Main Article Content
Abstract
The bending of the rectangular plate exists for a large length comparing with its width as we have considered the simply supported plate. Also, it gets the accuracy, if the plate is attached between enough distance from the ends. This paper concern with the study of bending moment in the rectangular plate by using the thermal stresses. In this paper, we have considered the mathematical model of the unsteady state three-dimensional heat conduction equation for a thick rectangular plate with non-zero temperature initially. We have determined the thermal stresses and the bending moment in the rectangular plate by using the reduced differential transform method. The results are discussed by considering the special cases for copper material. Also, results are shown graphically. The graphs are drawn by using mathematical software Scilab.
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References
- Barletta, A. and Zanchini, E.,"Three dimensional propagation of in a solid bar with rect-angular cross section hyperbolic thermal waves", International Journal of Heat and Mass Transfer,42(1999),219-229.
- Boley, B.A. and Weiner, J. H., Theory of Thermal Stresses, New York, 1960.
- Cattaneo, C., "A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation", Compte Rendus , 247 (1958), 431-433.
- Chaudhari Kamini K. and Sutar C. S. , "Thermoelastic modelling of a Rectangular plate under the hyperbolic heat conduction with an internal heat source", International Journal of
- Mechanical and Production Engineering Research and Development , (9)6 (2019), 859-872.
- Chen, P., "Transient thermal stresses in rectangular plate due to nonuniform heat transfer coecient", Journal of Thermal Stresses , (11)2 (1988), 115-125.
- Deshmukh K.C., Khandait M.V. and Kumar Rajneesh , "Thermal stresses in a simply sup-ported plate with thermal bending moments with heat sources", Materials Physics and Me-
- chanics , 21 (2014), 135-146.
- Jane K.C. and Hong C.C.,"Thermal bending analysis of laminated orthotropic plates by the generalized differential quadrature method", Mechanics Research Communications , (27)2
- (2000), 157-164.
- Mallick, A.,Ranjan R.and Sarkar, P.K., "Effect of heat transfer on thermal stresses in an an-nular hyperbolic n: an approximate analytical solution", Journal of Theoretical and applied Mechanics , (54)2 (2016), 437-448.
- Manseld E.H.Manseld,The bending and stretching of plates (Second Edition ed.) , Cam-bridge University Press.1989.
- Mehta R. C., "Direct search optimization technique for the solution of inverse nonlinear heat conduction problem", Indian Journal of Engineering and Material Sciences, 19 (2012),67-71.
- Mohammed O. Al-Amr, "New applications of reduced differential transform method",Alexandria Engineering Journal , 53 (2014), 243-247.
- Morimoto, T., Tanigawa Y. and Kawamura R., "Thermal bukling analysis of inhomogeneous rectangular plate due to uniform heat supply", Journal of Thermal Stresses , (26)11-12
- (2003), 1151-1170.
- Noda, N., Hetnarski, R.B., Tanigawa, Y., Thermal Stresses, Taylor and Francis, 2003.
- Nowacki, W. , "The state of stress in a thick circular plate due to temperature eld.",Bull.Sci.Acad.Polon Sci. Tech., 5 (1957).
- Ozicik, M., Heat Conduction (Second Edition ed.), John Wiley and Sons,Inc.,1993.
- Sherief, H.H and Anwar,M.N, "Two-dimensional generalized thermoelasticity problem for an innitely long cylinder", Journal of Thermal Stresses , (17)2 (1994), 213-227.
- Srivastava Vineet K., Awasthi Mukesh K. and Chaurasia R.K., "Reduced differential trans-form method to solve two and three dimensional second order hyperbolic telegraph equations", Journal of King Saud University- Engineering Sciences, 29 (2017), 166-171.
- Taha, B. A., "The Use of Reduced Differential Transform Method for Solving Partial Differential Equations with Variable Coecients", Journal of Basrah Researches((Sciences)),(37)4 (2011), 226-233.
- Timoshenko S.and Woinowsky-Krieger S.,Theory of Plates and Shells (Second Edition ed.),McGraw-Hill,1989.
- Yos Sompornjaroensuk and Kraiwood Kiattikomol ,"Bending behaviours of simply supported rectangular plates with an internal line sagged and unsagged supports", Songklanakarin Journal of Science and Technology , (30)1 (2008), 101-107.
