Plastic mechanism analysis of the resistance of ship longitudinal girders in grounding and collision

A theoretical model for ship bottom longitudinal girders being crushed during accidental raking process has been proposed and developed on the basis of nonlinear finite element analysis. Focus is placed on establishing the basic folding mechanism, and identifying the major energy dissipation pattern. Using the plastic methods of analysis, the simplified analytical expression for total energy dissipation, which is composed of bending and membrane energy, has been formulated. Subsequently, the mean horizontal resistance is derived. It depends on two free parameters, namely crushing distance and wave angle. It is noted that the optimality condition could not be achieved by minimising the energy expression or mean crushing force with respect to these free parameters. Therefore, empirical expressions, which agree reasonably with the results from finite element simulations, have been employed. Three series of parametric/sensitivity studies have been carried out by using LS-DYNA code. Comparisons between the proposed simplified method and simulations have been made. In some cases, excellent agreement is obtained. However, some discrepancy between theory and numerical simulations is also noticed and needs further investigation. The theory presented is not only pertinent to longitudinal girders in ship bottom structure during raking but is also relevant to side stringers in sliding collision situations. The simplified method developed will contribute substantially to the establishment of efficient methods for fast and reliable assessment of the outcome of accidental collisions and grounding events. Such methods may in turn be incorporated into decision support tools for crisis handling in emergency situations, e.g. for tankers in disabled conditions.

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