A new flat shell finite element for the linear analysis of thin shell structures
Keywords:
Flat shell element, thin shell, strain based approach, static condensationAbstract
In this paper, a new rectangular flat shell element denoted ‘ACM_RSBE5’ is presented. The new element is obtained by superposition of the new strain-based membrane element ‘RSBE5’ and the well-known plate bending element ‘ACM’. The element can be used for the analysis of any type of thin shell structures, even if the geometry is irregular. Comparison with other types of shell elements is performed using a series of standard test problems. A correlation study with an experimentally tested aluminium shell is also conducted. The new shell element proved to have a fast rate of convergence and to provide accurate results.
Downloads
References
Abed-Meraim, F., & Combescure, A. (2009). An improved assumed strain solidâ shell element
formulation with physical stabilization for geometric non-linear applications and elasticâ
plastic stability analysis. International Journal for Numerical Methods in Engineering, 80,
–1686.
Abed-Meraim, F., & Combescure, A. (2007). A physically stabilized and locking-free
formulation of the SHB8PS solid-shell element. European Journal of Computational
Mechanics, 16, 1037–1072.
Abed-Meraim, F., Trinh, V., & Combescure, A. (2012). Assumed strain solid–shell formulation
for the six-node finite element SHB6: Evaluation on non-linear benchmark problems.
European Journal of Computational Mechanics, 21, 52–71.
Abed-Meraim, F., Trinh, V., & Combescure, A. (2013). New quadratic solid–shell elements and
their evaluation on linear benchmark problems. Computing, 95, 373–394.
Adini, A., & Clough, R. W. (1961). Analysis of plate bending by the finite element method (Report
to the Nat. Sci. Found., G 7337), Arlington, TX, USA.
Alves de Sousa, R. J., Cardoso, R. P. R., Fontes Valente, R. A., Yoon, J. W., Grácio, J. J., & Natal
Jorge, R. M. N. (2005). A new one-point quadrature enhanced assumed strain (EAS) solidshell
element with multiple integration points along thickness: Part I – geometrically linear
applications. International Journal for Numerical Methods in Engineering, 62, 952–977.
Ashwell, D. G., & Sabir, A. B. (1972). A new cylindrical shell finite element based on simple
independent strain functions. International Journal of Mechanical Sciences, 14, 171–183.
Bathe, K. J., & Wilson, E. L. (1976). Numerical methods in finite element analysis. Englewood
Cliffs, NJ: Prentice Hall.
Batoz, J. L., & Dhatt, G. (1992). Modélisation des structures par éléments finis, (Vol. 3). Coques,
Ed. Paris: Hermès.
Belarbi, M. T. (2000). Développement de nouveaux éléments finis basés sur le modèle en
déformation. Application linéaire et non linéaire [Development of new finite elements based
on the strain model: Application to linear and nonlinear problems] (Thèse de Doctorat
d’état). Université de Constantine, Algérie.
Beles, A. A., & Soare, M. V. (1975). Elliptic and hyperbolic paraboloidal shells used in
construction. Bucharest (pp. 145–146). London: Editura Academiei. S.P. Christie.Bogner, F. K., Fox, R. L., & Schmit, L. A. (1967). A cylindrical shell discrete element. AIAA
Journal, 5, 745–750.
Cantin, G., & Clough, R. W. (1968). A curved, cylindrical-shell, finite element. AIAA Journal,
, 1057–1062.
Cardoso, R. P. R., Yoon, J. W., & Valente, R. A. (2006). A new approach to reduce membrane
and transverse shear locking for one-point quadrature shell elements: Linear formulation.
International Journal for Numerical Methods in Engineering, 66, 214–249.
Cardoso, R. P., Yoon, J. W., Mahardika, M., Choudhry, S., Alves de Sousa, R. J., & Fontes Valente,
R. A. (2008). Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods
for one‐point quadrature solid‐shell elements. International Journal for Numerical Methods
in Engineering, 75, 156–187.
Corner, J. J., Brebbia, C. (1967). Stiffness matrix for shallow rectangular shell element. Journal
of Engineering Mechanics (ASCE), 93, 43–65.
