Showing papers in "Journal of Thermal Stresses in 2008"

Thermo-Mechanical Bending of Functionally Graded Plates

Abstract: In this work the deformations of a simply supported, functionally graded, rectangular plate subjected to thermo-mechanical loadings are analysed, extending Unified Formulation by Carrera. The governing equations are derived from the Principle of Virtual Displacements accounting for the temperature as an external load only. The required temperature field is not assumed a priori, but determined separately by solving Fourier's equation. Numerical results for temperature, displacement and stress distributions are provided for different volume fractions of the metallic and ceramic constituent as well as for different plate thickness ratios. They correlate very well with three-dimensional solutions given in the literature.

Pull-In Instabilities in Functionally Graded Microthermoelectromechanical Systems

Abstract: We study pull-in instabilities in a functionally graded microelectromechanical system (MEMS) due to the heat produced by the electric current. Material properties of two-phase MEMS are assumed to vary continuously in the thickness direction. It is shown that the pull-in voltage strongly depends upon the variation through the thickness of the volume fractions of the two constituents. It is probably the first work to consider Joule's heating, dependence of the electric conductivity upon the temperature, and the gradation of material properties in studying the pull-in instability in micro-thermo-electro-mechanical plates.

A Well-Posed Problem for the Three-Dual-Phase-Lag Heat Conduction

Abstract: The three-dual-phase-lag theory based on the constitutive law q(P, t + τ q ) = −(k∇T(P, t + τ T ) + k∗∇ν(P, t + τν)), was proposed by Roy Choudhuri as an extension of the theory by Tzou where the recent theories of Greeen and Naghdi could be recover. Although it proposes a law that could be compatible with our intuition, when we adjoin it with the energy equation −∇q(x, t) = c[Tdot](x, t), we obtain an ill-posed problem, that is, a problem which has a sequence of eigenvalues such that their real part are positive (and go to infinity). A consequence of this fact is that the problem is always unstable and we cannot obtain continuous dependence on the initial data. In this note we combine this constitutive equation with two-temperature heat conduction theory and we show in this new context that the problem is well-posed.

Generalized Theory of Thermoelastic Diffusion for Anisotropic Media

Abstract: The equations of generalized thermoelastic diffusion, based on the theory of Lord and Shulman with one relaxation time, are given in anisotropic media. A variational principle for the governing equations is obtained. Then we show that the variational principle can be used to obtain a uniqueness theorem under suitable conditions. A reciprocity theorem for these equations is given. The obtained results are valid for some special cases that can be deduced from our generalized model.

Thermomechanical Response of Variable Stiffness Composite Panels

Abstract: Analysis of non-traditional Variable Stiffness (VS) laminates, obtained by steering the fiber orientation as a spatial function of location, have shown to improve buckling load carrying capacity of flat rectangular panels under axial compressive loads. In some cases the buckling load of simply supported panels doubled compared to the best conventional laminate with straight fibers. Two distinct cases of stiffness variation, one due to fiber orientation variation in the direction of the loading, and the other one perpendicular to the loading direction, were identified as possible contributors to the buckling load improvements. In the first case, the increase was attributed to the favorable distribution of the transverse in-plane stresses over the panel platform. In the second case, a higher degree of improvement was obtained due to the re-distribution of the applied in-plane loads. Experimental results, however, showed substantially higher levels of buckling load improvements compared with theoretical pred...

Thermal Stress Analysis by Refined Multilayered Composite Shell Theories

Abstract: This paper considers the thermal stress uncoupled problem of multilayered composite shells. An assumed linear distribution of temperature through the thickness is considered for thick/thin cylindrical and spherical shells including carbon fiber reinforced layers and/or a central soft core. The Carrera's Unified Formulation (CUF) and the Principle of Virtual Displacements (PVD) are extended to derive differential governing equations for the thermal analysis of shells with constant radii of curvature. Classical and refined two-dimensional models are treated in a unified form. Both Equivalent Single Layer (ESL) and Layer-Wise (LW) approaches are considered along with variable order of expansion in the thickness direction, from linear to fourth order. In the case of ESL, the typical zig-zag form of the displacement is accounted for via the Murakami's function. Classical models have also been considered for comparison purposes. The obtained results demonstrate the effectiveness of refined models for a correct ...

Some Theorems in the Isotropic Theory of Microstretch Thermoelasticity with Microtemperatures

Abstract: This article is concerned with the linear theory of microstretch thermoelastic bodies with microtemperatures. It is shown that there is exists the coupling of microtation vector field with the microtemperatures for isotropic bodies. The existence of a generalized solutions is proved by means of the semigroup of linear operators theory and the asymptotic behavior of the solutions is studied.

