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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 75
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and Z. Bittnar
Paper 77

Nonlinear Behaviour of the RFNS Element - Large Displacements and Rotations

D. Briassoulis

Department of Agricultural Engineering, Agricultural University of Athens, Greece

Full Bibliographic Reference for this paper
D. Briassoulis, "Nonlinear Behaviour of the RFNS Element - Large Displacements and Rotations", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 77, 2002. doi:10.4203/ccp.75.77
Keywords: shell finite elements, geometrical nonlinear analysis, large displacements, large rotations.

Summary
The reformulated four-node shell element proposed in [1] has been shown to exhibit an excellent behaviour with respect to a well-known set of benchmark tests established over the last years specifically for shell elements. This shell element does not experience any locking phenomena or zero energy modes, performing equally well in flat as well as in warped shell element configurations. Its performance has been found to be favourably compared to that of other well established elements. Recently the performance of the RFNS element was re-confirmed in terms of its asymptotic behaviour by means of classical and new limit tests [1,2].

In the present paper, the RFNS formulation is extended to incorporate geometrically nonlinear behaviour, including membrane action, large displacements and large rotations. The nonlinear formulation of the RFNS element is based on the same assumptions that are employed in the linear formulation. Thus, lines perpendicular to the shell midsurface are assumed to remain straight during the element deformation and normal stress in the transverse direction is assumed to be zero. The total Lagrangian formulation is employed. The effect of thickness change, important for finite strain problems, is not considered in the present formulation and thus the shell director is assumed non-extensible. The present geometrical nonlinear approach represents a first approach to investigate the basic nonlinear behaviour of the RFNS element without resorting to any special techniques for line-search procedures to pass limit points and trace post-buckling behaviour.

The formulation is numerically investigated against selected classical nonlinear problems. An efficient performance of the new nonlinear shell element formulation is confirmed for the applications investigated. It is also shown that an efficient modeling of membrane action is achieved as compared to results obtained numerically by employing other numerical approaches, commercial finite element programs and full- scale experiments.

References
1
Briassoulis D. "The Four-node Shell Element Reformulated", Int. J. Numer. Meth. Eng.,39, 2417-2455, 1996. doi:10.1002/(SICI)1097-0207(19960730)39:14<2417::AID-NME959>3.0.CO;2-0
2
Briassoulis D., "Testing the Asymptotic Behaviour of Shell Elements, Part I. The Classical Benchmark Tests", Int. J. Numer. Meth. Eng, 54, 3, 421-452, 2002. doi:10.1002/nme.436
3
Briassoulis D., "Testing the Asymptotic Behaviour of Shell Elements, Part II. New limit tests: Analytical Solutions and the RFNS Element Case", Int. J. Numer. Meth. Eng., to be published, 2002. doi:10.1002/nme.435

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