Improved finite element models for the analysis of plate and shell structures

Abstract

The present work is concerned with the development of improved finite element models for the analysis of plate and shell structures. The original Ahmad``s degenerated shall element has good performances for moderately thick situations. However, the element suffer from shear/membrane locking phenomena for thin shells when normal integration is used to evaluate the stiffness matrix. Although reduced or selective integration technique has been proposed to alleviate these deficiencies, such scheme is not always successful in overcoming locking behavior. Furthermore, the use of reduced integration technique leads to elements which can produce not only rigid body motions but also extra zero-energy modes in some cases and eventually give the erratic solutions. In the present study, the application of reduced or selective integration technique, the addition of nonconforming displacement modes, and their coupling to Ahmad``s degenerated shell elements to improve their basic behavior and solve the locking phenomena are reviewed and the establishments of a seris of new plate and shell elements by combined use of these schemes are presented. The new elements have the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy modes. It is shown that the results obtained by new elements converged to the exact solutions very rapidly as the mesh is refined and exhibited reliable solutions even for severely distorted meshes through numerical studies for standard benchmark problems. These elements are shown to overcome the shear/membrane locking problems completely so that they are applicable to the wide range of plate and shell problems, giving a high accuracy for both thick and thin structures.