Showing papers in "Journal of Thermal Stresses in 2006"
TL;DR: In this paper, a generalized theory of thermoelasticity with one relaxation time was proposed for micro-/nanobeams vibrating at very high frequencies, such as encountered in micro/nanoelectromechanical systems (MEMS/NEMS).
Abstract: The operation of micro-/nanobeams vibrating at very high frequencies, such as encountered in micro-/nanoelectromechanical systems (MEMS/NEMS), hinges on the minimization of intrinsic material losses. We study the associated thermoelastic damping in such beams from the standpoint of a generalized theory of thermoelasticity with one relaxation time. Some of our results relate to: (i) the cooling (instead of heating) in the compressed surface of the beam; (ii) the existence of not one damping peak appearing in the classical theory, but many peaks, with a decreasing amplitude as the frequency tends to infinity; (iii) the relevance of thermoelasticity with finite wave speeds for frequencies on the order of 1012 Hz.
78 citations
TL;DR: In this article, the theoretical treatment of transient thermoelastic problem involving a functionally graded hollow cylinder due to uniform heat supply is concerned with the theoretical analysis by the method of Laplace transformation.
Abstract: This paper is concerned with the theoretical treatment of transient thermoelastic problem involving a functionally graded hollow cylinder due to uniform heat supply. The transient one-dimensional temperature is analyzed by the method of Laplace transformation. The thermal and thermoelastic constants of the hollow cylinder are expressed as power functions of the radial coordinate. We obtain the one-dimensional solution for the temperature change in a transient state, and thermoelastic response of a functionally graded hollow cylinder. Some numerical results for the temperature change, the displacement and the stress distributions are shown. Furthermore, the influence of the nonhomogeneity of the material upon the temperature change, displacement and stresses is investigated.
74 citations
TL;DR: In this article, the linear theory of thermoelasticity with microtemperatures is considered, and the representation theorem of Galerkin type of the system of equations of steady oscillations (vibrations) is presented.
Abstract: In the present paper the linear theory of thermoelasticity with microtemperatures is considered. First, the representation of Galerkin type solution of equations of motion is obtained. Then, the representation theorem of Galerkin type of the system of equations of steady oscillations (vibrations) is presented. Finally, the general solution of the system of homogeneous equations of steady oscillations in terms of nine metaharmonic functions is established.
56 citations
TL;DR: In this paper, a 3D finite element method was used for nonlinear bending analysis of functionally graded plates subjected to uniform pressure and thermal loads using a simple power law distribution, and the thermal loads were assumed as uniform, linear and sinusoidal temperature rises across the thickness direction.
Abstract: Nonlinear bending analysis of functionally graded plates subjected to uniform pressure and thermal loads is investigated using a 3-D finite element method. Material properties are varied continuously in the thickness direction according to a simple power law distribution. A three-dimensional solid element is used for more accurate modeling of material properties and temperature field in the thickness direction. The Green–Lagrange nonlinear strain-displacement relation is used to account for large deflection due to uniform pressure and thermal loads and the incremental formulation is applied for nonlinear analysis. The thermal loads are assumed as uniform, linear and sinusoidal temperature rises across the thickness direction. In numerical studies, the nonlinear bending responses of Al2O3-Ni FGM plates due to temperature field, volume fraction distribution, and system geometric parameters are presented, in detail.
54 citations
TL;DR: In this paper, the analysis of axisymmetric mechanical and thermal stresses for a long hollow cylinder made of functionally graded material, as functions of radial and longitudinal directions, is developed.
Abstract: The analysis of axisymmetric mechanical and thermal stresses for a long hollow cylinder made of functionally graded material, as functions of radial and longitudinal directions, is developed. The material properties are graded along the radial direction according to power functions of radial direction. The temperature and Navier equations are solved analytically, using the generalized Bessel function and complex form of Fourier integral. A direct method of solution of Navier equations is presented, rather than potential functions method.
