Static and Dynamic Analysis of Mooring Lines by Nonlinear Finite Element Method

This study has focused on developing numerical procedures for the static and dynamic nonlinear analysis of mooring lines. A geometrically nonlinear finite element method using isoparametric cable element with two nodes is briefly presented on the basis of the total Lagrangian formulation. The static and dynamic equilibrium equations of mooring lines are established. An incremental-iterative method is used to determine the initial static equilibrium state of cable systems under the action of self weights, buoyancy and current. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method, and examine the effect of various parameters.

Dynamic Analysis of Semi-Submersible Production Platform Under the Failure of Mooring Lines

This paper quantitatively studies the transient dynamic response of a semi-submersible production platform with the loss of one or several positioning mooring lines.A semi-submersible platform,production risers,and positioning mooring lines are all included in the numerical simulation.Increased motion of the semi-submersible platform,tension variation of the remaining mooring lines/risers and the risk of mooring line or riser clashing are all investigated through fully coupled time-domain analysis.Combined environmental loads are selected from irregular waves and the steady current varying from very rough to extreme sea conditions.Three dimension radiation/diffraction theories and Morison’s equation are applied to calculate first-order wave force and second-order mean drift force of floating semi-submersible platform.Nonlinear time-domain finite element methods are employed to analyze the behavior of mooring lines and risers.Results show that the failure of mooring lines seriously reduce the platform’s stability performance.The tension of the rest lines is also increased accordingly.Remaining lines which are closer to the failed lines will have larger tension increase to compensate.Line-Line distance provides practical information for the risk of clashing investigation.

Investigation of Motion of Two Hinged Bodies Moored by Mooring Lines in Waves

In this paper, the motions are studied of a multi-body which is composed of two plates hinged together and moored by eight mooring lines in regular waves. The experimental results are compared with computational results. The linear potential theory and the perturbation method are combined to study this complicated system. The former is used to calculate the wave forces acting on the plates and the motion responses of them, while the latter is used to describe the dynamic character of the eight mooring lines coupled with the two hinged plates. Some response results of each plate are presented and comparisons between calculated results and experimental data are given. All the calculations are confined to regular beam waves.

Snap Tension in Mooring Lines of Deepwater Platform

Based on the theory of impact dynamics, the motion equations for a mooring line-floating body system before and after impact loading are established with consideration of the viscoelastic property of mooring lines. The factors that influence the taut-slack conditions of a mooring system are analyzed through classifying the taut-slack regions, which are defined by non-dimensional ratios of displacement, frequency, and damping of the system. The mooring system of Jip spar platform is analyzed, and the snap tension characteristics of mooring lines are given. The factors that influence the maximum tension in mooring lines, including the mass of the floating body, length of mooring lines, frequency and amplitude of external excitation, and pretension in mooting lines, are also analyzed through computing the dynamic response of system and parametric study. It is shown that the maximum tension increases with the increasing mass of the floating body, external excitation and pretension. Also, it is found that the influence of the non-dimensional ratio of damping increases with the increase of the pretension in mooring lines.

Mooring Model Experiment and Mooring Line Force Calculation

Mooring model experiment and mooring line tension determination are of significance to the design of mooring systems and berthing structures. This paper mainly involves: (a) description and analysis of a mooring model experiment; (b) derivation of static equilibrium equations for a moored ship subjected to wind, current and waves; (c) solution of mooring equations with the Monte Carlo method; (d) qualitative analysis of effects of pier piles on mooring line forces. Special emphasis is placed on the derivation of static equilibrium equations, solution method and the mooring model experiment.

Design Curves for Mooring Lines of Turret Mooring Systems

This paper presents a series of design curves to aid in the selection of turret mooring systems for tankers based Floating Production Storage and Offloading (FPSO) systems. These curves are appropriate to water depths ranging from 100 m to 600 m. The curves can be used as a preliminary design tool, allowing the designer to quickly evaluate alternative mooring system configurations, including the number of mooring lines, the characteristics of chain and wire rope to be deployed and the. initial tension. With a knowledge of the total environmental force and vessel motion characteristics, the designer can determine the appropriate system for closer evaluation.