Nonaxisymmetric Thermomechanical Analysis of Functionally Graded Hollow Cylinders

Abstract: Analytical solutions for nonaxisymmetric, thermomechanical response of functionally graded hollow cylinders are obtained in this article The hollow cylinders are assumed to be subjected to nonaxisymmetric mechanical and transient thermal loads Properties of functionally graded material are considered as temperature-independent and continuously varying in radial direction Employing complex Fourier series and Laplace transform techniques, analytical solutions of time-dependent temperature and thermomechanical stresses are obtained Numerical values of temperature and stresses of a FGM hollow cylinder under assumed thermomechanical loads are presented in graphical form

Thermal Stress in a Nonhomogeneous Curved Beam

Abstract: The thermoelastic stress field in a functionally graded curved beam, where the elastic stiffness varies in the radial direction, is considered. An analytical solution is obtained where the radial variation of the stiffness is represented by a fairly general form. The stress fields corresponding to two different cases for the elastic properties are examined: first, the elastic properties representing a coating on the outer surfaces of the curved beam; secondly, the elastic properties obtained from experimental data. The flexural stress in the curved beam is then compared with that of a solid ring. Finally, a relatively simple approximate solution is developed and this is shown to be in good agreement with the analytical results.

Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere

Abstract: This paper is concerned with the theoretical treatment of transient piezothermoelastic problem involving a functionally graded thermopiezoelectric hollow cylinder due to uniform heat supply. The transient one-dimensional temperature is analyzed by the method of Laplace transformation. The thermal, thermoelastic and piezoelectric 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 piezothermoelastic response of a functionally graded thermopiezoelectric hollow cylinder. Some numerical results for the temperature change, the displacement, the stress and electric potential distributions are shown. Furthermore, the influence of the nonhomogeneity of the material upon the temperature change, displacement, stresses and electric potential is investigated.

Transient temperature and thermal stress distributions in a hollow disk subjected to a moving uniform heat source

Abstract: This study presents numerical analyses of transient temperature and thermally induced stress distributions in a stationary hollow steel disk partially heated by a moving uniform heat source from its outer surface under stagnant ambient conditions. The moving heat source applied on a certain angular segment of the processed surface rotates with a constant angular speed (ω). The peak levels of the temperature gradients and the thermal stress ratios at the heated segments do not rise very much after 2–3 cycles. When the value of ω is increased, the maximum effective thermal stress ratio can be decreased in a considerable amount.

Coupled Thermoelasticity of Functionally Graded Beams

Abstract: 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.

Improved Efficient Zigzag and Third Order Theories for Circular Cylindrical Shells Under Thermal Loading

Abstract: An improved efficient zigzag theory (IZIGT) and an improved third order theory (ITOT) are presented for laminated circular cylindrical shells and shell panels under thermal loading. The transverse deflection is approximated nonuniformly to explicitly account for the transverse strain due to temperature. The inplane displacements are modelled in ITOT to have global cubic variation across the thickness and are modelled in IZIGT to have additional layerwise zigzag linear variation. The number of primary variables is reduced to 5 by imposing conditions on transverse shear at outer and inner surfaces for ITOT and also at layer interfaces for IZIGT. The governing equations and boundary conditions are derived using the principle of virtual work. The IZIGT, ZIGT, ITOT and TOT are assessed in comparison with exact 3D thermoelasticity solution for simply supported shells and shell panels of different lay-ups. The comparison reveals that IZIGT and ITOT are an improvement over ZIGT and TOT respectively, and in genera...

Stress Analysis of a Penny-Shaped Crack in a Magneto-Electro-Thermo-Elastic Layer Under Uniform Heat Flow and Shear Loads

Abstract: This article analyzes the mechanical behavior induced by a penny-shaped crack in a magneto-electro-thermal-elastic layer that is subjected to a heat flow. The surfaces of the magneto-electro-thermal-elastic layer are subjected to radial shear loads, and the crack is assumed to be thermally insulated. The Hankel transform technique is employed to reduce the problem to a Fredholm integral equation, which is then solved numerically. Shear stress intensity factors (SIFs) are obtained and discussed in detail. Numerical results reveals that in the case of only applied shear loads, the layer height has insignificant effects on the SIF when the ratio of the half-layer height h to crack radius a is larger than 2, and that in the case of only applied heat flow, the layer height also has insignificant effects on the crack extension force when h/a > 8. It is further interesting to note that for the magneto-electro-thermo-elastic layer under only applied heat flow, there exists a critical height as far as the stabilit...