51 citations
TL;DR: In this paper, a thermal buckling analysis of an imperfectically graded cylindrical shell is considered using the Wan-Donnell model for initial geometrical imperfections, based on the first-order classical shell theory using the Sanders nonlinear kinematic relations.
Abstract: A thermal buckling analysis of an imperfect functionally graded cylindrical shell is considered using the Wan–Donnell model for initial geometrical imperfections. Derivation of the equations is based on the first-order classical shell theory using the Sanders nonlinear kinematic relations. Results for the buckling loads are obtained in the closed form. The effects of shell geometry and volume fraction exponent of functionally graded material on the buckling load are investigated. The results are validated with known data in the literature.
47 citations
TL;DR: In this article, the generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Naghdi (GN) theories admit the second sound effect.
Abstract: The generalized thermoelasticity based on the Lord-Shulman (LS), Green-Lindsay (GL), and Green-Naghdi (GN) theories admit the second sound effect. By introducing some parameters all these theories are combined and a unified set of equations is rendered. These equations are then solved for a layer of isotropic and homogeneous material to study the thermal and mechanical wave propagations. The disturbances are generated by a sudden application of temperature to the boundary. The non-dimensionalized form of the governing equations are solved utilizing the Laplace transform method in time domain. Closed form solutions are obtained for the layer in Laplace transform domain, and a numerical inverse Laplace transform method is used to obtain the temperature, displacement, and stress fields in the physical time domain. The thermo-mechanical wave propagations and reflections from the layer boundaries are investigated.
42 citations
TL;DR: In this article, Tauschert et al. derived the governing equations for a thin spherical shell based on the Donnell-Mushtari-Vlasov theory and derived the equations using the Sanders simplified kinematic relations and variational method.
Abstract: In this paper, thermal instability of shallow spherical shells made of functionally graded material (FGM) is considered. The governing equations for a thin spherical shell based on the Donnell–Mushtari–Vlasov theory are obtained. The equations are derived using the Sanders simplified kinematic relations and variational method. It is assumed that the mechanical properties vary linearly through the shell thickness. The constituent material of the functionally graded shell is assumed to be a mixture of ceramic and metal. Analytical solutions are obtained for three types of thermal loading including Uniform Temperature Rise (UTR), Linear Radial Temperature (LRT), and Nonlinear Radial Temperature (NRT). The results are validated with the known data in the literature. Communicated by Theodore R. Tauschert on September 1, 2005.
42 citations
TL;DR: In this article, the exact treatment of penny-shaped crack in a magneto-electro-elastic solid subjected to uniform heat flow far away from the crack region is presented.
Abstract: The magnetoelectroelastic material possesses the dual feature that the application of magnetic field induces electric polarization and electric field induces magnetization. Piezoelectric-piezomagnetic materials exhibit magneto-electric effect. When magneto-electro-elastic materials are subjected to thermal flow, they can fracture prematurely due to their brittle behavior. Hence, it should be important to know the fracture behavior of magneto-electro- elastic materials. The penny-shaped crack problem in a medium possessing coupled electro-magneto-thermo-elastic is considered in this paper. It is assumed that the crack is isothermal. The analysis is an exact treatment of penny-shaped crack in a magneto-electroelastic solid subjected to uniform heat flow far away from the crack region. The governing equations of temperature, elastic displacements and electric potential as well as magnetic potential for an anisotropic magneto-electro-elastic medium are partial differential equations of second order, ...
35 citations
TL;DR: In this article, a simulation tool was developed and experimentally validated to predict out-of-plane deformation generated by double-sided fillet-welded attachments, with particular emphasis on the deformation of double-fillet attachments.
Abstract: Prediction and control of thermal distortion is particularly important for the design and manufacture of multiply stiffened welded structures. This study aimed to develop and experimentally validate a comprehensive simulation tool to predict distortion, with particular emphasis on out-of-plane deformation generated in double-sided fillet-welded attachments. Simulation was used to optimise the relative positions of a twin-arc configuration, to give minimum out-of-plane deformation consistent with reasonable production time for single stiffener, double-fillet attachments. The critical buckling load of the structure was approached and exceeded as the arcs were brought closer and simulation allowed the influence of this factor to be determined.
