Showing papers in "Journal of Thermal Stresses in 2016"

Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates

Abstract: The nonlinear thermomechanical vibration behavior of viscoelastic nanoplates is investigated based on nonlocal elasticity theory. Based on Kelvin–Voigt model and nonlinear strain–displacement relations, the geometrical nonlinearity is modeled while governing equations are solved applying semi-analytical differential quadrature method (DQM). The detailed derivations are presented while the emphasis is placed on investigating the effects of thermal environment, small scale effects, Winkler and Pasternak elastic coefficients and the viscidity and aspect ratio of the nanoplate on its nonlinear vibrational characteristics. Numerical results are presented to serve as benchmarks for the analysis of viscoelastic nanoplates, which are fundamental elements in nanoelectromechanical systems.

Thermoelastic diffusion with memory-dependent derivative

Abstract: The constitutive equations are derived for the thermoelastic diffusion in anisotropic and isotropic solids, in the context of a new generalized thermoelasticity theory with two time delays and kernel functions. The coupled thermoelastic diffusion and the Lord–Shulman theories result from the given theory as particular cases. For anisotropic solid, the reciprocity theorem is proved; the convolutional variational principle is given and the uniqueness theorem based on the variational principle is proved.

Thermal postbuckling of temperature-dependent sandwich beams with carbon nanotube-reinforced face sheets

Abstract: Thermal postbuckling response of a sandwich beam made of a stiff host core and carbon nanotube (CNT)-reinforced face sheets is analyzed in this research. Distribution of CNTs across the thickness of face sheets may be uniform or functionally graded. Material properties of the constituents are considered as temperature dependent. Properties of the face sheets are obtained by means of a modified rule of mixture approach. First-order shear deformation theory and von Karman type of geometrical nonlinearity are incorporated with the virtual displacement principle. Ritz method with polynomial basis functions is applied to the virtual displacement principle to obtain the matrix representation of the governing equations. An iterative displacement control algorithm is applied to solve the nonlinear eigenvalue problem and trace the postbuckling equilibrium path. It is shown that, graded profile of CNTs, length to thickness ratio, host thickness to face thickness ratio, volume fraction of CNTs, boundary cond...

Nonlinear vibration and dynamic response of shear deformable imperfect functionally graded double-curved shallow shells resting on elastic foundations in thermal environments

Abstract: In this article, nonlinear vibration and dynamic response of imperfect functionally graded materials (FGM) thick double-curved shallow shells resting on elastic foundations are investigated using Reddy's third-order shear deformation shell theory in thermal environments. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The FGM shells are subjected to mechanical, damping, and thermal loads. The Galerkin method and fourth-order \hboxRunge–Kutta method are used to calculate natural frequencies, nonlinear frequency–amplitude relation, and dynamic response of the shells. In numerical results, the effects of geometrical parameters, material properties, imperfections, shear deformation, the elastic foundations, mechanical, thermal and damping loads on the nonlinear dynamic response, and nonlinear vibration of FGM double-curved shallow shells are investigated....

Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations

Abstract: This paper investigates the nonlinear dynamic response of thick functionally graded materials (FGM) plates using the third-order shear deformation plate theory and stress function. The FGM plate is assumed to rest on elastic foundations and subjected to thermal and damping loads. Numerical results for dynamic response of the FGM plate are obtained by Runge–Kutta method. The results show the influences of geometrical parameters, the material properties, the elastic foundations, and thermal loads on the nonlinear dynamic response of FGM plates.

Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading

Abstract: Different from previous two-dimensional thermal weight function (TWF) method, a three-dimensional (3D) TWF method is proposed for solving elliptical interface crack problems in bimaterial structures under a transient thermal loading. The present 3D TWF method based on the Betti's reciprocal theorem is a powerful tool for dealing with the transient thermal loading due to the stress intensity factors (SIFs) of whole transient process obtained through the static finite element computation. Several representative examples demonstrate that the 3D TWF method can be used to predict the SIFs of elliptical interface crack subjected to transient thermal loading with high accuracy. Moreover, numerical results indicate that the computing efficiency can be enhanced when dealing with transient problems, especially for large amount of time instants.

