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Effects of thermal relaxations on thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity

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Abstract

Thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity are studied. The cavity surface is subjected to ramp-type heating of its internal boundary, which is assumed to be traction free. Lord–Shulman and Green–Lindsay models for the generalized thermoelasticity theories are selected since they allow for second-sound effects and reduce to the classical model for an appropriate choice of the parameters. The temperature, radial displacement, radial stress, and hoop stress distributions are computed numerically using the finite-element method (FEM). The results are presented graphically for different values of the thermal relaxation times using the three different theories of generalized thermoelasticity. Excellent agreement is found between the finite-element analysis and analytical and classical solutions.

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Abbreviations

C ij :

elastic moduli

ρ:

density of the medium

C v :

specific heat at constant strain

β ij :

stress–temperature coefficients

t :

time

T :

temperature

T o :

reference temperature

K r :

thermal conductivity

Q :

heat source

t 1, t 2, t 3 :

relaxation times

t o :

time of rise of temperature

Γ:

domain

δu, δT :

weighting functions

τ ij :

components of stress tensor

u i :

components of displacement vector

F i :

body-force vector

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

    Ibrahim A. Abbas & Abo-el-nour N. Abd-alla

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  1. Ibrahim A. Abbas
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  2. Abo-el-nour N. Abd-alla
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Correspondence to Ibrahim A. Abbas.

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Abbas, I.A., Abd-alla, Aen.N. Effects of thermal relaxations on thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity. Arch Appl Mech 78, 283–293 (2008). https://doi.org/10.1007/s00419-007-0156-7

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  • DOI: https://doi.org/10.1007/s00419-007-0156-7

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