The Buckling of Non-Homogeneous Truncated Conical Shells under a Lateral Pressure and Resting on a Winkler Foundation
محورهای موضوعی : EngineeringA.H Sofiyev 1 , A Valiyev 2 , P Ozyigit 3
1 - Department of Civil Engineering, Suleyman Demirel University, Isparta 32260, Turkey
2 - Chair of Mathematics and General Technical Subjects of Odlar Yurdu University, Baku, Azerbaijan
3 - Department of Civil Engineering, Suleyman Demirel University, Isparta 32260, Turkey
کلید واژه: Buckling, Non-homogeneous material, Truncated conical shell, Winkler foundation, Critical uniform lateral pressure,
چکیده مقاله :
In this paper, the buckling of non-homogeneous isotropic truncated conical shells under uniform lateral pressure and resting on a Winkler foundation is investigated. The basic relations and governing equations have been obtained for non-homogeneous truncated conical shells. The critical uniform lateral pressures of non-homogeneous isotropic truncated conical shells with or without a Winkler foundation are obtained. Finally, carrying out some computations, effects of the variations of truncated conical shell characteristics, the non-homogeneity and the Winkler foundation on the critical uniform lateral pressures have been studied. The results are compared with other works in open literature.
[1] Pasternak P.L., 1954, On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR (in Russian).
[2] Kerr A.D., 1964, Elastic and visco-elastic foundation models, ASME Journal of Applied Mechanics 31: 491-498.
[3] Bajenov V.A., 1975, The Bending of the Cylindrical Shells in an Elastic Medium, Kiev, Visha Shkola (in Russian).
[4] Sun B., Huang Y., 1988, The exact solution for the general bending problems of conical shells on the elastic foundation, Applied Mathematics and Mechanics 9(5): 455-469.
[5] Eslami M.R., Ayatollahi M.R., 1993, Modal-analysis of shell of revolution on elastic-foundation, International Journal of Pressure Vessels and Piping 56(3):351-368.
[6] Paliwal D.N., Pandey R.K., Nath T., 1996, Free vibration of circular cylindrical shell on Winkler and Pasternak foundation, International Journal of Pressure Vessels and Piping 69: 79-89.
[7] Ng T.Y., Lam K.Y., 2000, Free vibrations analysis of rotating circular cylindrical shells on an elastic foundation, Journal of Vibration and Acoustics 122: 85-89.
[8] Tj H.G., Mikami T., Kanie S., Sato M., 2006, Free vibration characteristics of cylindrical shells partially buried in elastic foundations, Journal of Sound and Vibration 290: 785-793.
[9] Lomakin V.A., 1976,The Elasticity Theory of Non-homogeneous Materials, Nauka, Moscow (in Russian).
[10] Awrejcewicz J., Krysko V.A., Kutsemako A.N., 1999, Free vibrations of doubly curved in-plane non-homogeneous shells, Journal of Sound and Vibration 225(4): 701-722.
[11] Shen H.S., 2003, Post-buckling analysis of pressure loaded functionally graded cylindrical shells in thermal environments, Engineering Structures 25: 487-497.
[12] Goldfeld Y., 2007, Elastic buckling and imperfection sensitivity of generally stiffened conical shells, AIAA Journal 45(3): 721–729.
[13] Sofiyev A.H., Omurtag M., Schnack E., 2009, The vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure, Journal of Sound and Vibration 319(3-5): 963-983.
[14] Najafizadeh M.M., Hasani A., Khazaeinejad P., 2009, Mechanical stability of functionally graded stiffened cylindrical shells, Applied Mathematical Modelling 33(2):1151-1157.
[15] Tomar J., Gupta D., Kumar V., 1986, Natural frequencies of a linearly tapered non-homogeneous isotropic elastic circular plate resting on an elastic foundation, Journal of Sound and Vibration 111: 1-8.
[16] Sofiyev A.H., 1987, The stability of non-homogeneous cylindrical shells under the effect of surroundings, Soviet Scientific and Technical Research Institute (VINITI), Moscow 3(189): 1-9 (in Russian).
[17] Sofiyev a.H., Keskin S.N., Sofiyev A.L.H., 2004, Effects of elastic foundation on the vibration of laminated non-homogeneous orthotropic circular cylindrical shells, Journal of Shock and Vibration 11: 89-101.
[18] Sheng G.G., Wang X., 2008, Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium, Journal of Reinforced Plastics and Composites 27(2): 117-134.
[19] Singer j., 1962, The effect of axial constraint on the instability of thin conical shells under external pressure, ASME Journal of Applied Mechanics, 212-214.
[20] Agamirov V.L., 1990, Dynamic Problems of Nonlinear Shells Theory, Moscow, Nauka (in Russian).
[21] Tong L., 1996, effect of axial load on free vibration of orthotropic conical shells, Journal of Vibration and Acoustics 118: 164-168.
[22] Liew K.M., Ng T.Y., Zhao X., 2005, Free vibration analysis of conical shells via the element-free KP-Ritz method, Journal of Sound and Vibration 281: 627-645.
