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Dynamic Analysis Of A Spar Type Offshore Floating Wind Turbine And Its Mooring System
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Book Synopsis Dynamic Analysis of a Spar-type Offshore Floating Wind Turbine and Its Mooring System by : Xue Xu
Download or read book Dynamic Analysis of a Spar-type Offshore Floating Wind Turbine and Its Mooring System written by Xue Xu and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The demand for developing sustainable and renewable energy is increasing due to the greenhouse gas effect and the reducing availability of fossil fuels. Wind energy is one of the cleanest and most sustainable renewable resources. People mainly use two types of wind turbines - onshore and offshore, to harvest the wind energy. Compared with onshore wind, offshore wind resources allow more reliable generation of electricity. In shallow water, bottom-fixed turbines may be used. However, as water depths increase it becomes increasingly difficult to build suitable fixed foundations, and floating offshore wind turbines become attractive. The OC3-Hywind is an offshore floating wind turbine (OFWT) supported by a spar platform and held in place with three mooring lines. It is important to study the dynamic responses of the floating platform and the mooring system behaviour so that the OFWT can be designed and constructed safely and economically and generate electricity with reliability. However, there are not many studies which have validated the numerical simulation results for floating offshore wind turbines with physical experiments while published studies rarely show the details of the mooring line motion behaviour for OFWTs. This thesis investigates the dynamic behaviour of a spar-type OFWT including its mooring systems, analysed under various environmental loads both by using state-of-the-art numerical software and conducting an experiment campaign at the Kelvin Hydrodynamics Laboratory. The free decay test has been carried out first to get the spar platform's motions natural frequencies and damping characteristics. A range of regular and irregular waves has been applied to the platform (both with and without realistic mooring lines) to obtain the platform motion RAO (response amplitude operator) - which can be used to predict the platform dynamic responses under other wave conditions - and to examine the reliability of the numerical predictions under realistic sea conditions. For the mooring line tensions and motion, the software shows its limitations in the calculation. A non-linear snatching phenomenon has been observed at the tank for some wave frequencies, which has rarely been discussed in published research. It is very important to study this non-linear behaviour as it is shown that snatching leads to the high instantaneous mooring line loads and platform accelerations, which could cause the failure of the mooring lines in the real structure.
Book Synopsis Offshore Structure Modeling by : Subrata Kumar Chakrabarti
Download or read book Offshore Structure Modeling written by Subrata Kumar Chakrabarti and published by World Scientific. This book was released on 1994-02-21 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the existing literature on offshore structures touch on model testing, a comprehensive text discussing the design, construction, instrumentation, testing and analysis of the physical model is lacking. This book fills that vacuum and provides, through its survey of the theoretical and practical aspects of physical modeling, an in-depth coverage of the technology of model testing. Its usefulness runs through the entire field of engineering, reaching far beyond its focus on offshore construction; and its breadth of scope should appeal not only to engineers and naval architects but to scientists interested in structural or hydraulic testing as well.
Book Synopsis Floating Offshore Wind Energy by : Joao Cruz
Download or read book Floating Offshore Wind Energy written by Joao Cruz and published by Springer. This book was released on 2016-08-20 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a state-of-the-art review of floating offshore wind turbines (FOWT). It offers developers a global perspective on floating offshore wind energy conversion technology, documenting the key challenges and practical solutions that this new industry has found to date. Drawing on a wide network of experts, it reviews the conception, early design stages, load & structural analysis and the construction of FOWT. It also presents and discusses data from pioneering projects. Written by experienced professionals from a mix of academia and industry, the content is both practical and visionary. As one of the first titles dedicated to FOWT, it is a must-have for anyone interested in offshore renewable energy conversion technologies.
