Generalized Thermo Elasticity in an Infinite Nonhomogeneous Solid Having a Spherical Cavity Using DPL Model

Author(s)
Ahmed Elsayed Abouelrega

Abstract

The induced temperature, displacement, and stress fields in an infinite nonhomogeneous elastic medium having a spherical cavity are obtained in the context dual-phase-lag model. The surface of the cavity is stress free and is subjected to a thermal shock. The material is elastic and has an in¬homogeneity in the radial direction. The type of non homogeneity is such that the elastic constants, thermal conductivity and density are propor¬tional to the nth power of the radial distance. The solutions are obtained analytically employing the Laplace transform technique. The numerical inversion of the transforms is carried out using Fourier series expansions. The stresses, temperature and displacement are computed and presented graphically. A comparison of the results for different theories is presented.

The induced temperature, displacement, and stress fields in an infinite nonhomogeneous elastic medium having a spherical cavity are obtained in the context dual-phase-lag model. The surface of the cavity is stress free and is subjected to a thermal shock. The material is elastic and has an in¬homogeneity in the radial direction. The type of non homogeneity is such that the elastic constants, thermal conductivity and density are propor¬tional to the nth power of the radial distance. The solutions are obtained analytically employing the Laplace transform technique. The numerical inversion of the transforms is carried out using Fourier series expansions. The stresses, temperature and displacement are computed and presented graphically. A comparison of the results for different theories is presented.

Keywords

Generalized Thermo Elasticity, Nonhomogeneous, Functionally Graded Material (FGM), Laplace Transform, Three-Phase-Lag Model

Generalized Thermo Elasticity, Nonhomogeneous, Functionally Graded Material (FGM), Laplace Transform, Three-Phase-Lag Model

Cite this paper

nullA. Abouelrega, "Generalized Thermo Elasticity in an Infinite Nonhomogeneous Solid Having a Spherical Cavity Using DPL Model,"*Applied Mathematics*, Vol. 2 No. 5, 2011, pp. 625-632. doi: 10.4236/am.2011.25083.

nullA. Abouelrega, "Generalized Thermo Elasticity in an Infinite Nonhomogeneous Solid Having a Spherical Cavity Using DPL Model,"

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