34 citations
TL;DR: In this article, four distinct theories describing the flexural motion of thermoelastic thin plates are compared, including the Lagnese and Lions model, Simmonds' model with an explicit formula for temperature in terms of plate deflection, and the Norris model.
Abstract: Four distinct theories describing the flexural motion of thermoelastic thin plates are compared. The theories are due to Chadwick [1], Lagnese and Lions [2], Simmonds [3] and Norris [4]. Chadwick's theory requires a 3D spatial equation for the temperature but is considered the most accurate as the others are derivable from it by different approximations. Attention is given to the damping of flexural waves. Analytical and quantitative comparisons indicate that the Lagnese and Lions model with a 2D temperature equation captures the essential features of the thermoelastic damping, but contains systematic inaccuracies. These are attributable to the approximation for the first moment of the temperature used in deriving the Lagnese and Lions equation. Simmonds' model with an explicit formula for temperature in terms of plate deflection is the simplest of all but is accurate only at low frequency, where the damping is linearly proportional to the frequency. It is shown that the Norris model, which is al...
TL;DR: In this paper, the authors investigated the thermoelectromechanical fracture behavior of a parallel crack in a piezoelectric strip under the same type of loading, where the crack faces were supposed to be insulated thermally and electrically.
Abstract: This paper investigates the thermoelectromechanical fracture behavior of a parallel crack in a piezoelectric strip under thermoelectric loading. The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to a system of singular integral equations, respectively, which are solved numerically. Numerical calculations are carried out, and the energy density factor as well as the stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the size and the location of the crack and the magnitude of the electric loading.
TL;DR: In this paper, the theoretical analysis of a transient piezothermoelastic problem is developed for a piezoelectric strip with a parallel crack under static electric loading and thermal shock loading conditions.
Abstract: In this study, the theoretical analysis of a transient piezothermoelastic problem is developed for a piezoelectric strip with a parallel crack under static electric loading and thermal shock loading conditions. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to a system of singular integral equations, respectively, which are solved numerically. Some numerical results for the temperature change, the stress and electric displacement distributions, and the energy density factor as well as the stress and electric displacement intensity factors in a transient state are shown in figures.
TL;DR: In this article, the wave propagation phenomenon in anisotropic thermoelastic media is represented by two systems of equations, one representing modified Christoffel equations for the medium and the other relating the temperature of the medium to the displacement of its particles.
Abstract: The wave propagation phenomenon in anisotropic thermoelastic media is represented by two systems of equations. One of them represents modified Christoffel equations for the medium and the other relates the temperature of the medium to the displacement of its particles. The frequency and thermal coefficients are grouped together to define three thermal parameters that steer the whole effect of thermodynamics on the wave propagation. The procedure is presented for the exact evaluation of the velocities and attenuations of four quasi-waves propagating in such a medium. Reduced cases are obtained for isotropic thermoelastic propagation and anisotropic elastic propagation. Analogy is established between thermoelastic propagation and poroelastic propagation of waves in the presence of general anisotropy. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed, for a realistic numerical model. The effect of frequency, thermal conductivity, relaxation time, ...
TL;DR: In this article, the generalized J-integral is converted to an equivalent domain integral around the crack tip for both plane stress and plane strain problems of thermoelasticity.
Abstract: This paper presents the formulation and finite element implementation of the equivalent domain integral (EDI) for fracture analysis of functionally graded materials (FGMs) under thermal stresses. By carrying out the neccesary modifications resulting from material nonhomogeneity and thermal strains, the generalized J-integral is converted to an equivalent domain integral around the crack tip for both plane stress and plane strain problems of thermoelasticity. The developed procedure is integrated in a fracture analysis code FRAC2D using graded and cubic finite elements in order to calculate the stress intensity factor under mode I steady-state and transient thermal loading conditions. Temperature distribution profiles in FGMs are calculated using the finite elements based heat transfer analysis code HEAT2D. Comparisons of the computed thermal stress intensity factors to the results available in the literature and to those calculated by an enriched finite element method show that developed EDI approach prod...
