Testing the asymptotic behaviour of shell elements - Part II: New limit tests: analytical solutions and the RFNS element case

The asymptotic behaviour of classical benchmark tests was investigated in the rst part of this work. In the present second part, the behaviour of some new limit problems, recently proposed as being speci cally applicable to benchmark testing of the asymptotic behaviour of shell elements, is analytically and numerically investigated. Exact analytical solutions are obtained based on Flugge’s theory for cylindrical shells. These analytical solutions are used along with, and in comparison to, the corresponding solutions obtained earlier by symbolic calculus using the Reissner–Mindlin shell model. The reformulated four-node shell (RFNS) element is employed in the numerical analyses in a parallel, supportive–comparative character, next to the analytical investigation of the asymptotic behaviour of the new limit tests. As with the case of the classical benchmark tests, in the course of the numerical investigation, the reliability and e ciency of the RFNS element is re-con rmed in all cases of the new asymptotic tests. A good agreement with the boundary layers described analytically is obtained even in very thin shell element applications. The various load-carrying mechanisms shown numerically to be active in the cases under investigation follow closely the analytical predictions. The energy components appear to be more sensitive to the modelling of boundary layers in cases of mixed mode problems. In several cases, the solutions obtained earlier by using symbolic calculus are shown to be inadequate