Coupled Thermoelastic Research Articles

Thermoelastic interactions in a functionally graded material with gravity and rotation under dual-phase-lag heat conduction

Present work is aimed to study the solution of a problem on thermoelastic interactions in a functionally graded material under dual-phase-lag model in the presence of rotation and gravity. By employing the normal mode technique, the analytical expressions for the displacement components, stresses and temperature field are obtained in the physical domain. These expressions are also calculated numerically and represented graphically in the presence and absence of gravity and rotation. Discussions have been made to highlight the effects of non-homogeneity, rotation and gravity on these physical fields. Moreover, the significant differences in the numerical results for three models known as dual-phase-lag (DPL) model, Lord–Shulman (L–S) model, and coupled thermoelastic (C-T) model are also observed for two different times. Some particular cases of interest have been inferred from the present study. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form i.e., thermally induced vibrations in a non-homogeneous thermoelastic material with rotation and gravity under DPL model has not been studied till now.

Coupled thermoelasticity analysis of FGM plate integrated with piezoelectric layers under thermal shock

Based on theory of piezoelectricity and using generalized coupled thermoelasticity, transient response of a simply supported functionally graded material rectangular plate embedded in sensor and actuator piezoelectric layers under applied electric field and thermal shock is studied. Thermoelastic properties of the plate vary continuously along the thickness direction according to exponential functions and Poisson ratio is assumed to be constant. Applying Fourier series state space technique to the basic coupled thermoelastic differential equations results in the ordinary differential equations which are solved analytically by using Laplace transform. Validation of the present approach is assessed by comparing the numerical results with the available results in literature. In parametric study, effect of the relaxation time, applied voltage and temperature and time history of the thermoelastic response of FGM plate attached to piezoelectric layers are investigated.

Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials

Abstract The finite element method (FEM) is developed for coupled thermoelastic crack problems if material properties are continuously varying. The weak form is utilized to derive the FEM equations. In conventional fracture theories the state of stress and strain at the crack tip vicinity is characterized by a single fracture parameter, namely the stress intensity factor or its equivalent, J-integral. In the present paper it is considered also the second fracture parameter called as the T-stress. For evaluation of both fracture parameters the quarter-point crack tip element is developed. Simple formulas for both fracture parameters are derived comparing the variation of displacements in the quarter-point element with asymptotic expression of displacement at the crack tip vicinity. The leading terms of the asymptotic expansions of fields in the crack-tip vicinity in a functionally graded material (FGM) are the same as in a homogeneous one with material coefficients taken at the crack tip.

Coupled thermoelasticity of a functionally graded cracked layer under thermomechanical shocks

This paper investigates linear-elastic response of cracked functionally graded layers subjected to thermomechanical loading; classical coupled thermoelastic equations are used in the calculations. The coupled dynamical system of equations obtained from the extended finite element discretization is solved by the Newmark method in the time domain. Micromechanical models for conventional composites are used to estimate properties of functionally graded layer. The interaction integral is then employed to calculate the stress intensity factors at each time step. In addition, crack propagation phenomenon under thermomechanical shocks is investigated in this paper. We have used MATLAB software to implement the algorithm and related code of problem.

Coupled thermoelasticity and second sound in finite length functionally graded thick hollow cylinders (without energy dissipation)

In this article, the coupled thermoelasticity behavior of functionally graded thick hollow cylinders is studied. The governing coupled thermoelasticity and the energy equations are solved for a finite length functionally graded cylinder subjected to thermal shock load. The coupled thermoelastic equations are considered based on Green–Naghdi theory. The mechanical properties of cylinder are graded across the thickness as a power law function of radius. The cylinder is assumed to be made of many isotropic sub-cylinders (layers) across the thickness. Functionally graded properties are created by suitable arrangement of layers and governing equations are expanded in longitudinal direction by means of trigonometric function expansion. The Galerkin Finite Element and Newmark Methods are used to analyze the cylinder. The dynamic behavior of temperature distribution, mechanical displacement and thermal stresses is obtained and discussed. The second sound and elastic wave propagation are determined for various kinds of variation in the mechanical properties. The comparison of present results with published data shows the excellent agreement.

Coupled Thermoelasticity of Functionally Graded Beams

This paper presents the finite element solution of an Euler–Bernoulli beam with functionally graded material (FGM) subjected to lateral thermal shock loads. The FGM beam is assumed to be graded across the thickness. The material properties across the thickness direction follow the volume fraction of the constitutive materials in power law form. The solution is obtained under coupled thermoelastic assumption. The equation of motion and the conventional coupled energy equation are simultaneously solved to obtain the transverse deflection and temperature distribution in the beam. The governing partial differential equations of the problem are solved simultaneously using the Galerkin finite element method with the C 1-continuous shape function leading to fast convergence of the solution. Results are presented for different power law indexes and coupling coefficients for simply supported boundary conditions. The results are verified with those reported in the literature.

