Equivalent Single-Layer and Layerwise Shell Theories and Rigid-Body Motions—Part I: Foundations

Abstract

The exact representation of rigid-body motions in the displacement patterns of the first-order equivalent single-layer (ESL) and layerwise (LW) shell elements is considered. This consideration requires the development of the strain–displacement relationships of the ESL and LW shell theories with regard to their consistency with rigid-body motions. The fundamental unknowns consist of six displacements of the face surfaces of the shell in the ESL theory and 3(N + 1) displacements of the face surfaces of layers in the LW shell theory, where N is a number of layers. Such a choice of displacements makes it possible to deduce strain–displacement relationships, which are objective, that is, invariant under rigid-body motions. To overcome thickness locking, three types of the modified material stiffness matrix corresponding to the generalized plane-stress state are employed.