Nonlinear effects from wave-induced maximum vertical bending moment on a flexible ultra-large containership model in severe head and oblique seas

Vertical bending moment (VBM) is of crucial importance in ensuring the survival of vessels in rough seas. With regard to conventional vessels, wave-induced maximum VBM is normally considered to be experienced in head seas. It is conservative to determine the extreme VBM based on either numerical simulations or model tests in long-crested head seas. Extensive model tests have been conducted in head seas with focus on the nonlinear vertical responses in severe seas, and the measured results were compared with numerical calculations for validation. Unexpected phenomena, however, were observed during the model tests of an ultra-large containership. The maximum sagging and hogging VBMs were encountered in oblique seas. Furthermore, the significant wave height used in oblique seas was even smaller than that used in head seas. The nonlinear vertical load effects in oblique seas require further investigations for this particular vessel. Limited experimental results in oblique seas have been reported, in which the lateral responses were always more concerned than the vertical responses. Up to now, rare systematic comparisons of the nonlinear vertical responses between head and oblique seas have been published, especially when the hydroelastic effects are also accounted for. A 13000-TEU ultra-large containership model, which was designed by Hyundai Heavy Industries (HHI), has been tested in the towing tank and the ocean basin at the Marintek center in Trondheim. The experimental results in regular waves are first compared between head and oblique seas. The statistical characteristics of the VBM amidships under nineteen irregular wave conditions are then investigated. Next, the extreme hogging and sagging VBMs are compared under different wave conditions with focus on the extreme hogging VBMs. At the end of the paper, the uncertainties in the experiments are discussed.     

Investigation on the nonlinear effects of the vertical motions and vertical bending moment for a wave-piercing tumblehome vessel based on a hydro-elastic segmented model test

Although the nonlinear effects of the ship motions, wave-induced loads and structural responses of conventional vessels have been investigated experimentally and numerically in recent years, similar studies on the wave-piercing tumblehome (WPTH) vessels are rare, in spite of the urgent necessary due to their extensive applications. This paper experimentally investigated the nonlinear effects of the vertical motions and vertical bending moment (VBM) for a WPTH vessel based on a hydro-elastic segmented model test. The model test was carried out in head regular waves for three amplitudes, in the towing tank at Harbin Engineering University. Based on the band-pass filter technique, four kinds of decomposed harmonics are defined by mean offset, linear wave-frequency response, nonlinear wave-frequency response and nonlinear high-frequency vibration. Meanwhile, based on mean offset, three kinds of combined responses are defined by considering linear wave-frequency response, nonlinear wave-frequency response and nonlinear high-frequency vibrations step by step. The transfer functions of vertical motions and VBM are presented as function of the incident wave frequency, and the measured data and VBM were compared with numerical calculations for validation. With the method proposed above, the results of VBM are analyzed by focusing on the influences of decomposed harmonics on the amplitudes and asymmetry of combined responses. Strong nonlinear effects are observed in the VBM. The nonlinearity of VBM can be identified by the significant amplitudes of decomposed harmonics, variation of amplitude with the wave amplitude and remarkable asymmetry about the zero axis. The hogging VBM of WPTH vessel can be even larger than the sagging VBM, which is in contrast to the general experiences from conventional vessels. Combined the calculated relative motion with the decomposed and combined histories of VBM, the occurrence of the transient impact and its characteristics are discussed, and these are then used to analyze the unconventional asymmetry of VBM. Furthermore, the influences of the bow shape over the vertical motions and VBM are discussed. At the end of the paper, the uncertainties in the test are provided.     