Book Synopsis Dynamic Analysis of a 5 Megawatt Offshore Floating Wind Turbine by : Evan Michael Harriger
Download or read book Dynamic Analysis of a 5 Megawatt Offshore Floating Wind Turbine written by Evan Michael Harriger and published by . This book was released on 2011 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offshore wind is a valuable source of renewable energy, as it is typically strong and steady. Turbines have been utilized offshore in parts of Europe and Asia, however only at shallow depths. Floating wind turbines must be implemented in deeper areas to be economical, but this technology is relatively new and untested. This paper describes a numerical analysis model that can be used to investigate the motion of a 5 MW floating turbine subjected to ocean conditions. Prototype designs for a spar buoy and barge platform are studied. The stiffness and damping effects brought about by the mooring lines are evaluated using a dynamic cable model. A boundary element model is used to calculate added mass and damping effects, as well as the forces on the structure caused by the wave-body interaction. The governing equations of motion include all the added mass, damping and stiffness components in the frequency domain. Response of the structure is found by solving the governing equation combined with a wave spectrum to represent actual ocean wave fields. Approximate bending moments at the base of each design are found by inputting the predicted base motion into a linear modal analysis model created in SAP2000. Based on the results found in this paper, incoming waves cause much greater motion of the barge design, especially in the pitching direction.
Book Synopsis Coupled Dynamic Analysis of Floating Offshore Wind Farms by : Sangyun Shim
Download or read book Coupled Dynamic Analysis of Floating Offshore Wind Farms written by Sangyun Shim and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past decade, the demand for clean renewable energy continues to rise drastically in Europe, the US, and other countries. Wind energy in the ocean can possibly be one of those future renewable clean energy sources as long it is economically feasible and technologically manageable. So far, most of the offshore wind farm research has been limited to fixed platforms in shallow-water areas. In the water depth deeper than 30m, however, floating-type wind farms tend to be more feasible. Then, the overall design and engineering becomes more complicated than fixed platforms including the coupled dynamics of platforms, mooring lines, and blades. In the present study, a numerical time-domain model has been developed for the fully coupled dynamic analysis of an offshore floating wind turbine system including blade-rotor dynamics and platform motions. As a test case, the TLP-type floater system with 3 blades of 70-m diameter designed by the National Renewable Energy Laboratory (NREL) is selected to analyze the dynamic coupling effects among floating system, mooring lines, and wind turbine. The performance of the selected system in a typical wind-wave-current condition has been simulated and analyzed. A similar study for the floater and rotor coupled dynamic analysis was conducted by MIT and NREL. However, in the present case, the dynamic coupling between platform and mooring lines are also considered in addition to the rotor-floater dynamic coupling. It is seen that the rotor-floater coupling effects increase with wind velocity and blade size. The increased coupling effects tend to increase the dynamic tension of TLP tethers. The developed technology and numerical tool are applicable to the new offshore floating wind farms planned in the future.
Book Synopsis Marine Hydrodynamics, 40th anniversary edition by : J. N. Newman
Download or read book Marine Hydrodynamics, 40th anniversary edition written by J. N. Newman and published by MIT Press. This book was released on 2018-01-26 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook that offers a unified treatment of the applications of hydrodynamics to marine problems. The applications of hydrodynamics to naval architecture and marine engineering expanded dramatically in the 1960s and 1970s. This classic textbook, originally published in 1977, filled the need for a single volume on the applications of hydrodynamics to marine problems. The book is solidly based on fundamentals, but it also guides the student to an understanding of engineering applications through its consideration of realistic configurations. The book takes a balanced approach between theory and empirics, providing the necessary theoretical background for an intelligent evaluation and application of empirical procedures. It also serves as an introduction to more specialized research methods. It unifies the seemingly diverse problems of marine hydrodynamics by examining them not as separate problems but as related applications of the general field of hydrodynamics. The book evolved from a first-year graduate course in MIT's Department of Ocean Engineering. A knowledge of advanced calculus is assumed. Students will find a previous introductory course in fluid dynamics helpful, but the book presents the necessary fundamentals in a self-contained manner. The 40th anniversary of this pioneering book offers a foreword by John Grue. Contents Model Testing • The Motion of a Viscous Fluid • The Motion of an Ideal Fluid • Lifting Surfaces • Waves and Wave Effects • Hydrodynamics of Slender Bodies
Book Synopsis Offshore Mechanics by : Madjid Karimirad