TL;DR: In this article, the linear theory of micropolar thermoelasticity without energy dissipation was studied in the case of steady oscillations in terms of elementary functions, and the fundamental solution of the system of differential equations was constructed.
Abstract: This paper concerns the linear theory of micropolar thermoelasticity without energy dissipation. We construct the fundamental solution of the system of differential equations in the case of steady oscillations in terms of elementary functions.
TL;DR: In this paper, the authors investigated the fracture behavior of a normal crack in a piezoelectric material strip subjected to a uniform heat flow far away from the crack region, where the crack faces were supposed to be insulated thermally and electrically.
Abstract: This paper investigates the electromechanical fracture behavior of a normal crack in a piezoelectric material strip subjected to a uniform heat flow far away from the crack region. The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to singular integral equations, respectively, which are solved numerically. Both the cases of an internal crack and an edge crack are studied. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the crack location and length on the temperature distribution and the stress intensity factors.
TL;DR: The Mathematical Theory of Elasticity (MTE) as discussed by the authors is a mathematical theory of elasticity with a focus on the problem of finding a solution to a given set of problems.
Abstract: Published by Taylor & Francis, New York and London 2004 XXVIII + 821 pages, 13 chapters, Notation, Name Index, Subject Index, 148 Examples, 116 Problems The new book Mathematical Theory of Elastici...
TL;DR: In this paper, a rapid convergent series solution for both the temperature and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form.
Abstract: Within the framework of the linear theory of thermoelasticity, the problem of circularly cylindrical layered media subjected to an arbitrary point heat source is considered and solved in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solutions to heat conduction and thermoelasticity problems for a three-phase multilayered cylinder are first derived. A rapid convergent series solution for both the temperature and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. Numerical results are provided for some particular examples to investigate the effect of material combinations on the interfacial stresses.
TL;DR: In this article, a perfectly conducting half-space, permeated by an initial magnetic field governed by the generalized equations of thermoelasticity is considered, and the bounding plane is acted upon by a combination of thermal and mechanical shock.
Abstract: A perfectly conducting half-space, permeated by an initial magnetic field governed by the generalized equations of thermoelasticity is considered. The bounding plane is acted upon by a combination of thermal and mechanical shock. The formulation is applied to the generalized thermoelasticity theories—Lord–Shulman, Green–Lindsay, and Chandrasekharaiah–Tzou—as well as to the uncoupled and the dynamic coupled theory. Laplace transform techniques together with the method of potentials are used. The expansions of the stress component, the temperature increment, and the displacement, in Laplace transform domain, in power series, and the exact inversions for arbitrary time, are given. The jump discontinuities are calculated for the five theories and the kinematical conditions of compatibility are verified. Numerical results for the temperature, stress, induced magnetic and electric field distributions are obtained and illustrated graphically. Comparisons are made with the results predicted by the five thermoelas...
TL;DR: In this article, a theory for porous thermoelastic shells using the model of Cosserat surfaces and the Nunziato-Cowin theory for materials with voids is presented.
Abstract: This paper presents a theory for porous thermoelastic shells using the model of Cosserat surfaces and the Nunziato–Cowin theory for materials with voids. To describe the porosity of the thin body, we introduce two scalar fields: one field accounts for the changes in volume fraction along the middle surface of the shell, and the other field characterizes the porosity variations along the shell's thickness. First, we postulate the principles of thermodynamics for these two-dimensional continua and we obtain the equations of the nonlinear theory. Then, we consider the linearized theory and prove the uniqueness of solution to the boundary initial value problem with no definiteness assumption on the constitutive coefficients. Finally, we consider the deformation of isotropic and homogeneous shells and determine the constitutive coefficients for Cosserat surfaces, by comparison with the results obtained from the three-dimensional approach to shell theory.
