Thermoelastic interactions without energy dissipation due to a line heat source (original) (raw)
Related papers
Materials
Many attempts have been made to investigate the classical heat transfer of Fourier, and a number of improvements have been implemented. In this work, we consider a novel thermoelasticity model based on the Moore–Gibson–Thompson equation in cases where some of these models fail to be positive. This thermomechanical model has been constructed in combination with a hyperbolic partial differential equation for the variation of the displacement field and a parabolic differential equation for the temperature increment. The presented model is applied to investigate the wave propagation in an isotropic and infinite body subjected to a continuous thermal line source. To solve this problem, together with Laplace and Hankel transform methods, the potential function approach has been used. Laplace and Hankel inverse transformations are used to find solutions to different physical fields in the space–time domain. The problem is validated by calculating the numerical calculations of the physical ...
The present study is concerned with the thermoelastic interactions in a two dimensional homogeneous, transversely isotropic thermoelastic solids without energy dissipation and with two temperatures in the context of Green -Naghdi model of type-II. The Laplace and Hankel transforms have been employed to find the general solution to the field equations. Concentrated normal force, normal force over the circular region and concentrated thermal source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stresses and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are depicted graphically to show the effect of two temperature and anisotropy on the components of normal stress, tangential stress and conductive temperature.
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.
Reciprocal and variational principles in linear thermoelasticity without energy dissipation
Mechanics Research Communications, 2010
In the present paper we consider the equations which govern the behavior of an anisotropic and inhomogeneous centrosymmetric material within the framework of the linear theory of thermoelasticity without energy dissipation. We establish a reciprocal relation which is based on a characterization of the boundary-initial value problem in which the initial conditions are incorporated into the field equations. Further, a variational principle is presented too.
On a two-dimensional model of generalized thermoelasticity with application
Scientific Reports
A 2D first order linear system of partial differential equations of plane strain thermoelasticity within the frame of extended thermodynamics is presented and analyzed. The system is composed of the equations of classical thermoelasticity in which displacements are replaced with velocities, complemented with Cattaneo evolution equation for heat flux. For a particular choice of the characteristic quantities and for positive thermal conductivity, it is shown that this system may be cast in a form that is symmetric t-hyperbolic without further recurrence to entropy principle. While hyperbolicity means a finite speed of propagation of heat waves, it is known that symmetric hyperbolic systems have the desirable property of well-posedness of Cauchy problems. A study of the characteristics of this system is carried out, and an energy integral is derived, that can be used to prove uniqueness of solution under some boundary conditions. A numerical application for a finite slab is considered ...
Generalized Thermoelastic Interaction in a Half-Space under a Nonlocal Thermoelastic Model
Mathematics
In the current article, the nonlocal thermoelastic theory is used to discuss the wave propagation in unbounded thermoelastic materials. Due to the inclusion of relaxation time in thermal conduction formulation and the equations of motion, this model was developed using Lord and Shulman’s generalized thermoelastic model. The theory of the nonlocal continuum proposed by Eringen is used to obtain this model. The integral transforms of the Laplace transform methods used to generate an analytical solution for physical variables are utilized to produce the analytical solutions for the thermal stress, displacement, and temperature distribution. The effects of nonlocal parameters and relaxation time on the wave propagation distributions of physical fields for material are visually shown and explored.
Communications in Computer and Information Science
The aim of this paper is to discuss about a new thermoelasticity theory for a homogeneous and anisotropic medium in the context of a recent heat conduction model proposed by Quintanilla (2011). The coupled thermoelasticity being the branch of science that deals with the mutual interactions between temperature and strain in an elastic medium had become the interest of researchers since 1956. Quintanilla (2011) have introduced a new model of heat conduction in order to reformulate the heat conduction law with three phase-lags and established mathematical consistency in this new model as compared to the three phase-lag model. This model has also been extended to thermoelasticity theory. Various Taylor's expansion of this model has gained the interest of many researchers in recent times. Hence, we considered the model's backward time expansion of Taylor's series upto second-order and establish some important theorems. Firstly, uniqueness theorem of a mixed type boundary and initial value problem is proved using specific internal energy function. Later, we give the alternative formulation of the problem using convolution which incorporates the initial conditions into the field equations. Using this formulation, the convolution type variational theorem is proved. Further, we establish a reciprocal relation for the model.
Thermoelastic Disturbances in Transversely Isotropic Half-Space
2008
In this article attempt is made to study the fracas due to a thermal line load in a homogeneous transversely isotropic half-space in linearized theory of generalized thermo elasticity. A combination of Fourier and Laplace transform technique is applied to obtain the solutions of governing equations. The transformed solutions are then inverted using Cagniard technique for small times. The results obtained theoretically, for temperature, thermal stresses are computed numerically for a crystal of zinc, and found that variations in stresses and temperature are more prominent at small times and decrease with passage of time. The
Thermoelastic Disturbances in a Transversely Isotropic Half-Space Due to Thermal Point Load
The objective of this paper is to study disturbances due to thermal point load in a homogeneous transversely isotropic half-space in genera-lized thermoelasticity. A combination of the Fourier and Hankel trans-form technique is applied to obtain the solutions to governing equations. Cagniared's technique is used to invert the transformed solutions for small times. Theoretically obtained results, for temperature, stresses are computed numerically for a zinc material. It is found that variations in stresses and temperature are more prominent at small times and decrease with passage of time. Theg results obtained theoretically are represented graphically at different values of thermal relaxation times.
Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc
European Journal of Mechanics - A/Solids, 2007
This paper deals with the problem of thermoelastic interactions in a homogeneous isotropic unbounded medium due to the presence of periodically varying heat sources in the context of the linear theory of generalized thermoelasticity with energy dissipation (TEWED). The governing equations are expressed in Laplace-Fourier transform domain. The inversion of Fourier transform is carried out analytically while that 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 and presented graphically. A comparison has been made with the results obtained earlier for thermoelasticity without energy dissipation (TEWOED).