Analysis of Thermal-Bending Stresses in a Simply Supported Annular Sector Plate

Document Type: Research Paper

Authors

1 Department of Mathematics, Mahatma Gandhi Science College, Armori, Gadchiroli, India

2 Department of Mathematics, Sushilabai Bharti Science College, Arni, Yavatmal, India

10.22034/jsm.2019.566121.1275

Abstract

The present article deals with the analysis of thermal-bending stresses in a heated thin annular sector plate with simply supported boundary condition under transient temperature distribution using Berger’s approximate methods. The sectional heat supply is on the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the solution of heat conduction is obtained by the classical method. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using thermally induce resultant moment and resultant forces. The numerical calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the results for temperature, deflection, resultant bending moments and thermal stresses have been illustrated graphically with the help of MATHEMATICA software.

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[1] Hetnarski R. B.,2012, Encyclopedia of Thermal Stresses, Springer.
[2] Nowacki W., 1962, Thermoelasticity, Addison Wesley, NY.
[3] Chia C. Y., 1978, Nonlinear Analysis of Plates, McGraw Hill.
[4] Berger H.M.,1955, A new approach to an analysis of large deflection of plates, Journal of Applied Mechanics 22: 465-472.
[5] Tauchert T. R., 2014, Large Plate Deflections, Berger’s Approximation, Encyclopedia of Thermal Stresses, Springer, Dordrecht.
[6] Basuli S., 1968, Large deflection of plate problems subjected to normal pressure and heating, Indian Journal of Mechanics and Mathematics 6(1): 1-14.
[7] Biswas P., 1976, Large deflection of a heated semi-circular plate under stationary temperature distribution, Proceedings Mathematical Sciences 83(5): 167-174.
[8] Datta S., 1976, Large deflection of a semi-circular plate on elastic foundation under a uniform load, Proceedings of the Indian Academy of Sciences - Section A 83(1): 21-32.
[9] Nowinski J.L., Ohnabe H., 1972, On certain inconsistencies in Berger equations for large deflections of elastic plates, International Journal of Mechanical Sciences 14: 165-170.
[10] Iwinski T., Nowinski J. L., 1957, The problem of large deflections of orthotropic plates, Archiwum Mechaniki Stosowanej 9: 593-603.
[11] Nowinski J. L., 1958, MRC Technical Summary Report No.34, Mathematics Research Center, US Army University of Wisconsin.
[12] Nowinski J. L., 1958, MRC Technical Summary Report No.42, Mathematics Research Center, US Army University of Wisconsin.
[13] Nowinski J. L., 1958, MRC Technical Summary Report No.67, Mathematics Research Center, US Army University of Wisconsin.
[14] Okumura I.A., Honda Y., Yoshimura J., 1989, An analysis for thermal-bending stresses in an annular sector by the theory of moderately thick plates, Structural Engineering 6(2): 347-356.
[15] Wang C.M., Lim G.T., 2000, Bending solutions of sectorial Mindlin plates from Kirchhoff plates, Journal of Engineering Mechanics 126(4): 367-372.
[16] Golmakani M.E., Kadkhodayan M., 2013, Large deflection thermoelastic analysis of functionally graded stiffened annular sector plates, International Journal of Mechanical Sciences 69(1): 94–106.
[17] Eren I., 2013, Analyses of large deflections of simply supported nonlinear beams, for various arc length functions, Arabian Journal for Science and Engineering 38(4): 947-952.
[18] Sitar M., Kosel F., Brojan M., 2014, A simple method for determining large deflection states of arbitrarily curved planar elastica, Archive of Applied Mechanics 84(2): 263-275.
[19] Bakker M.C.M., Rosmanit M., Hofmeyer H., 2008, Approximate large-deflection analysis of simply supported rectangular plates under transverse loading using plate post-buckling solutions, Thin-Walled Structures 46(11): 1224-1235.
[20] Jang T.S., 2014, A general method for analysing moderately large deflections of a non-uniform beam: an infinite Bernoulli-Euler-von Kármán beam on a nonlinear elastic foundation, Acta Mechanica 225(7): 1967-1984.
[21] Choi I.H., 2017, Low-velocity impact response analysis of composite pressure vessel considering stiffness change due to cylinder stress, Composite Structures 160(15): 491-502.
[22] Bhad P., Varghese V., Khalsa L., 2017, A modified approach for the thermoelastic large deflection in the elliptical plate, Archive of Applied Mechanics 87(4): 767-781.
[23] Boley B. A., Weiner J.H., 1960, Theory of Thermal Stresses, John Wiley and Sons, New York.
[24] Ventsel E., Krauthammer T., 2001, Thin Plates and Shells-Theory Analysis, and Applications Marcel Dekker, New York.
[25] Wang M. Z., Xu X.S.,1990, A generalization of Almansi’s theorem and its application, Applied Mathematical Modelling 14: 275-279.