Large-deflection and post-buckling analyses of isotropic rectangular plates by Carrera Unified Formulation

Abstract

Accurate predictions of the in-service nonlinear response of highly flexible structures in the geometrically nonlinear regime are of paramount importance for their design and failure evaluation. This paper develops a unified formulation of full geometrically nonlinear refined plate theory in a total Lagrangian approach to investigate the large-deflection and post-buckling response of isotropic rectangular plates. Based on the Carrera Unified Formulation (CUF), various kinematics of two-dimensional plate structures are consistently implemented via an index notation and an arbitrary expansion function of the generalized variables in the thickness direction, resulting in lower- to higher-order plate models with only pure displacement variables via the Lagrange polynomial expansions. Furthermore, the principle of virtual work and a finite element approximation are exploited to straightforwardly and easily formulate the nonlinear governing equations. By taking into account the three-dimensional full Green–Lagrange strain components, the explicit forms of the secant and tangent stiffness matrices of unified plate elements are presented in terms of the fundamental nuclei, which are independent of the theory approximation order. The Newton–Raphson linearization scheme combined with a path-following method based on the arc-length constraint is utilized to solve the geometrically nonlinear problem. Numerical assessments, including the large-deflection response of square plates subjected to transverse uniform pressure and the post-buckling analysis of slender plates under compression loadings, are finally conducted to confirm the capabilities of the proposed CUF plate model to predict the large-deflection and post-buckling equilibrium curves as well as the stress distributions with high accuracy.