Quasi-Static Transient Thermal Stresses in an Elliptical Plate due to Sectional Heat Supply on the Curved Surfaces over the Upper Face

Document Type : Research Paper

Authors
Lalsingh Khalsa 1
Ishaque Khan 1
Vinod Varghese 2
1 Department of Mathematics, M.G. College, Armori, Gadchiroli, India
2 Department of Mathematics, S.S.R. Bharti Science College, Arni, India
10.22055/jacm.2017.22068.1123
Abstract
This paper is an attempt to determine quasi-static thermal stresses in a thin elliptical plate which is subjected to transient temperature on the top face with zero temperature on the lower face and the homogeneous boundary condition of the third kind on the fixed elliptical curved surface. The solution to conductivity equation is elucidated by employing a classical method. The solution of stress components is achieved by using Goodier’s and Airy’s potential function involving the Mathieu and modified functions and their derivatives. The obtained numerical results are accurate enough for practical purposes, better understanding of the underlying elliptic object, and better estimates of the thermal effect on the thermoelastic problem. The conclusions emphasize the importance of better understanding of the underlying elliptic structure, improved understanding of its relationship to circular object profile, and better estimates of the thermal effect on the thermoelastic problem.
Keywords
Elliptical plate
Temperature distribution
Thermal stresses
Mathieu function
Subjects
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Journal of Applied and Computational Mechanics
Volume 4, Issue 1
Winter 2018
Pages 27-39