Showing papers in "Journal of Thermal Stresses in 2011"
TL;DR: In this paper, the generalized Cattaneo-type equations with time-fractional derivatives are considered and the corresponding theory of thermal stresses is formulated, interpolating the theory of Lord and Shulman and thermoelasticity without energy dissipation of Green and Naghdi.
Abstract: Following Compte and Metzler, the generalized Cattaneo-type equations with time-fractional derivatives are considered. The corresponding theory of thermal stresses is formulated. The proposed theory, on the one hand, interpolates the theory of Lord and Shulman and thermoelasticity without energy dissipation of Green and Naghdi and, on the other hand, generalizes theory of thermal stresses based on the fractional heat conduction equation. The fundamental solution to the nonhomogeneous fractional telegraph equation as well as the corresponding stresses are obtained in one-dimensional and axisymmetric cases.
219 citations
TL;DR: In this article, a new theory of thermodiffusion in elastic solids is derived using the methodology of fractional calculus, and a variational theorem is then obtained for the governing equations.
Abstract: In this work, a new theory of thermodiffusion in elastic solids is derived using the methodology of fractional calculus. The theories of coupled thermoelastic diffusion and of generalized thermoelastic diffusion problem with one relaxation time follow as limit cases. A variational theorem is then obtained for the governing equations. Finally, a uniqueness and reciprocity theorems for these equations are derived.
86 citations
TL;DR: In this paper, a new theory of generalized thermoelasticity has been constructed by taking into account two-temperature generalized thermodynamic theory for a homogeneous and isotropic body without energy dissipation.
Abstract: This paper deals with thermoelastic behavior without energy dissipation; it deals with linear theory of thermoelasticity. In particular, in this work, a new theory of generalized thermoelasticity has been constructed by taking into account two-temperature generalized thermoelasticity theory for a homogeneous and isotropic body without energy dissipation. The new theorem has been derived in the context of Green and Naghdi model of type II of linear thermoelasticity. Also, a general uniqueness theorem is proved for two-temperature generalized thermoelasticity without energy dissipation.
81 citations
SIDI1
TL;DR: In this paper, the authors presented a two-variable refined plate theory for the analysis of the thermoelastic bending of functionally graded sandwich plates, where the number of unknown functions involved is only four, as against five in case of other shear deformation theories.
Abstract: The thermoelastic bending analysis of functionally graded sandwich plates using the two-variable refined plate theory is presented in this paper Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson's ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents The core layer is still homogeneous and made of an isotropic ceramic
80 citations
TL;DR: In this article, two general models of fractional heat conduction law for nonhomogeneous anisotropic elastic solid are introduced and the constitutive equations for the two-temperature fractional thermoelasticity theory are obtained, uniqueness and reciprocal theorems are proved and the convolutional variational principle is established and used to prove a uniqueness theorem with no restrictions imposed on the elasticity or thermal conductivity tensors except symmetry conditions.
Abstract: Two general models of fractional heat conduction law for non-homogeneous anisotropic elastic solid is introduced and the constitutive equations for the two-temperature fractional thermoelasticity theory are obtained, uniqueness and reciprocal theorems are proved and the convolutional variational principle is established and used to prove a uniqueness theorem with no restrictions imposed on the elasticity or thermal conductivity tensors except symmetry conditions. The two-temperature dynamic coupled, Lord-Shulman and fractional coupled thermoelasticity theories result as limit cases. The reciprocity relation in case of quiescent initial state is found to be independent of the order of differintegration.
75 citations
TL;DR: The constitutive laws for two-temperature Green-Naghdi theories are given in this article, where it is proved that the theory of elasticity without energy dissipation is valid only when the twotemperatures coincide.
Abstract: The constitutive laws for two-temperature Green–Naghdi theories are given. It is proved that the two-temperature thermoelasticity theory admits dissipation of energy and the theory of elasticity without energy dissipation is valid only when the two-temperatures coincide. The uniqueness and reciprocal theorems are proved for a linear anisotropic and inhomogeneous thermoelastic centro-symmetric solid in the frame of two-temperature Green–Naghdi theories. The convolutional variational principle is established for the two-temperature Green–Naghdi theory of type III. A continuous dependence result is given for an isotropic solid.
61 citations
TL;DR: In this article, thermal buckling analysis of functionally graded material (FGM) plates resting on two-parameter Pasternak's foundations is investigated and equilibrium and stability equations of FGM plates are derived based on the trigonometric shear deformation plate theory and includes the plate foundation interaction and thermal effects.