Download or read book Offshore Mechanics written by Madjid Karimirad and published by John Wiley & Sons. This book was released on 2018-05-07 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers theoretical concepts in offshore mechanics with consideration to new applications, including offshore wind farms, ocean energy devices, aquaculture, floating bridges, and submerged tunnels This comprehensive book covers important aspects of the required analysis and design of offshore structures and systems and the fundamental background material for offshore engineering. Whereas most of the books currently available in the field use traditional oil, gas, and ship industry examples in order to explain the fundamentals in offshore mechanics, this book uses more recent applications, including recent fixed-bottom and floating offshore platforms, ocean energy structures and systems such as wind turbines, wave energy converters, tidal turbines and hybrid marine platforms. Offshore Mechanics covers traditional and more recent methodologies used in offshore structure modelling (including SPH and hydroelasticity models). It also examines numerical techniques, including computational fluid dynamics and finite element method. Additionally, the book features easy-to-understand exercises and examples. Provides a comprehensive treatment for the case of recent applications in offshore mechanics for researchers and engineers Presents the subject of computational fluid dynamics (CFD) and finite element methods (FEM) along with the high fidelity numerical analysis of recent applications in offshore mechanics Offers insight into the philosophy and power of numerical simulations and an understanding of the mathematical nature of the fluid and structural dynamics with focus on offshore mechanic applications Offshore Mechanics: Structural and Fluid Dynamics for Recent Applications is an important book for graduate and senior undergraduate students in offshore engineering and for offshore engineers and researchers in the offshore industry.
Download or read book MARE-WINT written by Wiesław Ostachowicz and published by Springer. This book was released on 2016-08-30 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a holistic, interdisciplinary overview of offshore wind energy, and is a must-read for advanced researchers. Topics, from the design and analysis of future turbines, to the decommissioning of wind farms, are covered. The scope of the work ranges from analytical, numerical and experimental advancements in structural and fluid mechanics, to novel developments in risk, safety & reliability engineering for offshore wind.The core objective of the current work is to make offshore wind energy more competitive, by improving the reliability, and operations and maintenance (O&M) strategies of wind turbines. The research was carried out under the auspices of the EU-funded project, MARE-WINT. The project provided a unique opportunity for a group of researchers to work closely together, undergo multidisciplinary doctoral training, and conduct research in the area of offshore wind energy generation. Contributions from expert, external authors are also included, and the complete work seeks to bridge the gap between research and a rapidly-evolving industry.
Book Synopsis Dynamic Response of Spar-type Offshore Floating Wind Turbines by : Roberts Proskovics
Download or read book Dynamic Response of Spar-type Offshore Floating Wind Turbines written by Roberts Proskovics and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a significant increase in the interest in floating offshore wind turbines from the wind energy industry, governments and academia. Partially driven by the recent nuclear disaster in Japan, but also by the lack or complete absence of shallow waters in various countries around the globe (making fixed offshore wind turbines infeasible), multiple different topology floating offshore wind turbines have been proposed and, in some cases, prototypes built and installed offshore. The most well-known of these is Hywind by Statoil, which has been operational off the coast of Norway since the end of 2009. While small scale prototypes had been installed even before Hywind, for example Blue-H in 2007, no guidelines have yet emerged that would give recommendations and guiding principles in designing new floating offshore wind turbines. The aim of this thesis is to provide some knowledge base for future design of floating offshore wind turbines by looking at what simplifications could be made and what effect these would have on the preliminary designs of new floating offshore wind turbines. This thesis starts by comparing different topology floating offshore wind turbines and choosing one, deemed the most promising, as the base case scenario for use in the subsequent analysis and calculations. This thesis also looks at the importance of unsteady representations of the aerodynamics compared with quasi-steady when designing a new floating offshore wind turbine, by comparing quasi-steady aerodynamic loads first with fully-attached unsteady loads and later with fully-unsteady (fully-attached, separated and dynamic stall). A chapter is allocated to identifying which degree-of-freedom of loading is the most damaging to the system, as floating offshore wind turbines operate in very harsh and unstable environments. Once identified, this knowledge can be used to further improve floating offshore wind turbines, hence making them even more feasible. Finally, the wind turbine previously chosen as a base case has its floating support shortened and four different draft designs proposed that would allow it to be deployed in medium-to-deep waters, in which fixed supports for wind turbines are not economical.
