Effect of Initial Imperfections on the Strength of Restrained Plates

Most common studies on the strength of plates under compressive longitudinal loading are related to plates having unrestrained edges which lead to a zero net load in the transverse direction. In ships, the framing system and the continuity of the plating in the transverse direction tend to induce rather different boundary conditions on the “unloaded” edges, which results in a completely different state of stresses when the external loads are applied. This is due to the surge of a significant level of induced membrane stresses in the direction perpendicular to loading. In this work, the behavior of long restrained plates under compressive axial loading is analyzed and compared with the one of plates having other boundary conditions. The finite element method is applied for the nonlinear analysis of the plates using a commercial package. Fifty-six cases are considered corresponding to different levels of plate slenderness which ranges between 0.35 and 3.46 covering the practical range of structural plates used in the shipbuilding industry. Various shapes of initial imperfections are considered in order to establish the minimum level of resistance. Also, the influence of the magnitude of the distortions associated to each mode is discussed. The study conducted to the establishment of the minimum compressive strength of restrained plates and it defines the expected range of strength's variation due to the magnitude level of distortions. The biaxial state of stresses resulting from these boundary conditions is characterized and its dependence from the plate's slenderness is quantified for the most common type of the hull plating.