Thermomechanical response of generalized thermoelastic diffusion with one relaxation time due to time harmonic sources

A general solution to the field equations of generalized thermodiffusion in an elastic solid has been obtained, in the transformed form, using the Fourier transform. Assuming the disturbances to be harmonically time dependent, the transformed solution is obtained in the frequency domain. As an application, concentrated and distributed sources have taken to illustrate the utility of the approach. The transformed solutions are inverted numerically, using a numerical inversion technique to invert the Fourier transform. The variations of concentration distribution, chemical potential distribution and effect of diffusion on the normal stress and temperature distribution have been depicted graphically for Lord and Shulman (L–S) and coupled thermoelastic (C-T) theories of thermoelasticity.

Coupled Thermoelasticity of Functionally Graded Disk

The coupled thermoelastic response of functionally graded annular disk based on the classical theory of thermoelasticity is studied in this paper. The disk is assumed to be under axi-symmetric thermal shock, applied to its inner surface. The disk material is considered to be graded along the radial direction, where a power law distribution is assumed. The method of Laplace transform is used to transform the governing equations into the space domain, where the Galerkin finite element method is employed to solve the resulting equations in the space domain. The inverse Laplace transform into the real time domain is obtained using a numerical inversion method. The time dependent temperature, radial displacement, radial stress, and hoop stress are obtained and plotted. The results are verified with the known data in the literature.

Coupled thermoelasticity of functionally graded cylindrical shells

The coupled thermoelastic response of a functionally graded circular cylindrical shell is studied. The coupled thermoelastic and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. A second-order shear deformation shell theory that accounts for the transverse shear strains and rotations is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain are used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The results are validated with the known data in the literature.

Coupled Thermoelasticity Problems of Shallow Shells

The derived differential equations govern a coupled linear thermoelastic behaviour in the frame of the Kirchhoff-Love model with the neglected effect of shell element rotary inertia. Then an abstract Cauchy problem for a coupled system by two differential equations in the Hilbert space is defined. It generalizes a series of coupled thermoelastic problems including those considered previously (Kirchhoff-Love and Timoshenko-type shells). All considerations are valid for a wide class of initial and boundary value problems.

Coupled thermoelasticity in laminated composite plates based on Green–Lindsay model

A new mixed finite element formulation is proposed to analyze transient coupled thermoelastic problems. The non-classical (Green–Lindsay) coupled model of dynamic thermoelasticity is selected for a laminated composite and a homogeneous isotropic plate. For the particular finite element developed here, there are 15 degrees of freedom at each node. Two simply supported plates are considered subjected to a half-sine mechanical and thermal loading. It is seen from a comparison of the present study with NISA II FEM code that the present method has good agreement and accuracy.

Galerkin Finite Element Displacement Formulation of Coupled Thermoelasticity Spherical Problems

When the time rate of change of the thermomechanical forces in a continuum is high enough to produce stress wave, the solution must be sought through the simultaneous consideration of the first law of thermodynamics and the equations of thermoelasticity. The general finite element formulation of coupled thermoelasticity along with a general discussion for inclusion of mechanical and thermal boundary conditions is presented. The case is then considered for a spherical symmetry and the governing coupled thermoelastic equations are reduced for a thick sphere. Based on the Galerkin method, a Kantrovich approximation is applied to the displacement and temperature field and the finite element formulation of the problem is obtained.

“EXACT” SOLUTION OF A MODEL PROBLEM FOR THE COUPLED THERMOELASTIC EQUATIONS WITH NONSMALL TEMPERATURE CHANGES

The coupled thermoelastic equations are derived for a material with Helmholtz free energy quadratic in the strains but with a temperature term that does not depend on (T — T0) /T0 being small, where T is the temperature and T0 the temperature of the body in its undeformed state. A solution is then derived for a thin-plane plate, a parabolic platelet, or a paraboloid, moving at a constant speed V in a thermoelastic medium, the constant plate temperature being T1, and (T1 — T0 ) /T0 is not necessarily small. The speed V of the plate is assumed to be small relative to elastic wave speeds of the thermoelastic medium and the plate itself is assumed to be rigid. The problem could be thought of as a model of a thin transformed plate in a solid-solid phase transformation (for a model in which elastic stresses are not considered) or as the inner solution for a plate that is not thin (for a nonlinear thermal problem of a thick rectangular rod) or as a model of a parabolic platelet or paraboloid shaped dendrite.

Coupled Thermoelasticity of Bars

Several boundary-value problems for semi-infinite bars made of a coupled thermoelastic material are solved by means of new functions. These arise in the solutions as “corrections” to classical tabulated functions such as the error function. However, they are not always small compared to their uncoupled equivalents. It turns out that the numerical differences in the solutions of a specific problem are usually small. But interesting phenomena are still found. The stresses produced in the coupled material are larger than those in the uncoupled one. The temperature generated on the face during impact of identical specimens is less than one might expect on simple intuitive grounds. Its time history is also quite interesting. Stress, strain, and thermal precursors exist but they do not propagate at a unique speed, while discontinuities propagate at the isothermal bar velocity. It is found that there is not much difference between the surface temperatures generated in a constant-velocity problem and one in which a constant acceleration is imposed. The temperature gradients are, however, different in these two problems.

A Transformation in Coupled Thermoelasticity Problems

It is shown that a simple transformation can uncouple the thermoelastic field equations but at the expense of coupled boundary conditions. A large class of coupled thermoelastic problems then becomes solvable using integral equations.