A shell superelement for mechanical analysis of cylindrical structures

Document Type : Research Paper


1 Mechanical Engineering Department, Amirkabir University of Technology

2 Amirkabir University of Technology


This paper aims at developing a new cylindrical shell element, called shell superelement. The element is defined based on the classical shell theory, and it consists of eight nodes each with six degree-of-freedoms (dofs). In this element, the trigonometric shape functions are incorporated along the angular direction of element while polynomials were used in other two directions. Therefore, there is no need for meshing a shell structure with cylindrical geometry through the angular direction. This property helps an engineer to deal with complicated analyses on cylindrical shell structures with less number of dofs. At the end, the defined element is used in the stress analysis of two different classical shell problems and the results are compared with the ones reported in the literature, and obtained by means of shell elements in a commercial software package.


Main Subjects

[1]     Koko T.S., “Super Finite Elements for Nonlinear Static and Dynamic Analysis of Stiffened Plate Structures”, Ph.D. Thesis, University of British Columbia, Vancouver, Canada, (1990).
[2]     Koko, T.S., and and Olson, M.D., “Vibration Analysis of Stiffened Plates by Superelements”, J. Sound Vib., Vol. 158, pp. 149-167, (1992).
[3]     Jiang, J., and Olson, M.D., “Vibration Analysis of Orthogonally Stiffened Cylindrical Shells using Super Finite Elements”, J. Sound Vib., Vol. 173, pp. 73-83, (1994).
[4]     Jiang, J., and Olson, M.D., “Nonlinear Analysis of Orthogonally Stiffened Cylindrical Shells by a Superelement Approach”, Finite Elem. Anal. Des., Vol. 18, pp. 99-110, (1994). 
[5]     Ahmadian, M.T., and Zanganeh, M.S., “Vibration Analysis of Orthotropic Rectangular Plates using Superelements”, Comput. Methods Appl. Mech. Eng., Vol. 191, pp. 2069-2075, (2002).
[6]     Ahmadian, M.T., and Zanganeh, M.S. “Application of Superelements to Free Vibration Analysis of Laminated Stiffened Plates”, J. Sound Vib., Vol. 259, pp. 1243-1252, (2003).
[7]     Kuntjoro, W., Abdul Jalil AMH, Mahmun J., “Wing Structure Analysis using Superelement”, Procedia Engineering, Vol. 41, pp. 1600-1606, (2012).
[8]     Tkachev, V.V., “The use of Superelement Approach for the Mathematical Simulation of Reactor Structure Dynamic Behavior”, Nuclear Engineering and Design, Vol. 196, pp. 101-104, (2000).
[9]     Ju, F., and Choo, Y.S., “Superelement Approach to Cable Passing through Multiple Pulleys”, Int. J. Solids Struct., Vol. 42, pp. 3533-3547, (2005).
[10]  He, Y.J., Zhou, X.H., and Hou, P.F., “Combined Method of Super Element and Substructure for Analysis of ILTDBS Reticulated Mega-structure with Single-layer Latticed Shell Substructures”, Finite Element in Analysis and Design, Vol. 46, pp. 563-570, (2010).
[11] Tahilramani, D.R., and Hitchins, J., “Application of Model Reduction Techniques within Cummins Inc.”, Proceedings of the ASME 2014 Internal Combustion Engine Division Fall Technical Conference, Columbus, USA, pp. 19-22, (2014).
[12]Danielczyk, P., “Parametric Optimization with the use of Numerically Efficient Finite Element Models”, Advances in Mechanical Engineering, Vol. 11, pp. 1-12, (2015).
[13]  Persson, P., Persson, K., and Sandberg, G., “Reduced order Modeling of Liquid-filled Pipe Systems”, Journal of Fluids and Structures, Vol. 61, pp. 205-217, (2016).
[14]Lu, C., Yang, W., Zheng, H., Liang, J., and Fu, G., “The Application of Superelement Modeling Method in Vehicle Body Dynamics Simulation”, SAE Technical Paper, doi: 2016-01-8050, (2016).
