Time-variant bulk carrier reliability analysis in pure bending intact and damage conditions

Time-variant reliability analysis of a corroded bulk carrier in intact and damage conditions is performed by First-Order (FORM), Second-Order (SORM) Reliability Methods and Importance Sampling simulation. Annual failure probabilities are determined up to 25-year ship lifetime, accounting for time-variant corrosion wastage of structural members contributing to hull girder strength. Statistical properties of hull girder capacity are determined by Monte Carlo simulation, applying three correlation models among corrosion wastages of structural members contributing to hull girder strength, namely no correlation, full correlation and full correlation among wastages of structural members belonging to the same category of compartments. A modified incremental-iterative method is applied, to account for instantaneous neutral axis rotation, in case of asymmetrical damage conditions, as for collision and grounding events. Incidence of intact/damage condition, as well as correlation among corrosion wastages, on annual sagging/hogging time-variant failure probability is investigated and discussed. Time-variant sensitivity analyses for intact and damage conditions are also performed, to investigate the incidence of random variables' uncertainties on the attained failure probability. Finally, the bulk carrier section scheme, benchmarked in the last ISSC Report, is applied as test case.     

点蚀损耗对船体梁极限强度的影响（英文）

The paper focuses on the assessment of the hull girder ultimate strength,combined with random pitting corrosion wastage,by the incremental-iterative method.After a brief review about the state of art,the local ultimate strength of pitted platings under uniaxial compression is preliminarily outlined and subsequently a closed-form design formula is endorsed in the Rule incremental-iterative method,to account for pitting corrosion wastage in the hull girder ultimate strength check.The ISSC bulk carrier is assumed as reference ship in a benchmark study,devoted to test the effectiveness of the incremental-iterative method,by a comparative analysis with a set of FE simulations,performed by Ansys Mechanical APDL.Four reference cases,with different locations of pitting corrosion wastage,are investigated focusing on nine combinations of pitting and corrosion intensity degrees.Finally,a comparative analysis between the hull girder ultimate strength,combined with pitting corrosion wastage,and the relevant values,complying with the Rule net scantling approach,is performed.Based on current results,the modified incremental-iterative method allows efficiently assessing the hull girder ultimate strength,combined with pitting corrosion wastage,so revealing useful both in the design process of new vessels and in the structural health monitoring of aged ships.     

腐蚀对双壳超大型原油运输船船体的影响研究（英文）

This study aims to examine and analyze the effect of corrosion wastage on the ship hull of a double hull very large crude oil carrier. To calculate the ultimate bending moment capacity, along with the neutral axis position at the limit state, section modulus, and moment of inertia, the incremental-iterative method is employed. This paper also considered the residual strength checking criteria of ship hull and the ultimate stress behaviors of the representative structural elements. Then, Paik's probabilistic corrosion, which employs two levels of corrosion rate and three different assumptions of coating life time, is applied to assess the corrosion effects. The calculation results obtained through relevant analyses are also presented.     

Time-variant ultimate longitudinal strength of corroded bulk carriers

Many bulk carrier losses have been reported of late, and one of the possible causes of such casualties is thought to be the structural failure of aging hulls in rough weather. In aging ships, corrosion and fatigue cracks are the two most important factors affecting structural safety and integrity. This paper uses a set of the time-dependent corrosion wastage models for 23 different member locations/categories of bulk carriers previously developed by the authors, based on the available corrosion measurements for existing large bulk carrier structures. Differences due to the location and corrosion severity of every member type are taken into account. The nominal design corrosion values for the primary members are suggested based on the annualized corrosion rates obtained in the present study. The effect of time-variant corrosion wastage on the ultimate hull girder strength as well as the section moduli is studied. The criteria for repair and maintenance of heavily corroded structural members so as to keep the ultimate longitudinal strength at an acceptable level are discussed. Important insights and conclusions developed are summarized.     