6750箱集装箱船非线性波激振动和颤振响应分析

本文采用三维时域非线性水弹性方法分析了一艘6750箱集装箱船的水弹性响应以及运动和垂向弯矩特征。通过考虑入射波力、静水恢复力、砰击效应的非线性,研究了在恶劣海况下船体的非线性运动和垂向弯矩响应,同时分析了波激振动及颤振对垂向弯矩的影响。数值计算结果表明:(1)非线性入射波力对运动的影响较小,但是对垂向弯矩的影响较大,使得其有明显的倍频成分,同时中垂弯矩显著大于中拱弯矩。另外,非线性入射波力也引起了明显的非线性波激振动;(2)非线性静水恢复力对运动和载荷的影响均较大,但是没有引起明显的非线性响应。非线性计算的垂荡响应小于线性结果,而纵摇和垂向弯矩响应大于线性结果;(3)砰击效应对运动的影响较小,但对垂向弯矩的影响较大,砰击效应引起了显著的船体弹性高频振动,增大了载荷幅值,但是其引起的合成中垂和中拱幅值相差不大;(4)非线性水动力的作用主要引起垂向弯矩的倍频响应,包括倍频可能引起的二节点垂向弯矩弹性共振,而砰击效应主要引起船体二节点垂向弯矩共振;(5)本文的非线性水弹性响应计算结果与Kim给出的数值计算结果吻合很好。     

江海直达船舶波浪载荷响应试验与数值计算研究（英文）

The ship motions and wave-induced loads of a new type of river-to-sea ship are investigated experimentally and numerically. A river-to-sea ship is an unconventional type of container ship characterized by high breadth to draft ratio and low length to breadth ratio, which makes it more prone to hydroelasticity than conventional ships of the same size. A segmented model was tested under two loading conditions, namely, ballast and loaded conditions, to determine the vertical motions and wave-induced loads under each condition. Results are compared with numerical simulations in the frequency domain. The wave-induced responses are calculated by a nonlinear time domain code at each time step. The response amplitude operators of vertical ship responses in regular waves are analyzed, and the wave-induced responses are consistent with the experimental results.     

S-175集装箱船舶波浪载荷的船模试验与线性切片理论计算的比较

本文就日本S-175集装箱船舶的波浪载荷进行了船模试验与线性切片理论计算的比较,发现线性切片理论对于波浪载荷沿船长的纵向分布以及中拱与中垂的不同分量都与试验值存在着相当大的差异,仅纵向运动较为满意;揭示了对于在高浪级下快速舰船的波浪载荷,特别是砰击载荷应致力于开展非线性理论和试验研究。     

Time-domain simulation of wave-induced nonlinear motions and loads and its applications in ship design

A nonlinear time-domain formulation for ship motions and wave loads and a nonlinear long-term statistics method are presented and applied to the S175 container ship. The general agreement between model tests and numerical results is very satisfactory. The calculated long-term vertical sagging and hogging moments amidships are comparable to those given by DNV rules. The approach described in this paper can be used as a way of more accurately evaluating extreme wave loads and other nonlinear responses in ship design.     

Comparison of numerical and experimental results of nonlinear wave-induced vertical ship motions and loads

 A nonlinear time-domain procedure is presented which is used to calculate the vertical responses of a container ship advancing in head waves. The method assumes linear radiation forces represented by time convolution of memory functions, infinite frequency added masses, and radiation restoring coefficients. The nonlinear hydrostatic restoring and Froude–Krilov forces are computed exactly over the instantaneous wetted surface of the ship's hull. Forces due to green water on deck are calculated using the momentum method. Nonlinear effects are identified on different vertical ship responses, namely on the heave and pitch motions, the vertical accelerations, and the vertical bending moment. These non-linear effects are expressed by the variation of the transfer function with the wave amplitude, the higher-order harmonics of the time signals, the offset of the time series, and the asymmetry of the peaks. The numerical results and the quantified nonlinear effects are compared with experimental results showing an ability to reproduce the main nonlinear effects. Received: December 17, 2001 / Accepted: January 31, 2002     

小方型系数船舶的船体波浪载荷综合研究

从船级社规范对于不符合主尺度比要求的船舶船体梁波浪载荷的规定出发,采用理论预报和船模试验2种综合方式,进行了小于0.6方型系数、高航速、高海况目标船的波浪载荷研究.从规范对波浪载荷的线性理论预报值进行的非线性修正,修正后中拱和中垂波浪弯矩绝对值之和与线性理论预报极值全幅值相等出发,阐述所研究船特殊主尺度比下的模型试验结果、三维非线性水弹性理论预报结果显示出的波浪载荷非线性行为;同时综合模型试验与理论预报的共同规律,研究不同波高、航速、浪向等非常规船型船体波浪载荷的强非线性行为,从而认为规范基于的线性理论预报值进行非线性修正的统一规定太过笼统,进而建议规范对波浪载荷的非线性修正予以进一步的明确区分和规定.     

