3D Thermoelastic Interactions in an Anisotropic Lastic Slab Due to Prescribed Surface Temparature

Subject Areas : Engineering

Gh Debkumar ¹ , L Abhijit ² , R Kumar ³ , R Surath ⁴

1 - Department of Mathematics, Jadavpur University, Kolkata, India
2 - Department of Mathematics, Jadavpur University, Kolkata, India
3 - Department of Mathematics, Kurukshetra University, India
4 - Department of Mathematics, Brainware College of Engineering, Barasat, Kolkata, India

Received: 2018-05-30 Accepted : 2018-07-04 Published : 2018-09-30

Keywords: eigenvalue, Differential equation, Generalized thermoelasticity, Normal mode analysis and vector-matrix,

Abstract :

The present paper is devoted to the determination of displacement, stresses and temperature from three dimensional anisotropic half spaces due to presence of heat source. The normal mode analysis technique has been used to the basic equations of motion and generalized heat conduction equation proposed by Green-Naghdi model-II [1]. The resulting equation are written in the form of a vector –matrix differential equation and exact expression for displacement component, stresses, strains and temperature are obtained by using eigen value approach. Finally, temperature, stresses and strain are presented graphically and analyzed.

References:

[1] Chandrasekharaiah D.S., Srinath K.S., 1998, Thermoelastic plane waves without energy dissipation in a rotating body, Mechanics Research Communications 24: 551-560.
[2] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[3] Green A.E., Naghdi P.M., 1991, A re- examination of the basic postulate of thermo-mechanics, Proceedings of the Royal Society of London 432: 171-194.
[4] Green A.E., Naghdi P.M., 1992, An unbounded heat wave in an elastic solid, Journal of Thermal Stresses 15: 253-264.
[5] Green A.E., Naghdi P.M., 1992, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189-208.
[6] Lord H.W., Shulman Y.A., 1967, Geeneralized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
[7] Roychoudhuri S.K., Bandyopadhyay N., 2004, Thermoelastic wave propagation in a rotating elastic medium without energy dissipation, International Journal of Mathematics and Mathematical Sciences 1: 99-107.
[8] Roychoudhuri S.K., Dutta P.S., 2005, Thermoelastic interaction without energy dissipation in an infinite solid with distributed periodically varing heat sources, International Journal of Solid and Structures 42: 4192-4203.
[9] Chattopadhyay A., Rogerson G.A., 2001, Wave reflection in slightly compressible finitely deformed elastic media, Archives of Applied Mathematics 71: 307-316.
[10] Sarkar N., Lahiri A., 2013, The effect of gravity field on the plane waves in a fiber- reinforced two temperature magneto thermoelastic medium under Lord- Shulman theory, Journal of Thermal Stresses 36: 895-914.
[11] Sarkar N., Lahiri A., 2012, A three dimensional thermoelastic problem for a half Space without energy dissipation, International Journal of Engineering Science 51: 310-325.
[12] Sharma J.N., Chouhan R.S., 1999, On the problem of body forces and heat sources in thermoelasticity without energy dissipation, Indian Journal of Pure and Applied Mathematics 30: 595-610.