Book Synopsis Fundamentals of Multibody Dynamics by : Farid Amirouche
Download or read book Fundamentals of Multibody Dynamics written by Farid Amirouche and published by Springer Science & Business Media. This book was released on 2007-05-24 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook – a result of the author’s many years of research and teaching – brings together diverse concepts of the versatile tool of multibody dynamics, combining the efforts of many researchers in the field of mechanics.
Book Synopsis Sea Loads on Ships and Offshore Structures by : O. Faltinsen
Download or read book Sea Loads on Ships and Offshore Structures written by O. Faltinsen and published by Cambridge University Press. This book was released on 1993-09-23 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: After introducing the theory of the structural loading on ships and offshore structures based on the motions of wind, waves and currents, this text demonstrates its applications to conventional and non-conventional sea vessels, including extensive exercises and examples.
Book Synopsis Reliability-Based Optimization of Floating Wind Turbine Support Structures by : Mareike Leimeister
Download or read book Reliability-Based Optimization of Floating Wind Turbine Support Structures written by Mareike Leimeister and published by Springer Nature. This book was released on 2023-01-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pursues the ambitious goal of combining floating wind turbine design optimization and reliability assessment, which has in fact not been done before. The topic is organized into a series of very ambitious objectives, which start with an initial state-of-the-art review, followed by the development of high-fidelity frameworks for a disruptive way to design next generation floating offshore wind turbine (FOWT) support structures. The development of a verified aero-hydro-servo-elastic coupled numerical model of dynamics for FOWTs and a holistic framework for automated simulation and optimization of FOWT systems, which is later used for the coupling of design optimization with reliability assessment of FOWT systems in a computationally and time-efficient manner, has been an aim of many groups internationally towards implementing a performance-based/goal-setting approach in the design of complex engineering systems. The outcomes of this work quantify the benefits of an optimal design with a lower mass while fulfilling design constraints. Illustrating that comprehensive design methods can be combined with reliability analysis and optimization algorithms towards an integrated reliability-based design optimization (RBDO) can benefit not only the offshore wind energy industry but also other applications such as, among others, civil infrastructure, aerospace, and automotive engineering.
Book Synopsis Coupled Dynamic Analysis of Multiple Unit Floating Offshore Wind Turbine by : Yoon Hyeok Bae
Download or read book Coupled Dynamic Analysis of Multiple Unit Floating Offshore Wind Turbine written by Yoon Hyeok Bae and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present study, a numerical simulation tool has been developed for the rotor-floater-tether coupled dynamic analysis of Multiple Unit Floating Offshore Wind Turbine (MUFOWT) in the time domain including aero-blade-tower dynamics and control, mooring dynamics and platform motion. In particular, the numerical tool developed in this study is based on the single turbine analysis tool FAST, which was developed by National Renewable Energy Laboratory (NREL). For linear or nonlinear hydrodynamics of floating platform and generalized-coordinate-based FEM mooring line dynamics, CHARM3D program, hull-riser-mooring coupled dynamics program developed by Prof. M.H. Kim's research group during the past two decades, is incorporated. So, the entire dynamic behavior of floating offshore wind turbine can be obtained by coupled FAST-CHARM3D in the time domain. During the coupling procedure, FAST calculates all the dynamics and control of tower and wind turbine including the platform itself, and CHARM3D feeds all the relevant forces on the platform into FAST. Then FAST computes the whole dynamics of wind turbine using the forces from CHARM3D and return the updated displacements and velocities of the platform to CHARM3D. To analyze the dynamics of MUFOWT, the coupled FAST-CHARM3D is expanded more and re-designed. The global matrix that includes one floating platform and a number of turbines is built at each time step of the simulation, and solved to obtain the entire degrees of freedom of the system. The developed MUFOWT analysis tool is able to compute any type of floating platform with various kinds of horizontal axis wind turbines (HAWT). Individual control of each turbine is also available and the different structural properties of tower and blades can be applied. The coupled dynamic analysis for the three-turbine MUFOWT and five-turbine MUFOWT are carried out and the performances of each turbine and floating platform in normal operational condition are assessed. To investigate the coupling effect between platform and each turbine, one turbine failure event is simulated and checked. The analysis shows that some of the mal-function of one turbine in MUFOWT may induce significant changes in the performance of other turbines or floating platform. The present approach can directly be applied to the development of the remote structural health monitoring system of MUFOWT in detecting partial turbine failure by measuring tower or platform responses in the future. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/149465
