Thermoelastic theories on elliptical profile objects: an overview & prospective. (English) Zbl 1370.74044

Bhad, Pravin; Varghese, Vinod; Khalsa, Lalsingh

Int. J. Adv. Appl. Math. Mech. 4, No. 2, 12-20 (2016).

Summary: The article investigates the present review of thermoelastic theories on elliptic objects in elliptical coordinate system published on paper after 1950. The main theme of the thermoelastic problems on elliptic structures is to establish operational methods to solve the governing differential equations. In the thermoelastic problems, we have considered few practical problems of technical interest taking into account the elliptical shape geometry by using numerical procedures. Furthermore, by considering a circle as a special kind of ellipse, it is seen that the temperature distribution and comparative study of a circular solution can be derived as a special case from the present mathematical solution.

MSC:

74F05	Thermal effects in solid mechanics
74-03	History of mechanics of deformable solids
01A60	History of mathematics in the 20th century
01A61	History of mathematics in the 21st century

Keywords:

elliptical objects; temperature distribution; thermal stresses; vibration; deflection; integral transform