Finite deformation analysis of the elastic circular plates under pressure loading

Abstract

As one of the most commonly used engineering components, thin plates usually undergo large deflections when subjected to intense pressure loadings. In addition to the material nonlinearity, such as plastic yielding, the geometric nonlinearity caused by this finite deformation also has a great influence over its total response. In this study, a finite deformation approximation solution is given theoretically for the elastic circular plate, based on the von Kármán equations and the uniform membrane strain assumption. Through comparisons with the corresponding finite element simulations and the existing theoretical solution, the present solution is confirmed to be both accurate and efficient, for thin plate under uniform pressure loading, in both static and dynamic loading conditions. Thereafter, the competing effects and the respective dominant ranges of bending and stretching are investigated.Besides, based on the accurate stress prediction provided by the proposed high-order deformation model, the limit state of the elastic stage is analyzed, including the location that first reached the elastic limit and the corresponding instant. Thus, the present approximate solution will be valuable in future studies of failure criteria and subsequent inelastic behavior.