A method for establishing ship design wave bending moment and its comparison with classification societies' rules

A procedure has been developed for the long-term distribution of the short-term extreme values of ship wave bending moments. The procedure has been applied in a systematic manner to investigate the effect of the principal ship characteristics on the design wave bending monent. The results have been compared to Classification Societies' Rules and demonstrate a rational way to improve them. The same procedure can also be applied to other ship responses or the responses of any structure excited by seaways.     

Prediction of short-term distributions of load extremes of offshore wind turbines

This paper proposes a new methodology to select an optimal threshold level to be used in the peak over threshold (POT) method for the prediction of short-term distributions of load extremes of offshore wind turbines. Such an optimal threshold level is found based on the estimation of the variance-to-mean ratio for the occurrence of peak values, which characterizes the Poisson assumption. A generalized Pareto distribution is then fitted to the extracted peaks over the optimal threshold level and the distribution parameters are estimated by the method of the maximum spacing estimation. This methodology is applied to estimate the short-term distributions of load extremes of the blade bending moment and the tower base bending moment at the mudline of a monopile-supported 5MW offshore wind turbine as an example. The accuracy of the POT method using the optimal threshold level is shown to be better, in terms of the distribution fitting, than that of the POT methods using empirical threshold levels. The comparisons among the short-term extreme response values predicted by using the POT method with the optimal threshold levels and with the empirical threshold levels and by using direct simulation results further substantiate the validity of the proposed new methodology.     

The evaluation method of total damage to ship in underwater explosion

Whipping response will happen when a ship is subjected to underwater explosion bubble load. In that condition, the hull would be broken, and even the survivability will be completely lost. A calculation method on the dynamic bending moment of bubble has been put forward in this paper to evaluate the impact of underwater explosion bubble load on the longitudinal strength of surface ships. Meanwhile the prediction equation of bubble dynamic bending moment has been concluded with the results of numerical simulation. With wave effect taken into consideration, the evaluation method of the total damage of a ship has been established. The precision of this evaluation method has been proved through the comparison with calculation results. In order to verify the validity of the calculation results, experimental data of real ship explosion is applied. Prediction equation and evaluation method proposed in this paper are to be used in ship structure design, especially in the preliminary prediction of the ultimate withstanding capability of underwater explosion damage for the integrated ship in preliminary design phase.     

Effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine

Floating wind turbine has been the highlight in offshore wind industry lately. There has been great effort on developing highly sophisticated numerical model to better understand its hydrodynamic behaviour. A engineering-practical method to study the nonlinear wave effects on floating wind turbine has been recently developed. Based on the method established, the focus of this paper is to quantify the wave nonlinearity effect due to nonlinear wave kinematics by comparing the structural responses of floating wind turbine when exposed to irregular linear Airy wave and fully nonlinear wave. Critical responses and fatigue damage are studied in operational conditions and short-term extreme values are predicted in extreme conditions respectively. In the operational condition, wind effects are dominating the mean value and standard deviation of most responses except floater heave motion. The fatigue damage at the tower base is dominated by wind effects. The fatigue damage for the mooring line is more influenced by wind effects for conditions with small wave and wave effects for conditions with large wave. The wave nonlinearity effect becomes significant for surge and mooring line tension for large waves while floater heave, pitch motion, tower base bending moment and pontoon axial force are less sensitive to the nonlinear wave effect. In the extreme condition, linear wave theory underestimates wave elevation, floater surge motion and mooring line tension compared with fully nonlinear wave theory while quite close results are predicted for other responses.     

Investigation of ship hydroelasticity

The importance of hydroelastic analysis of large and flexible container ships of today is pointed out. A methodology for investigation of this challenging phenomenon is drawn up and a mathematical model is worked out. It includes definition of ship geometry, mass distribution, structure stiffness, and combines ship hydrostatics, hydrodynamics, wave load, ship motion and vibrations. Based on the presented theory, a computer program is developed and applied for hydroelastic analysis of a flexible segmented barge for which model test results of motion and distortion in waves have been available. A correlation analysis of numerical simulation and measured response shows quite good agreement of the transfer functions for heave, pitch, roll, vertical and horizontal bending and torsion. The tool checked in such a way can be further used for reliable hydroelastic analysis of ship-like structures.     

