深水柔性立管非线性静动力分析
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摘要
传统柔性立管和钢悬链线立管(SCR)都属于海洋工程中的细长柔性杆件,它们有相同的动力响应特性:即二者都以其大位移及大角度的运动来抵抗浮式平台的运动和水动力荷载,也就是说几何非线性是其结构分析的一个突出特点和求解难题。正是从结构力学特性的角度,本文将传统的柔性立管和钢悬链线立管统一归结为柔性立管,并且主要关注其几何非线性特性。
在常用的求解大变形问题的三种方法中——集中质量法、有限差分法和有限元法,本文选取了一种特别的基于绝对坐标系的细长柔性杆有限元模型来分析柔性立管,该模型通用性强,可模拟海洋工程中的各种柔性杆件结构,如立管、锚线等。该模型的最大优点是其控制方程直接在全局坐标系下推导得到,而且包括了全部几何非线性,因而省却了在不同坐标系间进行坐标变换的繁琐。借鉴文献,本文并推导得到了考虑内流作用的细长柔性杆模型,然后对控制方程应用有限元法在空间域内进行离散。这样,柔性立管的静力分析问题可由非线性方程的经典解法—牛顿-拉弗森法(Newton-Raphson)迭代求解,针对其动力问题本文采用了Adams-Moulton和Newmark-β两种积分方法求解。在海床模拟方面,本文模型考虑了由海床提供的弹性阻尼力和摩擦力,其中海床提供的竖向支持力以二次弹簧来模拟。
作者基于上述理论编制了柔性立管计算分析程序,并对程序有效性进行了理论验证。随后对几个柔性立管——柔性软管、钢悬链线立管、懒惰型及陡峭型波浪立管的算例分析表明,该程序可以胜任一些典型柔性立管的分析工作,为进一步精细研究柔性立管在海洋运行环境中各荷载作用下的结构力学特性和响应行为提供了源代码基础。
Both conventional flexible risers, which are made of concentric extruded polymer and reinforcing helical metallic layers, and steel catenary risers (SCRs) fall into the category of slender structures that are commonly used in ocean engineering, as they behave with similar dynamic response characteristics, accommodating floating platform motion and hydrodynamic loading by changing their shape significantly. In other words, geometric nonlinearity is dominant in their structural analysis. Bearing this in mind, this thesis uses flexible risers to represent both conventional flexible risers and SCRs hereafter, and seeks to tackle the relatively difficult geometric nonlinearity problem.
Among the three main modeling methods that are capable of tackling large displacement, namely lumped mass, finite difference, and finite element method (FEM), a special FEM absolute coordinate based slender rod model is adopted to analyze flexible risers. The model is formulated directly in a global coordinate system by employing global position displacements and their derivatives as nodal variables, and thus obviates all transformations involving trigonometric functions, which is typically required in traditional finite element method. The governing equation derived with internal flow in consideration is discretized using FEM in space domain. The static problem is then solved iteratively by the classic Newton-Raphson method, while the dynamic response is integrated in time domain by Adams-Moulton method and Newmark--βmethod, respectively. With respect to the riser-seabed interaction, both the seabed support and friction effect are considered, with the former modeled by a nonlinear quadratic spring, allowing for a consistent derivation of the tangent stiffness matrix.
Based on the above theory, the author developed a computer program to conduct static and dynamic analyses for flexible risers. The program has been validated against two theoretical examples. By analyzing several flexible risers-flexible jumper, steel catenary riser, lazy wave riser, and steep wave riser, it is demonstrated that this program is capable of dealing with structural analysis of typical flexible risers. And it serves as source code for further study about flexible risers’structural response behavior under various loadings in marine environment.
在常用的求解大变形问题的三种方法中——集中质量法、有限差分法和有限元法,本文选取了一种特别的基于绝对坐标系的细长柔性杆有限元模型来分析柔性立管,该模型通用性强,可模拟海洋工程中的各种柔性杆件结构,如立管、锚线等。该模型的最大优点是其控制方程直接在全局坐标系下推导得到,而且包括了全部几何非线性,因而省却了在不同坐标系间进行坐标变换的繁琐。借鉴文献,本文并推导得到了考虑内流作用的细长柔性杆模型,然后对控制方程应用有限元法在空间域内进行离散。这样,柔性立管的静力分析问题可由非线性方程的经典解法—牛顿-拉弗森法(Newton-Raphson)迭代求解,针对其动力问题本文采用了Adams-Moulton和Newmark-β两种积分方法求解。在海床模拟方面,本文模型考虑了由海床提供的弹性阻尼力和摩擦力,其中海床提供的竖向支持力以二次弹簧来模拟。
作者基于上述理论编制了柔性立管计算分析程序,并对程序有效性进行了理论验证。随后对几个柔性立管——柔性软管、钢悬链线立管、懒惰型及陡峭型波浪立管的算例分析表明,该程序可以胜任一些典型柔性立管的分析工作,为进一步精细研究柔性立管在海洋运行环境中各荷载作用下的结构力学特性和响应行为提供了源代码基础。
Both conventional flexible risers, which are made of concentric extruded polymer and reinforcing helical metallic layers, and steel catenary risers (SCRs) fall into the category of slender structures that are commonly used in ocean engineering, as they behave with similar dynamic response characteristics, accommodating floating platform motion and hydrodynamic loading by changing their shape significantly. In other words, geometric nonlinearity is dominant in their structural analysis. Bearing this in mind, this thesis uses flexible risers to represent both conventional flexible risers and SCRs hereafter, and seeks to tackle the relatively difficult geometric nonlinearity problem.