Abstract: In this article, thermal buckling analysis of functionally graded material (FGM) plates resting on two-parameter Pasternak's foundations is investigated. Equilibrium and stability equations of FGM plates are derived based on the trigonometric shear deformation plate theory and includes the plate foundation interaction and thermal effects. The material properties vary according to a power law form through the thickness coordinate. The governing equations are solved analytically for a plate with simply supported boundary conditions and subjected to uniform temperature rise and gradient through the thickness. Resulting equations are employed to obtain the closed-form solution for the critical buckling load for each loading case. The influences of the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the buckling temperature difference are discussed.
60 citations
TL;DR: In this article, the governing equations of flexural vibrations in a transversely isotropic thermoelastic beam are derived in closed form based on Euler-Bernoulli theory.
Abstract: The governing equations of flexural vibrations in a transversely isotropic thermoelastic beam are derived in closed form based on Euler–Bernoulli theory. The out-of- plane vibrations have been studied under different beam dimensions and boundary conditions. The analytical expressions for thermoelastic damping and frequency shift of vibrations are obtained. The damping and frequency shift of beam vibrations significantly depend on thermal relaxation time and surface conditions at resonance. The expressions for displacement and temperature fields in the beam resonator are obtained. Some numerical results with help of MATLAB software have been computed and presented graphically for silicon material beams.
55 citations
TL;DR: In this article, the Euler-Bernoulli beam theory and nonlinear strain-displacement relation are used to obtain the governing equations of piezoelectric FGM beam.
Abstract: Buckling analysis of functionally graded material (FGM) beams with surface-bonded piezoelectric layers which are subjected to both thermal loading and constant voltage is studied. The material nonhomogeneous properties are assumed to vary smoothly by distribution of power law through the beam thickness. The Euler-Bernoulli beam theory and nonlinear strain-displacement relation are used to obtain the governing equations of piezoelectric FGM beam. Beam is assumed under three types of thermal loading and various types of boundary conditions. For each case of thermal loading and boundary conditions, closed-form solutions are obtained. The effects of the applied actuator voltage, beam geometry, boundary conditions, and power law index of functionally graded material on the buckling temperature are investigated.
52 citations
TL;DR: In this paper, a review of the state-of-the-art in linear and nonlinear aero-thermo-elasticity of FGM panels with emphasis on the authors contributions to the topic is presented.
Abstract: Functionally Graded Materials (FGM) have attracted significant interest as heat-shielding materials for space vehicle, skin sub-structures, gas turbine blades technologies, and many other high-temperature industrial applications. This paper reviews the state-of-the-art in linear and nonlinear aero-thermo-elasticity of FGM panels with emphasis on the authors’ contributions to the topic. An overview of the pertinent literature discussing the linear and nonlinear behavior of flat and curved panels when exposed to high temperature supersonic flow fields is presented first. The effect of material property dependency on temperature is also discussed. The study addresses divergence and flutter and methodologies used to determine these aero-thermo-elastic instabilities. In particular, critical and post-critical behaviors for panels in presence of thermal loads are addressed, along with a series of divergence, flutter, and post-flutter results obtained with linear/nonlinear dynamics approaches. Regular and chaotic...
52 citations
TL;DR: In this article, the generalized thermo-piezoelectricity model in an isotropic elastic medium with temperature-dependent mechanical properties is established and the modulus of elasticity is taken as a linear function of the reference temperature.
Abstract: The generalized thermoelasticity theory that, based on a fractional order model, is used to solve a one-dimensional boundary value problem of a semi-infinite piezoelectric medium. The resulting formulation is applied to a half-space subjected to ramp-type heating and traction free. The generalized thermo-piezoelectricity model in an isotropic elastic medium with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of the reference temperature. The Laplace transform technique is used to obtain the general solution for any set of boundary conditions. The inverse Laplace transforms are numerically computed using the Fourier expansion techniques. The effects of fractional order and the ramping of heating parameters are studied and comparison with different theories of thermoelasticity are considered. The results are also compared to results obtained in the case of a temperature-independent modulus of elasticity.
TL;DR: In this article, a cracked layer is considered under thermal shock and is analyzed once by the Lord-Shulman theory and once by classical theory, and the effect of second sound of the Shulman Theory on the cracked layer was investigated.
Abstract: In this study, a cracked layer is considered under thermal shock and is analyzed once by the Lord–Shulman theory and once by classical theory. In this way the effect of second sound of Lord–Shulman theory on a cracked layer is investigated. The Galerkin method is invoked to obtain finite element modeling of the cracked layer. The eight node rectangular element is used and the nodes near the crack tip are replaced to introduce the crack tip singularity (Barsoum element). The discretized form of Navier and energy equations are solved simultaneously in time domain by Newmark integration algorithm. The J integral formulation in dynamical thermal form is implemented to obtain stress intensity factors from the finite element solution of the problem.