Wave propagation in a generalized thermoelastic plate using eigenvalue approach

Abstract: In the present work, we obtain a dispersion relation for Rayleigh–Lamb wave propagation in a plate of thermoelastic material. For this aim, we consider the theory of generalized thermoelasticity with one relaxation time. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be isothermal and free from stresses. We obtain the analytical solution for the temperature, displacement components, and stresses using an eigenvalue approach. Finally, we derive a dispersion relation for the plate in closed form taking into account isothermal boundary conditions for wave mode propagation. To obtain the phase velocity and attenuation coefficients of propagating wave mode, we use the function iteration numerical scheme to solve the complex dispersion relation. The phase velocity and attenuation coefficients for the first five modes of waves are represented graphically for Lord–Shulman and classical coupled dynamical theories.

Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation

Abstract: Buckling and post-buckling thermomechanical deformations of a functionally graded material (FGM) Timoshenko beam resting on a two-parameter non-linear elastic foundation and subjected to only a temperature rise have been numerically investigated with the shooting method. The material properties are assumed to vary only in the thickness direction according to a power law function. Through-the-thickness temperature distribution is determined by numerically solving the one-dimensional heat conduction equation. Geometric non-linearities in the strain-displacement relations and the non-linear traction-displacement relations at the interface between the beam and the foundation are considered. For clamped-clamped and immovable simply supported beams, critical values of the ratio of temperatures of the top and the bottom surfaces of the beam for transitions in buckling modes to occur are determined. Post-buckled equilibrium paths and configurations of the heated FGM beam are illustrated for different valu...

Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties

Abstract: In this article, the nonlinear free vibration behavior of functionally graded (FG) spherical shell panel is examined under nonlinear temperature field. The functionally graded material (FGM) constituents are assumed to be the function of temperature and the thermal conductivity. The effective \hboxmaterial properties of the FGM are obtained using the Voigt micromechanical model through power-law distribution. The mathematical model of the shell panel is developed using Green–Lagrange nonlinear kinematics in the framework of the higher order shear deformation theory. The desired governing \hboxequation of the FG shell panel under thermal environment is obtained using the classical Hamilton's principle. The domain is discretized with the help of the \hboxisoparametric finite element steps and the responses are computed using the direct \hboxiterative method. The convergence behavior of the present nonlinear numerical model has been checked and compared with the previous reported results. Numerous ex...

Thermal stress analysis of laminated structures by a variable kinematic MITC9 shell element

Abstract: A linear static thermal stress analysis of composite shell structures is carried out by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are both Equivalent Single Layer (ESL) and Layer Wise (LW) and they are grouped in the Unified Formulation by Carrera (CUF). These models permit the distribution of displacements, stresses and temperature along the thickness of the multilayered shell to be accurately described. The Principle of Virtual Displacement (PVD) is employed to derive the governing equations. The Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon for a nine-node shell element. Cross-ply plate, cylindrical and spherical shells with simply supported edges and subjected to bi-sinusoidal thermal load are analyzed and various thickness ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions ...

Modal characteristics of P- and S-FGM plates with temperature-dependent materials in thermal environment

Abstract: The present article copes with the analysis of free vibration of functionally graded plates with temperature-dependent materials in thermal environment. The functionally graded material (FGM) can be produced by continuously varying the constituents of multiphase materials in a predetermined profile defined by the variation of the volume fraction. In the proposed study, two different volume fractions are considered: (i) power-law function (P-FGM) and (ii) sigmoid function (S-FGM). As the difference between the material properties of the FGM constituents used is relatively small, it is then possible to successfully apply the rule of mixture with no loss of accuracy with respect to the Mori–Tanaka method. The analysis is performed using advanced hierarchical higher order equivalent single-layer plate theories developed using the method of power series expansion of displacement components. The modal characteristics of the P- and S-FGM plates are investigated while subjected to a temperature gradient. ...

Thermomechanical vibration of curved functionally graded nanobeam based on nonlocal elasticity

Abstract: In this article, thermal buckling and natural frequency of a curved functionally graded (FG) nanobeam in a thermal environment based on Eringen’s theory is investigated. Dimension of structure is in small scale, its geometric is curved, and properties of material vary in radial direction. In order to develop differential equation and boundary condition, Hamilton’s principle is adopted. Properties of material are a function of two variables of radial thickness and temperature. After developing equation of motion in thermal environment, analytical solution has been employed in order to obtain the amount of frequency and thermal buckling. Free vibration of a curved FG nanobeam subjected to in-plane thermal load may show zero frequency magnitude at a certain temperature, which specifies the existence of bifurcation type of instability. In numerical section, frequency responses have been studied one time based on temperature-dependent material property and another time based on temperature-independent ...