[15] Semenov, S., Nikhamkin, M., Sazhenkov, N., Semenov, I., and Mekhonoshin, G., “Simulation of Rotor System Vibrations using Experimentally Verified Super Elements”, Proceedings of the ASME International Mechanical Engineering Congress and Exposition (IMECE2016), Phoenix, Arizona, USA, pp. 11-17, (2016).
[16] Ahmadian, M.T., and Bonakdar, M., “A New Cylindrical Element Formulation and its Application to Structural Analysis of Laminated Hollow Cylinders”, Finite Elem. Anal. Des., Vol. 44, pp. 617-630, (2008).
[17] Taghvaeipour, A., Bonakdar, M., and Ahmadian, M.T., “Application of a New Cylindrical Element Formulation in Finite Element Structural Analysis of FGM Hollow Cylinders”, Finite Element Analysis Design, Vol. 50, pp, 1-7, (2012).
[18] Pourhamid, R., Ahmadian, M.T., Mahdavy Moghaddam, H., and Mohammadzadeh, A.R., “Mechanical Analysis of a Functionally Graded Cylinder-piston under Internal Pressure Due to a Combustion Engine using a Cylindrical Super Element and Considering Thermal Loading”, Scientia Iranica B, Vol. 22, pp. 493-503, (2015).
[19] Fatan A.R., and Ahmadian, M.T., “Vibration Analysis of FGM Rings using a Newly Designed Cylindrical Superelement”, Scientia Iranica B, Vol. 25, pp. 1179-1188, (2018).
[20] Nasiri Sarvi, M., and Ahmadian, M.T., “Design and Implementation of a New Spherical Superelement in Structural Analysis”, Appl. Math. Comput., Vol. 218, pp. 7546-7561, (2012).
[21] Nasiri Sarvi, M., and Ahmadian, M.T., “Static and Vibrational Analysis of Fullerene using a Newly Designed Spherical Element”, Scientia Iranica B, Vol. 19, pp. 1316-1323, (2012).
[22] Ahmadian, M.T., Movahhedy, M.R., and Rezaei, M.M., “Design and Application of a New Tapered Superelement for Analysis of Revolving Geometries”, Finite Elem. Anal. Des., Vol. 47, pp. 1242-1252, (2011).
[23] Shamloofard, M., and Movahhedy, M.R., “Development of Thermo-elastic Tapered and Spherical Superelements”, Applied Mathematics and Computation, Vol. 265, pp. 380-399, (2015).
[24] Soleimani, I., Tadi Beni, Y., and Mehralian, F., “A New Size-Dependent Cylindrical Shell Element Based on Modified Couple Stress Theory”, Adv. Appl. Math. Mech., Vol. 10, pp. 819-844, (2017).
[25] Torabi, J., and Ansari, R., “A Higher-order Isoparametric Superelement for Free Vibration Analysis of Functionally Graded Shells of Revolution”, Thin-Walled Structures, Vol. 133, pp. 169-179, (2018).
[26] Shamloofard, M., Hosseinzadeh, A., and Movahhedy, M.R., “Development of a Shell Superelement for Large Deformation and Free Vibration Analysis of Composite Spherical Shells”, Engineering with Computers, (2020). https://doi.org/10.1007/s00366-020-01015-w.
[27] Venstel, E., and Krouthammer, T., “Thin Plates and Shells, Theory, Analysis, and Applications”, First Ed, Marcel Dekker, New York, USA, (2001).
[28] Reddy, J. N., and Lio, C. F., “A Higher-order Shear Deformation Theory of Laminated Elastic Shells”, International Journal of Engineering Science, Vol. 23, pp. 319-330, (1985).
[29] Eslami, M.R., “Finite Elements Methods in Mechanics”, First Ed, Springer, Switzerland, (2014).
[30] Rao, S.S., “The Finite Element Method in Engineering”, Fifth Ed, Butterworth-Heinemann, United Kingdom, (2011).
[31] Jin, G., Ye, T., Chen, Y., Su, Z., and Yan, Y., “An Exact Solution for the Free Vibration Analysis of Laminated Composite Cylindrical Shells with General Elastic Boundary Conditions”, Composite Structures, Vol. 106, pp. 114-127, (2013).
[32] Blaauwendraad, J., and Hoefakker, J.H., “Structural Shell Analysis (Understanding and Application)”, First Ed, Springer, New York, USA, (2014).
[33] Timoshenko, S., and Woinowski-Krieger, S., “Theory of Plate and Shells”, Second Ed, McGraw-Hill, New York, USA, (1959).
[34] Felippa, C., “Introduction to Finite Element Methods (ASEN 5007)”, Lecture Notes, Department of Aerospace Engineering Sciences, University of Colorado at Boulder, USA,