Fundamental solutions of thermoelasticity with a recent heat conduction model with a single delay term

Kumari, Bharti; Mukhopadhyay, Santwana

doi:10.1080/01495739.2017.1281715

Cited by 7 publications

(2 citation statements)

References 28 publications

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“…Meanwhile, many non-Fourier thermoelastic theories have been proposed successively to solve the thermoelastic problem in a very short time, such as L-S non-Fourier theory, G-L non-Fourier theory, and G-N non-Fourier theory. Based on the above non-Fourier thermoelastic theories, Sherief et al [2][3], Kumari and Mukhopadhyay [4], Wei et al [5] studied the thermo-elastic problem.…”

Section: Introductionmentioning

confidence: 99%

A non-Fourier magneto-thermo-viscoelastic problem of a two-dimensional plate

Zhang

2023

J. Phys.: Conf. Ser.

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Viscoelastic materials is a kind of damping materials which has been wildly applied in vibration control of ocean and civil engineering, and viscoelastic materials mostly work in a complex thermoelectric multi-field coupled environment. In this work, a two-dimensional viscoelastic plate is studied with stain relaxation time and viscoelastic relaxation time. The two-dimensional viscoelastic plate is placed in a magnetic field, and the upper surface is subjected to a thermal shock. The problem is investigated by a modified L-S thermo-viscoelastic model with stain, viscoelastic relaxation time, and magnetic field. Normal mode analysis is used to achieve exact analytical expressions of temperature distribution, displacement component and thermal stresses. Numerical computations are conducted for copper-like material and dimensionless results are illustrated graphically. Based on the results, the influence of magnetic field on the distributions of the nondimensional temperature, displacement and stresses are discussed.

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Section: Introductionmentioning

confidence: 99%

A non-Fourier magneto-thermo-viscoelastic problem of a two-dimensional plate

Zhang

2023

J. Phys.: Conf. Ser.

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“…This heat conduction equation has been complemented with other equations to obtain a thermoelastic problem and several contributions has been dedicated to study it. We recall some of them [13][14][15][16][17][18]22].…”

Section: Introductionmentioning

confidence: 99%

Numerical Resolution of an Exact Heat Conduction Model With a Delay Term

Campo¹,

Fernández²,

Quintanilla³

2019

jaac

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In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.

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On fundamental solution of Moore–Gibson–Thompson (MGT) thermoelasticity theory

Singh

Mukhopadhyay

2023

Z. Angew. Math. Phys.

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Fundamental solutions of thermoelasticity with a recent heat conduction model with a single delay term

Cited by 7 publications

References 28 publications

A non-Fourier magneto-thermo-viscoelastic problem of a two-dimensional plate

A non-Fourier magneto-thermo-viscoelastic problem of a two-dimensional plate

Numerical Resolution of an Exact Heat Conduction Model With a Delay Term

On fundamental solution of Moore–Gibson–Thompson (MGT) thermoelasticity theory

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