内河船舶船体梁极限弯曲能力统计特性研究

针对内河船舶船体梁极限弯曲能力的计算与统计特性问题,将影响船体梁极限弯曲能力的主要因素作为随机变量,分别讨论了材料屈服强度与板厚的概率分布参数选取。采用增量迭代方法与改进Rosenblueth方法,计算得到船体梁极限弯曲能力及其分布参数。研究表明,极限弯曲能力计算时可不考虑板厚变异的影响,内河船舶船体梁极限弯曲能力具有统计上的稳定性。     

复合材料船体纵向极限强度可靠性分析

把船体甲板或船底板结构视为是一系列加筋板单元的组合，然后利用复合材料梁柱理论计算船体加筋板单元构件的极限承载能力，最后用Smith法计算复合材料船体的极限承载能力。由于复合材料船体纵向极限强度的极限状态方程不能简单地用船体各参数显式表达，故将近年发展起来的响应面法与JC法相结合，对复合材料船体纵向极限强度进行了可靠性分析。并讨论了影响船体纵向极限强度可靠性各变量的敏感性。     

破损船体非对称弯曲极限强度分析及可靠性评估

在船体发生破损后,其剩余有效剖面是非对称的,船体还可能倾斜。本文首先对破损船体非对称弯曲进行了弹性和塑性分析,在此基础上假设了破损船体发生整体破坏时的剖面应力分布,给出了破损船体非对称弯曲极限强度分析方法,并采用了比较精细的方法计算加筋板格的屈曲极限强度。以箱型梁模型和超大型油船为例,将本文的计算结果与试验、ＩＳＵＭ法及解析公式的结果进行了比较。基于破损船体极限强度,结合重要性样本法,对６５,００     

CFRP修复的FPSO点蚀船体梁极限强度分析

采用非线性有限元法对中拱和中垂工况条件下碳纤维增强聚合物(Carbon Fiber Reinforced Polymer, CFRP)修复的浮式生产储卸油装置(Floating Production Storage and Offloading, FPSO)点蚀船体梁极限强度进行仿真分析。对比FPSO的完整船体梁、点蚀船体梁和CFRP修复的点蚀船体梁的中拱极限弯矩和中垂极限弯矩，分析CFRP对FPSO点蚀船体梁的修复效果，并分析胶层失效规律。结果表明，CFRP可为船舶的高效修复提供一种新的方式。     

船体梁抗弯能力的计算

在船舶纵弯曲强度的可靠性分析中,需要计算船体梁的抗弯能力,本文提供一种实用计算方法。在此方法中取材料厚度(或剖面积)和屈服限、弹性模量等均为随机变量,利用随机函数的线性化原理,求得船体断面几何要素以及抗弯能力的统计特征值。文中还介绍了国产船用钢材的厚度和屈服极限的变异系数,并利用组合梁模型试验资料对采用梁模型带来的计算误差及其修正办法作了讨论。该计算方法采用了造船人员熟悉的常规强度计算中的格式,便于在船舶设计中应用。     

基于完整船体极限强度和搁浅剩余强度的协调共同结构规范对比分析

文章基于Smith法,根据国际船级社协会发布的2013版协调共同结构规范(HCSR)中破损模型、失效模式和载荷模型,考虑材料屈服、结构单元屈曲及后屈曲的特性,应用FORTRAN程序设计语言编写船体极限强度计算程序,以某76000吨散货船为算例,对完整船体的极限强度进行计算,对搁浅状态下破损船体的剩余强度进行计算并校核承载能力。通过在中拱和中垂工况下与其他规范的对比验证,2013版HCSR指定的剩余强度校核公式及船体梁载荷计算公式中选取的安全系数要求更高,校核更严格。     

Reliability analysis of a bulk carrier in ultimate limit state under combined global and local loads in the hogging and alternate hold loading condition

The alternate hold still-water loading in hogging combined with wave loading is critical for the safe design of bulk carriers. The ultimate longitudinal strength of the hull girder of bulk carriers in this condition has been found to be considerably reduced by the action of local lateral pressure loads. In the present paper, an interaction equation based on the ultimate hull girder strength assessment obtained by nonlinear finite element analyses is adopted to consider the relationship between ultimate longitudinal bending capacity and average external sea pressure over the bottom. This interaction equation is used as the basis for the failure function. The annual probability of failure is obtained by FORM analysis considering two typical load cases, namely, pure longitudinal hogging bending moment and combined global hogging bending moment and local lateral pressure loads. The effect of heavy weather avoidance on the failure probability is evaluated. The results show that the local lateral pressure has a significant influence on the annual probability of failure of bulk carriers in the hogging and alternate hold loading condition.     

