Abstract
This article is concerned with the determination of temperature, displacement, and thermal stresses in a thin circular plate due to uniform internal energy generation within it. The fixed circular edge (r=a) is kept at zero temperature and the upper (z=h) and lower (z=0) surfaces are thermally insulated. The governing heat conduction equation has been solved using finite Hankel transform technique. The results are obtained in a series form in terms of Bessel’s functions. The results for temperature, displacement, and stresses have been computed numerically and illustrated graphically.
Highlights
During the second half of the twentieth century, non-isothermal problems of the theory of elasticity became increasingly important
The results presented here should prove useful in engineering problem in the determination of the state of strain in thin circular plate
To obtain the expression of the function (r, z), we develop the finite Hankel transform and its inverse transform over the variable r in the range 0 ≤ r ≤ a defined in Sneddon (1972) as a
Summary
During the second half of the twentieth century, non-isothermal problems of the theory of elasticity became increasingly important. Studying the two-dimensional steady-state temperature distribution of a thin circular plate due to uniform internal energy generation. Nowacki (1957) determined the steady-state thermal stresses in a circular plate subjected to an axisymmetric temperature distribution on the upper surface with zero temperature on the lower surface and with the circular edge thermally insulated. Gaikwad and Ghadle (2010) solved the quasi-static thermal stresses of an infinitely long circular cylinder having constant initial temperature under steady-state field. Gaikwad and Ghadle (2012) solved non-homogeneous heat conduction problem and obtained thermal deflection due to internal heat generation in a thin hollow circular disk. No literature on steady-state temperature distribution and thermal stresses of a thin circular plate due to internal heat generation has been published. The results presented here should prove useful in engineering problem in the determination of the state of strain in thin circular plate
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