Torsional Stability of Cylindrical Shells with Functionally Graded Middle Layer on the Winkler Elastic Foundation

Document Type : Research Paper


Department of Civil Engineering of Suleyman Demirel University


In this study, the torsional stability analysis is presented for thin cylindrical with the functionally graded (FG) middle layer resting on the Winker elastic foundation. The mechanical properties of functionally graded material (FGM) are assumed to be graded in the thickness direction according to a simple power law and exponential distributions in terms of volume fractions of the constituents. The fundamental relations and basic equations of three-layered cylindrical shells with a FG middle layer resting on the Winker elastic foundation under torsional load are derived. Governing equations are solved by using the Galerkin method. The numerical results reveal that variations of the shell thickness-to-FG layer thickness ratio, radius-to-shell thickness ratio, lengths-to-radius ratio, foundation stiffness and compositional profiles have significant effects on the critical torsional load of three-layered cylindrical shells with a FG middle layer. The results are verified by comparing the obtained values with those in the existing literature.


[1] Yamanouchi M., Koizumi M., Hirai T., Shiota I., 1990, Proceedings of First International Symposium on Functionally Gradient Materials, Sendai, Japan.
[2] Koizumi M., The concept of FGM ceramic transactions, Ceramic Transactions FunctionallyGradientMaterials 34: 3-10.
[3] Jin Z.H., Batra, R.C., 1996, Some basic fracture mechanics concepts in functionally graded materials, Journal of Mechanics and Physics of Solids 44: 1221-1235.
[4] Reddy J.N., Chin C.D., 1998, Thermo-mechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 21: 593-626.
[5] Najafizadeh M.M., Eslami M.R., 2002, Buckling analysis of circular plates of functionally graded materials under uniform radial compression, International Journal of Mechanical Sciences 44: 2479-2493.
[6] Sofiyev AH, Schnack E., 2004, The stability of functionally graded cylindrical shells under linearly increasing dynamic torsional loading, Engineering Structures 26: 1321-1331.
[7] Sofiyev A.H., 2005,The torsional buckling analysis for cylindrical shell with material non–homogeneity in thickness direction under impulsive loading, Structural Engineering and Mechanics 19: 231-236.
[8] Batra R.C., 2006, Torsion of a functionally graded cylinder, AIAA Journal 44: 1363-1365.
[9] Arghavan S., Hematiyan M.R. 2009, Torsion of functionally graded hollow tubes, European Journal of Mechanics - A/Solids 28: 551-559.
[10] Shen H.S., 2009, Torsional buckling and postbuckling of FGM cylindrical shells in thermal environments, International Journal of Non-Linear Mechanics 44: 644-657.
[11] Huang H.W., Han Q., 2010,Nonlinear buckling of torsion–loaded functionally graded cylindrical shells in thermal environment, European Journal of Mechanics - A/Solids 29: 42-48.
[12] Singh B.M., Rokne J., Dhaliwal R.S., 2006, Torsional vibration of functionally graded finite cylinders, Meccanica 41: 459-470.
[13] Wang H.M., Liu C.B., Ding H.J., 2009, Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders, Acta Mechanica Sinica 25:555-563.
[14] Shen H.S., 2009, Functionally Graded Materials, Nonlinear Analysis of Plates and Shells, CRC Press, Florida.
[15] Pitakthapanaphong S., Busso E.P., 2002, Self–consistent elasto–plastic stress solutions for functionally graded material systems subjected to thermal transients, Journal of Mechanics and Physics of Solids 50: 695-716
[16] Li S.R., Batra R.C., 2006, Buckling of axially compressed thin cylindrical shells with functionally graded middle layer, Thin Walled Structures 44: 1039-1047.
[17] Liew K.M., Yang J., Wu Y.F., 2006, Nonlinear vibration of a coating–FGM–substrate cylindrical panel subjected to a temperature gradient. Computer Methods in Applied Mechanics and Engineering 195: 1007–1026.
[18] Sofiyev, A.H., 2007, Vibration and stability of composite cylindrical shells containing a FG layer subjected to various loads, Structural Engineering and Mechanics 27: 365-391.
[19] Kargarnovin M. H., Hashemi M., 2012, Free vibration analysis of multilayered composite cylinder consisting fibers with variable volume fraction, Composite Structures 94: 931-944
[20] 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: 117-134.
[21] Shen H.S., 2009, Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium, International Journal of Mechanical Sciences 51: 372-383.
[22] Shen H.S., Yang J., Kitipornchai S., 2010, Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium, European Journal of Mechanics A-Solids 29: 448-460.
[23] Sofiyev A.H., Avcar M., 2010, The stability of cylindrical shells containing a FGM layer subjected to axial load on the Pasternak foundation, Engineering 2: 228-236.
[24] Sofiyev A.H., 2010, Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation, Mechanics Research Communications 37: 539-544.
[25] Bagherizadeh E., Kiani Y., Eslami M.R., 2011, Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Composite Structures 93: 3063-3071.
[26] Volmir, A.S., 1967, The Stability of Deformable Systems, Nauka, Moscow (in Russian).