Equivalent Single-Layer and Layerwise Shell Theories and Rigid-Body Motions—Part II: Computational Aspects

Abstract

The precise representation of rigid-body motions in the displacement patterns of the first-order equivalent single-layer (ESL) and layer-wise (LW) shell elements has been considered in the companion paper (Part I). In this paper, computational aspects of the ESL shell formulation are discussed in detail. To overcome shear and membrane locking and have no spurious zero energy modes, the assumed strain and stress resultant fields are invoked. On the basis of this approach, a family of four-node curvedESL shell elements is designed. All elemental stiffness matrices have six, and only six, zero eigenvalues and require only direct substitutions. Besides, they are evaluated by using the full exact analyticalintegration. To demonstrate the efficiency and accuracy of the developed formulation, extensive numerical studies are presented.