Abstract
This paper presents a new discrete layer finite element method modeling thin and moderately thick orthotropic and laminated composite cylindrical shells. The element formulation is based on the first order shear deformation theory of shells. A twentydegrees- of-freedom plane stress element is utilized and modeled with in-plane displacements defined at the interfaces of the element layers in addition to the radial displacement. A field consistency approach is implemented to insure that the element is free from locking due to membrane tangential, shear and transverse shear strains. The field consistency approach used eliminates inconsistent terms from the original displacement shape functions that correspond to the targeted strains. The new element is validated through a series of benchmark problems and has shown accurate and fast converging results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ahmad, S., Irons, B.M. & Zienkiewicz, O.C. 1970. Analysis of thick and thin shell structures by curved finite elements. International Journal for Numerical Methods in Engineering 2: 419-451.
Alam, N. & Asnani, N.T. 1984. Vibration and damping analysis of a multilayered cylindrical shell, Part I: theoretical analysis. AIAA Journal 22: 803-810.
Alves de Sousa, R.J., Natal Jorge, R.M., Fontes Valente, R.A. & César de Sá, J.M.A. 2003. A new volumetric and shear locking-free 3D enhanced strain element. Engineering Computations 20: 896-925.
Arciniega, R.A. & Reddy, J.N. 2005. Consistent third-order shell theory with application to composite circular cylinders. AIAA 43: 2024-2038.
Ashwell, D.G. & Sabir, A.B. 1972. A new cylindrical shell finite element based on simple independent strain functions. International Journal for Mechanical Sciences 14: 171-183.
Ausserer, M.F. & Lee, S.W. 1988. An eighteen node solid element for thin shell analysis. International Journal for Numerical Methods in Engineering 26: 1345-1364.
Belytschko, T. & Leviathan, I. 1994. Physical stabilization of the 4-node shell element with one point quadrature. Computer Methods in Applied Mechanics and Engineering 113:321-350.
Bletzinger, K.U., Bischoff, M. & Ramm, E. 2000. A unified approach for shear-locking-free triangular and rectangular shell finite elements. Computers and Structures 75: 321-334.
Bogner, F.K., Fox, R.L. & Schmit, L.A. 1967. A cylindrical shell discrete element. AIAA Journal 5: 745-750.
Carrera, E. & Brischetto, S. 2008. Analysis of thickness locking in classical, refined and mixed theories for layered shells. Composite Structures 85: 83-90.
Cheng, Z.Q., He, L.H. & Kitipornaci, S. 2000. Influence of imperfect interfaces on bending and vibration of laminated composite shells. International Journal of Solids and Structures 37: 2127-2150.
Connor, J.J. & Brebbia, C. 1967. Stiffness matrix for shallow shell rectangular shell element. Proceedings of the American Society of Civil Engineers, Journal of Engineering Mechanics 93: 43-65.
Djoudi, M.S. & Bahai, H. 2004. A cylindrical strain-based shell element for vibration analysis of shell structures. Finite Elements in Analysis and Design 40: 1947-1961.
Dvorkin, E.N. & Bathe K.J. 1984. A continuum mechanics based four-node shell element for general non-linear analysis. Engineering Computations 1:77-88.
Fontes Valente, R.A., Alves de Sousa, R.J. & Natal Jorge, R.M. 2004. An enhanced strain 3D element for large deformation elastoplastic thin-shell applications. Computational Mechanics 34: 38-52.
Hrennikoff, A. & Tezcan, S.S. 1966. Analysis of cylindrical shells by the finite element method. Symposium on Problems of Interdependence of Design and Construction of Large-Spam Shells for Industrial and Civic Buildings, Leningrad, USSR.
Jeung, Y.S. & Shen, Y. 2001. Development of isoparametric, degenerate constrained Layer element for plate and shell structures. AIAA Journal 39: 1997-2005.
Khdeir A.A. & Reddy JN. 1990. Influence of edge conditions on the modal characteristics of cross-ply laminated shells. Computers and Structures 34: 817-826.
Kim, K.D., Lomboy, G.R. & Voyiadjis, G.Z. 2003. A 4-node assumed strain quasi-conforming shell element with 6 degrees of freedom. International Journal for Numerical Methods in Engineering 58: 2177-2200.
Koschnick, F., Bischoff, M., Camprub, N. & Bletzinger, K.U. 2005. The discrete strain gap method and membrane locking. Computer Methods in Applied Mechanics and Engineering 194:2444-2463.
