Thermoelastic Coupling Response of an Unbounded Solid with a Cylindrical Cavity Due to a Moving Heat Source (original) (raw)
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Honam Mathematical Journal, 2016
This paper investigates the effect of dual-phase-lags on a thermoviscoelastic orthotropic solid with a cylindrical cavity. The cylindrical cavity is subjected to a thermal shock varying heat and its material is taken to be of Kelvin-Voigt type. The phase-lag thermoelastic model, Lord and Shulman's model and the coupled thermoelasticity model are employed to study the thermomechanical coupling, thermal and mechanical relaxation (viscous) effects. Numerical solutions for temperature, displacement and thermal stresses are obtained by using the method of Laplace transforms. Numerical results are plotted to illustrate the effect phase-lags, viscoelasticity, and the variability thermal conductivity parameter on the studied fields. The variations of all field quantities in the context of dual-phase-lags and coupled thermoelasticity models follow similar trends while the Lord and Shulman's model may be different. The influence of viscosity parameter and variability of thermal conductivity is very pronounced on temperature and thermal stresses of the thermoviscoelastic solids.
2016
This article investigates the thermoelastic interactions in an orthotropic unbounded solid containing a cylindrical cavity with variable thermal conductivity. A generalized solution is developed in the context of the one relaxation time thermoelasticity theory. The surface of the cylinder is constrained and subjected to a harmonically varying heat. The governing equations are treated to be timeless dependence by using the Laplace transform. Finally, the transformed equations are inverted by the numerical inversion of the Laplace transform. A numerical example has been calculated to illustrate the effects of the variability thermal conductivity parameter and the angular frequency of the thermal vibration on all fields.
A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity
Computers & Mathematics with Applications, 2008
The aim of the present paper is to study the thermoelastic interactions in an unbounded elastic medium with a spherical cavity in the context of four different theories of thermoelasticity, namely: the classical coupled dynamical thermoelasticity, the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation in a unified way. The cavity surface is assumed to be stress free and is subjected to a smooth and time-dependent-heating effect. The solutions for displacement, temperature and stresses are obtained with the help of the Laplace transform procedure. Firstly the short-time approximated solutions for four different theories have been obtained analytically. Then following the numerical method proposed by Bellman et al. [R. Bellmen, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Pub. Co., New York, 1966] for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained for the theory of thermoelasticity without energy dissipation with the results of other thermoelasticity theories.
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017
In this work, the generalized thermoelasticity theory with phase lags is used to solve a thermoelastic problem for an orthotropic infinite unbounded body containing a cylindrical cavity by approximate techniques. The thermal conductivity of the present body is assumed to vary linearly with the temperature. The surface of the cylinder is traction free and subjected to a uniform step temperature. The general solutions for the temperature, displacement, and thermal stresses are obtained by the method of Laplace transforms. The effects of dual phase lags and the variable thermal conductivity parameter on the studied fields for a cobalt material are discussed.
Materials Research Express
The linear generalized Green-Naghdi thermoelasticity theory without energy dissipation is employed. The study of thermoelastic interactions in a hollow cylinder under a continuous heat source is carried out. Firstly, Laplace and Hankel transforms are employed to solve the problem without the time domain. Then, the state space approach is employed to get the exact solution of the problem in the space domain. Once again, the inverse Laplace transforms is used to get the solutions in the time domain. Accurate terminologies for the temperature, thermoelastic potential, axial displacement, dilatation, and stresses are derived. Numerical outcomes for field variables are presented with the view of illustrating the theoretical results.
Archive of Mechanical Engineering
In the present article, we introduced a new model of the equations of generalized thermoelasticity for unbounded orthotropic body containing a cylindrical cavity. We applied this model in the context of generalized thermoelasticity with phase-lags under the effect of rotation. In this case, the thermal conductivity of the material is considered to be variable. In addition, the cylinder surface is traction free and subjected to a uniform unit step temperature. Using the Laplace transform technique, the distributions of the temperature, displacement, radial stress and hoop stress are determined. A detailed analysis of the effects of rotation, phase-lags and the variability thermal conductivity parameters on the studied fields is discussed. Numerical results for the studied fields are illustrated graphically in the presence and absence of rotation.
2018
In this work, we study the thermoelastic interactions in an unbounded medium with a spherical cavity in the context of a very recently proposed heat conduction model established by Quintanilla (2011). This model is a reformulation of three-phase-lag conduction model and is an alternative heat conduction theory with a single delay term. We make an attempt to study the thermoelastic interactions in an isotropic elastic medium with a spherical cavity subjected to three types of thermal and mechanical loads in the contexts of two versions of this new model. Analytical solutions for the distributions of the field variables are found out with the help of the integral transform technique. A detailed analysis of analytical results is provided by short-time approximation concept. Further, the numerical solutions of the problems are obtained by applying numerical inversion of Laplace transform. We observe significant variations in the analytical results predicted by different heat conduction ...
Generalized Thermoelastic Problem of an Infinite Body with a Spherical Cavity under Dual-Phase-Lags
Прикладная механика и техническая физика, 2016
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.
Journal of Thermal Stresses, 2008
The aim of the present article is to study the thermoelastic interactions in an infinite elastic medium with a cylindrical hole in the context of generalized thermoelasticity III, recently developed by Green and Nagdhi [1]. The boundary of the hole is assumed to be stress free and is subjected to a ramp type heating. In order to make a comparison between this thermoelastic model with other thermoelastic models, the problem is formulated on the basis of three different theories of thermoelasticity, namely: the extended thermoelasticity proposed by Lord and Shulman [2], the thermoelasticity without energy dissipation (Green and Nagdhi [3]) and thermoelasticity with energy dissipation (thermoelasticity type III [1]) in a unified way. The solutions for displacement, temperature and stresses are obtained with the help of Laplace transform procedure. Firstly the short time approximated solutions for three different theories have been obtained analytically. Then following a numerical method for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained from different models of generalized thermoelasticity.
2015
This article presents an analytical solution for the effect of phase-lags on a generalized plane strain thermoviscoelastic orthotropic medium with a cylindrical cavity subjected to a thermal shock from varying heat. It is assumed that the cylindrical cavity is made of Kelvin–Vogt type material. The general solutions for field quantities are obtained using the method of Laplace transforms. The results are graphically presented to illustrate the effect of phase-lags, viscoelasticity and variability of thermal conductivity on the studied fields. Comparisons are also presented with those in the absence of viscosity and variability of thermal conductivity.