, the inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand is obtained numerically in complex domain by using Laguerre’s method and the inversion of Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The solution to the analogous problem for homogeneous isotropic material is obtained by taking nonhomogeneity parameter suitably. Finally the results obtained are presented graphically to show the effect of nonhomogeneity on displacement, temperature, stress and strain.     

不同排水条件下非饱和土中柱孔扩张问题的解析分析

现有的圆柱孔扩张理论已可为诸如石油工程中井筒稳定性鉴定、 及旁压和圆锥贯入实验分析等提供理论依据, 但在非饱和地基压力注浆, 复合地基处理等实际工程问题中却鲜有应用. 基于弹塑性理论和非饱和土力学原理, 采用统一强度理论, 对非饱和土中柱形小孔扩张问题进行了解析研究. 首先将柱孔周围土体分为弹性区和塑性区, 并考虑在弹性区遵循小应变理论, 在塑性区遵循大应变理论, 同时考虑了中间主应力及粒间吸力对非饱和土体强度的影响. 其次应用有效应力表示的统一强度准则, 在本构关系、几何方程、动量平衡方程等基本方程的基础上, 结合相应的边界条件, 最终获得了不同排水条件下柱孔扩张时周围弹塑性区域内的应力场、应变场、位移场及极限扩孔压力的解析表达式. 通过数值算例和参数分析, 在与现有的饱和及非饱和土中柱孔扩张理论进行退化验证的同时, 分析了吸力、剪胀参数、中主应力效应参数及初始径向有效应力等对弹塑性区域内的应力场、应变场及位移场的影响规律, 验证了本文理论的正确性及有效性, 以期为实际工程问题提供合理的理论依据.      

热冲击载荷作用下的含球形空腔的广义热弹性功能梯度球形各向同性体

This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.     

Three-dimensional vibration analysis of a thermoelastic cylindrical panel with voids

In this paper, based on three-dimensional linear generalized thermoelasticity, an exact analysis of free vibration of a simply supported homogeneous isotropic, thermally conducting, cylindrical panel with voids initially at uniform temperature and undeformed state has been presented. Three displacement potential functions are introduced for solving the equations of motion, heat conduction and volume fraction field. The purely transverse wave gets decoupled from rest of motion and is not affected by thermal and volume fraction (voids) fields. After expanding the displacement potentials, volume fraction and temperature functions with orthogonal series, the equations of the considered vibration problem are reduced to five-second order coupled ordinary differential equations whose formal solution can be expressed by using Bessel functions with complex arguments. The corresponding results for thermoelastic panel without voids, elastic panel with and without voids have been deduced as special cases from the present analysis. In order to illustrate the analytical results, the numerical solutions of various relations and equations have been obtained to compute the lowest frequency as function of different cylindrical panel parameters. The computer simulated results have been presented graphically.     

Effects of thermal relaxations on thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity

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.     

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅰ)──MICROPOLAR THERMOELASTICITY

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Effect of rotation in magneto-thermoelastic transversely isotropic hollow cylinder with three-phase-lag model

This article deals with the various heat source responses in a transversely isotropic hollow cylinder under the purview of three-phase-lag (TPL) generalized thermoelasticity theory. In presence of magnetic field and due to the rotating behavior of the cylinder, the governing equations are redefined for generalized thermoelasticity with thermal time delay. In order to obtain the stress, displacement and temperature field, the field functions are expressed in terms of modified Bessel functions in Laplace transformed domain. When the outer radius of hollow cylinder tends to infinity, the corresponding results are discussed. Finally an appropriate Laplace transform inversion technique is adopted.     

激光脉冲加热的二维广义热弹性问题研究

基于L-S广义热弹性理论,研究了半无限大板局部受到激光脉冲加热时的广义热弹性问题.为避免常规积分变换方法求解带来的精度丢失,采用有限元法直接在时间域进行求解,得到了激光脉冲加热时板中的温度、位移及应力的变化规律.结果表明,直接求解方法可以准确描述热在介质中以有限的速度传播,同时发现,激光脉冲加热过后,结构的最高温度随着时间的推移逐渐降低,且最高温度的位置总在热波波前附近,此处的应力也明显高于其他区域.     

Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.     

Interactions due to mechanical/thermal sources in a micropolar thermoelastic medium possessing cubic symmetry

The present problem is the deformation of micropolar thermoelastic solids with cubic symmetry under the influence of various sources acting on the plane surface. Analytic expressions for displacement components, microrotation, force stress, couple stress, and temperature distribution are obtained in the physical domain for Lord–Shulman (L–S) and Green–Lindsay (G–L) theories of thermoelasticity by applying integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically for a particular model.     

Two-dimensional thermoelastic problem of an infinite magneto-microstretch homogeneous isotropic plate

In this work, the magneto-thermoelastic problem of an infinite microstretch homogeneous isotropic plate placed in a transverse magnetic field is studied in the context of different theories of generalized thermoelasticity. The upper surface of the infinite plate is subjected to a zonal time-dependent heat shock. The problem is investigated by applying finite element method. The solution is obtained by solving finite element governing equations of the problem in time domain directly. The results, including temperature, stresses, displacements, microrotation, microstretch, induced magnetic field, and induced electric field, are presented graphically. Comparison is made in the results predicted by different theories of generalized thermoelasticity, to show that the micropolar effect has a slight influence on the results while the microstretch effect has a great influence on the results. Finally, a parameter study provides an idea about the influence of the respective terms of the theories.     

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.     

SH波作用下界面任意形状孔洞附近的动应力集中

采用Green函数和复变函数法求解了平面SH波在界面任意形状孔洞上的散射问题.首先,取含有任意形状凹陷的弹性半空间,在其水平表面上任意一点承受时间谐和的反平面线源荷载作用时的位移场作为Green函数.然后,按契合方式构造出界面任意形状孔洞对SH波的散射模型,利用所得Green函数按界面位移连续条件建立求解问题的定解积分方程组,求解界面孔附近的动应力集中系数.最后,给出了界面上椭圆孔和方孔边缘动应力集中系数的数值结果,并讨论了不同介质参数和孔洞形状对孔附近动应力集中系数的影响.