Design Method of the Ship Bottom Frame Based on Yield Reliability

LIU Yachong; WU Jiameng; TANG Yamin; HAN Tao; ZHU Junxia; XU Bo

doi:10.7643/issn.1672-9242.2026.10.003

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Equipment Environmental Engineering ›› 2026, Vol. 23 ›› Issue (10) : 28-36. DOI: 10.7643/issn.1672-9242.2026.10.003

Special Topic——Theoretical Analysis and Design Methods for Ships and Ocean Engineering Equipment

Design Method of the Ship Bottom Frame Based on Yield Reliability

LIU Yachong^1,2, WU Jiameng^1,2, TANG Yamin^1,2, HAN Tao¹, ZHU Junxia^1,2, XU Bo^1,2

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Abstract

The work aims to investigate the stress state and reliability level of the ship bottom frame in real marine environments, and design the component dimensions based on the target reliability. By constructing a yield stress state equation reflecting the true stress state of the components, the wave bending moment and hydrodynamic pressure were expressed as three-parameter expressions related to the sea wave environment. The First-Order Second-Moment (FOSM) method was adopted for structural reliability calculation to conduct a reliability check on the component dimensions initially determined by the rules, and the component dimensions satisfying the reliability requirements were determined based on the target reliability index. The reliability of the outer bottom plate determined based on the rules was significantly higher than that of the bottom stiffeners, revealing an imbalance in the safety margin between the two. To meet the target reliability (generally taken as 3.0), the thickness of the outer bottom plate could be appropriately reduced, while the section modulus of the bottom stiffeners should be appropriately increased. The traditional design based on the rules suffers from an uneven distribution of safety among components. Through the inverse deduction method based on the target reliability, the safety levels of various components can be effectively balanced, achieving a rational allocation of materials while ensuring the overall safety of the structure.

Key words

reliability method / FOSM method / stress state equation / bottom shell plating / bottom stiffener / target reliability

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LIU Yachong, WU Jiameng, TANG Yamin, HAN Tao, ZHU Junxia, XU Bo. Design Method of the Ship Bottom Frame Based on Yield Reliability[J]. Equipment Environmental Engineering. 2026, 23(10): 28-36 https://doi.org/10.7643/issn.1672-9242.2026.10.003

