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

by Zhiyao Zhu 1,2, Huilong Ren 1,2, Chenfeng Li 1,2,* and Xueqian Zhou 1,2,*
1
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
2
International Joint Laboratory of Naval Architecture and Offshore Technology between Harbin Engineering University and Lisbon University, Harbin 150001, China
*
Authors to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2020, 8(2), 117; https://doi.org/10.3390/jmse8020117
Received: 24 January 2020 / Revised: 9 February 2020 / Accepted: 12 February 2020 / Published: 14 February 2020
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. View Full-Text
Keywords: PSO-based Smith method; ultimate limit state function; piecewise polynomial fitting; damaged ship; combined loads PSO-based Smith method; ultimate limit state function; piecewise polynomial fitting; damaged ship; combined loads
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Zhu, Z.; Ren, H.; Li, C.; Zhou, X. Ultimate Limit State Function and Its Fitting Method of Damaged Ship under Combined Loads. J. Mar. Sci. Eng. 2020, 8, 117.

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