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: The present paper deals with the flexural vibrations
of homogeneous, isotropic, generalized micropolar microstretch
thermoelastic thin Euler-Bernoulli beam resonators, due to
Exponential time varying load. Both the axial ends of the
beam are assumed to be at simply supported conditions. The
governing equations have been solved analytically by using Laplace
transforms technique twice with respect to time and space variables
respectively. The inversion of Laplace transform in time domain
has been performed by using the calculus of residues to obtain
deflection.The analytical results have been numerically analyzed with
the help of MATLAB software for magnesium like material. The
graphical representations and interpretations have been discussed
for Deflection of beam under Simply Supported boundary condition
and for distinct considered values of time and space as well. The
obtained results are easy to implement for engineering analysis and
designs of resonators (sensors), modulators, actuators.
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: Fundamental basics of pure and applied research in the area of magneto-thermo-mechanical numerical analysis and design of innovative electromagnetic devices (modern induction heaters, novel thermoelastic actuators, rotating electrical machines, induction cookers, electrophysical devices) are elaborated. Thus, mathematical models of magneto-thermo-mechanical processes in electromagnetic devices taking into account main interactions of interrelated phenomena are developed. In addition, graphical representation of coupled (multiphysics) phenomena under consideration is proposed. Besides, numerical techniques for nonlinear problems solution are developed. On this base, effective numerical algorithms for solution of actual problems of practical interest are proposed, validated and implemented in applied 2D and 3D computer codes developed. Many applied problems of practical interest regarding modern electrical engineering devices are numerically solved. Investigations of the influences of various interrelated physical phenomena (temperature dependences of material properties, thermal radiation, conditions of convective heat transfer, contact phenomena, etc.) on the accuracy of the electromagnetic, thermal and structural analyses are conducted. Important practical recommendations on the choice of rational structures, materials and operation modes of electromagnetic devices under consideration are proposed and implemented in industry.
Abstract: In this article, we used the residual correction method
to deal with transient thermoelastic problems with a hollow spherical
region when the continuum medium possesses spherically isotropic
thermoelastic properties. Based on linear thermoelastic theory, the
equations of hyperbolic heat conduction and thermoelastic motion
were combined to establish the thermoelastic dynamic model with
consideration of the deformation acceleration effect and non-Fourier
effect under the condition of transient thermal shock. The approximate
solutions of temperature and displacement distributions are obtained
using the residual correction method based on the maximum principle
in combination with the finite difference method, making it easier and
faster to obtain upper and lower approximations of exact solutions.
The proposed method is found to be an effective numerical method
with satisfactory accuracy. Moreover, the result shows that the effect
of transient thermal shock induced by deformation acceleration is
enhanced by non-Fourier heat conduction with increased peak stress.
The influence on the stress increases with the thermal relaxation time.
Abstract: Two micromechanical models for 3D smart composite
with embedded periodic or nearly periodic network of generally
orthotropic reinforcements and actuators are developed and applied to
cubic structures with unidirectional orientation of constituents.
Analytical formulas for the effective piezothermoelastic coefficients
are derived using the Asymptotic Homogenization Method (AHM).
Finite Element Analysis (FEA) is subsequently developed and used
to examine the aforementioned periodic 3D network reinforced smart
structures. The deformation responses from the FE simulations are
used to extract effective coefficients. The results from both
techniques are compared. This work considers piezoelectric materials
that respond linearly to changes in electric field, electric
displacement, mechanical stress and strain and thermal effects. This
combination of electric fields and thermo-mechanical response in
smart composite structures is characterized by piezoelectric and
thermal expansion coefficients. The problem is represented by unitcell
and the models are developed using the AHM and the FEA to
determine the effective piezoelectric and thermal expansion
coefficients. Each unit cell contains a number of orthotropic
inclusions in the form of structural reinforcements and actuators.
Using matrix representation of the coupled response of the unit cell,
the effective piezoelectric and thermal expansion coefficients are
calculated and compared with results of the asymptotic
homogenization method. A very good agreement is shown between
these two approaches.
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: In this study, thermo elastic stress analysis is performed on a cylinder made of laminated isotropic materials under thermomechanical loads. Laminated cylinders have many applications such as aerospace, automotive and nuclear plant in the
industry. These cylinders generally performed under thermomechanical loads. Stress and displacement distribution of the laminated cylinders are determined using by analytical method both thermal and mechanical loads. Based on the results, materials combination plays an important role on the stresses distribution along the radius. Variation of the stresses and displacements along the radius are presented as graphs. Calculations program are prepared using MATLAB® by authors.
Abstract: The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The Integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.
Abstract: This paper presents the results of thermo-mechanical
characterization of Glass/Epoxy composite specimens using Infrared
Thermography technique. The specimens used for the study were
fabricated in-house with three different lay-up sequences and tested
on a servo hydraulic machine under uni-axial loading. Infrared
Camera was used for on-line monitoring surface temperature changes
of composite specimens during tensile deformation.
Experimental results showed that thermomechanical
characteristics of each type of specimens were distinct. Temperature
was found to be decreasing linearly with increasing tensile stress in
the elastic region due to thermo-elastic effect. Yield point could be
observed by monitoring the change in temperature profile during
tensile testing and this value could be correlated with the results
obtained from stress-strain response. The extent of prior plastic
deformation in the post-yield region influenced the slopes of
temperature response during tensile loading. Partial unloading and
reloading of specimens post-yield results in change in slope in elastic
and plastic regions of composite specimens.
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: This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a distributed piezoelectric actuators. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations.
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: In this work, thermoelastic damping effect on the hemi- spherical shells is investigated. The material is selected silicon, and heat conduction equation for thermal flow is solved to obtain the temperature profile in which bending approximation with inextensional assumption of the model. Using the temperature profile, eigen-value analysis is performed to get the natural frequencies of hemispherical shells. Effects of mode numbers, radii and radial thicknesses of the model on the natural frequencies are analyzed in detail. Furthermore, the quality factor (Q-factor) is defined, and discussed for the ring and hemispherical shell.
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: This paper studies questions of continuous data dependence and uniqueness for solutions of initial boundary value problems in linear micropolar thermoelastic mixtures. Logarithmic convexity arguments are used to establish results with no definiteness assumptions upon the internal energy.
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.