Ultimate strength of ship hulls under torsion

For a ship hull with large deck openings such as container vessels and some large bulk carriers, the analysis of warping stresses and hatch opening deformations is an essential part of ship structural analyses. It is thus of importance to better understand the ultimate torsional strength characteristics of ships with large hatch openings. The primary aim of the present study is to investigate the ultimate strength characteristics of ship hulls with large hatch openings under torsion. Axial (warping) as well as shear stresses are normally developed for thin-walled beams with open cross sections subjected to torsion. A procedure for calculating these stresses is briefly described. As an illustrative example, the distribution and magnitude of warping and shear stresses for a typical container vessel hull cross section under unit torsion is calculated by the procedure. By theoretical and numerical analyses, it is shown that the influence of torsion induced warping stresses on the ultimate hull girder bending strength is small for ductile hull materials while torsion induced shear stresses will of course reduce the ship hull ultimate bending moment.     

Prediction of Long-Term Extreme Response of Fish Cage Using Environmental Contour Method

The fish cage design requires accurate predictions of long-term extreme loads and responses. Compared with the time-consuming full long-term analysis method integrating all the probability distribution of the short-term extremes,the environmental contour method gains much attention in predicting the long-term extreme values due to the less computational effort. This paper investigates the long-term extreme response of a fish cage using the environmental contour method. The fish cage is numerically simulated based on the lumped-mass method and the curved beam theory. Based on the one-dimensional(1D) and two-dimensional(2D) environmental contour, the extreme responses,including the surge and heave motions, mooring force, and vertical bending of the floater, are predicted for different return periods and compared with the full long-term analysis results. Results indicate that the 1D method greatly underestimates the extreme values. The 2D environmental contour method with a higher percentile level, namely90%, provides reasonable estimations and seems to be suitable for the long-term value analysis. Sensitivity studies show that the mooring arrangement and the bending stiffness have great effects on the bending moment and the mooring force and the mooring line pre-tension has minor effects on the fish cage response.     

Design similar scale model of a 10,000 TEU container ship through combined ultimate longitudinal bending and torsion analysis

This paper firstly figures out a similar scale model regarding ultimate strength experiment of a typical ultra large container ship (ULCS) through combined ultimate longitudinal bending and torsion analysis, in which the similarity theory is proposed to design the scale model for reflecting the progressive collapse behaviors of true ships in ultimate strength model test. The present study presents the similarity between scale model and true ship in cross-section considering the height of neutral axis, the section modulus, the inertia moment about neutral axis and the polar inertia moment should fit the geometrical similarity theory, and in strength considering buckling strength and shear ultimate strength of plates and stiffened panels should fit the strength similarity theory. Numerical investigations are conducted on the ultimate strength of a 10,000 TEU container ship and the similar scale model under pure hogging bending, pure torsion and combined bending and torsion, respectively. The nonlinear finite element method (NFEM) is adopted considering the effects of initial deformations and both material and geometric nonlinearities. Finally, the numerical results are compared with each other and discussed showing a good agreement in both elastic and inelastic range during the progressive collapse behaviors, which means the similar scale model can represent the true ship regarding ultimate strength test. And the similarity theory is verified quite stable after the uncertainty analysis.     

三向载荷联合作用下的大型集装箱船结构可靠性研究

大型集装箱船（LCS）具有较大的甲板开口，抗扭刚度非常低。在恶劣海况下航行时，大型集装箱船可能会遭遇斜浪的作用，此时船体将受到三向载荷的联合作用，水平波浪弯矩和扭转波浪弯矩可能会接近甚至超过垂向波浪弯矩，船体可能因发生组合变形而破坏。因此有必要研究大型集装箱船在三向载荷联合作用下的结构可靠性。在研究三向载荷联合作用下各维度极限强度的相互关系的基础上，提出了大型集装箱船的极限承载能力的可靠性评估方法，并对目标船在各浪向角下的结构可靠性进行评估。结果表明：目标船在0°浪向角下的失效概率最高；考虑水平波浪弯矩影响后目标船的结构可靠性有所降低；扭转波浪弯矩对目标船船中剖面的结构可靠性影响较小。     

Strength Analysis of Turret Mooring Productive/Storage Tanker

The longitudinal strength of turret mooring productive/storage tanker is studied.A numeri-cal example has been implemented according to the method presented in this paper to give practical il-lustration.From the results of the numerical example,it is concluded that the turret hole located near theforward of the amidships has small effect on the longitudinal strength of the ship hull.As for design ex-treme value of wave bending moment of storage tanker,statistic method is a more reasonablemethodology,especially with the consideration of the servere environmental conditions.The primary esti-mation of design section modulus of turret storage tanker can be determined by this design bending mo-ment.     

