非线性混合海况下近海风机塔筒底部载荷的动力响应

本文主要研究在非线性混合海况(即风浪和涌浪组合海况)下,以NREL 5MW_Baseline Monopile近海风机为研究对象,对其塔筒底部(基线)所受到的剪力和弯矩载荷的动力响应进行仿真。在近海风机的时域仿真中,选用了Ochi-Hubble六参数波浪谱,并编制了该谱的程序嵌入到FAST中进行编译。计算过程中,共进行了20次10 min的仿真分析。对于得到的短期载荷,给出了波高程,塔筒底部首尾向剪力和弯矩在线性与非线性不规则波作用下的时程曲线对比图。采用分块最大值法对每一次的短期载荷提取极值,并基于20次仿真所得的极值,给出了塔筒底部首尾向剪力与弯矩在线性与非线性不规则波作用下的超越概率曲线对比图。研究表明,在非线性混合海况下进行近海风机塔筒底部载荷的动力响应研究,计算结果对工程实际应用具有指导意义。     

Efficient estimation of extreme long-term stresses by considering a combination of longitudinal bending stresses

Longitudinal stresses due to combined horizontal and vertical bending moments in ships, corresponding to a return period of 20 years, are estimated by linear response analysis. In principle, the stress should be obtained by combining the stress in all sea states that can occur over a long-term period. A method to determine the desired long-term extreme stress by considering only a few short-term sea states is presented. The sea states have a certain probability of occurrence, and are each identified by a contour line in the (H _s, T _p)-plane. This approach makes it possible to estimate the extreme loads on the vessel in a practical and accurate manner. Moreover, it is shown that the long-term stress can be estimated by combining the individual long-term extreme stresses due to vertical and horizontal bending moments by using the sum-of-squares approach and accounting for the correlation between stresses. It was found that the correlation coefficient can be taken as the largest of the ones calculated along the contour line. It is shown that this correlation coefficient can even be approximated by the normalized phase angle at the wave length where the dominant response has its peak value. A comparison with the results obtained using well-known combination rules is presented. While linear analysis has been used here, it is believed that the approach can be generalized to stresses with nonlinear behavior, and hence represent a significant improvement in calculation efficiency. Received: September 18, 2001 / Accepted: December 18, 2001     

Structural loads induced in a containership by abnormal wave conditions

An analysis is presented of the vertical bending moments induced in a containership by a set of abnormal waves measured at different locations and on different occasions. A systematic investigation was carried out by using a large set of wave traces that included abnormal waves. In this way it was possible to assess the influence of the height, length, and shape of the abnormal waves on the wave-induced structural loads. The probability distributions of the ship responses to the sea states that included the abnormal waves were also calculated and were compared to the responses induced by the abnormal waves and to fitted distributions. Finally, the structural loads induced by the abnormal waves were compared with rule values and with long-term predictions.     

Experimental study on the nonlinear pressure acting on a high-speed vessel in irregular waves

The present study focuses on the nonlinear behavior of pressure on the hull surface of a high-speed vessel in irregular waves, particularly the pressure responses of alternately wet and dry areas near the waterline and on the bow zone. The vessel has high deadrise angles that may be subject to slight impact and water pile-up effects. A series of experiments in regular and irregular head waves were conducted, and the validity of applying Volterra modeling was investigated. In a previous article using experimental data in regular waves, it was confirmed that the approximate third-order Volterra model adequately simulated the variation of pressure responses in regular waves of different steepness up to a wave amplitude with a wavelength ratio of 0.01, even for the highly nonlinear pressures acting on the abovementioned areas of the hull surface. In this article, further validation for the second part of the study was obtained using experimental data in irregular waves. The frequency response functions obtained from the previous study’s experimental data in regular waves were applied to the third-order Volterra model by combining the input of irregular waves to simulate the responses in irregular waves of sea state five. Then, the spectra and statistics were analyzed. For the motions, accelerations, and pressure responses in irregular waves (as well as for the simulated time histories) variance spectra and statistics such as cumulative distributions of peak values and probability density functions were compared with the experimental results. It was confirmed that even for highly nonlinear and non-Gaussian pressures on the abovementioned areas of the hull surface, the approximate third-order Volterra model simulates the pressure responses in irregular head waves up to a sea state of five with adequate accuracy on deterministic and statistical bases.     

