Comparative study of primal- and dual-mixed finite element models for cylindrical shells

Abstract

Dedicated to Professor Barna Szabó on the occasion of his eightieth birthdayand to Professor Imre Kozák on the occasion of his eighty-fifth birthdayAbstract. Analytical and numerical comparisons of a primal-mixed, a dual-mixed and a consistent primal-dual mixed finite element formulation are presented for cylindrical shells using the lowest possible order, constant and linear, polynomial approximations within the framework of the Naghdi shell model. The stiffness matrices and the load vectors of the mixed elements are explicitly derived and compared to each other and to that of the standard displacement-based shell element for axisymmetric deformations. It is pointed out that the stiffness matrices of the dual-mixed and the primal-dual mixed elements can be related to that of the standard shell element through two geometry-, material-and mesh-dependent coefficients. One of these coefficients turns out to be a reliable shear locking indicator which can be used to transform the standard displacement-based shell element into a shear locking-free dual-mixed one, independently of the thickness and the loading of the shell. The numerical comparisons indicate that the dual-mixed element is the only element that gives second-order rates of asymptotic convergence for all the variables, including the bending moment and shear force computations.Mathematical Subject Classification: 05C38, 15A15