Among the three main modeling methods that are capable of tackling large displacement, namely lumped mass, finite difference, and finite element method (FEM), a special FEM absolute coordinate based slender rod model is adopted to analyze flexible risers. The model is formulated directly in a global coordinate system by employing global position displacements and their derivatives as nodal variables, and thus obviates all transformations involving trigonometric functions, which is typically required in traditional finite element method. The governing equation derived with internal flow in consideration is discretized using FEM in space domain. The static problem is then solved iteratively by the classic Newton-Raphson method, while the dynamic response is integrated in time domain by Adams-Moulton method and Newmark--βmethod, respectively. With respect to the riser-seabed interaction, both the seabed support and friction effect are considered, with the former modeled by a nonlinear quadratic spring, allowing for a consistent derivation of the tangent stiffness matrix.
Based on the above theory, the author developed a computer program to conduct static and dynamic analyses for flexible risers. The program has been validated against two theoretical examples. By analyzing several flexible risers-flexible jumper, steel catenary riser, lazy wave riser, and steep wave riser, it is demonstrated that this program is capable of dealing with structural analysis of typical flexible risers. And it serves as source code for further study about flexible risers’structural response behavior under various loadings in marine environment.
引文
[1]李洪春.顶张力立管顺流向动力响应及疲劳研究:[硕士学位论文].青岛:中国海洋大学,2010
[2] Machado, Z.L., and Dumay, J.M., Dynamic Production Riser on Enchova Field Offshore Brazil. Offshore Brazil Conference, Latin America Oil Show, Rio de Janeiro, June 1980.
[3] R.Chandwani, I.Larsen. Design of Flexible Risers Workshop on Subsea Pipelines, COPPE/UFRJ-Federal University of Brasil, Rio de Janeiro, Brasil, December 8-9 1997
[4] Bai, Y. and Bai. Q., Subsea Pipelines and Risers. Elsevier, Amsterdam, 2005
[5] Jain, A.K. Review of flexible risers and articulated storage systems. Ocean Engineering, 1994, 21: 733–750
[6] Patel, H.M., Seyed, F.B. Review of flexible riser modeling and analysis techniques. Engineering Structures, 1995, 17: 293–304
[7] SINTEF. RIFLEX Theory Manual , 2005
[8] Larsen, C. M. Flexible riser analysis– comparison of results from computer programs, Marine Structures, 1992, 5: 103-119
[9] Patel M. H., Seyed F. B. Internal flow induced behaviour of flexible risers. Engng. Struct. (Flexible risers-special issue) , 1989, 11: 266~280
[10] Seyed F. B., Patel M. H. Mathematics of flexible risers including pressure and internal flow effects. Marine Struct. (flexible riser-special issue), 1992, 5: 121~150
[11]白兴兰.基于惯性耦合的深水钢悬链线立管非线性分析方法研究:[博士学位论文].青岛:中国海洋大学,2009
[12] Stephen A. Hatton, Neil Willis. Steel Catenary Risers for Deepwater Environment. Proceedings-Offshore Technology Conference. Houston, OTC8607, USA, 1998
[13] Egil Giertsen, Richard Verley and Knut Schroder. CARISIMA a Catenary Riser/Soil Interaction Model for Global Riser Analysis. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering. OMAE2004, Vol. 1, 633-640
[14] Ghadimi, R. A simple and efficient algorithm for the static and dynamic analysis of flexible marine risers, Computers and Structures. 1988, 29 (4): 541~544
[15] Boom, H.J.J., Dekker, J.N. and van Elsacker, A.W. Dynamic Aspects of Offshore Riser and Mooring Concepts, 19th Annual OTC, Houston, Texas, 1987
[16] Orcina Ltd. Orcaflex Manual, 2005
[17] Raman-Nair, W. and Baddour, R. E. Three-dimensional dynamics of a flexible marine riser undergoing large elastic deformations, Multibody System Dynamics, 2003, 10 (3): 393~423
[18] Bradley J. Buckham. Dynamics modelling of low-tension tethers for submerged remotely operated vehicles, Ph. D dissertation, University of Victoria, 2003
[19] Low, Y. M. and Langley, R. S. Dynamic analysis of a flexible hanging riser in the time and frequency domain, Proceedings of 25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, 2006
[20] Jason I. Gobat. The Dynamics of Geometrically Compliant Mooring Systems, Ph. D dissertation, S.M., MIT/WHOI Joint Program, 2000
[21] Sophia, T. S. Analysis of the elastica with applications to vibration isolation. Ph. D dissertation, Duke University, 2007
[22] Chatjigeorgiou, I.K. A finite differences formulation for the linear and nonlinear dynamics of 2D catenary risers. Ocean Engineering, 2008, 35: 616~636
[23] Kodaissi, E., Lemerchand, E. and Narzul, P. State of the Art on Dynamic Programs for Flexible Riser Systems, ASME Ninth International Conference on Offshore Mechanics and Arctic Engineering, Houston, 1990
[24] O'Brien, P.J. and McNamara, J.F, Significant Characteristics of Three-Dimensional Flexible Riser Analysis, J. of Engineering Structures, 1989, 11: 223~233.