Ultimate strength analysis of a bulk carrier hull girder under alternate hold loading condition,Part 2: Stress distribution in the double bottom and simplified approaches

This is the second of two companion papers dealing with nonlinear finite element modelling and ultimate strength analysis of the hull girder of a bulk carrier under Alternate Hold Loading (AHL) condition. The methodology for nonlinear finite element modelling as well as the ultimate strength results from the nonlinear FE analyses was discussed in the companion paper (Part 1). The purpose of the present paper is to use the FE results to contribute towards developing simplified methods applicable to practical design of ship hulls under combined global and local loads. An important issue is the significant double bottom bending in the empty hold in AHL due to combined global hull girder bending moment and local loads. Therefore, the stress distributions in the double bottom area at different load levels i.e. rule load level and ultimate failure load level are presented in detail. The implication of different design pressures obtained by different rules (CSR-BC rules and DNV rules) on the stress distribution is investigated. Both (partially) heavy cargo AHL and fully loaded cargo AHL are considered. Factors of influence of double bottom bending such as initial imperfections, local loads, stress distribution and failure modes on the hull girder strength are discussed. Simplified procedures for determination of the hull girder strength for bulk carriers under AHL conditions are also discussed in light of the FE analyses.     

Effect of pitting corrosion on local strength of hold frames of bulk carriers (2nd Report)—Lateral-distortional buckling and local face buckling

Pitting corrosion is typical corrosion observed on coated hold frames of bulk carriers which exclusively carry coal and iron ore. In order to secure the safety of these types of bulk carriers, it is important to understand the effect of pitting corrosion on local strength of hold frames.

In order to investigate this effect, a series of 4- and 3-point bend tests on structural models which consist of web, shell and face plates has been carried out. Artificial pitting was created on the web plate to simulate pitting. In the 4-point bend tests, two equal concentrated loads have been applied vertically at the one-third points of simply supported models so that compression load due to bending would act on the face plate. In this testing condition, lateral-distortional buckling occurred before reaching the ultimate strength and local buckling of the face plate was observed after reaching the ultimate strength. The effect of web plate pitting on the lateral-distortional buckling strength was found to be small but the ultimate strength decreases with increase in the degree of pitting intensity. In the 3-point bend tests, concentrated load has been applied vertically at the center of simply supported models so that compression load due to bending would act on the face plate. In this testing condition, local face buckling occurred just after reaching the ultimate strength. The ultimate strength is found to be decreasing with increase in the degree of pitting intensity.

A series of non-linear FE analyses has been performed to simulate the deformation behavior observed in the tests. It has been revealed that even in the case of randomly distributed pitting corrosion the ultimate strength of the structural models was almost the same as that of the structural models with uniform corrosion corresponding to the average thickness loss.     

船体在疲劳和腐蚀损伤下的可靠性

在疲劳和腐蚀作用下，船体梁舯剖面模数折减，导致极限承载能力下降，在此基础上进行可靠性分析。文中腐蚀率是一个有常数平均值的随机变量，疲劳裂纹根据Paris公式计算，当静水弯矩和波浪弯矩的组合值超过船体梁极限承载能力时，发生船体梁失效。以一艘散货船为例，计算其可靠性随时间的变化。计算结果可为船东和船级社评估船舶营运期间疲劳和腐蚀对船舶可靠性的影响提供参考。     

散货船隔舱重载下极限强度简易计算方法研究

散货船在装载矿石等重货时,通常只装载在奇数货舱内,这就是所谓的隔舱重载工况。在这种工况下,中间舱的双层底结构除受到总纵弯曲作用外,还会受到邻舱重货引起的局部弯曲作用,而且该局部弯曲的作用会降低中拱状态下船体梁的极限强度。文章提出了一种简易计算方法,顶边舱结构和底边舱结构可以看作两根梁,双层底结构可视作正交异性板,运用双梁理论和正交异性板理论可推导出局部弯曲的影响。然后,考虑该局部弯曲的作用,用Smith法计算船体梁的极限强度。最后,将文中方法计算的结果与FEM结果进行比较,并对结果进行了分析。     

Ultimate hull girder strength of a bulk carrier under combined global and local loads in the hogging and alternate hold loading condition using nonlinear finite element analysis

For bulk carriers in hogging, the most critical situation is the alternate hold loading (AHL) condition with odd numbered holds loaded with high density cargoes and even numbered holds empty. The effect of the local lateral pressure loads should be considered in the assessment of ultimate hull girder strength in the hogging and AHL conditions. In the present paper the ultimate strength of a Capesize bulk carrier hull girder under combined global and local loads in the hogging and AHL condition is extensively and systematically investigated using nonlinear finite element (FE) analysis with ABAQUS software. Since the bulk carrier used as a reference vessel in this study is an old design we also studied the effect of modified scantlings by multiplying the plate thickness in the bottom structure by a design modification factor (DMF). In particular, it should be noted that a DMF of 1.4 gives a design in accordance with the new CSR rules. Based on the results obtained by nonlinear FE analyses, a practical interaction equation is established between global hogging bending capacity and average external sea pressure over the bottom.     

