Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading

Abstract

This paper presents the problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity, and the surface is assumed initially quiescent. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite time of rise of temperature, stress, displacement, and strain. The problem has been solved analytically using a direct approach. The derived analytical expressions have been computed for a specific situation. Numerical results for the temperature distribution, thermal stress, displacement, and strain are represented graphically. A comparison is made with the results predicted by the three theories.

Generalized Magneto-thermo-microstretch Response of a Half-space with Temperature-dependent Properties During Thermal Shock

“…The second jump in stress σ zz distribution is elastic wave front. According to the speed of propagation of elastic wave, the location of the elastic wave front should be z=0.2 at t=0.2, we see that results given by Figure.6 are in good agreement with the predictions, while these phenomenon didn't appear in the previous studies (Sherief et al 1981(Sherief et al , 1986(Sherief et al , 2004Youssef et al , 2005Youssef et al , 2009Othman et al 2007Othman et al , 2014aOthman et al , 2014b. But at time point t=0.5, the location of the elastic wave front cannot be predicted exactly, this is because that the temperature dependent properties make the speed of the elastic wave increase significantly at time point t=0.5.…”

“…This further shows the results obtained by using FEM are accurate and reliable. In Figure.3, it can be seen that there exists a distinct temperature step on thermal wave front in the distribution of temperature at t=0.15 for generalized theory (G-L or L-S), while there isn't this phenomenon and the finite speed of propagation of thermal wave isn't depicted in the previous studies (Sherief et al 1981(Sherief et al , 1986(Sherief et al , 2004Youssef et al , 2005Youssef et al , 2009Othman et al 2007Othman et al , 2014aOthman et al , 2014b. The temperature step on thermal wave front in the distribution of temperature shown at t=0.5 in Figure.1).…”

“…In the last three decades, many problems that have been solved were in the context of the theory of L-S or G-L. The researches can be divided into two categories: one is to study the transient responses in time domain, such as, Sherief et al (1981Sherief et al ( , 1986Sherief et al ( , 2004, Youssef et al ( , 2005Youssef et al ( , 2009), Tian et al (2005Tian et al ( , 2006Tian et al ( , 2011aTian et al ( , 2011b, Othman et al (2007Othman et al ( , 2014aOthman et al ( , 2014b and the other is to investigate the response of steady state in frequency domain, for example, Kumar et al (2014aKumar et al ( , 2014b and Sihgh (2010Sihgh ( , 2011. Here the main attention is paied to the transient responses in time domain for thermal shock problem.…”

State-space approach to vibration of gold nano-beam induced by ramp type heating

“…Youssef with many authors investigated many applications in which the ramp-type heating is used [15][16][17][18][19][20][21].…”

Two-Temperature Generalized Thermopiezoelasticity for One Dimensional Problems – State Space Approach

“…Piezoelectric rod direction be parallel with the axial direction. The corresponding boundary conditions may be written as follows [20]:…”