Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements

Two simple displacement-based 4-node quadrilateral elements RDKQ-NL20 and RDKQ-NL24 are developed in this paper for geometrically nonlinear analysis of thin to moderately thick laminated composite plates. The proposed quadrilateral nonlinear laminated composite plate elements are based on the first-order shear deformation theory (FSDT) and von-Karman’s large deflection theory, and the total Lagrangian approach is employed to formulate the elements. The deflection and rotation functions of the element boundary are obtained from Timoshenko’s laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates. The linear displacement interpolation functions of the standard 4-node quadrilateral isoparametric plane element and the in-plane displacement functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements of elements RDKQ-NL20 and RDKQ-NL24, respectively. The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that they are accurate and efficient for large deformation, small rotation nonlinear analysis of thin to moderately thick laminated composite plates.