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 load analysis of a 10 MW offshore monopile wind turbine incorporating fully nonlinear irregular wave kinematics

Loads from storm waves can in some cases be dimensioning for offshore wind turbine substructures. Accurate determination of nonlinear wave loads is therefore important for a safe, yet economic design. In this paper, the fully nonlinear waves, realized by a fully nonlinear potential wave solver OceanWave3D, are incorporated into coupled aero-servo-hydro-elastic simulations for a reduced set of wave-sensitive design load cases, in comparison with the widely used linear and constrained waves. The coupled aero-elastic simulations are performed for the DTU 10 MW reference wind turbine on a large monopile at 33 m water depth using the aero-elastic code HAWC2. Effect of the wave nonlinearity is investigated in terms of the ultimate sectional moments at tower bottom and monopile mudline. Higher ultimate moments, 5% at tower bottom and 13% at monopile mudline as maximum, are predicated when the nonlinear waves are used. It could be explained by the fact that the extreme nonlinear waves, that are close to the breaking limit, can induce resonant ringing-type responses, and hereby dominate the ultimate load responses. However, the constrained wave approach shows marginal difference compared to the standard linear wave approach. It can be concluded at least for the present configuration that the industry standard approaches (linear and constrained wave approach) underestimate the ultimate load responses on offshore wind turbines in severe sea states.     

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.     

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.     

Sea state estimation based on vessel motion responses: Improved smoothness and robustness using Bézier surface and L1 optimization

Floating structures oscillate in waves, where these wave-induced motions may be critical for various marine operations. An important consideration is thereby given to the sea states at the planning and operating stages for an offshore project. The most important information extracted from a sea state is the directional wave spectrum, indicating wave direction, significant wave height, and wave spectrum peak period. Among several available methods of measuring and estimating the directional wave spectrum, the wave buoy analogy technique based on vessel motion responses is an in situ and almost real-time solution without extra costs of devices. If the forms of the wave spectra are not predefined in the estimation, the method is called a nonparametric approach. Its most remarkable advantage is the flexible form, but the smoothness should be regulated. After the discrete Fourier transform has been applied to the measured vessel motions, smoothing is necessary. However, this process results in disturbed vessel cross-spectra and a lowpass characteristic of the windowing function. This paper presents a nonparametric approach for directional wave spectrum estimation based on vessel motion responses. It introduces novel smoothness constraints using Bézier surface and includes a more robust estimate using L1 optimization. Both techniques are applied to the wave buoy analogy for the first time. Numerical simulations are conducted to verify the proposed algorithm.     

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.     

Difference in ship motion and wave load in long and short crested irregular waves北大核心CSCD

[Objective]To investigate ship motion and load responses in realistic 3D waves and overcome the limitations of the traditional 2D wave assumption, this paper develops a method for predicting ship motion and load responses in short-crested waves. [Method]The long- and short-term responses of ship motion and load in long- and short-crested waves are numerically predicted using the spectral analysis and statistical probability methods, respectively. The influence of directional function on ship response is also numerically analyzed. Moreover, tank model tests and a large-scale model sea trial are comparatively conducted to validate the difference between ship response and statistics in long- and short-crested irregular waves. [Results]The results show that when navigating against the waves in the same sea condition, the long-crested wave assumption overestimates the statistical mean value of ship load response, but underestimates extreme load in real seas. For long-crested waves, the ship motion and acceleration power spectrum is concentrated around a certain frequency band. [Conclusion]Ship motion and load responses in realistic 3D waves are significantly different from those in 2D long-crested waves. The directional function of short-crested waves also has a significant effect on ship motion and load responses. © 2023 The Author(s).     

Discussion on the parameters of design waves

In order to respond the discredit on the design wave standard and to recommend new consideration on design wave parameters, based on the long-term distribution of statistic characteristics of waves and the short-term probability properties of sea state defined by giving the return period, the calculation of the return period, the height, the period, and the oceanic wave parameters of the design wave and the forecasting methods are discussed in this paper. To provide references for the operation reliability of floating structures in the extreme sea state, the method of determining the design wave parameters is resurveyed. A proposal is recommended that the design wave, which can be either significant wave with 500-year of the return period, or the maximum wave with 1/N of exceeding probability, 100-year of the return period, can be applied in the engineering design practice.     

