Advanced Finite Elements for Geometrically Nonlinear Analysis of Rectangular Plates under Various In-Plane Loadings Accounting for the Boundary Conditions of the Stiffeners

Abstract

Highly flexible plate structures are subjected to various loading and edge conditions in many engineering applications, such as in the aerospace and civil industries. In this paper, the post-buckling response of rectangular plates subjected to axial and shear loadings is investigated by employing the Carrera Unified Formulation (CUF). As in previous works, only isolated plates have been considered, regardless of the effects of the stiffeners and boundary conditions imposed by the surroundings. However, in this research, different plate models are implemented, and the effects of boundary conditions imposed by the stiffeners are evaluated precisely. Comprehensive assessments are provided for the geometrically nonlinear equilibrium curves of the plate structures using the Newton–Raphson linearization method with the path-following constraint. Furthermore, the comparisons of different geometrically nonlinear assumptions according to the full Green–Lagrange nonlinear model and von Kármán nonlinear plate theory are presented. The importance of strain–displacement relationships and stiffeners’ effects in the nonlinear response of plate structures is highlighted. As a result, the accuracy and effectiveness of the presented CUF-2D model are demonstrated.