Simple method for monitoring transient thermal stresses in pipelines

Abstract: This paper presents a seminumerical method for solving inverse heat conduction problems (IHCP) encountered in the monitoring of thermal stresses in pressurized thick-walled elements of steam boilers. The objective is to give a simple and quick method of determining transient temperature histories in thick-walled components based on temperature measurements on the outer thermally insulated surface. The method is suitable for solving one-dimensional problems. However, it can be extended to multidimensional temperature fields. The IHCP will be solved using the control volume approach. The accuracy of the method is demonstrated by comparing computational and experimental results. Gram orthogonal polynomials are used to smooth the measured time-dependent temperature and for evaluating time derivatives of noisy data with high accuracy. Due to the simplicity of the final formulations, the developed method is very useful for estimating the thermal stresses and controlling the fatigue damage of boiler comp...

Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory

Abstract: In this article, an analytical model for the wave propagation analysis of inhomogeneous functionally graded (FG) nanobeam in thermal environment is developed based on nonlocal strain gradient theory, in which the stress accounts for not only the nonlocal elastic stress field but also the strain gradients stress field. The nanobeam is modeled through a higher order shear deformable refined beam theory which has a trigonometric shear stress function. The temperature field supposed to have a nonlinear distribution across the nanobeam thickness. Temperature-dependent material properties of nanobeams are spatially graded based on Mori–Tanaka model. The governing equations of the temperature-dependent functionally graded (FG) nanobeam are derived using the Hamilton’s principle. Numerical examples show that the characteristics of the wave propagation of FG nanobeam are influenced by various parameters such as nonlocality parameter, length scale parameter, gradient index, and temperature changes.

Thermomechanics of damage and fatigue by a phase field model

Abstract: In this paper, we present an isothermal model for describing damage and fatigue by the use of the Ginzburg–Landau (G–L) equation. Fatigue produces progressive damage, which is related with a variation of the internal structure of the material. The G–L equation studies the evolution of the order parameter, which describes the constitutive arrangement of the system and, in this framework, the evolution of damage. The thermodynamic coherence of the model is proved. In the last part of the work, we extend the results of the paper to a nonisothermal system, where fatigue contains thermal effects, which increase the damage of materials.

Thermal–structural analysis of large deployable space antenna under extreme heat loads

Abstract: Large deployable space antennas may be exposed to severe thermal environments in future space missions; extreme heat loads will result in considerable thermal stresses and deformations which seriously affects the accuracy of the antenna's parabolic surface. In this study, thermal–structural finite element analysis of a deployable AstroMesh antenna under extreme heat loads was presented. Considering position and orientation with respect to the Sun and Earth, the antenna's temperature changing law under orbital heat fluxes was first evaluated to find the worst condition as loading point. Analyses for the antenna under different levels of extreme heat loads were then performed to obtain the temperature distributions utilizing an equivalent quarter antenna model. Based on the temperature calculation results and prestress designs, structural analyses were finally made to gain the resulting stresses and deformations. The analysis results show that the existing antenna may generate significant performanc...

Fractional heat conduction in a space with a source varying harmonically in time and associated thermal stresses

Abstract: Time-nonlocal generalization of the classical Fourier law with the “long-tail” power kernel can be interpreted in terms of fractional calculus (theory of integrals and derivatives of noninteger order) and leads to the time-fractional heat conduction equation with the Caputo derivative. Fractional heat conduction equation with the harmonic source term under zero initial conditions is studied. Different formulations of the problem for the standard parabolic heat conduction equation and for the hyperbolic wave equation appearing in thermoelasticity without energy dissipation are discussed. The integral transform technique is used. The corresponding thermal stresses are found using the displacement potential.

The effect of axially variable thermal and mechanical loads on the 2D thermoelastic response of FG cylindrical shell

Abstract: This article presents two-dimensional thermoelastic analysis of a functionally graded cylindrical pressure vessel subjected to axially variable thermal and mechanical loads. Thermal and mechanical properties are assumed to be variable along the radius based on the power law variation. Two-dimensional heat transfer equation along the axial and radial directions is analytically solved before thermoelastic analysis of the problem. First-order shear deformation theory is used for description of displacement field. Energy method as well as Euler equation is used to obtain final constitutive differential equations of the system. Four differential equations of the system are solved using the eigenvalue and eigenvector method for various patterns of axially variable loadings. Axial and radial distributions of displacement, strain, and stress components are calculated in terms of different parameters such as variable thermal and mechanical loadings and nonhomogeneous index. The obtained results indicate th...

