A Method for Analyzing Elastic Large Deflection Behavior of Perfect and Imperfect Plates With Partially Rotation-Restrained Edges

Abstract

The edge condition of the plating in a continuous stiffened-plate structure is neither simply supported nor clamped because the torsional rigidity of the support members at the plate edges is neither zero nor infinite. In a robust ship structural design, it is necessary to accurately take into account the effect of the edge condition in analyses of plate behavior in terms of buckling and post-buckling behavior. The aim of this study is to develop a new method for analyzing the geometric nonlinear behavior (i.e., elastic large deflection or post-buckling behavior) of plates with partially rotation-restrained edges in association with the torsional rigidity of the support members and under biaxial compression. An analytical method was developed to solve this problem using the nonlinear governing differential equations of plates. The validity of the developed method was confirmed by comparison with nonlinear finite element method solutions with varying values for the torsional rigidity of the support members, plate aspect ratio, and biaxial loading ratio. The developed method was found to give reasonably accurate results for practical design purpose in terms of the large deflection analysis of plates with partially rotation-restrained edges, and it will be useful for the robust design of ship structures in association with buckling and ultimate strength of plates surrounded by support members.