TL;DR: The extension of the thermoelasticity theory by weakly non-local dual internal variables enriched by an extra entropy flux for the thermomechanical description of the behavior of microstructured solids is presented in this article.
Abstract: The extension of the thermoelasticity theory by weakly non-local dual internal variables enriched by an extra entropy flux for the thermomechanical description of the behavior of microstructured solids is presented. The internal variables take into account the distributed effect of microdeformations or microtemperatures (and their gradients) on the overall macroscopic behavior. The evolution equations for microtemperatures can be hyperbolic, which can induce wave-like propagation for macrotemperature due to the coupling of equations.
TL;DR: In this article, a generalized solution for the vibration of gold nano-beam resonator induced by ramp type heating is developed in the context of the Green and Naghdi model of generalized thermoelasticity.
Abstract: In the nanoscale beam, the effect of the coupling between temperature and strain rate becomes domineering. In the present study, a generalized solution for the vibration of gold nano-beam resonator induced by ramp type heating is developed in the context of the Green and Naghdi model of generalized thermoelasticity. The solution takes into account the above effect. State-space and Laplace transform methods are used to determine the lateral vibration, temperature, displacement, stress and strain energy of the beam. A numerical example of gold nano-beam in femtoseconds scale has been calculated to illustrate the effect of the ramping time parameter on all the studied fields.
TL;DR: In this paper, the thermal buckling behavior of single-walled carbon nanotubes (SWCNTs) embedded in an elastic medium is studied based on the nonlocal Timoshenko beam theory into which the effect of the elastic medium was incorporated, and the generalized differential quadrature method was employed to discretize the governing differential equations and to consider different commonly used boundary conditions.
Abstract: In this paper, the thermal buckling behavior of single-walled carbon nanotubes (SWCNTs) embedded in an elastic medium is studied. To this end, the SWCNTs are modeled based on the nonlocal Timoshenko beam theory into which the effect of the elastic medium is incorporated The generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations and to consider different commonly used boundary conditions (BCs). For simply supported BCs, the results obtained from the present analysis are compared with the ones from the exact solution and an excellent agreement has been achieved. The effects of the aspect ratio, nonlocal parameter and the Winkler parameter on the dimensionless critical buckling temperature are carefully investigated.
TL;DR: In this article, the dual-phase lag theory of two temperature thermoelasticity with two phase-lags has been considered and a uniqueness theorem has been established for a homogeneous and isotropic body.
Abstract: The present paper is concerned with the theory of two temperature thermoelasticity with two phase-lags in which the theory of heat conduction in deformable bodies depends on two distinct temperatures – the conductive temperature and the thermodynamic temperature. A generalized heat conduction law with dual-phase-lag effects was proposed by Tzou (1995) for the purpose of considering the delayed response in times due to the microstructural interactions in the heat transport mechanism. Recently, Quintanilla (2008) has proposed to combine this constitutive equation with a two temperature heat conduction theory and has proved that a dual-phase-lag theory with two temperatures is a well-posed problem. In the present work we consider the basic equations concerning this dual-phase lag theory of two temperature thermoelasticity and make an attempt to establish some important theorems in this context. A uniqueness theorem has been established for a homogeneous and isotropic body. An alternative characterization of ...
TL;DR: In this article, thermal buckling of shell made of functionally graded material (FGM) under thermal loads is investigated, where the material properties of FGM are assumed to be graded in the axial direction according to a simple power law distribution in terms of the volume fractions of the constituents.
Abstract: In the present research, thermal buckling of shell made of functionally graded material (FGM) under thermal loads is investigated. The material properties of functionally graded materials (FGMs) are assumed to be graded in the axial direction according to a simple power law distribution in terms of the volume fractions of the constituents. In the previous articles that published, these properties are assumed to be graded in the thickness direction. Nonlinear kinematic (strain-displacement) relations are considered based on the first order shear deformation shell theory. By substituting kinematic and stress-strain relations of functionally graded shell in the total potential energy equation and employing Euler equations, the equilibrium equations are obtained. Applying Euler equations to the second variation of total potential energy equation leads to the stability equations. Then, buckling analysis of functionally graded shell under three types of thermal loads is carried out resulting into closed-form so...
TL;DR: In this paper, the geometrically nonlinear vibrations of functionally graded cylindrical shells under the combined effect of thermal fields and mechanical excitations are analyzed by using the von Karman non-linear theory.
