Nonconforming Finite Element Analysis of Shells

By selectively adding nonconforming displacement modes to the low order isoparametric elements, new highly improved shell elements have been established. To select the best set of nonconforming modes to use, various combinations of modes were added to the original elements. A linear element and a quadratic element, each of which have two nonconforming modes added to the in-plane displacement, four to the out-of-plane displacement, and no additional modes added to the modal rotations have been found to be most effective in terms of the number of nonconforming modes used versus the improvement obtained. These elements have been tested by use on deep beam, plate, and various shell problems. A cylindrical shell and a spherical shell are investigated in order to demonstrate the versatility of the newly developed nonconforming elements. The results obtained from these investigations compare very satisfactorily with the results from well-established analysis methods.