Magneto-thermoelastic problem in non-homogeneous isotropic cylinder

In the present paper, we investigate the generation of thermal stresses in a nonhomogeneous anisotropic solid cylinder rotating about the z-axis at a constant angular velocity in the presence of a magnetic field. The governing equations are solved numerically using the boundary-element method (BEM) and numerical results are obtained for the variation of the temperature, displacements, and stresses along x-axis. The effect of nonhomogeneity is investigated.

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“…In nondimensional form the two-dimensional thermoelastic problem is described by the following system of equations (see [3,7])…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…For further details on the simplified Maxwell's equations for perfectly conducting elastic medium and for the adjoining free space, refer to the recent work of Abd-Alla et al [3].…”

Section: Displacement Fieldmentioning

confidence: 99%

Magneto-thermo-elastic problem of a rotating nonhomogeneous anisotropic solid cylinder

2007

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“…In general, it is not easy to obtain analytical solutions to a dynamical magneto-thermo-viscoelastic problem in anisotropic materials. therefore, an important number of engineering and mathematical papers devoted to the numerical solution have studied the overall behavior of such materials (Oden and Armstrong, 1971;Ting and Chen, 1982;Dargush and Banerjee, 1991;Misra, et al, 1992;Chen, et al, 2009;Tsai, 2009;Xing and Makinouchi, 2002;El-Naggar, et al, 2002Abd-Alla, et al, 2003, 2008Wu and Chu, 2004;Baksi, et al, 2006;Hosseini, et al, 2007;Huang and Rosakis, 2007;Fahmy, 2008Fahmy, , 2009Fahmy and El-Shahat, 2008;Feng, et al, 2008;Othman and Song, 2008;Damanpack, et al (2013);Rafieipour, et al (2013)). …”

Section: Introductionmentioning

confidence: 99%

A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures

Fahmy

2014

Lat. Am. j. solids struct.

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A numerical computer model, based on the dual reciprocity boundary element method (DRBEM) for studying the generalized magneto-thermo-visco-elastic stress waves in a rotating functionally graded anisotropic thin film/substrate structure under pulsed laser irradiation is established. An implicit-implicit staggered algorithm was proposed and implemented for use with the DRBEM to get the solution for the temperature, displacement components and thermal stress components through the structure thickness. A comparison of the results for different theories is presented in the presence and absence of rotation. Some numerical results that demonstrate the validity of the proposed method are also presented. Key wordsMagneto-Thermoviscoelasticity; Rotation; Functionally graded materials; Anisotropic; Dual Reciprocity Boundary Element Method; Distribution.A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures 1 INTRODUCTION Biot (1956) introduced the theory of coupled thermoelasticity to overcome the first shortcoming in the theory of uncoupled thermoelasticity introduced by Duhamel (1837) and Neuman (1885) where it predicts two phenomena not compatible with physical observations. First, the equation of heat conduction of this theory does not contain any elastic terms. Second, the heat equation is of a parabolic type, predicting infinite speeds of propagation for heat waves. Later on, generalized theories of thermoelasticity were introduced in order to eliminate the shortcomings of the uncoupled thermoelasticity. Lord and Shulman (1967) developed the theory of coupled thermoelasticity with one relaxation time by constructing a new law of heat conduction to replace the classical Fourier's law. This law contains the heat flux vector as well as its time derivative. It contains also new constant that acts as relaxation time. Since the heat equation of this theory is of the wave-type, it automatically ensures finite speeds of propagation for heat and elastic waves. Green and Lindsay (1972) cluded a temperature rate among the constitutive variables to develop a temperature-ratedependent thermoelasticity that does not violate the classical Fourier's law of heat conduction when the body under consideration has a center of symmetry; this theory also predicts a finite speed of heat propagation. This theory is known as the theory of thermoelasticity with two relaxation times. According to these theories, heat propagation should be viewed as a wave phenomenon rather than diffusion one Relevant theoretical developments on the subject were made by Naghdi (1992, 1993) they developed three models for generalized thermoelasticity of homogeneous isotropic materials which are labeled as model I, II and III. These theories of thermoelasticity LS, GL and GN theories are known as the generalized theories of thermoelasticity with finite thermal wave speed. In general, it is not easy to obtain analytical solutions to a dynamical magneto-...

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“…Thus, two kinds of stress are generated: one is magnetic stress caused by Lorentz's force and the other is the thermal stress caused by eddy current loss. Many investigations have been conducted in the field of magnetoelasticity or magnetothermoelasticity [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. However, up to now, there have only been a few studies of the magnetothermoelastic behavior of functionally gradient materials.…”

Section: Introductionmentioning

confidence: 99%

“…Using the finite-difference method, Abd-Alla et al [9,10], solved the magnetothermoelastic problem of a non-homogeneous isotropic cylinder in the presence of a heat source. Wang and Lu [11] presented an analytical method to analyze the magnetothermoelastic waves and perturbation of the magnetic field vector produced by thermal shock in a solid conducting cylinder.…”

Section: Introductionmentioning

confidence: 99%

Magnetothermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields

et al. 2008

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In this article, an analytical method is developed to obtain the response of magnetothermoelastic stress and perturbation of the magnetic field vector for a thick-walled spherical functionally graded materials (FGM) vessel. The vessel, which is placed in a uniform magnetic field, is subjected to an internal pressure and transient temperature gradient. Using the Hankel and Laplace transform techniques, the dynamic equation of magnetothermoelastic is solved and the radial and circumferential stresses as well as the perturbation of the magnetic field vector for a typical material are obtained. Moreover, the effect of magnetic field vector and material inhomogeneity on the stresses is investigated.Keywords Magnetothermoelasticity · Functionally graded material · Thick hollow sphere · Perturbation of magnetic field vector · Transient response List of symbols U , u r displacement vector and radial displacement (m), σ rr , σ θθ radial and circumferential stresses (N/m 2 ) λ 0 , G 0 , γ 0 , ρ 0 , and Lame's constant (N/m 2 ), shear modulus (N/m 2 ), thermal µ 0 modulus (N/Km 2 ), mass density (kg/m 3 ) and magnetic permeability coefficient (H/m), respectively m material grading exponent r radius (m) T (r, t) temperature change (K) t, a, b time (s), inner and outer radii of the FGM hollow sphere (m) H , h magnetic intensity vector, perturbation of magnetic field vector J electric current density vector e perturbation of electric field vector f φφ Lorentz's force (kg/m 2 , s 2 ) P i (t), P o (t) internal and external pressure of FGM hollow sphere (N/m 2 ) u r 0 (r ), v r 0 (r ) initial radial displacement (m), initial speed (m/s) V e elastic wave speed of homogeneous sphere (m/s) V t magnetothermoelastic wave speed (m/s) ω natural frequency of the FGM hollow sphere (1/s)

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Magneto-thermoelastic problem in non-homogeneous isotropic cylinder

Cited by 55 publications

References 10 publications

Magneto-thermo-elastic problem of a rotating nonhomogeneous anisotropic solid cylinder

Magneto-thermo-elastic problem of a rotating nonhomogeneous anisotropic solid cylinder

A Comuputerized DRBEM model for generalized magneto-thermo-visco-elastic stress waves in functionally graded anisotropic thin film/substrate structures

Magnetothermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields

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