Thermoelastic Analysis of Annular Sector Plate Under Restricted Boundaries Amidst Elastic Reaction
الموضوعات :
1 - Department of Mathematics, Mahatma Gandhi Science College, Armori, Gadchiroli, India
2 - Department of Mathematics, Smt. Sushilabai Bharti Science College, Arni, Yavatmal, India
الکلمات المفتاحية: integral transform, Internal heat sources, Thermal deflection, Thermal stresses, Heat conduction, Sector plate,
ملخص المقالة :
An analytical framework is developed for the thermoelastic analysis of annular sector plate whose boundaries are subjected to elastic reactions. The exact expression for transient heat conduction with internal heat sources is obtained using a classical method. The fourth-order differential equation for the thermally induced deflection is obtained by developing a new integral transformation in accordance with the simply supported elastic supports that are subjected to elastic reactions. Here it is supposed that the movement of the boundaries is limited by an elastic reaction, that is, (a) shearing stress is proportional to the displacement, and (b) the reaction moment is proportional to the rate of change of displacement with respect to the radius. Finally, the maximum thermal stresses distributed linearly over the thickness of the plate are obtained in terms of resultant bending momentum per unit width. The calculation is obtained for the steel, aluminium and copper material plates using Bessel's function can be expressed in infinite series form, and the results are depicted using a few graphs.
[1] Khdeir A.A., Reddy J.N., 1991, Thermal stresses and deflections of cross-ply laminated plates using refined plate theories, Journal of Thermal Stresses 14(4): 419-438.
[2] Tsai H.H., Hocheng H., 1998, Analysis of transient thermal bending moments and stresses of the workpiece during surface grinding, Journal of Thermal Stresses 21(6): 691-711.
[3] Kim K.S., Noda N., 2002, A Green's function approach to the deflection of Definitely FGM plate under transient thermal loading, Archive of Applied Mechanics 72(127): 127-137.
[4] Na K.S., Kim J.H., 2006, Nonlinear bending response of functionally graded plates under thermal loads, Journal of Thermal Stresses 29(3): 245-261.
[5] Qian H., Zhou D., Liu W., Fang H., 2014, 3-D Elasticity solutions of simply supported laminated rectangular plates in uniform temperature field, Journal of Thermal Stresses 37(6): 661-677.
[6] Hasebe N., Han J.J., 2016, Green's function for infinite thin plate with elliptic hole under bending heat source and interaction between elliptic hole and crack under uniform bending heat flux, Journal of Thermal Stresses 39(2): 170-182.
[7] Bhad P., Varghese V., Khalsa L., 2017, Heat source problem of thermoelasticity in an elliptic plate with thermal bending moments, Journal of Thermal Stresses 40(1): 96-107.
[8] 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.
[9] Bhad P., Varghese V., Khalsa L., 2017, Thermoelastic-induced vibrations on an elliptical disk with internal heat sources, Journal of Thermal Stresses 40(4): 502-516.
[10] Dhakate T., Varghese V., Khalsa L., 2017, Integral transform approach for solving dynamic thermal vibrations in the elliptical disk, Journal of Thermal Stresses 40(9): 1093-1110.
[11] Bhoyar S., Varghese V., Khalsa L., 2019, A method to derive thermoelastic free vibration in a simply supported annulus elliptic plate, Journal of Thermal Stresses 43(2): 247-267.
[12] Mirzaei M., 2018, Thermal buckling of temperature-dependent composite super elliptical plates reinforced with carbon nanotubes, Journal of Thermal Stresses 41(7): 920-935.
[13] Elsheikh A.H., Guo J., Lee K.M., 2019, Thermal deflection and thermal stresses in a thin circular plate under an axisymmetric heat source, Journal of Thermal Stresses 42(3): 361-373.
[14] Marchi E., Diaz M., 1966, Elastic vibrations in the crowns of thin plates: part 1, Atti della Accademia delle Scienze di Torino 101(5): 739-747.
[15] Zgrablich G., Diaz M., 1966, Elastic vibrations in crowns of thin circular plate: part 2, Atti della Accademia delle Scienze di Torino 101(5): 763-770.
[16] Timoshenko S., Woinowsky-Krieger S., 1959, Theory of Plates and Shells, McGraw-Hill, New York.
[17] Ventsel E., Krauthammer T., 2001, Thin Plates and Shells, Marcel Dekker, New York.
