GENERALIZED THERMOELASTICITY OF AN INFINITE BODY WITH A CYLINDRICAL CAVITY AND VARIABLE MATERIAL PROPERTIES

ABSTRACT

The equations of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with temperature-dependent mechanical and thermal properties are established. The modulus of elasticity and the thermal conductivity are taken as linear function of temperature. A problem of an infinite body with a cylindrical cavity has been solved by using Laplace transform techniques. The interior surface of the cavity is subjected to thermal and mechanical shocks. The inverse of the Laplace transform is done numerically using a method based on Fourier expansion techniques. The temperature, the displacement, and the stress distributions are represented graphically. A comparison was made with the results obtained in the case of temperature-independent mechanical and thermal properties.     

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

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.     

State Space Approach for Conducting Magneto-Thermoelastic Medium with Variable Electrical and Thermal Conductivity Subjected to Ramp-Type Heating

The equations of magneto-thermoelasticity with one relaxation time with variable electrical and thermal conductivity for one-dimensional problems are cast into matrix form using the state-space and Laplace transform techniques. The resulting formulation is applied to a half-space subjected to ramp-type heating and traction free. The inversion of the Laplace transform is carried out using a numerical approach. Numerical results for the temperature, the displacement and the stress distributions are given and illustrated graphically.     

A sub-interface thermal crack problem for bonded dissimilar plates with interfacial thermal resistance

The present work aims to investigate the effect of interfacial thermal resistance on thermal fracture behavior of bonded and composite materials. We consider a sub-interface crack parallel to the interface between two semi-infinite dissimilar plates subjected to remote heat flux thermal loading. A constant thermal resistance is assumed to exist along the interface. The temperature distribution along the crack, the thermal stress intensity factors (TSIFs), and the crack opening/sliding displacements (COD/CSD) are obtained using an integral transform/superposition method. The numerical results for Al₂O₃/Si₃N₄ bimaterial systems show that the magnitude of the mode I TSIF generally decreases with increasing thermal resistance of the interface but increases with increasing thermal resistance for cracks that are very close to the interface. On the other hand, the model II TSIF increases with increasing thermal resistance if the crack is in the Al₂O₃ semi-infinite plate, and decreases if the crack is in the Si₃N₄ semi-infinite plate. The COD/CSD are also significantly influenced by the thermal resistance of the interface.     

A Two-Dimensional Problem for Two Media in the Generalized Theory of Thermoelasticity

The two-dimensional problem for an elastic half-space with a thick layer on its top is considered with the context of the theory of generalized thermoelasticity with one relaxation time. The half-space and the thick layer are composed of different elastic materials. The surface of the upper layer is traction free and subjected to the effect of a thermal shock. Laplace and Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transform.     

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

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks of different lengths in a piezoelectric material strip under thermal loading. The crack faces are assumed to be insulated thermally and electrically. Fourier transform techniques are used to reduce the mixed boundary value problems to two systems of 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 and electric displacement intensity factors.     

THERMAL SINGULAR STRESSES NEAR A CIRCUMFERENTIAL EDGE CRACK IN A SPHERICAL CAVITY UNDER UNIFORM AXIAL HEAT FLOW

The linear thermoelastic problem of a spherical cavity with a circumferential edge crack is solved. The thermal stresses are caused by a uniform heat flow disturbed by the presence of the crack and the cavity. The surfaces of the crack and the cavity are assumed to be insulated. Integral transform techniques are used to reduce the problem concerning the temperature and thermoelastic fields to that of solving two singular integral equations of the first kind. The integral equations are solved numerically and the variation of the thermal stress intensity factor with the crack depth and the crack opening displacement are shown graphically.     

Three-dimensional generalized thermoelastic diffusion and application for a thermoelastic half-space subjected to rectangular thermal pulse

In this article, a model of three-dimensional generalized thermo-diffusion in a half-space thermoelastic medium subjected to permeating gas and the rectangular thermal pulse has been constructed. The half-space is considered to be made of an isotropic homogeneous thermoelastic material. The chemical potential is also assumed to be known on the bounding plane. Laplace transform techniques have been applied, and the solution is obtained in the Laplace transform domain using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method based on a Riemann-sum approximation for the inversion of Laplace transform. The temperature increment, stress, strain, diffusion concentration, and chemical potential distributions are represented graphically. The nonzero value of the relaxation time parameter predicts the finite speed of thermal, mechanical, diffusion waves.     

