LAUSR

Abstract The present study is undertaken based on a nonlinear finite element study carried out by the same authors for estimation of ultimate strength of cracked continuous unstiffened plates used in ship structures under in-plane longitudinal compression. Investigations show that in addition to the magnitude of ultimate strength, the deflection shape and plastic collapse mechanism will also change completely. Results show that deflection in the cracked half wave increases more rapidly than other half waves. Consequently generated half waves in a cracked plate will not have identical length and amplitude. This implies that the conventional plastic collapse mechanism cannot be used to predict the behavior of cracked plates in the post ultimate strength region. A new plastic collapse mechanism based on the FEM results is suggested and the principle of virtual work is used to derive the axial stress-deflection relation of the plate. However, due to inequality of the length and amplitude of generated half waves, the axial stress-deflection relation cannot be directly derived from the principle of virtual work. Therefore, in order to solve the virtual work equation, some auxiliary relations between the involved parameters are required. Auxiliary equations are derived using regression analysis based on FEM results. Finally, a semi-analytical formulation is derived to estimate post ultimate strength behavior of cracked plates. It is shown that the proposed semi-analytical formulation can predict both magnitude and slope of the stress-deflection curves with better accuracy compared to the conventional plastic collapse mechanism. The formulation can be used within the defined ranges of simulated crack lengths, slenderness and aspect ratios.