A Singular Perturbation Method for Parametric Investigation on J-lay Installation of Deepwater Pipelines

The maximum bending moment or curvature in the neighborhood of the touch down point (TDP) and the maximum tension at the top are two key parameters to be controlled during deepwater J-lay installation in order to ensure the safety of the pipe-laying operation and the normal operation of the pipelines. In this paper, the non-linear governing differential equation for getting the two parameters during J-lay installation is proposed and solved by use of singular perturbation technique, from which the asymptotic expression of stiffened catenary is obtained and the theoretical expression of its static geometric configuration as well as axial tension and bending moment is derived. Finite element results are applied to verify this method. Parametric investigation is conducted to analyze the influences of the seabed slope, unit weight, flexural stiffness, water depth, and the pipe-laying tower angle on the maximum tension and moment of pipeline by this method, and the results show how to control the installation process by changing individual parameters.     

Dynamics of ship collisions

This paper described a procedure for simulation of the outer dynamics in ship collisions.The simulation procedure is derived using the transient equations for the horizontal motion of a ship. The hydrodynamic forces acting on the ships' hull during the collision are calculated by a strip method, where the forces acting on each section are described by means of unit response functions. These functions are determined by cosine transformation of the sectional dampings. The sectional added masses and dampings, and thereby also the sectional unit response functions, are calculated by an approximate method. The deformations of the slip structures during the collisions are modelled as non-linear springs.The resulting system of non-linear equations is solved using a numerical time-integration procedure.A number of different collision situations are simulated by means of the procedure.     

Numerical prediction of hydrodynamic forces on a berthed ship induced by a passing ship in different waterway geometries

An investigation has been conducted to quantify the effect of waterway geometry on the form and magnitude of forces and moment experienced by a berthed ship due to a passing ship.By using the dynamic mesh technique and solving the unsteady RANS equations in conjunction with a RNG k?ε turbulence model,numerical simulation of the three-dimensional unsteady viscous flow around a passing ship and a berthed ship in different waterway geometries is conducted,and the hydrodynamic forces and moment acting on the berthed ship are calculated.The proposed method is verified by comparing the numerical results with existing empirical curves and a selection of results from model scale experiments.The calculated interaction forces and moment are presented for six different waterway geometries.The magnitude of the peak values and the form of the forces and moment on the berthed ship for different cases are investigated to assess the effect of the waterway geometry.The results of present study can provide certain guidance on safe maneuvering of a ship passing by a berthed ship.     

Numerical and experimental study on seakeeping performance of a SWATH vehicle in head waves

The seakeeping characteristics of a Small Waterplane Area Twin Hull (SWATH) vehicle equipped with fixed stabilizing fins was investigated by experimental and numerical methods The calculation methods range from viscous CFD simulation based on an unsteady RANS approach to Boundary Element Method (BEM) based on Three Dimensional Translating-pulsating Source Green Function (3DTP). Responses of ship motions in head regular waves and nonlinear effects on motion responses with increasing wave amplitude were analyzed. Numerical simulations have been validated by comparisons with experimental tests. The results indicate that the heave and pitch transfer functions depict two peaks with the increase of wave length. Comparisons amongst experimental data and different numerical calculations illustrate that the RANS method predicts ship motions with higher accuracy and allows the detection of nonlinear effects. The heave and pitch transfer functions see a downward trend with the increasing wave amplitude in the resonant zone at low speed.     

Investigation of Hydroelastic Ship Responses of An ULOC in Head Seas

Investigation of hydroelastic ship responses has been brought to the attention of the scientific and engineering world for several decades. There are two kinds of high-frequency vibrations in general ship responses to a large ocean-going ship in its shipping line, so-called springing and whipping, which are important for the determination of design wave load and fatigue damage as well. Because of the huge scale of an ultra large ore carrier (ULOC), it will suffer seldom slamming events in the ocean. The resonance vibration with high frequency is springing, which is caused by continuous wave excitation. In this paper, the wave-induced vibrations of the ULOC are addressed by experimental and numerical methods according to 2D and 3D hydroelasticity theories and an elastic model under full-load and ballast conditions. The influence of loading conditions on high-frequency vibration is studied both by numerical and experimental results. Wave-induced vibrations are higher under ballast condition including the wave frequency part, the multiple frequencies part, the 2-node and the 3-node vertical bending parts of the hydroelastic responses. The predicted results from the 2D method have less accuracy than the 3D method especially under ballast condition because of the slender-body assumption in the former method. The applicability of the 2D method and the further development of nonlinear effects to 3D method in the prediction of hydroelastic responses of the ULOC are discussed.     