SHORT TIME SOLUTION FOR A PROBLEM IN MAGNETOTHERMOELASTICITY WITH THERMAL RELAXATION

In this work, we study a problem in electromagnetothermoelasticity with thermal relaxation for a half-space whose surface is subjected to a thermal shock and is laid on a rigid foundation. Laplace transform techniques are used to obtain the solution by a direct approach. Wave propagation in the elastic medium and in the free space, bounding it, is investigated. The solution of the problem is obtained analytically using asymptotic expansions valid for short times. The temperature, displacement, stress, and the induced magnetic and electric field distributions are obtained analytically. The numerical values of these functions are represented graphically.     

Application of fractional order theory of thermoelasticity to a bilayered structure with interfacial conditions

In this work, fractional order theory of thermoelasticity is applied to a bilayered structure being in imperfect thermal and mechanical contact. The model is subjected to a sudden heating at the traction-free end, assumed to be undisturbed at infinity. The heat conduction in each medium is described by the time-fractional heat conduction equations with two fractional order parameters, respectively. An analytical technique based on Laplace transform is adopted. Numerical results are computed and represented graphically, from which the effects of fractional derivative parameters of both media, thermal contact resistance, elastic wave impedance ratio on the responses are discussed.     

A SHORT TIME SOLUTION FOR A PROBLEM IN THERMOELASTICITY OF AN INFINITE MEDIUM WITH A SPHERICAL CAVITY

The problem of a thermoelastic infinite medium with a spherical cavity is considered within the context of the theory of thermoelasticity with two relaxation times. The surface of the cavity is stress free and suddenly subjected to a time-dependent thermal shock. Laplace transform techniques are used. The inverse Laplace transforms are obtained analytically using asymptotic expansions valid for small values of time. Numerical computations for the temperature, the displacement, and stress distribution are carried out and represented graphically.     

THERMAL STRESSES IN A CIRCULAR CYLINDER WITH A CIRCUMFERENTIAL EDGE CRACK UNDER UNIFORM HEAT FLOW

The linear thermoelastic problem of an infinitely long circular cylinder with a circumferential edge crack is solved. The thermal stresses are caused by a uniform heat flow disturbed by the presence of the crack. The crack surfaces and the cylindrical surface are assumed to be insulated. Integral transform techniques are used to reduce the problem to that of solving two singular integral equations of the first kind. The equations are solved numerically, and the variation of the stress intensity factor with the crack depth is shown graphically.     

Thermal Stresses in Multilayer Gun Barrel with Interlayer Thermal Contact Resistance

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 response analysis of a spherical shell embedded in an infinite thermoelastic medium based on a memory-dependent generalized thermoelasticity

In the context of a memory-dependent generalized thermoelasticity, the thermal-induced transient response in an infinite elastic body containing a spherical shell is investigated. A thermal shock is applied on the inner surface of the spherical shell. The infinite body and the spherical shell are assumed to be isotropic but two dissimilar materials. By using an analytical technique based on the Laplace transform along with its numerical inversion, the governing equations of the problem are solved and the non-dimensional physical quantities in the two materials, i.e., temperature, displacement and stress, are obtained and illustrated graphically respectively. In simulation, the accuracy of memory-dependent derivative (MDD) is verified by degrading the present model into L-S model to compare the results obtained from the cases with interfacial thermal resistance and without interfacial thermal resistance. In addition, the effects of the different kernel functions as well as the ratios of the two materials, including the ratios of the density, the thermal-conductivity and the time-delay, on the distributions of the considered variables are obtained and demonstrated graphically respectively.     