Hygrothermal buckling analysis of magnetically actuated embedded higher order functionally graded nanoscale beams considering the neutral surface position

Abstract: In this article, the effects of humidity and thermal loads on buckling behavior of functionally graded (FG) nanobeams resting on elastic foundation and subjected to a unidirectional magnetic field is investigated. The nanobeam is modeled using different higher order refined beam theories which capture shear deformation influences needless of shear correction factors. The neutral axis position for all proposed beam models is determined. The material properties of FG nanobeam are temperature dependent and change gradually in spatial coordinate through the sigmoid and power-law models. Small-scale behavior of the nanobeam is described applying nonlocal elasticity theory of Eringen. Nonlocal governing equations for an embedded nanosize functionally graded material beam under hygrothermal loads obtained from Hamilton's principle are solved by an analytic method which satisfies various boundary conditions including S–S, C–S, and C–C. The validation of developed refined beam model has been proved with co...

Frictional contact problem between a functionally graded magnetoelectroelastic layer and a rigid conducting flat punch with frictional heat generation

Abstract: In this study, we consider the frictional sliding contact problem between a functionally graded magnetoelectroelastic (MEE) layer resting on a perfectly insulated rigid half plane and a perfectly conducting rigid flat punch with frictional heat generation. The punch is subjected to magnetoelectromechanical loads. The graded layer is modeled as a nonhomogeneous medium with a transversely isotropic stress–strain law and an exponential variation of the magnetoelectrothermoelastic properties along the thickness direction. Neglecting inertia effects and assuming a constant friction coefficient, the solution is obtained within the framework of steady-state plane magnetoelectrothermoelasticity under plane strain conditions. The heat equation is first solved using Fourier transform to yield the temperature field in the layer which is then substituted in the MEE governing equations. These equations are solved analytically using the same transform leading to three coupled Cauchy-type singular integral equat...

Waves and uniqueness in multi-porosity elasticity

Abstract: In this article, we present and review equations which describe the evolutionary behavior of double and triple porosity elastic materials. Uniqueness and continuous dependence results are described for a double porosity anisotropic elastic body when the elastic coefficients are positive, in a precise sense. We then review work on uniqueness and continuous dependence when the elastic coefficients are not required to be sign definite. With the advent of auxetic materials, and other materials which have negative Poisson ratios, sign indefinite elastic coefficients are important. We further establish uniqueness for a double porosity elastic body which occupies an unbounded spatial domain. This is not a trivial extension from the bounded domain case since the pressures and deformation and their derivatives are allowed to have substantial growth in space at infinity and so classical techniques like the energy method fail. After this we review work on acceleration wave evolution in a linear elastic doubl...

Finite element analysis of thermal buckling in automotive clutch plates

Abstract: A finite element analysis is performed to investigate the stability boundaries of thermal buckling in automotive clutches. It is found that the radial variation of temperature considerably affects the critical buckling temperature. A linear or monotonic temperature profile always leads to a dominant coning mode. Whereas a temperature profile with the maximum temperature located in the middle leads to a dominant non-axisymmetric buckling mode, and the associated critical temperature is typically much higher. The numerical solutions for periodic variations of temperature with multiple waves along the circumference were also tentatively obtained.

Optimum heating of pressure components of steam boilers with regard to thermal stresses

Abstract: A method for determining time–optimum fluid temperature changes is presented. In contrast to current standards, stepwise fluid temperature changes are allowed. The optimum fluid temperature changes are assumed in the form of a simple time function. It is possible to increase the fluid temperature stepwise, and then the fluid temperature can be increased with a constant rate at the beginning of the heating process. The permissible rates of the fluid temperature change determined by the proposed method are smaller than those obtained by boiler standards. But, due to the abrupt increase in fluid temperature, the heating time of a thick-walled component is of the same order as in the case of calculations according to EN 12952-3 European Standard. However, the total circumferential stresses on the edge of the hole do not exceed the allowable value.

Analytical solution of generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads

Abstract: In this article, a fully analytical solution of the generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads, based on Lord–Shulman model, is presented. The general forms of axisymmetric thermal and mechanical boundary conditions as arbitrary time-dependent heat transfer and traction, respectively, are considered at the inner and outer radii of the disk. The governing equations are solved analytically using the principle of superposition and the Fourier–Bessel transform. The general closed form solutions are presented for temperature and displacement fields. To validate the solutions, the results of this study are compared with the numerical results available in the literature, which show good agreement. For the temperature, displacement and stresses, radial distributions, and time histories are plotted and discussed. The propagation of thermoelastic waves and their reflection from the boundary of the disk are clearly shown. Moreover, effects ...