On the parametric rolling of ships using a numerical simulation method

This paper has shown a numerical motion simulation method which can be employed to study on parametric rolling of ships in a seaway. The method takes account of the main nonlinear terms in the rolling equation which stabilize parametric rolling, including the nonlinear shape of the righting arm curve, nonlinear damping and cross coupling among all 6 degrees of freedom. For the heave, pitch, sway and yaw motions, the method uses response amplitude operators determined by means of the strip method, whereas the roll and surge motions of the ship are simulated, using nonlinear motion equations coupled with the other 4 degrees of freedom. For computing righting arms in seaways, Grim's effective wave concept is used. Using these transfer functions of effective wave together with the heave and pitch transfer functions, the mean ship immersion, its trim and the effective regular wave height are computed for every time step during the simulation. The righting arm is interpolated from tables, computed before starting the simulation, depending on these three quantities and the heel angle. The nonlinear damping moment and the effect of bilge keels are also taken into account. The numerical simulation tool has shown to be able to model the basic mechanism of parametric rolling motions. Some main characteristics of parametric rolling of ships in a seaway can be good reproduced by means of the method. Comprehensive parametric analyses on parametric rolling amplitude in regular waves have been carried out, with that the complicated parametric rolling phenomena can be understood better.     

Manoeuvring behaviour of ships in extreme astern seas

In an attempt to contribute to efforts for a robust and effective numerical tool addressing ship motion in astern seas, this paper presents the development of a coupled non-linear 6-DOF model with frequency dependent coefficients, incorporating memory effects and random waves. A new axes system that allows straightforward combination between seakeeping and manoeuvring, whilst accounting for extreme motions, is proposed. Validation of the numerical model with the results of benchmark tests commissioned by ITTC's Specialist Group on Stability demonstrated qualitative, yet not fully satisfactory agreement between numerical and experimental results in line with other predictive tools. The numerical results indicate that the inclusion of frequency coefficients definitely affects the accuracy of the predictions. In order to enhance further the numerical model and obtain useful information on motion coupling, extensive captive and free running model tests were carried out. Good agreement with the experimental results was achieved. These studies provide convincing evidence of the capability of the developed numerical model to predict the dangerous conditions that a ship could encounter in extreme astern seas. As a result, it could offer new insights towards establishing relationships linking ship behaviour to design, environmental and operational parameters.     

筏式海水养殖设施在波浪作用下的水弹性分析

由于台风等恶劣海洋条件的影响,海上浮筏式养殖结构极易遭受破坏。浮筏式海水养殖结构系统由多个浮子、连接走板和系泊缆组成。文中研究了不同走板材料对浮筏结构在波浪中动力响应的影响。通过基于势流理论的软件WAMIT计算获得了浮子的附加质量系数。利用海洋工程软件OrcaFlex计算模拟了浮筏结构在波浪中的时历响应,并分析比较了采用不同走板材料的浮筏结构在海浪中的水弹性差异。研究结果表明,木制浮筏相对新型高密度聚乙烯（high density polyethylene,简称HDPE）材料在波浪中受到的弯矩更大,可能更容易受到破坏。另外,对比分析了直接计算的结构最大响应和基于瑞利分布预测的最大响应值（MPM）,结果表明结构最大垂向运动基本符合瑞利分布,而水平运动最大值由于受系泊系统非线性影响,与瑞利分布有一定差异。     

Analysis of Wave Loads on A Semi-Submersible Platform

For the global and structural fatigue strength analysis of a semi-submersible platform, wave loads under design conditions are calculated by use of the three-dimensional boundary element method. Methods for calculating the forward-speed free-surface Green function are discussed and a computer program with this Green function is developed. According to the special rules, the wave loads under several typical design conditions of the platform are calculated. The maximum vertical bending moment, torsion moment and horizontal split force are determined from a series of contour maps of wave loads for the wave period of 5 to 18 seconds at a certain interval and the wave phase of 0°to 360°at a certain interval. The wave height is determined by the function of wave period with a given exceedance probability. The maximum wave loads under the combination of wave parameters are used as the input of hydrodynamic pressure in the three-dimensional finite element analysis process. The transfer functions of wave loads     

Stochastic inverse modeling of nonlinear roll damping moment of a ship

This work presents an application of stochastic inverse method for the determination of nonlinear roll damping moment of a ship at zero forward speed. Nonlinear roll damping moment was estimated from the measured dynamic responses through stochastic inverse model. It is shown that this method enables nonlinear characteristic of the roll damping to be estimated without any assumption on its form of nonlinearity, including its confidence intervals given noisy data. The accuracy and practicability were assessed with laboratory tests related to both free-decay and forced rolling motions. The estimation results of the nonlinear damping moment show good agreement in all cases.