Two simple and efficient displacement-based quadrilateral elements for the analysis of composite laminated plates

Two simple 4-node 20-DOF and 4-node 24-DOF displacement-based quadrilateral elements named RDKQ-L20 and RDKQ-L24 are developed in this paper based on the first-order shear deformation theory (FSDT) for linear analysis of thin to moderately thick laminates. The deflection and rotation functions of the element sides are obtained from Timoshenko's laminated composite beam functions. Linear displacement interpolation functions of the standard 4-node quadrilateral isoparametric plane element and displacement functions of a quadrilateral plane element with drilling degrees of freedom are taken as in-plane displacements of the proposed elements RDKQ-L20 and RDKQ-L24, respectively. Due to the application of Timoshenko's laminated composite beam functions, convergence can be ensured theoretically for very thin laminates. The elements are simple in formulation, and shearlocking free for extremely thin laminates even with full integration. A hybrid-enhanced procedure is employed to improve the accuracy of stress analysis, especially for transverse shear stresses. Numerical tests show that the new elements are convergent, not sensitive to mesh distortion, accurate and efficient for analysis of thin to moderately thick laminates.