Mechanical Behavior of Rectangular Plates with Functionally Graded Coefficient of Thermal Expansion Subjected to Thermal Loading

Abstract: This study analyzed an elastic, rectangular, and simply supported functionally graded material (FGM) plate with medium thickness subjected to linear temperature change in the z direction. Young's modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies continuously throughout the thickness direction in relation to the volume fraction of constituents defined by power-law, sigmoid, or exponential functions. The series solutions for the power-law FGM (P-FGM), sigmoid FGM (S-FGM), or exponential FGM (E-FGM) plates subjected to thermal loading are obtained based on the classical plate theory and Fourier series expansion. The analytical solutions for P-, S-, and E-FGM plates are verified by numerical results obtained with the finite element technique.

Two-Temperature Generalized Thermopiezoelasticity of Finite Rod Subjected to Different Types of Thermal Loading

Abstract: In this work the theory of two-temperature generalized thermoelasticity, based on the theory of Youssef is used to solve boundary value problems of one-dimensional finite piezoelectric rod with loading on its boundary with different types of heating. The governing equations are solved in the Laplace transform domain by using a direct approach. The general solution obtained is applied to specific problems of a finite piezoelectric rod subjected to two types of heating: a thermal shock type, and a ramp type. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. The conductive temperature, the dynamical temperature, the stress, the strain and the displacement distributions are shown graphically.

A Problem on Thermoelastic Interactions in an Infinite Medium with a Cylindrical Hole in Generalized Thermoelasticity III

Abstract: The aim of the present article is to study the thermoelastic interactions in an infinite elastic medium with a cylindrical hole in the context of generalized thermoelasticity III, recently developed by Green and Nagdhi [1]. The boundary of the hole is assumed to be stress free and is subjected to a ramp type heating. In order to make a comparison between this thermoelastic model with other thermoelastic models, the problem is formulated on the basis of three different theories of thermoelasticity, namely: the extended thermoelasticity proposed by Lord and Shulman [2], the thermoelasticity without energy dissipation (Green and Nagdhi [3]) and thermoelasticity with energy dissipation (thermoelasticity type III [1]) in a unified way. The solutions for displacement, temperature and stresses are obtained with the help of Laplace transform procedure. Firstly the short time approximated solutions for three different theories have been obtained analytically. Then following a numerical method for the inversion of ...

Thermal Stresses in Multilayer Gun Barrel with Interlayer Thermal Contact Resistance

Abstract: A hybrid numerical method of the Laplace transformation and the finite difference is applied to solve the transient heat transfer problem of a gun barrel, in which the interlayer thermal contact resistance between the steel cylinder and the chrome coating is taken into account in the boundary conditions The general solutions of the governing equations are first solved in the transform domain Then the inversion to the real domain is completed by the method of Fourier series technique The transient distributions of temperature and thermal stresses for the gun barrel in the real domain are calculated numerically

Transient thermomechanical analysis of a layered cylinder by the parametric finite-volume theory

Abstract: The recently developed parametric finite-volume theory for functionally graded materials is employed to investigate the response of a layered cylinder under transient thermal loading that simulates a cyclic thermal shock durability test. The results reveal a potential for the occurance of two distinct failure modes that may be activated due to two different stress components reaching critical values during different portions of the thermal cycle at different locations. These are delamination of the ceramic top coat from the bond coat, and radial cracking of the top coat that potentially initiates at the outer surface subjected to concentrated transient thermal load. Steady-state analysis substantially underestimates the magnitude of the radial and hoop stresses and, moreover, does not predict the stress reversals during cooldown that likely initiate radial cracks at the outer surface. The fidelity with which local stress fields are captured provides a convincing evidence that the parametric finite-volume ...

Generalized thermoelastic problem of a spherically isotropic infinite elastic medium containing a spherical cavity

Abstract: This paper is concerned with the determination of thermoelastic stresses and temperature in a spherically isotropic infinite elastic medium having a spherical cavity in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). The surface of the cavity is stress free and is subjected to a thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by the eigenvalue approach. The numerical inversion of the transforms is carried out using the Bellman method. The stresses and temperature are computed and presented graphically. A comparison with isotropic body has also been studied.

Thermal Stresses in Anisotropic and Radially Inhomogeneous Annular Domains

Abstract: This paper presents an analytical approach for construction of solutions to the plane quasi-static, non-axially-symmetric elasticity and thermoelasticity problems for cylindrically anisotropic and radially inhomogeneous hollow cylinders and disks subjected to in-plane external force loadings and temperature distribution. This approach is based upon the direct integration of equilibrium equations, which are independent of material properties. The original problems are reduced to integral equations of Volterra type. By application of the resolvent technique, solutions of the governing integral equations are constructed in explicit form, which is convenient for analysis and appropriate for various kinds of inhomogeneity.