Longitudinal strength of ships with accidental damages

This paper presents an investigation of the longitudinal strength of ships with damages due to grounding or collision accidents. Analytical equations are derived for the residual hull girder strength and verified with direct calculations of sample commercial ships for a broad spectrum of accidents. Hull girder ultimate strengths of these sample vessels under sagging and hogging conditions are also calculated, based on which correlation equations are proposed. To evaluate a grounded ship, using the section modulus to the deck would be optimistic, while using the section modulus to the bottom would be conservative. On the contrary, to evaluate a collided ship, using the section modulus to the deck would be conservative, while using the section modulus to the bottom would be optimistic. The derived analytical formulae are then applied to a fleet of 67 commercial ships, including 21 double hull tankers, 18 bulk carriers, 22 single hull tankers and six container carriers. The mean values, standard deviations and coefficients of variation for the coefficients in these new analytical formulae are obtained. The ship length exhibits little influence on these coefficients because they are close to the mean values although ship length spans from 150 to 400 m. The ship type shows some influence on the residual strength. Uniform equations are proposed for commercial ships which do not depend on a ship's principal dimensions. These formulae provide very handy tools for predicting the residual strength in seconds, without performing step-by-step detailed calculations, an obvious advantage in cases of emergency or salvage operation.     

循环载荷下箱型梁极限强度性能实验研究

通过系列箱型梁模型实验,研究了箱型梁在极值循环弯曲载荷下的极限承载性能。分别对四个加筋箱型梁模型进行了循环载荷下的四点纯弯实验,实验分别采取单向及双向循环载荷两种施加方式。在单向循环弯曲实验中,模型的后续循环的极限强度与前一循环的后极限强度阶段的卸载点接近,但塑性变形有明显增加,极限承载能力下降显著;双向循环弯曲中,反向弯矩虽然抵消了部分塑性变形,但箱型梁的极限承载能力仍有明显下降。实验表明,实验加载过程中,箱型梁在承受极值循环载荷初期,其构件崩溃速率较缓,而一旦进入后极限阶段,崩溃速率显著加快;箱型梁在极值循环弯曲载荷下的极限承载性能,即后极限强度性能,相比一次性极限强度值逐步下降。     

Effect of pitting corrosion on the ultimate strength of steel plates subjected to in-plane compression and bending

Corrosion pits with a circular cone shape are typically observed on coated hold frames of aged bulk carriers which carry exclusively coal and iron ore. In order to ensure the safety of these types of bulk carrier, it is necessary to understand the effect of pitting corrosion on the local strength of hold frames. In order to investigate this effect, a series of nonlinear finite-element (FE) analyses has been performed with pitted plates subjected to in-plane compressive loads and bending moments. It has been shown that the ultimate compression load or bending moment of pitted plates is smaller than that of uniformly corroded plates in terms of average thickness loss, and that predictions of the ultimate strength using the average thickness loss at the minimum cross section would be conservative. In order to establish a method of evaluating strength reduction due to pitting corrosion, it is important to identify the failure mode that would be most detrimentally affected by pitting corrosion. It was found that the reduction of the ultimate compressive load or bending moment due to pitting corrosion is smaller than that of the tensile strength in terms of equivalent thickness.     

Structural reliability of two bulk carrier designs

The paper aims at quantifying the changes in notional reliability levels that result from redesigning a traditional single-hull bulk carrier to become a double-hull structure. The probability of failure is calculated using a first-order reliability method. The evaluation of the wave-induced load effects that occur during long-term operation of the ship in the seaway is carried out. The still water loads are defined on the basis of a statistical analysis that accounts for the ship type. The ultimate collapse bending moment of the midship cross section is used as the basis for the reliability formulation. It is shown that by introducing the double-hull in the bulk carriers their level of structural safety can be increased up to values typical of tankers. Additionally, the time-dependent degrading effect of corrosion on the ultimate moment is also taken into account in the reliability assessment of bulk carriers.