Generalized Thermoelastic Problem of a Thick Plate Under Axisymmetric Temperature Distribution

Sherief, Hany H.; Hamza, Farid A.

doi:10.1080/01495739408946271

Cited by 69 publications

(30 citation statements)

References 12 publications

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“…The fundamental solutions for the spherically symmetric spaces were obtained by Sherief [45]. Sherief and Hamza [46] have solved some two-dimensional problems and studied the wave propagation in this theory. El-Maghraby and Youssef [47] used the state-space approach to solve a thermomechanical shock problem.…”

Section: Introductionmentioning

confidence: 98%

Two-Temperature Generalized Thermoelastic Interactions in an Infinite Body with a Spherical Cavity

Banik

Kanoria

2011

Int J Thermophys

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This paper is concerned with the determination of the thermoelastic displacement, stress, conductive temperature, and thermodynamic temperature in an infinite isotropic elastic body with a spherical cavity in the context of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature Green-Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation introducing the unified parameters. The medium is assumed initially quiescent. 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 (a) the state-space approach and (b) the eigenvalue approach for any set of boundary conditions. The general solution obtained is applied to a specific problem when the boundary of the cavity is subjected to thermomechanical loading. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The computed results for thermoelastic stresses, conductive temperature, and thermodynamic temperature are shown graphically for the Lord Shulman model and for two models of Green-Naghdi and the effects of two temperatures are discussed. A comparative study of the two methods has also been carried out.

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Section: Introductionmentioning

confidence: 98%

Two-Temperature Generalized Thermoelastic Interactions in an Infinite Body with a Spherical Cavity

Banik

Kanoria

2011

Int J Thermophys

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“…The fundamental solutions for the spherically symmetric spaces were obtained by Sherief [34]. Sherief and Anwar [31,32] have solved some two dimensional problems, while Sherief and Hamza [33] have solved some two dimensional problems and studied the wave propagation in this theory. El-Maghraby and Youssef [18] used the state space approach to solve a thermomechanical shock problem.…”

Section: Introductionmentioning

confidence: 98%

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

Youssef

Al-Harby

2007

Arch Appl Mech

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In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech 26(4):470-475 2005a, IMA J Appl Math, pp 1-8, 2005). The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and ramp-type heating). The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters.

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“…. , 8). Proper selection of these constants will effect solution duration time and solution convergence.…”

Section: <1mentioning

confidence: 97%

Generalized coupled thermoelasticity of functionally graded cylindrical shells

Bahtui

Eslami

2006

Numerical Meth Engineering

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SUMMARYIn this paper, the response of a circular cylindrical thin shell made of the functionally graded material based on the generalized theory of thermoelasticity is obtained. The governing equations of the generalized theory of thermoelasticity and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. Thermoelasticity with second sound effect in cylindrical shells based on the Lord-Shulman model is compared with the Green-Lindsay model. A second-order shear deformation shell theory, that accounts for the transverse shear strains and rotations, is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain is used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The effects of temperature field for linear and non-linear distributions across the shell thickness are examined. The results are validated with the known data in the literature.

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Generalized Thermoelastic Problem of a Thick Plate Under Axisymmetric Temperature Distribution

Cited by 69 publications

References 12 publications

Two-Temperature Generalized Thermoelastic Interactions in an Infinite Body with a Spherical Cavity

Two-Temperature Generalized Thermoelastic Interactions in an Infinite Body with a Spherical Cavity

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

Generalized coupled thermoelasticity of functionally graded cylindrical shells

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