TL;DR: In this article, a hereditary non-Fourier constitutive law for the heat flux and some heat power constitutive equation with linear memory were derived in the framework of the well-established theory, due to Gurtin and Pipkin.
Abstract: In this paper we investigate mathematical models describing deformations and thermal variations of a thin homogeneous thermoviscoelastic plate A hereditary non-Fourier constitutive law for the heat flux and some heat power constitutive equation with linear memory are considered The resulting models are derived in the framework of the well-established theory, due to Gurtin and Pipkin, and according to the standard approximation procedure for the Reissner–Mindlin plate model
TL;DR: In this article, the authors considered the problem of an embedded partially insulated crack in a graded coating bonded to a homogeneous substrate under thermal and mechanical loading and applied a crack-closure algorithm to avoid interpenetration.
Abstract: The problem of an embedded partially insulated crack in a graded coating bonded to a homogeneous substrate under thermal and mechanical loading is considered. The heat conduction and the plane elasticity equations are converted into singular integral equations which are solved to yield the temperature and the displacement fields in the medium as well as the crack tip stress intensity factors. A crack-closure algorithm is applied to avoid interpenetration. The main objective of the paper is to study the effect of the coating nonhomogeneity parameters, partial insulation of the crack surfaces and crack-closure on the crack tip stress intensity factors for the purpose of gaining better understanding of the thermo-mechanical behavior of graded coatings.
TL;DR: In this article, the authors studied the propagation of straight and circularly crested Lamb waves in homogeneous, transversely isotropic, piezothermoelastic plates subjected to stress-and charge-free, thermally insulated/isothermal and stress free, and electrically shorted boundary conditions.
Abstract: This paper concentrates on the study of propagation of straight and circularly crested Lamb waves in homogeneous, transversely isotropic, piezothermoelastic plates subjected to: stress- and charge-free, thermally insulated/isothermal and stress free, thermally insulated/isothermaland electrically shorted boundary conditions in the context of generalized theories of thermoelasticity. The motion of purely transverse shear horizontal (SH) modes get decoupled from rest of the motion and do not interact with other fields. Secular equations for wave propagation modes in the plate are derived from a coupled system of governing partial differential equations of linear piezothermoelasticity. It is shown that the Rayleigh–Lamb secular equation also governs circular crested piezothermoelastic waves in a plate. Although the frequency wave number relationship holds whether the waves are straight or circularly crested the displacement, stress, electric and temperature fields vary according to Bessel functions rather th...
TL;DR: In this article, an approximate mathematical model for the heat transfer analysis in a laminated conductor is proposed, which decomposes the heat conduction problem into an independent boundary-layer problem for temperature fluctuations and a problem of finding the averaged temperature.
Abstract: In the contribution it is shown that a temperature distribution in a laminated rigid conductor can suffer certain near-boundary and near-initial fluctuations. These fluctuations are caused by periodic heterogeneity of a conductor. The aim of the research is to investigate the above fluctuations. To this end a certain approximate mathematical model for the heat transfer analysis in a laminated conductor is proposed. The main feature of the model is a decomposition of the heat conduction problem into an independent boundary-layer problem for temperature fluctuations and a problem of finding the averaged temperature. This fact makes it possible to satisfy boundary and initial conditions for temperature not only by its averaged part but also by temperature fluctuations. For selected problems the obtained results are compared with those derived from the homogenized model as well as from the exact Fourier heat transfer equation. It is shown that in contrast to the known homogenized model the proposed model desc...
TL;DR: In this article, a boundary element method using the Laplace transform in time domain is presented for the analysis of fracture mechanics under thermal shock using the Green and Lindsay (GL) theory of thermoelasticity.
