Formulation and evaluation of incompatible but convergent rational quadrilateral membrane elements

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