A Simple Locking-Alleviated 3D 8-Node Mixed-Collocation C0 Finite Element with Over-Integration, for Functionally-Graded and Laminated Thick-Section Plates and Shells, with & without Z-Pins

a simple locking-alleviated 3D 8-node mixed-collocation C0 finite element (denot-ed as CEH8) is developed in this study, for the modeling of functionally-graded or laminated thick-section composite plates and shells, without using higher-order or layer-wise zig-zag plate and shell theories which are widely popularized in the current literature. The present C0 element independently assumes an 18-parameter linearly-varying Cartesian strain field. The independently assumed Cartesian s-trains are related to the Cartesian strains derived from mesh-based Cartesian dis-placement interpolations, by exactly enforcing 18 pre-defined constraints at 18 pre-selected collocation points. The constraints are rationally defined to capture the basic kinematics of the 3D 8-node C0 element, and to accurately model each basic deformation mode of tension, bending, shear, and torsion. A 2×2×2 Gauss quadra-ture is sufficient for evaluating the stiffness matrix of CEH8 C0 3D elements for homogeneous materials, but over-integration (with a higher-order Gauss Quadra-ture, a layer-wise Gauss Quadrature, or a simple Trapezoidal Rule in the thickness direction) is used for functionally-graded materials or thick-section laminated com