Probability Distribution of the Hull Motion and Mooring Line Tension of Two Floating Systems

The statistical and distribution characteristics of the responses of a floater and its mooring lines are essential in designing floating/mooring systems.In general,the dynamic responses of offshore structures obey a Gaussian distribution,assuming that the structural system,and sea loads are linear or weakly nonlinear.However,mooring systems and wave loads are considerably nonlinear,and the dynamic responses of hull/mooring systems are non-Gaussian.In this study,the dynamic responses of two types of floaters,semi-submersible and spar platforms,and their mooring lines are computed using coupled dynamic analysis in the time domain.Herein,the statistical characteristics and distributions of the hull motion and mooring line tension are discussed and compared.The statistical distributions of the dynamic responses have strong non-Gaussianity and are unreasonably fitted by a Gaussian distribution for the two floating and mooring systems.Then,the effects of water depth,wave parameters,and low-frequency and wave-frequency components on the non-Gaussianity of the hull motion,and mooring line tension are investigated and discussed.A comparison of the statistical distributions of the responses with various probability density functions,including the Gamma,Gaussian,General Extreme Value,Weibull,and Gaussian Mixture Model(GMM)distributions,shows that the GMM distribution is better than the others for characterizing the statistical distributions of the hull motion,and mooring line tension responses.Furthermore,the GMM distribution has the best accuracy of response prediction.

An Investigation on Low Frequency Fatigue Damage of Mooring Lines Applied in a Semi-Submersible Platform

Assessing the fatigue life of mooring systems is important for deep water structures. In this paper, a comprehensive fatigue analysis is conducted on the mooring lines applied in a semi-submersible platform with special focus on the low frequency(LF) fatigue damage. Several influential factors, including water depth, wave spectral parameters, and riser system, are considered. Numerical simulation of a semi-submersible platform with the mooring/riser system is executed under different conditions, and the fatigue damage of mooring lines is assessed by using the time domain analysis method as a benchmark. The effects of these factors on the mooring line tension and the fatigue damage are investigated and discussed in detail. Research results indicate that the LF fatigue damage only accounts for a very small portion of the total damage, although the LF components dominate the global motion response and the mooring line tension of the semi-submersible platform. However, it is demonstrated that the LF fatigue damage is clearly affected by the influential factors. The increase in water depth and spectral peak periods, and the existence of risers can weaken the contribution of the LF components to the mooring line fatigue damage, while the fatigue damage due to the LF components increases with the increase of significant wave height.

Investigation on the Dynamic Responses of a Truss Spar Platform for Different Mooring Line Groups

任何漂浮的平台的动态回答依赖于团，僵硬和身体以及系在的系统的抑制特征。因此，学习对能最后帮助他们的费用到节俭的系统的单个贡献的效果是很必要的。这份报纸在一个 truss 圆材平台的回答上集中于系在的僵硬的效果，由线的不同组织获得了。学习是我们关于包括线虚荣，直径和方位角角度的效果的系在的系统的现在的研究的部分。站台与三 degrees-of-freedom 作为僵硬身体被建模，它的运动用含蓄的 Newmark 贝它技术在时间域被分析。系在的线恢复力量旅行关系用一条伪静电干扰途径被评估。有线的系在的系统以恢复力量以及平台的吝啬的位置在组展览的更少的数字安排了更好的性能，这被观察。然而，站台的动态运动为不同的线组仍然保持未受影响。

Time Domain Simulation of a One Line Failure for a DP-assisted Mooring System

这篇论文集中于与一个帮助 DP 的绳索系统装备的一个半能沉入水中的平台的研究。基于帮助 DP 的绳索系统的工作原则和平台运动的模型，一个时间域模拟程序被使用分析影响在一线失败的情况中，在平台运动上，驱动推进器和系在的线的紧张的消费。结果显示出那，在 10 年的风下面主导，一线失败几乎没在系在的线的紧张上有很少影响。当失败线是上风的时，电源消费将与精确性的一个削弱的位置极大地增加。然而失败线是什么时候下风，电源消费将与精确性的一个部分加强的位置被减少。

Numerical Investigation of Mooring Line Damping and the Drag Coefficients of Studless Chain Links

The chain/wire rope/chain combination is a common choice for mooring offshore floating platforms. However, data of the drag coefficients of chain links are rather limited, resulting in uncertainties with the calculations of the drag force, and hence the damping of the mooring system. In this paper, the importance of the selection of the drag coefficient is first investigated. The computational fluid dynamics(CFD) method is then used to determine the drag coefficients of a studless chain under steady flows. Numerical model validation is first completed by simulating a smooth circular cylinder under steady flows. In particular, the performance of different turbulence models is assessed through the comparisons between the calculations and the experimental results. The large eddy simulation(LES) model is finally selected for the simulation of steady flows past a chain. The effects of the Reynolds number on the drag coefficient of a stud-less chain is also studied. The results show that the calculated drag coefficients of a stud-less chain are fairly consistent with the available experimental data.

