# Two-Temperature Generalized Thermoelasticity in a Fiber-Reinforced Hollow Cylinder Under Thermal Shock

22 May 2013-International Journal for Computational Methods in Engineering Science and Mechanics (Taylor & Francis Group)-Vol. 14, Iss: 5, pp 367-390

TL;DR: In this paper, the Laplace transform is used to transform the coupled equations into a Laplace transformed domain and numerical inversion of the transform is carried out using Fourier series expansion techniques.

Abstract: This paper deals with the thermoelastic interactions in a transversely isotropic, infinite hollow cylinder in which the boundaries are stress-free. There is no temperature in the inner boundary and heat flux is applied on the outer boundary. In the context of two-temperature generalized thermoelasticity theory, the three-phase-lag thermoelastic model and Green Naghdi model III (GN-III) are employed to study the thermophysical quantities. The Laplace transform is used to transform the coupled equations into the Laplace transformed domain. Then two different methods, the Galerkin finite element technique and eigen-value approach, are employed to solve the resulting equations in the transformed domain. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The physical quantities have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (GN-III and three-phase-lag model) and for two different...

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01 Jan 1997TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

1,820 citations

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01 Jan 1995TL;DR: In this chapter, the fundamentals of the finite element method are reviewed and the notation which will be used throughout the book is introduced.

Abstract: This work assumes a basic familiarity with the finite element method. For those readers desiring a better understanding of the method, there are a number of excellent books varying from an introductory treatment to advanced topics listed in the bibliography [1] [2] [3] [4] [5]. In this chapter, we will review the fundamentals of the finite element method and introduce the notation which will be used throughout the book. For the examples shown in this book, either first or second order elements were used. For the worked examples first order triangles are used. The use of first order triangular elements simplifies the arguments and in no way reduces generality. In all cases the procedures given in this book can be used with high order and/or curved elements.

125 citations

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TL;DR: In this article, the problem of two-temperature generalized thermoelastic thin strip is investigated in the context of Green and Lindsay theory, and a particular type of moving heuristic is proposed.

Abstract: The problem of two-temperature generalized thermoelastic thin slim strip is investigated in the context of Green and Lindsay theory. As an application of the problem, a particular type of moving he...

65 citations

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TL;DR: In this article, the problem of thermoelastic interactions in a homogeneous, isotropic three-dimensional medium whose surface suffers a time dependent thermal loading is treated on the basis of three-phaselag model and dual-phase-lag model with two temperatures.

Abstract: The present paper deals with the problem of thermoelastic interactions in a homogeneous, isotropic three-dimensional medium whose surface suffers a time dependent thermal loading. The problem is treated on the basis of three-phase-lag model and dual-phase-lag model with two temperatures. The medium is assumed to be unstressed initially and has uniform temperature. Normal mode analysis technique is employed onto the non-dimensional field equations to derive the exact expressions for displacement component, conductive temperature, thermodynamic temperature, stress and strain. The problem is illustrated by computing the numerical values of the field variables for a copper material. Finally, all the physical fields are represented graphically to analyze the difference between the two models. The effect of the two temperature parameter is also discussed.

34 citations

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TL;DR: A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders to study thermoalastic interaction in an isotropic homogenous semi-infinite generalized therMOelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading.

Abstract: A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter.

20 citations

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01 Jan 1950

TL;DR: In this paper, the solution of two-dimensional non-steady motion problems in two dimensions is studied. But the solution is not a solution to the problem in three dimensions.

Abstract: 1. Introduction 2. Foundations of the thoery 3. General theorems 4. The solution of plastic-elastic problems I 5. The solution of plastic-elastic problems II 6. Plane plastic strain and the theory of the slip-line field 7. Two-dimensional problems of steady motion 8. Non-steady motion problems of steady motion 9. Non-steady motion problems in two dimensions II 10. Axial symmetry 11. Miscellaneous topics 12. Platic anisotropy

7,810 citations

### "Two-Temperature Generalized Thermoe..." refers background in this paper

...Figure 27 depicts the equivalent stress [65] σe versus r for t = 1 and ω = 0....

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TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.

Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.

3,266 citations

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01 Jan 1997TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

1,820 citations

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TL;DR: In this article, a general uniqueness theorem for linear thermoelasticity without energy dissipation is proved and a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress.

Abstract: This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the linearized theory of thermoelasticity discussed possesses the following properties: (a) the heat flow, in contrast to that in classical thermoelasticity characterized by the Fourier law, does not involve energy dissipation; (b) a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress; and (c) it permits the transmission of heat as thermal waves at finite speed. Also, a general uniqueness theorem is proved which is appropriate for linear thermoelasticity without energy dissipation.

1,649 citations

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TL;DR: In this article, the authors focused on the thermal properties of the constitutive response functions in the context of both nonlinear and linear theories, and provided an easy comparison of the one-dimensional version of the equation for the determination of temperature in the linearized theory.

Abstract: This paper is concerned with thermoelastic material behavior whose constitutive response functions possess thermal features that are more general than in the usual classical thermoelasticity. After a general development of the constitutive equations in the context of both nonlinear and linear theories, attention is focused on the latter. In particular, the one-dimensional version of the equation for the determination of temperature in the linearized theory provides an easy comparative basis of its predictive capability: In one special case where the Fourier conductivity is dominant, the temperature equation reduces to the classical Fourier law of heat conduction, which does not permit the possibility of undamped thermal waves; however,'in another special case in which the effect of conductivity is negligible, the equation has undamped thermal wave solutions without energy dissipation.

1,143 citations