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.     

Ultimate strength of container ships subjected to combined hogging moment and bottom local loads part 1: Nonlinear finite element analysis

This paper is the first of two companion papers concerning the ultimate hull girder strength of container ships subjected to combined hogging moment and bottom local loads. In the midship part of container ships, upward bottom local loads are usually larger than the downward ones. This leads to the increase of biaxial compression in the outer bottom plating and the reduction of the ultimate hull girder strength in the hogging condition. In this Part 1, the collapse behavior and ultimate strength of container ships under combined hogging moment and bottom local loads are analyzed using nonlinear finite element method. Buckling collapse behavior of bottom stiffened panels during the progressive collapse of a hull girder is closely investigated. It has been found that major factors of the reduction of ultimate hogging strength due to bottom local loads are (1) the increase of the longitudinal compression in the outer bottom and (2) the reduction of the effectiveness of the inner bottom, which is on the tension side of local bending of the double bottom. The obtained results will be utilized in the Part 2 paper to develop a simplified method of progressive collapse analysis of container ships under combined hogging moment and bottom local loads.     

Vertical and horizontal bending moments on the hydroelastic response of a large-scale segmented model in a seaway

Wave-induced vertical bending moment (VBM) and horizontal bending moment (HBM) on a large-scale segmented model with a box-type backbone beam in short-crested irregular seas are systematically analyzed using sea trial measurement data. New insights into the relationship between nonlinear VBM and HBM of the ship sailing in short-crested sea waves are explored and presented. The results indicate that the HBM significantly contributes to the total sectional loads when the ship is sailing in a seaway and the HBM has a strong correlation with VBM in both magnitude and tendency. Therefore, design loads of HBM and the corresponding lateral structural strength issues should also be concerned in addition to VBM at the ship design phase.     

Numerical computation of motions and structural loads for large containership using 3D Rankine panel method

In this paper, we present the results of our numerical seakeeping analyses of a 6750-TEU containership, which were subjected to the benchmark test of the 2 nd ITTC–ISSC Joint Workshop held in 2014. We performed the seakeeping analyses using three different methods based on a 3D Rankine panel method, including 1) a rigid-body solver, 2) a flexible-body solver using a beam model, and 3) a flexible-body solver using the eigenvectors of a 3D Finite Element Model(FEM). The flexible-body solvers adopt a fully coupled approach between the fluid and structure. We consider the nonlinear Froude–Krylov and restoring forces using a weakly nonlinear approach. In addition, we calculate the slamming loads on the bow flare and stern using a 2D generalized Wagner model. We compare the numerical and experimental results in terms of the linear response, the time series of the nonlinear response, and the longitudinal distribution of the sagging and hogging moments. The flexible-body solvers show good agreement with the experimental model with respect to both the linear and nonlinear results, including the high-frequency oscillations due to springing and whipping vibrations. The rigid-body solver gives similar results except for the springing and whipping.     

规则波和不规则波中船舶艉砰击及其振动响应的试验研究

在拖曳水池中对某船舶进行了艉砰击及其振动响应的试验研究.在规则波以及不规则波中的零航速、艉随浪情况下观察到了严重的艉砰击现象.试验数据分析表明,合成弯矩可以分成由波浪载荷引起的低频成分以及由砰击载荷引起的高频成分.由于严重艉砰击载荷的作用,发现在某次规则波试验中合成弯矩比波浪弯矩要大出44%,在3.24m不规则波中合成弯矩增加了43%.不规则波中的试验数据统计表明合成弯矩分布范围服从Weibull分布.推导了服从Weibull分布随机变量的短期概率极值预报公式,针对试验数据进行了预报.还讨论了试验数据分析中的不确定性问题.试验研究表明,对于艉部平坦肥大的船舶,在设计和使用中需要引起对艉砰击及其振动响应问题的重视.     

船舶航线优化中任意浪向的航速损失预测模型（英文）

This paper proposes a semi-empirical model to predict a ship's speed loss at arbitrary wave heading.In the model,the formulas that estimate a ship's added resistance due to waves attacking from different heading angles have been further developed.A correction factor is proposed to consider the nonlinear effect due to large waves in power estimation.The formulas are developed and verified by model tests of 5 ships in regular waves with various heading angles.The full-scale measurements from three different types of ships,i.e.,a PCTC,a container ship,and a chemical tanker,are used to validate the proposed model for speed loss prediction in irregular waves.The effect of the improved model for speed loss prediction on a ship's voyage optimization is also investigated.The results indicate that a ship's voyage optimization solutions can be significantly affected by the prediction accuracy of speed loss caused by waves.     

