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An attempt is made in the current research to obtain the fundamental buckling torque and the associated buckled shape of an annular plate. The plate is subjected to a torque on its outer edge. An isotropic homogeneous plate is considered. The governing equations of the plate in polar coordinates are established with the aid of the Mindlin plate theory. Deformations and stresses of the plate prior to buckling are determined using the axisymmetric flatness conditions. Small perturbations are then applied to construct the linearised stability equations which govern the onset of buckling. To solve the highly coupled equations in terms of displacements and rotations, periodic auxiliary functions and the generalised differential quadrature method are applied. The coupled linear algebraic equations are a set of homogeneous equations dealing with the buckling state of the plate subjected to a unique torque. Benchmark results are given in tabular presentations for combinations of free, simply-supported, and clamped types of boundary conditions. It is shown that the critical buckling torque and its associated shape highly depend upon the combination of boundary conditions, radius ratio, and the thickness ratio.
Wydawca
Czasopismo
Rocznik
Tom
Strony
209--227
Opis fizyczny
Bibliogr. 25 poz., rys., tab.
Twórcy
autor
- Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran
autor
- Faculty of Engineering, Shahrekord University, Shahrekord, Iran
autor
- Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran
Bibliografia
- [1] W. R. Dean. The elastic stability of anannular plate. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 106(737):268–284, 1924. doi: 10.1098/rspa.1924.0068.
- [2] J. Tani and T. Nakamura. Dynamic stability of annular plates under pulsating torsion. Journal of Applied Mechanics, 47(3):595–600, 1980. doi: 10.1115/1.3153739.
- [3] J.Tani. Dynamic stability of orthotropic annular plates under pulsating torsion. The Journal of the Acoustical Society of America, 69(6):1688–1694, 1981. doi: 10.1121/1.385948.
- [4] D. Durban and Y. Stavsky. Elastic buckling of polar-orthotropic annular plates in shear. International Journal of Solids and Structures, 18(1):51–58, 1982. doi: 10.1016/0020-7683(82)900154.
- [5] T. Irie, G. Yamada, and M. Tsujino. Vibration and stability of a variable thickness annular plate subjected to a torque. Journal of Sound and Vibration, 85(2):277–285, 1982. doi: 10.1016/0022460X(82)90522-3.
- [6] T. Irie, G. Yamada, and M. Tsujino. Buckling loads of annular plates subjected to a torque. Journal of Sound and Vibration, 86(1):145–146, 1983. doi: 10.1016/0022-460X(83)90951-3.
- [7] J. Zajączkowski. Stability of transverse vibration of a circular plate subjected to a periodically varying torque. Journal of Sound and Vibration, 89(2):273–286, 1983. doi: 10.1016/0022460X(83)90394-2.
- [8] H. Doki and J. Tani. Buckling of polar orthotropic annular plates under internal radial load and torsion. International Journal of Mechanical Sciences, 27:429–437, 1985. doi: 10.1016/00207403(85)90033-5.
- [9] M. Hamada and T. Harima. In-plane torsional buckling of an annular plate. Bulletin of JSME, 29(250):1089–1095, 1986. doi: 10.1299/jsme1958.29.1089.
- [10] E. Ore and D. Durban. Elastoplastic buckling of annular plates inpure shear. Journal of Applied Mechanics, 56(3):644–651, 1989. doi: 10.1115/1.3176141.
- [11] Chang-Jun Cheng and Xiao-an Lui. Buckling and post-buckling of annular plates in shearing, Part I: Buckling. Computer Methods in Applied Mechanics and Engineering, 92(2):157–172, 1991. doi: 10.1016/0045-7825(91)90237-Z.
- [12] Chang-Jun Cheng and Xiao-an Lui. Buckling and post-buckling of annular plates in shearing, Part II: Post-buckling. Computer Methods in Applied Mechanics and Engineering, 92(2):173–191, 1991. doi: 10.1016/0045-7825(91)90238-2.
- [13] P. Singhatanadgid and V. Ungbhakorn. Scaling laws for buckling of polar orthotropic annular plates subjected to compressive and torsional loading. Thin-Walled Structures, 43(7):1115– 1129, 2005. doi: 10.1016/j.tws.2004.11.004.
- [14] T.X. Wu. Analytical study on torsional vibration of circular and annular plate. Journal of Mechanical Engineering Science, 220(4):393–401, 2006. doi: 10.1243/09544062JMES167.
- [15] R. Maretic, V. Glavardanov, and D. Radomirovic. Asymmetric vibrations and stability of a rotating annular plate loaded by a torque. Meccanica, 42(6):537–546, 2007. doi: 10.1007/s11012007-9080-8
- [16] S. E. Ghiasian, Y. Kiani, M. Sadighi, and M. R. Eslami. Thermal buckling of shear deformable temperature dependent circular annular FGM plates. International Journal of Mechanical Sciences, 81:137–148, 2014. doi: 10.1016/j.ijmecsci.2014.02.007.
- [17] H. Bagheri, Y. Kiani, and M. R. Eslami. Asymmetric thermal buckling of temperature dependent annular FGM plates on a partial elastic foundation. Computers & Mathematics with Applications, 75(5):1566–1581, 2018. doi: 10.1016/j.camwa.2017.11.021.
- [18] H. Bagheri, Y. Kiani, and M. R. Eslami. Asymmetric compressive stability of rotating annular plates. European Journal of Computational Mechanics, 2019. doi: 10.1080/17797179.2018.1560989.
- [19] J. N. Reddy. Mechanics of Laminated Composite Plates and Shells, Theory and Application. CRC Press, 2nd Edition, 2003.
- [20] H. Bagheri, Y. Kiani, and M.R. Eslami. Asymmetric thermal buckling of annular plates on a partial elastic foundation. Journal of Thermal Stresses, 40(8):1015–1029, 2017. doi: 10.1080/01495739.2016.1265474.
- [21] H. Bagheri, Y. Kiani, and M. R. Eslami. Asymmetric thermo-inertial buckling of annular plates. Acta Mechanica, 228(4):1493–1509, 2017. doi: 10.1007/s00707-016-1772-5.
- [22] D. O. Brush and B. O. Almroth. Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, 1975.
- [23] M. R. Eslami. Thermo-Mechanical Buckling of Composite Plates and Shells, Amirkabir University Press,Tehran, 2010.
- [24] Y. Kiani Y and M. R. Eslami. An exact solution for thermal buckling of annular FGM plates on an elastic medium. Composites Part B: Engineering, 45(1):101–110, 2013. doi: 10.1016/j.compositesb.2012.09.034.
- [25] F. Tornabene, N. Fantuzzi F. Ubertini, and E. Viola. Strong formulation finite element method based on differential quadrature: a survey. Applied Mechanics Reviews, 67(2):020801-02080155, 2015. doi: 10.1115/1.4028859.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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