Mathematical Modeling of Thermoelastic State of a Thick Hollow Cylinder with Nonhomogeneous Material Properties

Journal of Solid Mechanics

مقاله 11، دوره 10، شماره 1، خرداد 2018، صفحه 142-156   

نوع مقاله: Research Paper

نویسندگان

V. R Manthena^{* 1}؛ N.K Lamba²؛ G.D Kedar¹

¹Department of Mathematics, RTM Nagpur University, Nagpur, India

²Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India

چکیده

The object of the present paper is to study heat conduction and thermal stresses in a hollow cylinder with nonhomogeneous material properties. The cylinder is subjected to sectional heating at the curved surface. All the material properties except for Poisson’s ratio and density are assumed to be given by a simple power law in the axial direction. A solution of the two-dimensional heat conduction equation is obtained in the transient state. The solutions are obtained in the form of Bessel’s and trigonometric functions. For theoretical treatment, all the physical and mechanical quantities are taken as dimensional, whereas we have considered non-dimensional parameters, for numerical analysis. The influence of inhomogeneity on the thermal and mechanical behaviour is examined. The transient state temperature field and its associated thermal stresses are discussed for a mixture of copper and tin metals in the ratio 70:30 respectively. Numerical calculations are carried out for both homogeneous and nonhomogeneous cylinders and are represented graphically.

کلیدواژه‌ها

Hollow cylinder؛ Heat conduction؛ Thermal stresses؛ Inhomogeneity؛ Shear modulus

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