Djoudi, M. S., & Bahai, H. (2003). A shallow shell finite element for the linear and non-linear
analysis of cylindrical shells. Engineering Structures, 25, 769–778.
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.
Flugge, W., & Fosberge, K. (1966). Point load on shallow elliptic paraboloid. Journal of Applied
Mechanics, 33, 575–585.
Hamadi, D. (2006). Analysis of structures by non-conforming finite elements (PhD thessis). Civil
Engineering Department, Biskra University, Algeria, pp. 130.
Hartmann, F., & Kats, C. (2007). Structural Analysis with finite element methods. (2nd ed.).
Berlin: Springer-Verlag.
Jones, R. E., Strome, D. R. (1966). Direct stiffness method analysis of shells of revolution
utilizing curved elements. AIAA Journal, 4, 1519–1525.
Kulikov, G. M., & Plotnikova, S. V. (2010). A family of ANS four-node exact geometry shell
elements in general convected curvilinear coordinates. International Journal for Numerical
Methods in Engineering, 83, 1367–1406.
Melosh, D., & Belarbi, M. T. (2006). Basis for derivation of matrices for the direct stiffness
method. AIAA Journal, 7, 525–549.
Melosh, R. J. (1963). Basis of derivation of matrices for the direct stiffness method. Journal of
AIAA, 1, 1631–1637.
Mousa, A. I. (1992). Triangular finite element for analysis of spherical shell structures (UWCC
Publications, Internal Report). Cardiff: University of Wales, college Cardiff.
Mousa, A. I., & EL Naggar, M. H. (2007). Shallow spherical shell rectangular finite element for
analysis of cross shaped shell roof. Electronic Journal of Structural Engineering, 7, 769–778.
Mousa, A. I., & Sabir, A. B. (1994). Finite element analysis of fluted conical shell roof structures.
Computational Structural Engineering in Practice, Civil Comp. press- ISRN O-948 748- 30x,
–181.
Reese, S. (2007). A large deformation solid-shell concept based on reduced integration with
hourglass stabilization. International Journal for Numerical Methods in Engineering, 69,
–1716.
Sabir, A. B. (1997). Strain based shallow spherical shell element. Proc. Int. Conf on the Math.
Finite elements and application, Brunel University, England.
Sabir, A. B., & Charchaechi, T. A. (1982). Curved rectangular and general quadrilateral shell
finite elements for cylindrical shells. In J. R. Whiteman (Ed.), The math of finite element and
application (pp. 231–239). London: Academic Press.
Sabir, A. B., & Djoudi, M. S. (1990). A shallow shell triangular finite element for the analysis
of hyperbolic parabolic shell roof. FEMCAD. Struct. Eng. and Optimization, 49–54.
Sabir, A. B., & Djoudi, M. S. (1998). A shallow shell triangular finite element for the analysis
of spherical shells. Structural Analysis Journal, 51–57.Sabir, A. B., & Lock, A. C. (1972). A curved cylindrical shell finite element. IJMS, 14, 125–135.
Sabir, A. B., & Ramadhani, F. (1985). A shallow shell finite element for general shell analysis.
Variation Method in Engineering, Proceedings of the 2nd International Conference,
University of Southampton, England.
Schwarze, M., & Reese, S. (2009). A reduced integration solid-shell finite element based on
the EAS and the ANS concept-geometrically linear problems. International Journal for
Numerical Methods in Engineering, 80, 1322–1355.
Scordelis, A. C., & Lo, K. S. (1969). Computer analysis of cylindrical shells. Journal of American
Concrete Institute, 61, 539–561.
Simo, J. C., & Rifai, M. S. (1990). A class of mixed assumed strain methods and the method
of incompatible modes. International Journal for Numerical Methods in Engineering, 29,
–1638.
Zienkiewics, O. C. (1977). The finite element method (3rd ed.). London: McGraw Hill.
Zienkiewics, O. C., & Taylor, R. L. (2000). The finite element method, Vol. solid mechanics (5th
ed.). Butterworth: Heinemann.