Long-term correlation structure of wave loads using simulation

This paper proposes a new method for combining the lifetime wave-induced sectional forces and moments that are acting on the ship structure. The method is based on load simulation and can be used to determine the exceedance probabilities of any linear and nonlinear long-term load combination. It can also be used to determine the long-term correlation structure between these loads in the form of the long-term correlation coefficients. They are essential part of the load combination procedures in design and strength evaluations as well as in the fatigue and reliability analysis of ship structures.The simulation method treats the non-stationary wave elevations during the ship’s entire life (long-term) as a sequence of different stationary Gaussian stochastic processes. It uses the rejection sampling technique for the sea state generation, depending on the ship’s current position and the season. Ship’s operational profile is then determined conditional on the current sea state and the ship’s position along its route. The sampling technique significantly reduces the number of sea state-operational profile combinations required for achieving the convergence of the long-term statistical properties of the loads. This technique can even be used in combination with the existing long-term methods in order to reduce the number of required weightings of the short-term CDFs. The simulation method does, however, rely on the assumption that the ship is a linear system, but no assumptions are needed regarding the short-term CDF of the load peaks.The load time series are simulated from the load spectra in each sea state, taking into account the effects of loading condition, heading, speed, seasonality, voluntary as well as involuntary speed reduction in severe sea states and the short-crested nature of the ocean waves. During the simulation procedure, special care has been given to maintaining the correct phase relation between all the loads. Therefore, time series of various load combinations, including the nonlinear ones, can be obtained and their correlation structure examined. The simulation time can be significantly reduced (to the order of minutes rather than hours and days) by introducing the seasonal variations of the ocean waves into a single voyage simulation. The estimate of the long-term correlation coefficient, obtained by simulating only a single voyage with the correct representation of seasonality, approaches the true correlation coefficient in probability. This method can be applied to any ship and any route, or multiple routes as long as the percentage of the ship’s total lifetime spent in each of them is known.A study has been conducted to investigate the effects of ship type, route and the longitudinal position of the loads on the values of the correlation coefficients between six different sectional loads; vertical, horizontal and twisting moments, as well as shear, horizontal and axial forces. Three ocean-going ship types have been considered; bulk carrier, containership and tanker, all navigating on one of the three busy ship routes; North America-Europe, Asia-North America and Asia-Europe. Finally, the correlation coefficient estimates have been calculated for five different positions along the ship’s length to investigate the longitudinal variation of the correlation coefficient.     

随机横浪中船舶倾覆过程模拟与安全域计算

研讨了随机海浪中船舶非线性随机横摇运动倾覆过程和安全域问题.考虑非线性阻尼、非线性复原力矩和随机波浪,建立了随机横浪中船舶运动的随机非线性微分方程.考虑两参数海浪谱和不同的有义波高,计算随机波浪力矩,采用简谐加速度数值计算方法求解随机微分方程,进行了随机倾覆过程的数值模拟.考虑船舶运动的瞬时状态,发展了胞映射方法计算随机非线性横摇运动安全域的方法,并编制了计算机程序.模拟了一条渔船不同有义波高作用下横摇倾覆过程,考虑不同的初始条件及随机波浪参数,在初始值平面上采用胞映射法构造了渔船航行的安全域.波高较小时,安全域是一个连续的区域;随着有义波高增大,安全域面积减小并且不再连续,倾覆域和安全域相互包围.计算结果表明,船舶运动的瞬时状态对安全域具有重要影响,而且随机海浪中安全域具有随机特性.     

Experimental and numerical study of containership responses in severe head seas

An accurate determination of the global load effects in a ship is vital for the design of the vessel. This paper addresses an experimental and numerical study of containership responses in severe head seas. Experimental results were obtained using a flexible model of a containership of newer design. The experiments showed that, taking hull flexibility into account, the fourth and sixth harmonic of the vertical bending moments had a maximum value of between 25% and 50% of the first harmonic. We also demonstrated that hull flexibility can increase the vertical bending moment by up to 35% in sea states relevant for design. Comparisons of moments found experimentally with results from a nonlinear hydroelastic strip theory method showed that the effect of nonlinearities on the rigid body moments was slightly over-predicted in the aft body. The method also tends to over-predict the increase of the bending moments due to hull flexibility. In general however, the numerical results compared reasonably well with the experimental ones.     