- Yuemei Liu and Rui Li, "Accurate bending analysis of rectangular plates with two adjacent edges free and the others clamped or simply supportedbased on new symplectic approach",
- Applied Mathematical Modelling, 34 (2010), 8556-865.
References
Barletta, A. and Zanchini, E.,"Three dimensional propagation of in a solid bar with rect-angular cross section hyperbolic thermal waves", International Journal of Heat and Mass Transfer,42(1999),219-229.
Boley, B.A. and Weiner, J. H., Theory of Thermal Stresses, New York, 1960.
Cattaneo, C., "A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation", Compte Rendus , 247 (1958), 431-433.
Chaudhari Kamini K. and Sutar C. S. , "Thermoelastic modelling of a Rectangular plate under the hyperbolic heat conduction with an internal heat source", International Journal of
Mechanical and Production Engineering Research and Development , (9)6 (2019), 859-872.
Chen, P., "Transient thermal stresses in rectangular plate due to nonuniform heat transfer coecient", Journal of Thermal Stresses , (11)2 (1988), 115-125.
Deshmukh K.C., Khandait M.V. and Kumar Rajneesh , "Thermal stresses in a simply sup-ported plate with thermal bending moments with heat sources", Materials Physics and Me-
chanics , 21 (2014), 135-146.
Jane K.C. and Hong C.C.,"Thermal bending analysis of laminated orthotropic plates by the generalized differential quadrature method", Mechanics Research Communications , (27)2
(2000), 157-164.
Mallick, A.,Ranjan R.and Sarkar, P.K., "Effect of heat transfer on thermal stresses in an an-nular hyperbolic n: an approximate analytical solution", Journal of Theoretical and applied Mechanics , (54)2 (2016), 437-448.
Manseld E.H.Manseld,The bending and stretching of plates (Second Edition ed.) , Cam-bridge University Press.1989.
Mehta R. C., "Direct search optimization technique for the solution of inverse nonlinear heat conduction problem", Indian Journal of Engineering and Material Sciences, 19 (2012),67-71.
Mohammed O. Al-Amr, "New applications of reduced differential transform method",Alexandria Engineering Journal , 53 (2014), 243-247.
Morimoto, T., Tanigawa Y. and Kawamura R., "Thermal bukling analysis of inhomogeneous rectangular plate due to uniform heat supply", Journal of Thermal Stresses , (26)11-12
(2003), 1151-1170.
Noda, N., Hetnarski, R.B., Tanigawa, Y., Thermal Stresses, Taylor and Francis, 2003.
Nowacki, W. , "The state of stress in a thick circular plate due to temperature eld.",Bull.Sci.Acad.Polon Sci. Tech., 5 (1957).
Ozicik, M., Heat Conduction (Second Edition ed.), John Wiley and Sons,Inc.,1993.
Sherief, H.H and Anwar,M.N, "Two-dimensional generalized thermoelasticity problem for an innitely long cylinder", Journal of Thermal Stresses , (17)2 (1994), 213-227.
Srivastava Vineet K., Awasthi Mukesh K. and Chaurasia R.K., "Reduced differential trans-form method to solve two and three dimensional second order hyperbolic telegraph equations", Journal of King Saud University- Engineering Sciences, 29 (2017), 166-171.
Taha, B. A., "The Use of Reduced Differential Transform Method for Solving Partial Differential Equations with Variable Coecients", Journal of Basrah Researches((Sciences)),(37)4 (2011), 226-233.
Timoshenko S.and Woinowsky-Krieger S.,Theory of Plates and Shells (Second Edition ed.),McGraw-Hill,1989.
Yos Sompornjaroensuk and Kraiwood Kiattikomol ,"Bending behaviours of simply supported rectangular plates with an internal line sagged and unsagged supports", Songklanakarin Journal of Science and Technology , (30)1 (2008), 101-107.
Yuemei Liu and Rui Li, "Accurate bending analysis of rectangular plates with two adjacent edges free and the others clamped or simply supportedbased on new symplectic approach",
Applied Mathematical Modelling, 34 (2010), 8556-865.