Investigation of springing in ship structures using experimental methods and 3-D hydroelastic theory

Large and long ships experience springing behavior. Depending on the trade routes and design of such ocean-going ships, wave-induced vibrations may be due to springing and whipping effects. In this paper, we address the wave-induced vibrations in an ultra-large ore carrier under fully loaded and ballast conditions. The experimental measurements from tests performed using a flexible model of the ship were compared with the numerical predictions from 3-D hydro-elastic theory (THAFTS) (Wu, Hydroelasticity of floating bodies. PH.D thesis, Brunel University, 1984). The measurements showed multiple frequencies between the encountered wave frequency and the 2-node bending frequency that occurred only in ballast conditions, whereas the springing vibrations were more apparent with forward speed under ballast conditions in both regular and irregular waves. The numerical method predicted the vertical bending moment quite well in the fully loaded condition but underestimated it in the ballast condition. This result was primarily due to an inability to capture the prediction of the multiple frequencies between the encountered wave frequency and the 2-node bending frequency. Using THAFTS, a new ship form with a deep draft was introduced, and this vessel was shown to reduce springing vibrations.     

一种减小中拱中垂对测深表影响的方法

针对实船测试数据反映出的中拱、中垂变形会对测深表的精度产生影响的问题,采用曲线拟合的方法精确计算船舶的实际倾斜状态,计算结果表明,使用经过曲线模拟推导出的纵倾修正公式后,计算的舱容数据更接近实际情况。通过这种方法可以有效减少中拱中垂对测深表的影响。     

Numerical and experimental investigations into the application of response conditioned waves for long-term nonlinear analyses

The coefficient of contribution method, in which the extreme response is determined by considering only the few most important sea states, is an efficient way to do nonlinear long-term load analyses. To furthermore efficiently find the nonlinear short-term probability distributions of the vessel responses in these sea states, response conditioned wave methods can be used. Several researchers have studied the accuracy of response conditioned wave methods for this purpose. However, further investigations are necessary before these can become established tools. In this paper we investigate the accuracy by comparing the short-term probability distributions obtained from random irregular waves with those from response conditioned waves. We furthermore show how response conditioned wave methods can be fitted into a long-term response analysis. The numerical and experimental investigations were performed using a container vessel with a length between perpendiculars of 281 m. Numerical simulations were done with a nonlinear hydroelastic time domain code. Experiments were carried out with a flexible model of the vessel in the towing tank at the Marine Technology Centre in Trondheim. The focus was on the probability distributions of the midship vertical hogging bending moments in the sea states contributing most to the hogging moments with a mean return period of 20 years and 10 000 years. We found that the response conditioned wave methods can very efficiently be used to accurately determine the nonlinear short-term probability distributions for rigid hulls, but either accuracy or efficiency is to a large effect lost for flexible hulls, when slamming induced whipping responses are accounted for.     

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.     

关于船舶规范中计算载荷的分析

本文利用非线性切片理论，以两条不同类型的船舶为例，具体分析了现行规范中关于波浪弯矩、砰击振动弯矩以及弯矩迭加计算时存在的一些问题；指出了在确定计算载荷时应当计及船舶在波浪中的失速，所谓的谐振波不一定就是最危险的规则子波，按动量冲击理论计算以底部砰击为主的船舶是不合适的，不应把波浪弯矩和砰击报动弯矩的最大值简单相加来确定合成弯矩。     

船体非线性波浪载荷的水弹性分析

本文采用水弹性分析方法研究船舶在规则波及不规则波中迎浪航行时的结构动力响应（运动、剪力和弯矩等）。确定流体载荷时应用了扩展的切片理论，其中计及由于船体的非直舷、剖面吃水的瞬时变化和船体振荡的非简谐特性所导致的非线性，同时还考虑了波浪冲击、出水和上浪的影响。运动方程是在时域内步进求解。数值计算结果与规则波中的模型试验相比较，符合程度令人满意。