Abstract: This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.
Abstract: In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.
Abstract: Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.
Abstract: In this study, fracture analysis of a fibrous composite
laminate with variable fiber spacing is carried out using Jk-integral
method. The laminate is assumed to be under thermal loading.
Jk-integral is formulated by using the constitutive relations of plane
orthotropic thermoelasticity. Developed domain independent form
of the Jk-integral is then integrated into the general purpose finite
element analysis software ANSYS. Numerical results are generated
so as to assess the influence of variable fiber spacing on mode I
and II stress intensity factors, energy release rate, and T-stress. For
verification, some of the results are compared to those obtained
using displacement correlation technique (DCT).
Abstract: In this study, thermal elastic stress distribution occurred on long hollow cylinders made of functionally graded material (FGM) was analytically defined under thermal, mechanical and thermo mechanical loads. In closed form solutions for elastic stresses and displacements are obtained analytically by using the infinitesimal deformation theory of elasticity. It was assumed that elasticity modulus, thermal expansion coefficient and density of cylinder materials could change in terms of an exponential function as for that Poisson’s ratio was constant. A gradient parameter n is chosen between - 1 and 1. When n equals to zero, the disc becomes isotropic. Circumferential, radial and longitudinal stresses in the FGMs cylinders are depicted in the figures. As a result, the gradient parameters have great effects on the stress systems of FGMs cylinders.
Abstract: This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.
Abstract: The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.
Abstract: Analysis for the generalized thermoelastic Lamb
waves, which propagates in anisotropic thin plates in generalized
thermoelasticity, is presented employing normal mode expansion
method. The displacement and temperature fields are expressed by a
summation of the symmetric and antisymmetric thermoelastic modes
in the surface thermal stresses and thermal gradient free orthotropic
plate, therefore the theory is particularly appropriate for waveform
analyses of Lamb waves in thin anisotropic plates. The transient
waveforms excited by the thermoelastic expansion are analyzed for
an orthotropic thin plate. The obtained results show that the theory
provides a quantitative analysis to characterize anisotropic
thermoelastic stiffness properties of plates by wave detection. Finally
numerical calculations have been presented for a NaF crystal, and the
dispersion curves for the lowest modes of the symmetric and
antisymmetric vibrations are represented graphically at different
values of thermal relaxation time. However, the methods can be used
for other materials as well
Abstract: Thermoelastic temperature, displacement, and
stress in heat transfer during laser surface hardening are solved
in Eulerian formulation. In Eulerian formulations the heat flux
is fixed in space and the workpiece is moved through a control
volume. In the case of uniform velocity and uniform heat flux
distribution, the Eulerian formulations leads to a steady-state
problem, while the Lagrangian formulations remains transient.
In Eulerian formulations the reduction to a steady-state
problem increases the computational efficiency. In this study
also an analytical solution is developed for an uncoupled
transient heat conduction equation in which a plane slab is
heated by a laser beam. The thermal result of the numerical
model is compared with the result of this analytical model.
Comparing the results shows numerical solution for uncoupled
equations are in good agreement with the analytical solution.