A simplified approach to assess the resistance of a ship sliding on elliptic paraboloïd rock

Abstract

This paper presents a simplified method for predicting the resistance of a ship bottom structure sliding over a rock idealised as an elliptic paraboloid. The derived analytical model may be considered as an extension of a previous work by the authors on the response of such structure in raking condition. The approach consist in splitting the structure into several independent super-elements and to derive closed-form expressions giving the plastic resistance force of each of them. Theoretical developments are based on plastic limit analysis with the objective to capture the main deformation modes of the outer shell plating, transverse floors, and longitudinal girders. Situations where the rock impacts the structure between two girders and below one girder are investigated as well as the general case where the ship bottom is not horizontal but inclined. For each situation, the proposed analytical formulations are confronted to numerical simulations performed with Ls-Dyna finite element solver, considering different rocks, friction coefficients and penetration heights. A good correlation between analytical predictions and numerical simulations is found for the majority of the sliding scenarios investigated but some limitations of the proposed model are also highlighted, more specifically when the grounding event involves a very sharp rock. Finally, it is shown that both the ship bottom inclination and its friction with the rock have a significant influence on the results.