Transient responses of a cylindrical lining in a thermoelastic medium based on the discontinuous interfacial model

Abstract

As an important supporting structure in underground engineering, the lining is continuously exposed to harsh environments, such as high temperature and shock. This study takes lining and soil as the thermoelastic mediums of the Lord–Shulman model to investigate the transient responses of a cylindrical lining in thermoelastic mediums under the action of ramp-type heating. By considering the effects of thermal contact resistance and thermal wave impedance of the lining–soil interface, a discontinuous interfacial model was built for the lining–soil interface by adopting a thermal contact resistance model and the reflection and transmission principles of thermal waves. Based on the Laplace transform and its inversion, the solution of the dynamic response of the lining–soil system under the action of ramp-type heating was then obtained. The influences of the thermal contact resistance, thermal wave impedance ratio, thermal conductivity ratio, and specific heat ratio on the temperature increment and displacement were also explored. The comparison of the calculated results with the existing ones verifies the correctness of the results in this study.     

GENERATION OF GENERALIZED MAGNETOTHERMOELASTIC WAVES BY THERMAL SHOCK IN A PERFECTLY CONDUCTING HALF-SPACE

The problem of distribution of thermal stresses and temperature is considered in a perfectly conducting half-space, in contact with a vacuum, permeated by an initial magnetic field when the bounding plane is suddenly heated to a constant temperature. The problem is in the context of generalized magnetothermoelasticity with one relaxation time. The solution is obtained using the method of potentials. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using asymptotic expansions valid for small values of time. Numerical computations for the temperature and stress distributions are carried out and represented graphically. A comparison is made with the results obtained in the absence of a magnetic field.     

Thermal Stress Analysis of an Embedded Crack in a Graded Orthotropic Coating-Substrate Structure

An analysis of a coupled plane thermoelastic problem for a graded orthotropic coating-substrate structure is performed under thermomechanical loading conditions. The crack direction is parallel to the free surface. Applying the superposition principle and Fourier integral transform, the heat conduction and plane elasticity equations lends themselves to the derivation of two sets of Cauchy-type singular integral equations. The thermal stress intensity factors are defined and evaluated. In the numerical results, the effects of the orthotropy parameters, thermoelastic non-homogeneity parameters, and dimensionless thermal resistance on the temperature distribution and the thermal stress intensity factors (TSIFs) are studied. The obtained results can be used to design graded orthotropic coating-substrate structures under thermomechanical loading.     

Nonlocal Thermoelasticity Theory for Thermal-Shock Nanobeams with Temperature-Dependent Thermal Conductivity

In this work, a model of nonlocal generalized thermoelasticity with one thermal relaxation time is used to consider the vibration behavior of an Euler-Bernoulli (E-B) nanobeam. The thermal conductivity of the nanobeam is assumed to be temperature-dependent. The nonlocality brings in an internal length scale in the formulation and, thus, allows for the interpretation of size effects. The governing partial differential equations are solved in the Laplace transform domain by adopting the state-space approach of modern control theory. The inverse of Laplace transforms are numerically computed using Fourier expansion techniques. The distributions of the lateral vibration, the temperature, the axial displacement and the bending moment of the nanobeam are determined. The effect of thickness and variability of thermal conductivity, as well as the influence of the nonlocal parameter are investigated.     

Wave packet enriched finite element for generalized thermoelasticity theories for thermal shock wave problems

A unified enriched finite element (FE) formulation for two generalized thermoelsaticity theories is developed for the transient thermal shock problems in one and two dimensional domains. Both the displacement and temperature field interpolations are enriched with harmonic functions defined in the local element coordinates. The coupled field finite element equations are derived using the generalized Hamilton’s principle and solved directly in time domain using the standard Newmark-β time integration technique as opposed to the transform techniques usually adopted for thermal shock problems. The method is assessed in comparison with the Laplace transform based analytical solutions and FE solutions with dynamic meshing available in the literature. It is shown that the present solution with a static uniform mesh captures the sharp discontinuities in the temperature and displacement fields and the wave properties of heat conduction very accurately, practically eliminating the severe drawbacks of the conventional FE solutions such as the spurious undulations and flattening out, while maintaining better computational e?ciency.