Thermal Stress Intensity Factors for Two Coplanar Cracks in a Piezoelectric Strip

Abstract: This work is concerned with the thermoelectromechanical fracture behavior of two coplanar cracks in a piezoelectric material strip under a uniform heat flow far away from the crack region. The crack faces are supposed to be insulated thermally and electrically. Fourier transforms are used to reduced the mixed boundary value problems to singular integral equations. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the geometric parameters on the thermal stress intensity factors.

A Two-Dimensional Generalized Thermoelasticity Problem for a Half-Space Under the Action of a Body Force

Abstract: In this work, we consider a two-dimensional problem of distribution of thermal stresses and temperature in a generalized thermoelastic half-space under the action of a body force and subjected to a thermal shock on the bounding plane. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.

Qualitative Aspects in the Coupled Theory of Thermoelastic Diffusion

Abstract: In this paper we derive some qualitative results of the coupled theory of thermoelastic diffusion for anisotropic media. We establish a reciprocity relation, which involves two thermoelastic diffusion processes at different instants. We show that this relation can be used to obtain reciprocity, uniqueness and continuous dependence theorems. The reciprocity theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. The uniqueness theorem is derived without the positive definiteness assumption on the elastic, conductivity and diffusion tensors. We prove also that the reciprocal relation leads to a continuous dependence theorem studied on external body loads. Finally, we prove the existence of a generalized solution by means of the semigroup of linear operators theory.

Stability for a transmission problem in thermoelasticity with second sound

Abstract: We consider a semilinear transmission problem for a coupling of an elastic and a thermoelastic material. The heat conduction is modeled by Cattaneo's law removing the physical paradox of infinite propagation speed of signals. The damped, totally hyperbolic system is shown to be exponentially stable, and the existence of a global attractor is shown.

Transient Thermoelectromechanical Response of a Piezoelectric Strip with Two Parallel Cracks of Different Lengths

Abstract: This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks of different lengths in a piezoelectric material strip under thermal shock loading. 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 two systems of singular integral equations, respectively, which are solved numerically. A numerical method is employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated and presented in graphical forms. Temperature change, the stress and electric displacement distributions in a transient state are also included.

Stress Analysis of an Infinite Plate with a Coated Elliptic Hole Under a Remote Uniform Heat Flow

Abstract: A thermoelastic solution to a coated elliptic hole embedded in an infinite matrix subjected to a remote uniform heat flow is provided in this article. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stresses in the coated layer and the matrix are derived explicitly in a series form. Some numerical results are provided to investigate the effects of the material combinations and geometric configurations on the interfacial stresses. It is found that a coated layer has a strong effect on thermal stresses of the problem with an elliptic hole embedded in an infinite plate.

Theoretical Modeling and Experimental Validation of Thermal Response of Metal-Ceramic Functionally Graded Beams

Abstract: A third-order zigzag theory based finite element model in conjunction with the modified rule of mixtures and Wakashima–Tsukamoto model for estimating effective modulus of elasticity and coefficient of thermal expansion, respectively, is presented for layered functionally graded beams under thermal loading. The model is validated through experiments with two systems, Al/SiC and Ni/Al2O3, fabricated using powder metallurgy and thermal spraying techniques, respectively. The predicted thermal deflections for simply supported and cantilever FGM beams are found to be in good agreement with the experimental values for both systems. For nonlinear variation of FGM composition across the thickness, two models for thickness discretization with equal thickness and equal change in volume fraction, respectively, are evaluated in terms of magnitude of axial stress and its jump at the interfaces. The effect of inhomogeneity parameter and number of layers in the FGM on the reduction of thermal stress and its jump at the i...

Thermal Post-Buckling and Vibration Analysis of Composite Conical Shell Structures Using Layerwise Theory

Abstract: The thermal post-buckling and vibration characteristics of composite conical shells are investigated using a finite element method. Based on the layerwise theory and the von Karman displacement strain relationships, the nonlinear finite element equations of motion are derived for the thermoelastic response of the composite conical shell structure. The cylindrical arc-length method is used to account for the snapping phenomenon. The influence of the structural parameters, such as the semi-cone angle, thickness ratio, and shallowness angle (curvature), on the structural stability of the composite conical shell subjected to the thermal load is also observed.

Thermoelectromechanical Interaction Between Two Parallel Cracks in a Piezoelectric Strip

Abstract: This article investigates the thermoelectromechanical interaction between two parallel cracks 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 systems of singular integral equations, respectively, which are solved numerically. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the geometric parameters and the electric loading on the stress and electric displacement intensity factors.