Estimation of nonlinear long-term extremes of hull girder loads in ships

This paper deals with a estimation of long-term extreme value for a given return period, say D=100 yr. In principle, this response is obtained by combining the response in all the sea states. The long-term response for a linear system can be effectively obtained by determining the response for each sea state, specified by the significant wave height, H_s, and the peak period, T_p, in the frequency domain. However, if the response is nonlinear, time domain simulation and a long time series would be required, to limit statistical uncertainty. Therefore, the long-term analysis becomes rather complicated and time consuming. For the long-term analysis, it is crucial to introduce ways to improve the efficiency in the calculation. In this work, it is shown that, the long-term extremes can be estimated by considering only a few short-term sea states. A long-term analysis based on identifying the most important sea state, defined by the coefficient of contribution, using linear analysis is applied. An iteration procedure is thereafter used to find the nonlinear long-term extreme values. It is concluded that only a limited number of sea states is necessary to get an acceptable estimate of the nonlinear D-year response as long as the most important sea states are included, i.e., the sea state with the maximum coefficient of contribution.     

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.     

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.     

超深水钻井隔水管动力分析理论研究与数值模拟

随着钻井作业向深水(500～1 500m)和超深水(1 500m以上)发展,在交变海洋环境载荷波浪力、海流力和浮式钻井平台运动的共同作用下,隔水管的动态响应更加显著.文中探讨了隔水管侧向振动的数学模型、动态特性分析中的结构与环境载荷建模技术及其非线性动力分析方法,研究并对比了不同分析方法在计算效率、计算精度和工程适用性等方面的差异.介绍了时域内应用ABAQUS软件进行超深水钻井隔水管非确定性动力分析的算法与详细流程,算例比较了不同边界条件对深水钻井隔水管动态特性的影响.研究表明,时域非确定性分析最为精确但需要时间最长,且只能采用线性AIRY波浪理论;理论上,海流主要引起隔水管动态响应的时不变部分,但该时不变部分不等同于海流引起的隔水管静态响应,一种简化方法只将海浪与钻井船运动作为动载荷而不考虑海流对动态响应的贡献;钻井船运动和波浪载荷是隔水管动态响应分析主要的动载荷,对于超深水隔水管来说,钻井船运动是首要的动载荷,其慢漂运动对隔水管性能有重要影响,而波浪仅对隔水管局部产生作用.     

New insight into the wave-induced nonlinear vertical load effects of ultra-large container ships based on experiments

Accurate estimation of the wave-induced extreme hogging vertical bending moment (VBM) is of vital importance for the design of container ships because container ships are normally under hogging conditions in still water. According to the empirical formulas proposed by the classification society rules, the design hogging VBM can be approximately 20 % smaller than the design sagging VBM for vessels with small block coefficients. High-order harmonic components in the vertical load effects, which are induced by the nonlinearities in the hydrodynamic forces and ship hull geometry, contribute to the asymmetry. Previous studies have shown that the nonlinear hydrostatic and Froude–Krylov forces increase the sagging VBM significantly. Current numerical tools are able to reveal this asymmetry to a certain extent. There is, however, little focus on the nonlinear pressure under the bow bottom, which is a more likely contributor to the hogging VBM. Several unexpected phenomena have been observed for large container ships. The wave-frequency sagging and hogging VBMs followed each other closely, and hence did not reflect the significant nonlinear factors as expected. In this paper, the test data of two (8600-TEU and 13000-TEU) ultra-large containership models in both regular and irregular head waves are systematically studied. In regular waves, the influence of the second and third harmonics on the fundamental hogging peaks and sagging troughs is estimated by comparing both the amplitude and phase difference relative to the first harmonic peaks. In irregular waves, the focus is on the statistical characteristics of the wave-induced nonlinear vertical load effects. To achieve a balance between results in regular and irregular waves, the influence of the second harmonics is evaluated through bispectral analysis.