Abstract: Considering rotary in-plane inertias, the geometrically non-linear vibrations of the functionally graded cylindrical shells under the combined effect of thermal fields and mechanical excitations are analysed by using the von Karman non-linear theory. The coupled non-linear partial differential equations are discretized based on a series expansion of linear modes and a multiterm Galerkin's method. The non-linear equation of motion is then solved by the fourth-order Runge-Kutta numerical method. Parametric studies are carried out in order to study the influence of temperature change, volume fraction exponent of functionally graded materials and the geometry parameters on the non-linear dynamic response of the functionally graded cylindrical shells.
TL;DR: In this paper, the authors investigated the thermoelastic interactions inside the medium by employing the fractional order theory of thermo-elasticity, recently advocated by Sherief et al (Int J Solids Struct, 47, 269,275, 2010).
Abstract: The present work is concerned with the solution of a problem on fractional order theory of thermoelasticity for an elastic medium We investigate the thermoelastic interactions inside the medium by employing the fractional order theory of thermoelasticity, recently advocated by Sherief et al (Int J Solids Struct, 47, 269–275, 2010) State space approach together with the Laplace transform technique is used to obtain the general solution of the problem The general solution is then applied to three specific problems on an elastic half space, whose boundary is subjected to (i) a thermal shock (ie, a step input in temperature and zero stress), (ii) a normal load (ie, a step input in stress and zero temperature change) and (iii) a ramp type increase in temperature and zero stress To observe the variations of displacement, temperature and stress inside the half-space we compute the numerical values of the field variables for a particular material by utilizing a numerical method of Laplace inversion T
TL;DR: In this article, a linear theory of thermoelasticity with microtemperatures is proposed, and the authors show how the logarithmic convexity arguments can be used in this theory.
Abstract: This paper is concerned with the linear theory of thermoelasticity with microtemperatures. Our main aim is to show how the logarithmic convexity arguments can be used in this theory. Results concerning uniqueness, instability and structural stability are consequences of the use of this method in the proposed thermomechanical theory. The main difficulty is the fact that the thermal and microthermal parts of the system of field equations do not define a self-adjoin problem. However the use of suitable weights permits to save the difficulties.
TL;DR: In this paper, an analytical elastic-plastic solution for thick-walled cylinders made of Functionally Graded Materials (FGMs) subjected to internal pressure and thermal loading is presented.
Abstract: In this article, an analytical elastic-plastic solution for thick-walled cylinders made of Functionally Graded Materials (FGMs) subjected to internal pressure and thermal loading is presented. Based on the experimental results, a mathematical model to predict the yielding through the thickness of FG AlA359/SiCp cylinder is developed. It is shown that under the temperature gradient loading, there is a point in the cylinder where the circumferential stress changes from compressive to tensile. The position of this point depends on the geometry and material properties of the FG cylinder and is independent of the temperature gradient.
TL;DR: In this paper, an original and practical finite difference model to investigate the thermoelastic response of suspended cables is presented and validated for various loading cases, including cable extensibility and large sag, as well as variability of temperature gradients and thermal properties.
Abstract: This paper presents and validates an original and practical finite difference model to investigate the thermoelastic response of suspended cables. The mathematical formulations are provided for various loading cases. The model includes the effects of cable extensibility and large sag, as well as variability of temperature gradients and thermal properties of the cable along its arc-length. The formulations are programmed and used to study suspended cables subjected to different thermomechanical loads. The results are validated against analytical or finite element solutions, and the proposed model is shown accurate and efficient in assessing the thermoelastic response of suspended cables.
TL;DR: In this paper, the effects of uncertainty in mechanical properties on transient behaviors of displacement and temperature fields in functionally graded materials under thermo-mechanical shock loading are studied in a cylindrical domain and the governing equations of a functionally graded thick hollow cylinder are solved.
Abstract: The main objective of this article is focused on stochastic analysis of wave propagation and effects of uncertainty in mechanical properties on transient behaviors of displacement and temperature fields in functionally graded materials under thermo-mechanical shock loading. The problem is studied in a cylindrical domain and the governing equations of a functionally graded thick hollow cylinder are solved. To assess the wave propagation, the generalized coupled thermoelasticty equations based on Green-Naghdi theory (without energy dissipation) are analyzed in a FG thick hollow cylinder. The FG cylinder is considered to have infinite length and axisymmetry conditions. The constitutive mechanical properties of FGM are assumed as random variables with Gaussian distribution and also the mechanical properties are considered to vary across thickness of FG cylinder as a nonlinear power function of radius. The FG cylinder is divided into many elements across thickness of cylinder and hybrid numerical method (Galer...
