Non-Linear Analysis of Asymmetrical Eccentrically Stiffened FGM Cylindrical Shells with Non-Linear Elastic Foundation

Document Type: Research Paper


Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran


In this paper, semi-analytical method for asymmetrical eccentrically stiffened FGM cylindrical shells under external pressure and surrounded by a linear and non-linear elastic foundation is presented. The proposed linear model is based on two parameter elastic foundation Winkler and Pasternak. According to the von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method, used for solving nonlinear problem. To finding the nonlinear dynamic response of fourth order Runge-Kutta method is used. The effect of parameters asymmetrical eccentrically stiffened on the nonlinear dynamic buckling response of FGM cylindrical shells have been investigated.


[1] Dung D. V., Nam V. H., 2014, Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium, European Journal of Mechanics - A/Solids 46: 42-53.
[2] Darabi M., Darvizeh M., Darvizeh A., 2008, Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading, Composite structures 83: 201-211.
[3] Sofiyev A. H., Schnack E., 2004, The stability of functionally graded cylindrical shells under linearly increasing dynamic torsional loading, Engineering Structures 26:1321-1331.
[4] Sheng G. G., Wang X., 2008, Thermo mechanical vibration analysis of a functionally graded shell with flowing fluid, European Journal of Mechanics - A/Solids 27:1075-1087.
[5] Sofiyev A. H., 2009, The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure, Composite structures 89: 356-366.
[6] Hong C. C., 2013, Thermal vibration of magnetostrictive functionally graded material shells, European Journal of Mechanics - A/Solids 40: 114-122.
[7] Huang H., Han Q., 2010, Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to a time-dependent axial load, Composite structures 92: 593-598.
[8] Budiansky B., Roth R. S., 1962, Axisymmetric Dynamic Buckling of Clamped Shallow Spherical Shells, NASA Technical Note D.1510.
[9] Pellicano F. , 2009, Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamic axial loads, Communications in Nonlinear Science and Numerical Simulation 14(8): 3449-3462.
[10] Duc N. D., Thang P. T., 2015, Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations, Aerospace Science and Technology 40: 115-127.
[11] Sofiyev A. H., 2011, Non-linear buckling behavior of FGM truncated conical shells subjected to axial load, International Journal of Non-Linear Mechanics 46: 711-719.
[12] Brush D. O., Almroth B. O., 1975, Buckling of Bars, Plates and Shells, McGraw-Hill. New York.
[13] Shao-Wen Y., 1979, Buckling of cylindrical shells with spiral stiffeners under uniform compression and torsion, Composite structures 11: 587-595.
[14] Najafizadeh M. M., Hasani A., Khazaeinejad P., 2009, Mechanical, stability of function-ally graded stiffened cylindrical shells, Applied Mathematical Modelling 33: 1151-1157.
[15] Shen H. S., 1998, Postbuckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and thermal loading, Applied Mathematics and Mechanics 19: 411-426.
[16] Ghiasian S. E., Kiani Y., Eslami M.R., 2013, Dynamic buckling of suddenly heated or compressed FGM beams resting on non-linear elastic foundation, Composite structures 106: 225-234.
[17] Huang H., Han Q., 2010, Research on nonlinear post-buckling of functionally graded cylindrical shells under radial loads, Composite structures 92:1352-1357.
[18] Volmir A. S., 1972, The Non-linear Dynamics of Plates and Shells, Science Edition, Russian.
[19] Sewall J. L., Naumann E. C., 1968, An Experimental and Analytical Vibration Study of Thin Cylindrical Shells with and Without Longitudinal Stiffeners, NASA Technical Note D-4705.
[20] Sewall J. L, Clary R. R., Leadbetter S. A., 1964, An Experimental and Analytical Vibration Study of a Ring-stiffened Cylindrical Shell Structure with Various Support Onditions, NASA Technical Note D-2398.
[21] 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.
[22] Sofiyev A. H., Avcar M., Ozyigit P., Adigozel S., 2009, The free vibration of non-homogeneous truncated conical shells on a Winkler foundation, International Journal of Engineering and Applied Sciences 1: 34-41.