A problem on thermoelastic interactions in an infinite medium with a cylindrical hole in generalized thermoelasticity III

The aim of the present article is to study the thermoelastic interactions in an infinite elastic medium with a cylindrical hole in the context of generalized thermoelasticity III, recently developed by Green and Nagdhi [1]. The boundary of the hole is assumed to be stress free and is subjected to a ramp type heating. In order to make a comparison between this thermoelastic model with other thermoelastic models, the problem is formulated on the basis of three different theories of thermoelasticity, namely. the extended thermoelasticity proposed by Lord and Shulman [2] the thermoelasticity without energy dissipation (Green and Nagdhi [3]) and thermoelasticity with energy dissipation (thermoelasticity type III [1]) in a unified way. The solutions for displacement, temperature and stresses are obtained with the help of Laplace transform procedure. Firstly the short time approximated solutions for three different theories have been obtained analytically. Then following a numerical method for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained from different models of generalized thermoelasticity.