The Effect of the First order Responses of Mooring Line on the Second order Mooring Line Damping

In this paper we investigated the effect of the first order responses of mooring line on the second order mooring line damping.In the study of the slow oscillating of a moored floating structure by perturbation method in frequency domain,the second order equations of the mooring line are divided into non homogeneous and homogeneous equations.The solutions are related to the first order responses of mooring line and second order floating structure oscillation respectively.In order to find the effect of the first order responses of mooring line,the second order mooring line tension and damping were determined by solving the non homogeneous equation and homogeneous equation.From the results,we found,although the second order mooring line tension obtained from the non homogenous equation is quite small compared with the total second order mooring line tension,the damping contributed from both of them are in the same order in quantity.So,in predicting the second order mooring line damping,the effect of the solution related to the non homogeneous equation can not be omitted.

Investigation on Effects of Mooring Line Fractures and Connector Failures for A Hybrid Modular Floating Structure System

The present work reports a Hybrid Modular Floating Structure(HMFS)system with typical malfunction conditions.The effects of both fractured mooring lines and failed connectors on main hydrodynamic responses(mooring line tensions,module motions,connector loads and wave power production)of the HMFS system under typical sea con-ditions are comparatively investigated.The results indicate that the mooring tension distribution,certain module motions(surge,sway and yaw)and connector loads(Mz)are significantly influenced by mooring line fractures.The adjacent mooring line of the fractured line on the upstream side suffers the largest tension among the remaining mooring lines,and the case with two fractured mooring lines in the same group on the upstream side is the most dangerous among all cases of two-line failures in view of mooring line tensions,module motions and connector loads.There-fore,one emergency strategy with appropriate relaxation of a proper mooring line has been proposed and proved effective to reduce the risk of more progressive mooring line fractures.In addition,connector failures substantially affect certain module motions(heave and pitch),certain connector loads(Fz and My)and wave power production.The present work can be helpful and instructive for studies on malfunction conditions of modular floating structure(MFS)systems.

Discrete Element Simulations of Ice Load and Mooring Force on Moored Structure in Level Ice

Moored structures are suitable for operations in ice-covered regions owing to their security and efficiency.This paper aims to present a new method for simulating the ice load and mooring force on the moored structure during ice-structure interaction with a spherical Discrete Element Method(DEM).In this method,the level ice and mooring lines consist of bonded sphere elements arranged in different patterns.The level ice model has been widely validated in simulation of the ice load of fixed structures.In the mooring line simulation,a string of spherical elements was jointed with the parallel bond model to simulate the chains or cable structure.The accuracy of the mooring line model was proved by comparing the numerical results with the nonlinear FEM results and model towing experiment results.The motion of the structure was calculated in the quaternion method,considering the ice load,mooring force,and hydrodynamic force.The hydrodynamic force comprised wave-making damping,current drag,and buoyancy force.Based on the proposed model,the interaction of a semi-submersible structure with level ice was simulated,and the effect of ice thickness on the ice load was analyzed.The numerical results show that the DEM method is suitable to simulate the ice load and mooring force on moored floating structures.

Prediction of the Mooring Force of a 2-D Floating Oil Storage Tank

A Constrained Interpolation Profile(CIP)-based model is developed to predict the mooring force of a two- dimensional floating oil storage tank under wave conditions, which is validated against to a newly performed experiment. In the experiment, a box-shaped floating oil storage apparatus is used. Computations are performed by an improved CIP-based Cartesian grid model, in which the THINC/SW scheme(THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A multiphase flow solver is adopted to treat the water-air-body interactions. The Immersed Boundary Method(IBM) is implemented to treat the body surface. Main attention is paid to the sum force of mooring line and velocity field around the body. It is found that the sum force of the mooring line increases with increasing wave amplitude. The body suffers from water wave impact and large body motions occur near the free surface. The vortex occurs near the sharp edge, i.e., the sharp bottom corners of the floating oil storage tank and the vortex shedding can be captured by the present numerical model. The present model could be further improved by including turbulence model which is currently under development. Comparison between the computational mooring forces and the measured mooring forces is presented with a reasonable agreement. The developed numerical model can predict the mooring line forces very well.

