Efficient unified hourglass stabilization for one point quadrature three dimensional shell elements

The application of the finite element method to large scale problems involving non-linear shells, necessitates the use of efficient element formulations. This can be achieved using single point quadrature to integrate linearly interpolated shell elements. However, the spurious hourglass deformation modes that may occur with such formulations must be controlled if useful results are to be obtained. In the past, simplified approximations have been utilized to obtain relatively successful hourglass stabilization for shell elements. Although these methods provide improved efficiency, they suffer from a number of drawbacks which include lack of interpretation for the hourglass coefficient, and deteriorating performance for highly distorted elements. In this paper, a revised approach to the complete three dimensional hourglass control theory, developed in a previous work, is applied to a three dimensional non-linear shell element formulation. The efficiency of the proposed technique is shown to be comparable to the approximate formulations, while providing accurate predictions in problems involving large deformation.