TL;DR: In this article, the linear theory of thermoelasticity with microtemperatures for isotropic microstretch solids is considered, and the representation of Galerkin type solution of equations of motion is obtained.
Abstract: Here, the linear theory of thermoelasticity with microtemperatures for isotropic microstretch solids is considered. First, the representation of Galerkin type solution of equations of motion is obtained. Then, the representation theorem of Galerkin type for the system of equations of steady vibrations is presented. Finally, the representation formula for general solution of the system of homogeneous equations of steady vibrations in terms of 10 metaharmonic functions is established.
TL;DR: Similarities and differences between thermo-elasticity and thermoviscoelas- ticity are critically examined and evaluated in this paper, where the full, partial or no possible applications of the elastic/vis-coelastic correspondence principle, including approximate approaches, are analyzed and discussed.
Abstract: Similarities and differences between thermo-elasticity and thermo-viscoelas- ticity are critically examined and evaluated. Topics include, among others, constitutive relations, Poisson's ratio, energy dissipation, temperature effects on material properties, thermal expansions, loading histories, failure criteria, lifetimes, 1–D beams, torsion, columns, plates, motions in time of neutral axes and shear centers, computational issues, wave propagation, torsional divergence, control reversal, aerodynamic derivatives, flutter and experimental determinations of viscoelastic properties. The full, partial or no possible applications of the elastic/viscoelastic correspondence principle, including approximate approaches, are analyzed and discussed.
TL;DR: In this paper, the authors established the domain of influence theorem for a potential-temperature disturbance under the generalized thermoelasticity with dual phase-lags and proved that for a finite time t ≥ 0, the potential related to the displacement and the temperature fields generate no disturbance outside a bounded domain.
Abstract: The aim of the present work is to establish the domain of influence theorem for a potential-temperature disturbance under the generalized thermoelasticity with dual phase-lags. We prove that for a finite time t > 0, the potential related to the displacement and the temperature fields generate no disturbance outside a bounded domain. The domain of influence is shown to be dependent on the thermoelastic coupling constant and two phase-lag parameters.
TL;DR: In this article, the Cesaro means of various parts of the total energy are introduced in the context of the linear theory of micromorphic thermopiezoelectricity.
Abstract: The Cesaro means of various parts of the total energy are introduced in the context of the linear theory of micromorphic thermopiezoelectricity. Then, using some Lagrange identities, the relations describing the asymptotic behavior of the Cesaro means are established.
TL;DR: In this article, the authors derived a continuum theory for a thermoviscoelastic composite with the help of an entropy production inequality proposed by Green and Laws, where the composite is modelled as a mixture of an elastic solid and a Kelvin-Voigt material.
Abstract: We derive a continuum theory for a thermoviscoelastic composite with the help of an entropy production inequality proposed by Green and Laws. The composite is modelled as a mixture of an elastic solid and a Kelvin-Voigt material. The theory is derived in lagrangian description. It is shown that the linear heat conduction tensor is symmetric and that the theory allows for “second sound” effects. In contrast with other theories of solid-fluid mixtures, in the present theory the diffusive force depends on both relative displacement and relative velocity. A uniqueness result in the linearized theory is presented. Finally, the effect of a concentrated heat source is investigated.
TL;DR: In this paper, the authors presented the application of the Trefftz functions method to solving direct and inverse problems of elasticity and thermoelasticity, where the system of equations for displacements is reduced to a system of wave equations.
Abstract: The Trefftz functions method has been developed very quickly. The paper presents the application of this method to solving direct and inverse problems of elasticity and thermoelasticity. The system of equations for displacements is reduced to a system of wave equations. Then the wave polynomials (Trefftz functions for wave equation) as base functions for several variants of Finite Element Method are used. In the paper, continuous FEMT and substructuring are considered. In the case of thermoelasticity, the temperature field occurs as inhomogeneity in one of the wave equations. It is shown how to get the particular solution in 2D and 3D. When using FEMT, the difference of solutions between the elements has to be minimized. The mechanical energy of the body depends on the velocity of the displacements. Therefore, the difference of the velocities between the elements is also minimized – it is a kind of physical regularization. The quality of the approximate solutions of direct and inverse problem was verified...
TL;DR: In this article, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat flux at the inner surface of a functionally graded hollow circular cylinder from the knowledge of temperature measurements taken within the cylinder.
Abstract: In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat flux at the inner surface of a functionally graded hollow circular cylinder from the knowledge of temperature measurements taken within the cylinder. Subsequently, the distributions of temperature and thermal stresses in the cylinder can be determined as well. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat flux, temperature distributions, and thermal stresses can be obtained for the test case considered in this study.