# Formulation and evaluation of incompatible but convergent rational quadrilateral membrane elements

• Batoz, J.L. (Universite de Technologie de Compiegne, Laboratoire de Genie Mecanique pour les Materiaux et les Structures) ;
• Hammadi, F. (Universite de Technologie de Compiegne, Laboratoire de Genie Mecanique pour les Materiaux et les Structures) ;
• Zheng, C. (Universite de Technologie de Compiegne, Laboratoire de Genie Mecanique pour les Materiaux et les Structures) ;
• Zhong, W. (Dalian University of Technology)
• Published : 2000.02.25

#### Abstract

This paper presents four incompatible but convergent Rational quadrilateral elements, two four-node elements (RQ4Z and RQ4B) and two five-node elements (RQ5Z and RQ5B). The difference between the so-called Rational Finite Element (Zhong and Zeng 1996) and the Free Formulation (Bergan and Nygard 1984) are discussed and compared. The importance of the mode completeness in these formulations is emphasized. Numerical results for several benchmark problems show the good performance of these elements. The two five-nodes elements RQ5Z and RQ5B, which can be viewed as complete quadratic mode elements (with seven stress modes), always give better results than the four nodes elements RQ4Z and RQ4B.

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#### Cited by

1. Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum vol.19, pp.5, 2002, https://doi.org/10.1108/02644400210435843