Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

Ghosh, Manasi; Kanoria, M.

doi:10.1007/s10483-008-1002-2

Cited by 28 publications

(5 citation statements)

References 32 publications

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“…Mukhopadhyay [ 27 ] discussed thermally induced vibrations of an unbounded viscoelastic body including a spherical hole in the framework of G–L theory. Ghosh and Kanoria [ 28 ] determined thermoelastic quantities in a functionally graded (FG) spherically unbonded body including a spherical hole in the framework of G–L theory. Kanoria and Ghosh [ 29 ] examined thermoelastic exchanges in an FG hollow sphere in the framework of the G–L model.…”

Section: Introductionmentioning

confidence: 99%

Magneto-Thermoelastic Response in an Unbounded Medium Containing a Spherical Hole via Multi-Time-Derivative Thermoelasticity Theories

2022

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This article introduces magneto-thermoelastic exchanges in an unbounded medium with a spherical cavity. A refined multi-time-derivative dual-phase-lag thermoelasticity model is applied for this reason. The surface of the spherical hole is considered traction-free and under both constant heating and external magnetic field. A generalized magneto-thermoelastic coupled solution is developed utilizing Laplace’s transform. The field variables are shown graphically and examined to demonstrate the impacts of the magnetic field, phase-lags, and other parameters on the field quantities. The present theory is examined to assess its validity including comparison with the existing literature.

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Section: Introductionmentioning

confidence: 99%

Magneto-Thermoelastic Response in an Unbounded Medium Containing a Spherical Hole via Multi-Time-Derivative Thermoelasticity Theories

2022

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“…Noda and Guo [34] have solved a thermal shock problem for an FGM plate with a surface crack where the thermomechanical properties of the plate were assumed to vary along the thickness direction. Ghosh and Kanoria studied the thermoelastic response in an FGM spherically isotropic infinite elastic medium having a spherical cavity [35] and in an FGM spherically isotropic hollow sphere [36] in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Kar and Kanoria [37] studied thermoelastic stresses, displacements and temperature distribution in an FGM orthotropic hollow sphere due to sudden temperature change on the stress-free boundaries of the hollow sphere in the context of the TEWOED, TEWED and 3P models of generalized thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Generalized thermoelastic interaction in a functionally graded isotropic unbounded medium due to varying heat source with three-phase-lag effect

Banik

Kanoria

2012

Mathematics and Mechanics of Solids

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This paper deals with the problem of thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of the three-phase-lag thermoelastic models, GN ii (TEWOED) and GN iii (TEWED). The governing equations of three-phase-lag thermoelastic model (3P), generalized thermoelasticity without energy dissipation (GN ii) and with energy dissipation (GN iii) for a functionally graded material (i.e., a material with spatially varying material properties) are established. The governing equations are expressed in a Laplace–Fourier double transform domain and solved in that domain. Then the inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand are obtained numerically in a complex domain by using Laguerre's method and the inversion of the Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the thermal displacement, temperature and thermal stress are obtained for a hypothetical material. The solution to the analogous problem for homogeneous isotropic material is obtained by taking a suitable non-homogeneity parameter. Finally, the results obtained are presented graphically to show the effect of non-homogeneity on thermal displacement, temperature and thermal stress. A comparison of the results for different theories (three-phase-lag model, GN ii and GN iii) is presented and the effect of non-homogeneity is also shown. In absence of non-homogeneity the results corresponding to the 3P model, GN ii and GN iii model agree with the results of the existing literature.

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“…Based on the classical plate theory, Yang and Shen [3] investigated the dynamic response of functionally graded rectangular thin plates initially stressed by in-plane load and transverse load. Ghosh and Kanoria [4] studied the solution of thermoelastic displacement, stress and temperature about a functionally graded solid isotropic infinite elastic medium containing a spherical cavity by the generalized thermoelastic linear theory (Green and Lindsay theory) which has two relaxation time parameters. The surface of the cavity is stress-free, but it withstands a thermal shock load which changes with time.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Buckling of FGM Shallow Conical Shells under Triangular Pulse Impact Loads

Lin¹,

Deng²,

Xu³

2012

AMR

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In this paper, nonlinear dynamic buckling of FGM shallow conical shells under the action of triangular pulse impact loads are investigated. The nonlinear dynamic governing equation of symmetrically FGM shallow conical shells is built. Using Galerkin method, the nonlinear dynamic governing equation is solved, and the nonlinear dynamic response equation of symmetrically FGM shallow conical shells is obtained. The Runge-Kutta method is introduced to numerically solve the nonlinear dynamic response equation and the impact response curve is achieved. Budiansky-Roth motion criterion expressed by the displacement of the peak of the shell is employed to determine the critical impact buckling load. The influences of geometric parameters and gradient constants on impact buckling are discussed as well.

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Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

Cited by 28 publications

References 32 publications

Magneto-Thermoelastic Response in an Unbounded Medium Containing a Spherical Hole via Multi-Time-Derivative Thermoelasticity Theories

Magneto-Thermoelastic Response in an Unbounded Medium Containing a Spherical Hole via Multi-Time-Derivative Thermoelasticity Theories

Generalized thermoelastic interaction in a functionally graded isotropic unbounded medium due to varying heat source with three-phase-lag effect

Nonlinear Dynamic Buckling of FGM Shallow Conical Shells under Triangular Pulse Impact Loads

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