Ultimate strength of container ships subjected to combined hogging moment and bottom local loads,Part 2: An extension of Smith's method

This paper is the second of two companion papers concerning the ultimate hull girder strength of container ships subjected to combined hogging moment and bottom local loads. The nonlinear finite element analysis in Part 1 has shown that local bending deformation of a double bottom due to bottom lateral loads significantly decreases the ultimate hogging strength of container ships. In this Part 2, extending Smith's method for pure bending collapse analysis of a ship's hull girder, a simplified method of progressive collapse analysis of ultimate hogging strength of container ships considering bottom local loads is developed. The double bottom is idealized as a plane grillage and the rest part of the cross section as a prismatic beam. An average stress-average strain relationship of plate/stiffened plate elements employed in Smith's method is transformed into an average stress-average plastic strain relationship, and implemented in the conventional beam finite element as a pseudo strain hardening/softening behaviors. The extended Smith's method is validated through a comparison with nonlinear finite element analysis.     

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.     

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.     

万箱集装箱船典型货舱结构极限承载能力计算

随着世界货运量的需求增加,集装箱船的大型化发展从未停止。近十年内,有2艘大型集装箱船先后在海上遭到极端载荷而丧失结构承载能力以致发生灾难性毁坏,给航运界敲响了警钟。为了避免今后大型集装箱船再次遭遇上述严重事故,保证营运中使用的安全性和航行时结构的可靠性,国际船级社协会专门针对集装箱船的规范要求进行修改,提高了载荷设计值,并且要求评估典型货舱结构的极限承载能力。本文针对万箱集装箱船典型货舱结构,基于逐步破坏法和有限元法,计算了垂向和水平方向的极限弯矩。结果表明,在初步设计阶段逐步破坏法有着快速高效的优势,但是考虑到载荷变化的多样性和船体结构的复杂性,还是需要应用非线性有限元法进行建模计算,给出最终评估结果。     

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。     

Experimental and numerical investigations of the ultimate torsional strength of an ultra large container ship

Structures of ultra large container ships (ULCS) are characterized by large deck openings and low torsional rigidity. It is essential to comprehensively figure out their collapse behaviors under pure torsion with both model experiments and numerical simulations, making an evaluation of their ultimate torsional strength. In this paper, a similar scale model of a 10,000TEU container ship has been designed and manufactured first, in which both geometric similarity and strength similarity are taken into account. Next the collapse behaviors of the test model are detailedly illustrated with both experimentally and numerically obtained results. Then discussions on warping or shear buckling deformations involved in the collapse process of the structure are conducted with extended numerical simulations. Finally, the ultimate torsional strength of the true ship is evaluated according to the similarity theory. Results show that it is the yielding and shear buckling of the side shells that causes the failure of the hull girder under pure torsion. Further nonlinear finite element analysis demonstrates that it may either have warping or shear buckling deformations in the torsional collapse process of the hull girder with a large deck opening, depending on the local rigidity distribution of side shells, which has a significant effect on the ultimate torsional strength of the hull girder.     

A proposal of reliability-based design formats for ultimate hull girder strength checks for bulk carriers under combined global and local loadings

The purpose of this paper is to provide a basis for the development of reliability-based design formats for ultimate hull girder strength checks for bulk carriers in hogging conditions under combined global and local loading and to estimate implied safety levels in current rule practices for hull girders. The effect of alternative definitions of characteristic still-water loads on the safety format and, hence, the safety factors is assessed. The effect of systematic (bias) model uncertainties associated with loads and strength on the reliability measures is investigated.     

波浪中船体梁后极限强度特性的实验评估(英文)

Experimental investigations into the collapse behavior of a box-shape hull girder subjected to extreme wave-induced loads are presented.The experiment was performed using a scaled model in a tank.In the middle of the scaled model,sacrificial specimens with circular pillar and trough shapes which respectively show different bending moment-displacement characteristics were mounted to compare the dynamic collapse characteristics of the hull girder in waves.The specimens were designed by using finite element(FE)-analysis.Prior to the tank tests,static four-point-bending tests were conducted to detect the load-carrying capacity of the hull girder.It was shown that the load-carrying capacity of a ship including reduction of the capacity after the ultimate strength can be reproduced experimentally by employing the trough type specimens.Tank tests using these specimens were performed under a focused wave in which the hull girder collapses under once and repetitive focused waves.It was shown from the multiple collapse tests that the increase rate of collapse becomes higher once the load-carrying capacity enters the reduction path while the increase rate is lower before reaching the ultimate strength.     

Compartment level progressive collapse analysis of lightweight ship structures

The continued development of large high speed ships, often constructed from aluminium alloy, has raised important issues regarding the response of lightweight hull girders under primary hull girder bending. In particular, the response of lightly framed panels in compression may be influenced by overall panel buckling over several frame spaces. Therefore, to provide improved ultimate strength prediction for lightweight vessels, an extended progressive collapse methodology is proposed. The method has capabilities to predict the strength of a lightweight aluminium midship section including compartment level buckling modes. Nonlinear finite element analysis is used to validate the extended progressive collapse methodology.     

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.     

