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.
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