Evaluation of geometrically nonlinear terms in the large-deflection and post-buckling analysis of isotropic rectangular plates

The nonlinear mechanical response of highly flexible plates and shells has always been of primary importance due to the widespread applications of these structural elements in many advanced engineering fields. In this study, the Carrera Unified Formulation (CUF) is used in a total Lagrangian framework to analyze the large-deflection and post-buckling behavior of isotropic rectangular plates based on different nonlinear strain assumptions. The scalable nature of the CUF provides us with the ability to tune the structural theory approximation order and the strain–displacement assumptions opportunely. In this work, the Newton–Raphson linearization scheme with a path-following constraint is used in the framework of the 2-D CUF to solve the geometrically nonlinear problems to draw important conclusions about the consistency of many assumptions made in the literature on the kinematics of highly flexible plates. In this regard, the effectiveness of the well-known von Kármán theory for nonlinear deformations of plates is investigated with different modifications such as the thickness stretching and shear deformations due to transverse deflection. The post-buckling curves and the related stress distributions for each case are presented and discussed. According to the results, the full Green–Lagrange nonlinear model could predict the nonlinear behavior of plates efficiently and accurately, whereas other approximations produce considerable inaccuracies in the case of thick plates subjected to large rotations and deflections.