Ultimate Limit State Function and Its Fitting Method of Damaged Ship under Combined Loads

Zhiyao Zhu,Xueqian Zhou,Chenfeng Li,Huilong Ren

doi:10.3390/jmse8020117

Zhiyao Zhu, Xueqian Zhou + Show 2 more

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https://doi.org/10.3390/jmse8020117

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Abstract

The ultimate limit state function is one of the premises for the assessment of structure strength and the safety of ships under severe conditions. In order to study the residual strength of damaged ships under the combined load of vertical and horizontal bending moments acting on the hull girder, the ultimate limit state function of a damaged ship under combined load, and its fitting methods are investigated in this paper. An improved Smith Method is adopted to calculate the residual load carrying capacity of damage ships, where the rotation and translation of the neutral axis of the damaged cross-section are obtained using a particle swarm optimisation method. Because the distribution curve of the residual load carrying capacity of a damaged ship under combined load is asymmetric, the application of traditional explicit polynomial fitting methods results in poor accuracy. In this study, a piecewise weighted least square fitting method is adopted so as to guarantee the continuity in the transitions, and a method is proposed for fitting the ultimate limit state function of a damaged ship under combined load. Calculations of the residual strength show that the improved Smith Method is more accurate than the original Smith Method for the accurate position of the neutral axis. The error analysis of the fitting methods shows that the ultimate limit state function that is fitted using a piecewise weight least square method is more accurate.

Highlights

Ships may encounter various types of dangers at sea; for instance, list due to stranding or hull damage due to collision
The accuracy of the Smith Method relies on the stress–strain relationship and the calculation of the neutral axis
(1) Compared to the implementations of the Smith Method, where only the translation of the neutral axis is considered, or the linear search method is applied to trace the position of the neutral axis, the Particle Swarm Optimisation (PSO)-based Smith Method is more accurate in obtaining the instantaneous position of the neutral axis, and helps produce more accurate results for the ultimate bending moment

Summary

Introduction

Ships may encounter various types of dangers at sea; for instance, list due to stranding or hull damage due to collision. Compared to ships floating in the upright position, the hydrostatic load acting on a damaged ship is very different. Researches have shown that the horizontal load acting on a damaged ship may be as large as 1.73 times the vertical load [1,2]. For this reason, the assessment of ship strength is more than just about dealing with the vertical bending moment; the ultimate limit state function of the ship under the action of combined loads must be assessed

Methods

Results

Conclusion