Book Synopsis Dynamics Modeling, Simulation and Analysis of a Floating Offshore Wind Turbine by : Mohammed Khair Al-Solihat
Download or read book Dynamics Modeling, Simulation and Analysis of a Floating Offshore Wind Turbine written by Mohammed Khair Al-Solihat and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: " Floating Offshore Wind Turbines (FOWTs) are a promising technology to harness the abundant offshore wind energy resources in open ocean areas. A FOWT consists of a floating platform, the moorings, and the wind turbine structure (tower + Rotor-Nacelle Assembly (RNA)). The main focus of this thesis is to develop multibody dynamic models that integrate the structural dynamics, and hydrostatic, hydrodynamic, aerodynamic and mooring system loads. Special efforts are also devoted to characterize the mooring and hydrostatic loads as main sources of systems stiffness that shapes the dynamic behavior of the system. Two approaches for modeling the platform/tower dynamics are developed, a rigid multibody model and a coupled rigid-flexible multibody model. Both models treat the platform, nacelle and rotor as six-degrees-of-freedom (6-DOF) rigid bodies. However, modeling the wind turbine tower dynamics differs between these approaches. The rigid model considers the tower as a 6-DOF rigid body while the flexible model represents the tower as a three-dimensional (3D) tapered damped Euler-Bernoulli beam undergoing coupled general rigid body and elastic motions. In both approaches, the wind turbine drivetrain dynamics is also considered to capture the rotor spin response. The equations of motions of both models are derived symbolically using Lagrange's equations. The hydrostatic restoring loads are evaluated through development of a novel nonlinear hydrostatic approach. This approach allows evaluating the exact hydrostatic force and moment and position of the center of buoyancy as function of the platform displacement and finite rotation. New exact expressions for the water plane area restoring moments are developed. The hydrostatic stiffness matrix at an arbitrary position and orientation of the platform is subsequently derived. A quasi-static approach is then developed to determine the cable tensions of the single-segment and multi-segment mooring system configurations proposed to moor the platform to the seabed. The approach uses different governing equations, depending on whether the mooring lines partially rest on the seabed; are suspended; or fully taut. The exact mooring stiffness is subsequently derived and the influence of several mooring system parameters on the mooring system stiffness is investigated. As an alternative to the quasi-static cable model, a lumped mass cable model incorporating the cable-seabed contact effect is developed to integrate the cable dynamics into the FOWT system dynamics. The equations of motion of the mooring line nodes are assembled for the two mooring system configurations under consideration. A new methodology is also presented to calculate the equilibrium profile of the mooring line lying on a seabed as desirable initial conditions for solving the discretized cable equations of motion. Finally, the theoretical models are implemented through a large simulation tool to analyze the dynamic behavior of the spar FOWT system under study. A series of simulations under defined external loads (load cases) are performed to validate the dynamic models. The simulation results are compared with similar results obtained from well-known offshore wind design codes. The simulation results are found to be in very good agreement with the reported results. Numerical experiments are also performed to investigate the influence of the tower flexibility, mooring system configuration, tower twist and cable dynamics on the system dynamic behavior. The results show that the system responses obtained from the rigid body model under-predict the platform yaw response and exhibit less damping than those obtained from the flexible model. It is also found that the mooring system configuration choice does not influence the platform roll and pitch responses or tower elastic deflections." --
Book Synopsis Offshore Wind Energy Technology by : Olimpo Anaya-Lara