Abstract: A boundary element method using the Laplace transform in time domain is presented for the analysis of fracture mechanics under thermal shock using the Green and Lindsay (GL) theory of thermoelasticity. The dynamic thermoelastic model of Green and Lindsay is selected to show the effect of thermal wave propagation at finite speed on crack tip stress intensity factor evaluation. The singular behavior of the temperature and displacement fields in the vicinity of the crack tip is modeled by the quarter-point elements. Thermal dynamic stress intensity factor for mode I is evaluated from computed nodal values, using the well-known displacement and traction formulas. The accuracy of the method is investigated through comparison of the results with the available data in literature. Condition where the inertia term plays important role is discussed and variations of dynamic stress intensity factor is investigated. Different relaxation times are chosen to briefly show their effects on stress intensity factor in the ...
TL;DR: In this paper, a closed form solution for the thermal stress distribution inside the substrate material is obtained for a stress-free boundary condition at the surface, which is the most practical situation in laser material processing.
Abstract: The closed form solution for the thermal stress distribution inside the substrate material is obtained for a stress-free boundary condition at the surface, which is the most practical situation in laser material processing. Since the molecules in the liquid and gas phases are free to move, the thermal strains in these phases are significantly small, so that the thermal stress field is formulated for the solid phase and the heat conduction equation for solid heating, therefore, considered only. It is found that the temperature in the region next to the surface vicinity drops sharply while the temperature reduces gradually in the surface vicinity due to the high amount of energy absorption from the irradiated field in this region. The variation in the temperature gradient in the surface region results in thermal stress waves propagating into the substrate material at a constant speed. Thermal stress below the surface is compressive due to high thermal strain developing in this region.
TL;DR: In this article, electric pulses are applied to the piezoelectric layers in order to suppress the vibration and the initiation and termination times of the pulse voltages are calculated according to a procedure similar to a method proposed earlier by the authors; amplitudes of the pulses are determined by various control strategies, including those based on speed feedback.
Abstract: Piezoelectric control of thermally induced vibrations of rectangular and circular plates exhibiting strain-rate damping is investigated. The plates consist of a thermoelastic structural layer bonded to two outer piezothermoelastic layers. Electric pulses are applied to the piezoelectric layers in order to suppress the vibration. The initiation and termination times of the pulse voltages are calculated according to a procedure similar to a method proposed earlier by the authors; amplitudes of the pulses are determined by various control strategies, including those based on speed feedback. Numerical results are presented for aluminum/PZT ceramic plates.
TL;DR: In this paper, the authors investigated the dynamic response of linear viscoelastic temperature-dependent prismatic columns under axial compressive loads and due to thermal stresses and moments to determine column life or survival times.
Abstract: The dynamic response of linear viscoelastic temperature-dependent prismatic columns is investigated under axial compressive loads and due to thermal stresses and moments. Creep buckling instabilities and probabilities of material failures are analyzed to determine column life or survival times. Optimum designer materials are studied to minimize thermal stress and axial load effects while concurrently lowering failure probabilities and extending survival times.
TL;DR: In this article, an axisymmetric analytical solution examines the radial and tangential thermal stresses and strains, and the radial displacements around a circular hole in a functionally graded material (FGM) plate.
Abstract: An existing axisymmetric analytical solution examines the radial and tangential thermal stresses and strains, and the radial displacements around a circular hole in a functionally graded material (FGM) plate. This solution is the point of departure to apply an inverse problem methodology to pose two inverse problems from measurements of the displacement and/or stress field: First, for known material distribution gradation function and material behavior the aim is to evaluate the thermal load. Second, for known thermal load and material behavior the objective is to define the gradation function coefficients relevant to determination of the properties. The inverse problem methodology explored in this paper for a FGM infinite plate with a hole provides a robust approach to determining the material gradation function and/or thermal loading conditions. It also demonstrates that careful attention needs to be paid to the analytical formulation of the behavior of FGMs so that the experimental necessity f...