Testing the asymptotic behaviour of shell elements - Part I: the classical benchmark tests

The asymptotic behaviour is considered to be one of the most demanding levels of benchmark testing for shell elements. In the present paper, the asymptotic behaviour of classical benchmark problems is analytically and numerically investigated. The aim is to examine the possibility of using the classical benchmark tests for testing the asymptotic behaviour of shell elements. Appropriate analytical approaches are introduced to investigate the asymptotic behaviour of the classical benchmark problems. The reformulated four-node shell element (RFNS) is employed in the numerical analyses. It is shown that the classical benchmark tests, in addition to testing the reliability and robustness of shell elements, also represent strong challenging tests for the asymptotic behaviour of shell elements. In the course of the numerical investigation of the asymptotic behaviour of the classical benchmark problems, the reliability and e ciency of the RFNS element already established by means of the classical con guration of the benchmark tests is re-con rmed in all cases of the corresponding asymptotic test con gurations