Two-dimensional thermoelastic analysis of FG cylindrical shell resting on the Pasternak foundation subjected to mechanical and thermal loads based on FSDT formulation

Abstract: Two-dimensional thermoelastic analysis of functionally graded thick-walled cylinder is investigated under thermal and mechanical loadings and based on the Pasternak foundation. The first-order shear deformation theory is used to describe the displacement field. Fundamental governing differential equations of system are obtained by energy method and Euler equations. Effect of gradation of material properties and Pasternak foundation parameters are considered as important results of this study. The obtained results indicate that the end supports have considerable effect on the longitudinal distribution of components. Furthermore, it can be concluded that with increasing the non-homogeneous index, both radial and axial displacements decreases.

Effect of gravity field on piezothermoelastic medium with three theories

Abstract: The present paper is aimed at studying the effect of gravity on piezothermoelastic medium. An exact solution to the problem is obtained using the normal mode analysis. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are also made with the results predicted by different theories (CT, L–S, and G–L) in the absence and presence of gravity.

SV-waves incidence at interface between solid-liquid media under electromagnetic field and initial stress in the context of three thermoelastic theories

Abstract: In this article, we studied the propagation of SV-waves under the effect of electromagnetic field and initial stress for three models in thermoelasticity: The couple and Green–Lindsay theories as well as the dual-phase-lag theory. The problem of reflection and transmission of thermoelastic waves at a solid–liquid interface in the presence of electromagnetic fields and initial stress we investigated subjected to certain boundary conditions. The appropriate expressions to find the amplitude ratios of the incident waves (SV-waves) were obtained. The reflection and transmission coefficients for the incident SV-waves were computed numerically. The effect of electric field, magnetic field, and initial stress were illustrated graphically. Comparisons were made with the obtained results in the presence and absence of considered variables and displayed graphically. The results indicate that the effect of electric field, magnetic field, and initial stress on SV-waves incidence at the interface between solid...

Thermal stability of eccentrically stiffened FGM plate on elastic foundation based on Reddy's third-order shear deformation plate theory

Abstract: This article studies the nonlinear thermal buckling and postbuckling of eccentrically stiffened functionally graded plates on elastic foundation subjected to mechanical, thermal, and thermomechanical loads. The noticeable point of this study is using the Reddy's higher order shear deformation plate theory and a general formula for the forces and moments of eccentrically stiffened functionally graded material (FGM) plate, which takes into account the influence of temperature on both the FGM plate and stiffeners. The article used the Galerkin method, stress function, and iterative method to determine the thermal buckling loads and postbuckling response of the eccentrically stiffened FGM plates in three different cases of boundary conditions. The effects of material, temperature-dependent material properties, elastic foundations, boundary conditions, outside stiffeners, and temperature on the buckling and postbuckling loading capacity of the FGM plates in thermal environments are analyzed and discuss...

Distinctive features of thermoelastic dissipation in microbeam resonators at nanoscale

Abstract: In this work, thermoelastic damping in microbeam resonators is evaluated using the generalized thermoelasticity theory based on the dual-phase-lagging thermal conduction model with relaxation between temperature increment and thermal expansion. An explicit formula of thermoelastic damping has been derived. Influences of various affecting factors on thermoelastic damping, such as the beam height, aspect ratio, and relaxation time between temperature increment and thermal expansion, are examined. Numerical results show that the thermoelastic damping, obtained by the generalized thermoelasticity theory in the present study, exhibits distinctive features at nanoscale. This work reveals that non-Fourier thermal conduction and relaxation between temperature increment and thermal expansion may play a nonnegligible role at nanometer scale.

Thermoelastic behavior of elastic media with temperature-dependent properties under transient thermal shock

Abstract: This article is concerned with thermoelastic behavior of an elastic media with temperature-dependent properties. The formulations of anisotropic media with variable material properties are proposed by the Clausius inequality and generalized theory of thermoelasticity with one relaxation time, where the higher-order expansion of the Helmholtz free energy with respect to increment temperature is used to obtain the relations between each parameter and real temperature. The governing equations of isotropic media with temperature-dependent properties are obtained based on these formulations. The problem of a half-space formed of an isotropic media with variable material properties and subjected to a sudden temperature rise in the boundary has been conducted. The propagations of thermoelastic wave and thermal wave, as well as the distributions of displacement, temperature, and stresses in the different cases, including constant properties and variable properties with specific temperature and real temper...