Generalized thermoelasticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

Abstract

In this paper, we construct the equations of generalized thermoelasticity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.

Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer

“…The copper material was chosen for purposes of numerical evaluations and the constants of the problem were taken as follows [20]: λ 0 =7.76×10 10 kg/(m·s 2 ), μ 0 =3.86×10 10 kg/(m·s 2 ), T 0 = 293 K, K 0 =3.86×10 2 kg·m/(K·s 3 ), c e =3.831×10 2 m 2 /(K·s 2 ), T 1 =1, l=4, ρ 0 =8.954×10 3 kg/m 3 , α t =17.8×10 −6 K −1 , τ T =0.1, τ q =0.15. Figures 1−3 display the temperature, displacement and the stress distributions for wide range of x 0≤x≤l for two different theories ( three-phase lag model 3PHL and Green-Naghdi model of type III GNIII) in presented two values of time t=0.5 and t=1 with n=0.5 and α=0.5.…”

Thermoelastic interaction in a thermally conducting cubic crystal subjected to ramp-type heating

“…This method is so general that it can be applied to a wide variety of engineering problems including heat transfer, fluid, mechanics, chemical processing etc. For the finite element analysis, one can refer [23][24][25][26][27][28][29][30][31][32][33][34][35]. In the finite element method, the displacement components u, w, and temperature change T are related to the corresponding nodal values by where m denotes the number of nodes per element, and N i are the shape functions.…”

Electro-magneto-thermo-elastic response of infinite functionally graded cylinders without energy dissipation

“…A further benefit of this method is that it allows physical effects to be visualized and quantified regardless of experimental limitations. On the other hand, the finite element method in different generalized thermoelastic problems has been applied by many authors (see for instant [23][24][25][26][27]). The finite element equations of a generalized thermoelasticity problem can be readily obtained by following standard procedure.…”