Fatigue Analysis of the Taut-Wire Mooring System Applied for Deep Waters

Precisely predicting the fatigue life of taut-wire mooring systems has become an interesting and important problem for scientists and engineers since there are still difficulties in the inspection and maintenance of mooring lines in a rough sea environment especially in deep waters. In this paper, a comprehensive fatigue analysis is performed for a polyester taut-wire mooring system of an FPSO based on the time domain dynamic theory, rainflow cycle counting method and linear damage accumulation rule of Palmgren-Miner. Three influential factors in the fatigue analysis including the pre-tension, dynamic stiffness and T-N curve are investigated in detail. Two polyester T-N curves, one is from the DNV- 0S-E301 and the other is from the API-RP-2SM, are adopted in the calculation. The fatigue analysis of the mooting system after one-line failure is also carried out. The calculation results indicate that the fatigue life is significantly affected by the T-N curve. The fatigue life decreases with increasing pre-tension, and is largely reduced if taking into account the dynamic stiffness caused by cyclic loading. The analysis also proves that one-line failure has remarkable effects on the fatigue lives of other mooting lines. The present parametric and comparative study is believed to be meaningful to further understanding of the taut-wire mooting system for deepwater applications.

Analysis of Optimization for Preliminary Design of Multi-Component Mooring Systems

Multi-component mooring systems become widely used in deep water position-keeping of drilling and production platforms. However, versatile materials make it difficult to design appropriate mooring lines made of several segments. Based on catenary equations of a multi-component mooring line at a specific water depth, this paper establishes a minimum model for designing this kind of lines. The model is solved by Genetic Algorithm and Multi-Objective Planning respectively. The model is verified by its application to a practical mooring design assignment—a quasi-static analysis for a large semi-submersible. The optimal result is finally obtained with the aid of design graphs.

Effect of Failure Mode of Taut Mooring System on the Dynamic Response of A Semi-Submersible Platform

Mooring system failure can lead to largely different dynamic response of floating structures when compared to the response under the condition of intact mooring system.For a semi-submersible platform with taut mooring system under extreme environmental conditions,the typical mooring system failure includes anchor line breaking failure due to the broken anchor line,and the anchor dragging failure caused by the anchor failure in the seabed soil due to the shortage of the anchor bearing capacity.However,study on the mooring failure caused by anchor failure is rare.The current work investigates the effect of three failure modes of taut mooring system on dynamic response of a semi-submersible platform,including one line breaking failure,two lines breaking failure,and one line breaking with one line attached anchor dragging failure.The nonlinear polynomial mooring line model in AQWA was used with integrating the load and displacement curve from the anchor pulling study to characterize the anchor dragging behavior for mooring system failure caused by the anchor failure.The offsets of the platform and the tension of mooring lines were analyzed for mooring system failure with 100-year return period.It is found that the mooring failure of one line breaking with one line attached anchor dragging is a case between the other two mooring failures.The traditional mooring analysis considering only the damaged condition with one line breaking is not safe enough.And the simple way of mooring analysis of two lines breaking is too conservative for the costly offshore engineering.

Current Status and Future Trends for Mooring Systems of Floating Offshore Wind Turbines

With the increasing demand of energy and the limitation of bottom-fixed wind turbines in moderate and deep waters,floating offshore wind turbines are doomed to be the right technical choice and they are bound to enter a new era of rapid development.The mooring system is a vital system of a floating wind turbine for station-keeping under harsh environmental con­ditions.In terms of existing floating wind turbine projects,this paper is devoted to discussing the current status of mooring systems and mooring equipment.This paper also presents the mooring analysis methods and points out the technical difficulties and challenges in mooring design,in­stallation,operation and maintenance stages.Finally,the developing trends of the mooring system are summarized,aiming to provide a reference for future mooring research.

浅水浮式风电结构非线性波浪荷载及动力响应特性研究

浮式风电结构在浅水海域中承受的波浪荷载及运动响应表现出非线性特征,对浮式风电安全性提出很高要求。本文建立了风机-浮式基础-系泊系统耦合分析模型,对于不同水深、不同波浪荷载计算方法下的频域水动力系数和时域计算结果分别进行了对比,讨论了水深以及波浪荷载计算方法对浮式风电结构响应和系泊张力的影响。结果表明:浮式风电结构的水动力性能和动力响应随水深变化显著。水深较浅时,浮体响应和系泊张力的低频部分明显增大,二阶波浪荷载的影响更加显著。同时,Newman近似方法与全二次传递函数方法相比,在浅水条件下会明显低估二阶波浪荷载效应,进而影响平台响应和系泊张力的分析。