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。     

Prediction of hull girder moment-carrying capacity using kinematic displacement theory

The hull girder moment capacity of a very large crude oil carrier (VLCC) called Energy Concentration (EC), for which many benchmark studies have been carried out using the simple progressive collapse method (SPCM), is predicted. In this study, three approaches are used to represent the load-shortening behavior, so-called average compressive strength, of a stiffened panel, comprising the hull section: 1) kinematic displacement theory (KDT); 2) nonlinear finite element analysis (FEA); and 3) simple formulas in the common structural rule (CSR) for tankers. Load-shortening curves for various kinds of stiffened panels in EC are compared for five different scenarios with variations of load-shortening approaches and initial imperfections. In order to verify the effect of load-shortening on the prediction accuracy of the hull girder moment-carrying capacity, load-shortening curves are imported into an SPCM-based in-house program called Ultimate Moment Analysis of Damaged Ships (UMADS). Comparison of the hull girder ultimate strength for general heeling conditions, including hogging and sagging conditions, reveals that the load-shortening curves significantly affect the hull girder moment-carrying capacities. Based on our comparison of these capacities with other benchmark results, it is concluded that nonlinear FEA provided the most conservative results, KDT provided the second most conservative results, and the CSR formulas predicted the upper bound.     

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.     

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。     

循环弯曲载荷下船体梁的极限纵强度

根据生破坏的强度准则，详细讨论了循环弯曲载荷下船体梁的非弹性变形性能。给出了循环弯曲载荷下船体梁极限强度的简化分析方法。进行了纵筋加强箱形薄壁梁模型的循环弯曲试验。理论计算与试验结果作了比较，两者吻合较好。     

A practical method for torsional strength assessment of container ship structures

Container ship structures are characterized by large hatch openings. Due to this structural property, they are subject to large diagonal deformations of hatch openings and warping stresses under complex torsional moments in waves. This necessitates torsional strength assessment of hull girder of container ships in their structural design stage. In this paper, a practical method for torsional strength assessment of container ship structures with transparent and consistent background is discussed based on the results from up-to-date analyses. In order to estimate the torsional response characteristics as accurately as possible, three-dimensional Rankine source method, after being validated by tank tests, is employed for estimation of wave loads on a container ship, and FE analyses are conducted on the entire-ship model under the estimated loads. Then, a dominant regular wave condition under which the torsional response of the container ship becomes maximum is specified. Design loads for torsional strength assessment that give torsional response equivalent to the long-term predicted values of torsional response are investigated based on the torsional moments on several container ships under the specified dominant wave condition. An appropriate combination of stress components to estimate the total hull girder stress is also discussed.     

Hydroelasto-plasticity approach to predicting the post-ultimate strength behavior of a ship’s hull girder in waves

Dynamic collapse behavior of a ship’s hull girder in waves is investigated; post-ultimate strength behavior is the focus. Firstly, a simulation method is proposed. Assuming that a plastic hinge is formed during the collapse of the hull girder, the whole ship is modeled as two rigid bodies connected amidship via a nonlinear rotational spring. The post-ultimate strength behavior, such as the reduction of load carrying capacity due to buckling and yielding, is reflected in the model. Hydrodynamic loads are evaluated by using nonlinear strip theory to account for the effect of large plastic deformations on the loads. A scaled model for validation of the simulation is designed and fabricated. Then a series of tank tests is conducted using the scaled model to validate the simulation results. Post-ultimate strength behavior characteristics in waves are clarified by using the numerical and tank test results. It is shown that the hull girder collapses rapidly after reaching ultimate strength, and then the plastic deformation grows until unloading starts at the collapsed section. Finally, several parametric dependencies of the extent of the collapse behavior are discussed based on a series of the simulations.     

Parametric dependencies of the post-ultimate strength behavior of a ship’s hull girder in waves

To rationally assess the consequence of a ship’s hull girder collapse, it is necessary to know the post-ultimate strength behavior of the hull girder including the global deformation and motions under extreme wave-induced loads. In the foregoing research, the authors proposed a numerical analysis system to predict the collapse behavior in waves including the post-ultimate strength behavior. The primary objective of the present paper is to clarify the parametric dependencies of the severity of the collapse in a rational manner. The parameters may include those related to load-carrying capacity and the extreme loads. To this end, an analytical solution to describe the post-ultimate strength behavior is derived. Assuming that a plastic hinge is formed at the midship during the collapse procedure, the whole ship is modeled as a two-rigid-bodies system connected to each other amidship via a nonlinear rotational spring, which represents the nonlinear relationship between the bending moment and the rotational angle. The relationship may be modeled as piece-wise linear curves. It is further assumed that large motions and elastic/plastic deformations of the hull girder may not affect the load evaluations, and that the hull girder is subjected to a large single wave. Some important parameters to predict the severity of the collapse are specified based on the analytical solution.     

Design safety margin of a 10,000 TEU container ship through ultimate hull girder load combination analysis

Assessment of the ultimate longitudinal strength of hull girders under combined waveloads can be of particular importance especially for ships with large deck openings and low torsional rigidity. In such cases the horizontal and torsional moments may approach or exceed the vertical bending moment when a vessel progresses in oblique seas. This paper presents a direct calculation methodology for the evaluation of the ultimate strength of a 10,000 TEU container ship by considering the combined effects of structural non-linearities and steady state wave induced dynamic loads on a mid ship section cargo hold. The strength is evaluated deterministically using non-linear nite element analysis. The design extreme values of principal global wave-induced load components and their combinations in irregular seaways are predicted using a cross-spectral method together with short-term and long-term statistical formulations. Consequently, the margin of safety between the ultimate capacity and the maximum expected moment is established.