A nonlinear stiffened-panel substructure method for efficient prediction of hull girder ultimate bending strength

The reliable prediction of hull girder ultimate strength has long been a cornerstone of ship structural design, but current numerical approaches either rely on oversimplified empirical formulas that lack generality or demand prohibitively high computational costs that hinder practical engineering applications. The core difficulty lies in the huge computation of nonlinear load-displacement characteristics for stiffened panels, which must account for strong coupling between large-deflection buckling and progressive plasticity. This paper overcomes these challenges by developing a nonlinear stiffened-panel substructure (NSPS) method with two key innovations. First, an improved plate superelement is formulated that explicitly enforces the large-deflection compatibility equation via the Airy stress function, inherently correcting the post-buckling membrane strains, and introduces a surface-differentiated von Mises plasticity correction to capture buckling-induced premature yielding. Second, a beam-column superelement is derived with an analytical post-buckling stiffness expression based on plastic hinge mechanism, enabling accurate simulation of the descending load-bearing branch. On this basis, a parametric substructure assembly strategy-grounded on principles of repetition, importance, and uniqueness-is proposed, allowing the entire hull section to be modeled using only tabular inputs without mesh generation. Critically, identical substructures are computed only once and their load-displacement curves are interpolated repeatedly, yielding drastic efficiency gains. Validation against FE simulations and experimental data for the Nishihara MST-3 box girder, one naval ship hull, one opening ship and Dow's frigate model demonstrates that the proposed method predicts ultimate bending strength with errors below 4.5%, while reducing computational time to lower than 17.9% of that required by conventional FE analyses. The proposed NSPS method offers a robust, computationally tractable alternative for preliminary design and parametric studies of complex ship structures.