References

[1] IACS C S R. Common Structural Rules for Bulk Carriers and Oil Tankers[S]. London: International Association of Classification Societies, 2014.
[2] 王庆丰, 吴怡, 辛利佳, 等. 基于分项安全系数的矿砂船极限强度可靠性分析[J]. 江苏科技大学学报(自然科学版), 2025, 39(4): 1-5.
WANG Q F, WU Y, XIN L J, et al.Reliability Analysis of the Ultimate Strength of the Ore Carrier Based on the Partial Safety Factors[J]. Journal of Jiangsu University of Science and Technology (Natural Science Edition), 2025, 39(4): 1-5.
[3] 辛利佳, 王庆丰, 吴怡, 等. 基于不确定性载荷组合的矿砂船船体梁安全裕量研究[J]. 江苏科技大学学报(自然科学版), 2025, 39(4): 20-25.
XIN L J, WANG Q F, WU Y, et al.Study on the Safety Margin of the Hull Beams for the Ore Carrierbased on the Uncertain Load Combination Method[J]. Journal of Jiangsu University of Science and Technology (Natural Science Edition), 2025, 39(4): 20-25.
[4] 李雨婷, 陈晓斌, 何鹏鹏. 砂土中海上锚板抗拔极限状态的可靠度分析[J]. 岩土力学, 2023, 44(12): 3495-3500.
LI Y T, CHEN X B, HE P P.Reliability of Offshore Plate Anchor Design in Sand for Uplift Limit State[J]. Rock and Soil Mechanics, 2023, 44(12): 3495-3500.
[5] Det Norske Veritas.Structural Reliability Analysis of Marine Structures[R]. Norway: Det Norske Veritas, 1992.
[6] CHOI J H, JENSEN J J.Extreme Value Predictions Using FORM for Ship Roll Motions[J]. Marine Structures, 2019, 66: 52-65.
[7] IVANOV L D.Reliability Estimation of Ship’s Hull Girder in Probabilistic Terms when Ultimate Strength Is Used as a Failure Mode[J]. Ships and Offshore Structures, 2013, 8(2): 141-153.
[8] 柳松. 基于Monte-Carlo法的破冰船船艏结构可靠性研究[D]. 哈尔滨: 哈尔滨工程大学, 2023.
LIU S.Research on the Reliability of Ice Breaker Bow Structure Based on Monte-Carlo Method[D]. Harbin: Harbin Engineering University, 2023.
[9] 何福志, 万正权, 张伟. 基于船体结构总纵极限强度的可靠性分析[J]. 船舶力学, 2002, 6(2): 27-45.
HE F Z, WAN Z Q, ZHANG W.Ultimate Longitudinal Strength Reliability Assessmentof a Corroded Ship Hull[J]. Journal of Ship Mechanics, 2002, 6(2): 27-45.
[10] 易家祥. 改进的序贯Kriging-蒙特卡洛可靠性分析方法及在船舶结构设计中的应用[D]. 武汉: 华中科技大学, 2021.
YI J X.Improved Sequential Kriging-Monte Carlo Simulation Reliability Analysis Methods and Their Applications to Ship Structural Design[D]. Wuhan: Huazhong University of Science and Technology, 2021.
[11] 李放. 基于集成学习法的船舶结构可靠性优化设计研究[D]. 上海: 上海交通大学, 2020.
LI F.Reliability-Based Design Optimization Research of Ship Structure Based on Ensemble Learning Method[D]. Shanghai: Shanghai Jiao Tong University, 2020.
[12] 刘婧, 王德禹. 基于SMOTE算法和动态代理模型的船舶结构可靠性优化[J]. 中国舰船研究, 2020, 15(5): 114-123.
LIU J, WANG D Y.Reliability-Based Design Optimization of Ship Structure Using SMOTE Algorithm and Dynamic Surrogate Model[J]. Chinese Journal of Ship Research, 2020, 15(5): 114-123.
[13] 昝森. 集装箱船极限强度评估及研究[D]. 上海: 上海交通大学, 2018.
ZAN S.Study on Ultimate Strength Calculation and Assessment of Container Ships[D]. Shanghai: Shanghai Jiao Tong University, 2018.
[14] 杨智宇, 沈丽骊, 郭力, 等. IACS Rec.No. 34 Rev. 2新海浪环境下CSR船型极限强度可靠度和分项安全因子优化研究[J].中国舰船研究, 2026, 21(9): 1-9.
YANG Z Y, SHEN L L, GUO L, et al.Study on Ultimate Strength Reliability and Calibration of Partial Safety Factors for CSR Ships under New IACS Rec. 34 Rev. 2 Wave Environment[J]. Chinese Journal of Ship Research, 2026, 21(9): 1-9.
[15] 沈丽骊, 曹晶, 郭力, 等. 考虑船型尺度参数的船体梁极限强度分项安全因子多参数优化研究[J]. 中国舰船研究, 2026, 21(4): 1-10.
SHEN L L, CAO J, GUO L, et al.Multi-Parameter Optimization of Partial Safety Factors for Hull Girder Ultimate Strength Considering Ship-Type Dimensional Parameters[J]. Chinese Journal of Ship Research, 2026, 21(4): 1-10.
[16] SHI G J, GAO D W, ZHOU H.Analysis of Hull Girder Ultimate Strength and Residual Strength Based on IACS CSR-H[J]. Mathematical Problems in Engineering, 2019, 2019: 2098492.
[17] 贡金鑫, 仲伟秋, 赵国藩. 结构可靠指标的通用计算方法[J]. 计算力学学报, 2003, 20(1): 12-18.
GONG J X, ZHONG W Q, ZHAO G F.A General Approach for Computing Structural Reliability Index[J]. Chinese Journal of Computational Mechanics, 2003, 20(1): 12-18.
[18] MELCHERS R E.Extreme Value Statistics and Long- Term Marine Pitting Corrosion of Steel[J]. Probabilistic Engineering Mechanics, 2008, 23(4): 482-488.
[19] 赵伟, 杨永增, 于卫东, 等. 长期极值统计理论及其在海洋环境参数统计分析中的应用[J]. 海洋科学进展, 2003, 21(4): 471-476.
ZHAO W, YANG Y Z, YU W D, et al.Long-Term Extreme Value Statistics Theory and Its Application Tothe Marine Environmental Parameter Statistics and Analysis[J]. Advances in Marine Science, 2003, 21(4): 471-476.
[20] 陈钰, 邓乐, 唐文勇. 内河船舶可靠性分析中的波浪弯矩统计与极值分布[J]. 船舶工程, 2016, 38(6): 6-9.
CHEN Y, DENG L, TANG W Y.Statistics and Extreme Value Distribution of Wave-Induced Bending Moment for Reliability Analysis of Inland Waterway Ships[J]. Ship Engineering, 2016, 38(6): 6-9.
[21] 周渝航, 冯国庆, 张旭辉. 三体船屈服强度的可靠性研究[J]. 中国舰船研究, 2020, 15(3): 117-122.
ZHOU Y H, FENG G Q, ZHANG X H.Research on Reliability of Trimaran Yield Strength[J]. Chinese Journal of Ship Research, 2020, 15(3): 117-122.
[22] International Association of Classification Societies. NO.34 Standard Wave Data: Rev. 1 Corr. 1[S]. London: International Association of Classification Societies, 2001.
[23] 谢永和, 吴剑国, 李俊来. 船舶结构设计[M]. 上海: 上海交通大学出版社, 2011.
XIE Y H, WU J G, LI J L.Ship Structural Design[M]. Shanghai: Shanghai Jiao Tong University Press, 2011.
[24] HESS P E, BRUCHMAN D, ASSAKKAF I A, et al.Uncertainties in Material and Geometric Strength and Load Variables[J]. Naval Engineers Journal, 2002, 114(2): 139-166.
[25] 中国船级社. 钢质海船入级规范(2025)[S]. 北京:中国船级社, 2025.
China Classification Society. Rules for Classification of Sea-Going Steel Ships(2025)[S]. Beijing: China Classification Society, 2025.