Download or read book Offshore Wind Energy Technology written by Olimpo Anaya-Lara and published by John Wiley & Sons. This book was released on 2018-05-11 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: A COMPREHENSIVE REFERENCE TO THE MOST RECENT ADVANCEMENTS IN OFFSHORE WIND TECHNOLOGY Offshore Wind Energy Technology offers a reference based on the research material developed by the acclaimed Norwegian Research Centre for Offshore Wind Technology (NOWITECH) and material developed by the expert authors over the last 20 years. This comprehensive text covers critical topics such as wind energy conversion systems technology, control systems, grid connection and system integration, and novel structures including bottom-fixed and floating. The text also reviews the most current operation and maintenance strategies as well as technologies and design tools for novel offshore wind energy concepts. The text contains a wealth of mathematical derivations, tables, graphs, worked examples, and illustrative case studies. Authoritative and accessible, Offshore Wind Energy Technology: Contains coverage of electricity markets for offshore wind energy and then discusses the challenges posed by the cost and limited opportunities Discusses novel offshore wind turbine structures and floaters Features an analysis of the stochastic dynamics of offshore/marine structures Describes the logistics of planning, designing, building, and connecting an offshore wind farm Written for students and professionals in the field, Offshore Wind Energy Technology is a definitive resource that reviews all facets of offshore wind energy technology and grid connection.
Book Synopsis Fully Coupled Dynamic Analysis of a Floating Wind Turbine System by : Jon E. Withee
Download or read book Fully Coupled Dynamic Analysis of a Floating Wind Turbine System written by Jon E. Withee and published by . This book was released on 2004 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of wind power is in a period of rapid growth worldwide and wind energy systems have emerged as a promising technology for utilizing offshore wind resources for the large scale generation of electricity Drawing upon the maturity of wind turbine and floater technologies developed by the wind energy and oil and gas industries, respectively, large offshore wind energy systems have been developed and are being proposed for operation in offshore areas where environmental restrictions are less restrictive, large wind resources exist, and open sea areas are available for wind farm development. A fully coupled dynamic analysis/technique was developed to predict the response of a floating wind turbine system in a stochastic wind and wave environment This technique incorporated both non-linear wave loading on the submerged floater and the aerodynamic loading on the wind turbine A tension leg spar buoy was designed to support the wind turbine This design was chosen due to its relatively small size and hence lower potential cost per wind turbine The system's tethers were attached to the ends of spokes which radiated out from the spar cylinder This arrangement of lines and spokes promised to be very stiff in the roll and pitch modes of motion.
Book Synopsis Dynamic Response Analysis of Spar Buoy Floating Wind Turbine Systems by : Sungho Lee (Ph. D.)
Download or read book Dynamic Response Analysis of Spar Buoy Floating Wind Turbine Systems written by Sungho Lee (Ph. D.) and published by . This book was released on 2008 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of alternative energy development has been dramatically increased by the dwindling supplies of oil and gas, and our growing efforts to protect our environment. A variety of meaningful steps have been taken in order to come up with cleaner, healthier and more affordable energy alternatives. Wind energy is one of the most reliable energy alternatives for countries that have sufficiently large wind sources. Due to the presence of steady and strong winds, and the distance from coastline residential, the offshore wind farm has become highly attractive as an ideal energy crisis solution. Floating wind turbine systems are being considered as a key solution to make the offshore wind farm feasible from an economic viewpoint, and viable as an energy resource. This paper presents the design of a synthetic mooring system for spar buoy floating wind turbines functioning in shallow water depths. Nacelle acceleration, static and dynamic tensions on catenaries, the maximum tension acting on the anchors are considered as design performances, and a stochastic analysis method has been used to evaluate those quantities based on sea state spectral density functions. The performance at a 100-year hurricane condition is being defined as a limiting case, and a linear wave theory has been the most fundamental theory applied for the present analysis.
