This thesis presents an eight-node hexahedral finite element, which is free of volumetric and shear locking, and possesses no spurious singular modes for nonlinear analysis of multi-layered shells. The underlying variational formulation is based on an assumed strain method. From a kinematical viewpoint, displacements and rotations are assumed finite while the strains are infinitesimal. The proposed model is cast in a corotational procedure which is derived consistently from the updated Lagrangian framework. The close relationship between the corotational procedure and its underlying updated Lagrangian procedure is presented to highlight the cost reduction for large and complicated geometric configurations. Some simple but mathematically consistent procedures for updating element stresses and calculating the internal force vector are also presented. The proposed model can accommodate an arbitrary number of elements through the thickness at the free edges where interlaminar peeling stresses can potentially lead to delamination and local buckling. The kinematic hypothesis results in independent shear deformation of the director associated with each individual layer and thus allows the warping of the composite cross-section. Rate independent elastoplasticity is considered in this study. The Associative J 2 flow rules with general nonlinear kinematics and isotropic hardening rules are considered. Numerical examples are presented to demonstrate the applicability of the proposed element.
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