Koziey, B.L. & Mirza, F.A. 1997. Consistent thick shell element. Computers and Structures 65:531-549.
Kulikov, G.M. & Plotnikova, S.V. 2006. Geometrically exact assumed stress-strain multilayered solidshell elements based on the 3D analytical integration. Computers and Structures 84: 1275-1287.
Lee, I., Oh, I.K., Shin, W.H., Cho, K.D. & Koo, K.N. 2002. Dynamic characteristics of cylindrical composite panels with co-cured and constrained viscoelastic layers. JSME Internatioal Journal Series C 45:16-25.
Liu, B., Xing, Y.F., Qatu, M.S & Ferreira A.J.M. 2012. Exact characteristic equations for the free vibrations of thin orthotropic circular cylindrical shells. Composite Structures 94: 484-493.
MacNeal, R.H. 1982. Derivation of element stiffness matrices by assumed strain distributions. Journal of Nuclear Engineering Design 70:3-12.
MacNeal, R.H. & Harder, R.L. 1985. A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design 1: 3-20.
Messina, A. & Soldatos, K.P. 1999. Influence of edge boundary conditions on the free vibratrions of cross-ply laminated circular cylindrical panels. Journal of the Acoustical Society of America 106: 2608-2620.
Mohr, GA. 1980. Numerically integrated triangular element for doubly curved thin shells. Computers and Structures 11: 565-571.
Mohr, G.A. 1981. A doubly curved isoparametric triangular shell element. Computers and Structures 14: 9-13.
Moreira, R.A.S., Alves de Sousa, R.J. & Fontes Valente, R.A. 2010. A solid-shell layerwise finite element for non-linear geometric and material analysis. Composite Structures 92: 1517-1523.
Nayak, A.K. & Shenoi, R.A. 2005. Free Vibration Analysis Of Composite Sandwich Shells Using Higher Order Shell Elements. 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Austin, Texas.
Prathap, G. 1985. A C0 continuous four-noded cylindrical shell element. Computers and Structures 21: 995-999.
Ramesh, T.C. & Ganesan, N. 1993. Vibration and damping analysis of cylindrical shells with a constrained damping layer. Computers and Structures 46: 751-758.
Reddy JN. 2003. Mechanics of laminated composite plates and shells; Theory and analysis. CRC Press, Boca Raton, FL, USA.
Shariyat M. 2011. An accurate double-superposition global-local theory for vibration and bending analyses of cylindrical composite and sandwich shells subjected to thermo-mechanical loads. Proceedings ofthe Institution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Sciences 225: 1816-1832.
Sheinman, I. & Greif, S. 1984. Dynamic analysis of laminated shells of revolution. Journal of Composite Materials 18: 200-215.
Simo, J.C. & Fox, D.D. & Rifai, M.S. 1989. On stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects. Computer Methods in Applied Mechanics and Engineering 73:53-92.
Simo, J.C. & Rifai, S. 1990. A class of mixed assumed strain methods and the method of incompatible models. International Journal for Numerical Methods in Engineering 29:1595-1638.
Stolarski, H. & Belytschko, T. 1982. Membrane locking and reduced integration for curved elements. Journal of Applied Mechanics 49:172-176.
Wang, H.J. & Chen, L.W. 2004. Finite element dynamic analysis of orthotropic cylindrical shells with a constrained damping layer. Finite Elements in Analysis and Design 40: 737-755.
Zienkiewicz, O.C. & Cheung, Y.K. 1966. Plate and shell problems, finite element displacement approach. International Symposium on the Use of Electrical Digital Computers in Structural Engineering, Newcastle, UK.
Zienkiewicz, O.C., Taylor, R.L. & Too JM. 1979. Reduced integration techniques in general analysis of plates and shells. International Journal for Numerical Methods in Engineering 3:275-290.
Acknowledgment
This work was done during the author’s sabbatical leave at the University of Maryland, College Park. The author is grateful to Prof. Amr Baz for his constant and invaluable support.
Author information
Authors and Affiliations
Corresponding author
Additional information
Open Access: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0) which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Al-Ajmi, M. A discrete layer finite element model for cylindrical shells. J Engin Res 3, 17 (2015). https://doi.org/10.7603/s40632-015-0017-4
Revised:
Accepted:
Published:
DOI: https://doi.org/10.7603/s40632-015-0017-4