Generalized Thermoelastic Problem of an Infinite Body with a Spherical Cavity under DualPhaseLags
R. Karmakar, A. Sur, M. Kanoria
University of Calcutta, Kolkata, West Bengal, India
Keywords: обобщенная двухтемпературная теория термоупругости, модель с двумя фазами запаздывания, пространство состояний, векторноматричное дифференциальное уравнение, twotemperature generalized thermoelasticity, dualphaselag model, statespace approach, vectormatrix differential equation
Abstract
The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the twotemperature generalized thermoelasticity theory (2TT). The twotemperature LordShulman (2TLS) model and twotemperature dualphaselag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the statespace approach. The expressions for the conductive temperature and elongation are obtained for at small times. The numerical inversion of the transformed solutions is carried out by using the Fourierseries expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the LordShulman and dualphaselag models.