[25] Felippa, C. A. and Haugen, B. Unified Formulation of Small-Strain Co-rotational Finite Elements: I. Theory, Computer Methods in Applied Mechanics and Engineering, Special Issue on Shells, 2005
[26] Yazdchi, M. and Crisfield, M.A. Buoyancy forces and the 2D finite element analysis of flexible offshore pipes and risers. International Journal for Numerical Methods in Engineering, 2002, 54: 61~88
[27] O’Brien P.J., Lane M., McNamara J.F. Improvements to the Convected Co-Ordinates Method for Predicting Large Deflection Extreme Riser Response. OMAE2002-28237, Oslo, 2002
[28] Romero, I. A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations, Multibody Syst Dyn, 2008, 20: 51~68
[29] Berzeri, M. and Shabana, A. A. Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation, Journal of Sound and vibration, 2000, 235(4): 539~565
[30] Nordgren RP. On computation of the motion of elastic rods. J Appl Mech 1974, 41:777–80.
[31] Garrett, D.L. Dynamic analysis of slender rods. Journal of Energy Resources Technology, 1982, 104: 302~306
[32] Paulling, J.R., Webster, W.C. A consistent large amplitude analysis of the coupled response of a TLP and Tendon System, Proceedings of the 5th OMAE Symposium, Japan, 1986 vol. III, 126~133
[33] Ran, Z. Coupled Dynamic Analysis of Floating Structures in Wave and Current. Ph. D Dissertation, Texas A&M University, College Station, TX, 2000
[34] Garrett, D.L. Coupled analysis of floating production system. Ocean Engineering, 2005, 32: 802–816
[35]宋儒鑫.深水开发中的海底管道和海洋立管.船舶工业技术经济信息,2003,218(8): 31-42
[36]黄维平,李华军.深水开发的新型立管系统——钢悬链线立管(SCR).中国海洋大学学报,2006(5): 775-780
[37]黄维平,白兴兰,李华军.国外深水钢悬链线立管研究发展现状中国海洋大学学报2009(2): 290-294
[38] LIANG Hui, Review of research on interactions between deepwater steel catenary risers and soft clay seabeds, J. Marine. Sci. Appl. (2009) 8: 163-167
[39]李凌.大尺度深水立管非线性振动特性研究:[硕士学位论文].天津:天津大学,2004
[40]李传凯.钢悬链线立管静力及波激疲劳分析:[硕士学位论文].大连:大连理工大学,2008
[41]傅俊杰,杨和振,深海钢悬链立管触地点动力响应分析.海洋工程, 2009(2): 36-40
[42] Sparks, C.P. The Influence of tension, pressure and weight on pipe and riser deformationsand stresses. Journal of Energy Resources Technology, 1984, 106: 46–54
[43] Roger Chang, STRAIGHT TALK ABOUT RISER TENSION AND MORE, Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, Hawaii, USA, OMAE2009-79759
[44]竺艳蓉.海洋工程波浪力学.天津:天津大学出版社,1991
[45]李效民.顶张力立管动力响应数值模拟及其疲劳寿命预测:[博士学位论文].青岛:中国海洋大学,2010
[46] DNV-OS-F201 Dynamic Risers, 2001
[47] William C. Webster. Mooring induced damping. Ocean Engineering, 1995, 22:571–591
[48] Arcandra. Hull/mooring/riser coupled dynamic analysis of a deepwater floating platform with polyester lines. PhD Thesis, Texas A and M University; 2001
[49] Chen X.H. Studies on dynamic interaction between deep-water floating structures and their mooring/tendon system. PhD Thesis, Texas A&M University, College Station, Texas, 2002
[50] Michael P. Paidoussis, Fluid-Structure Interactions, Volume 1. Slender Structures and Axial Flow, academic press
[51] Persio Leister de Almeida Barros, Renato Pavanello, Euclides Mesquita, and Celso Kazuyuki Morooka, SCR-Seafloor Interaction Modeling With Winkler, Pasternak and Kerr Beam-On-Elastic-Foundation Theories, OMAE2009-79459
[52] Liu Y. and Bergdahl L., Influence of current and seabed friction on mooring cable response-comparison between time-domain and frequency-domain analysis, Engineering Structures, 1997, 19(11): 945-953
[53] Orcina, Comparison of Orcaflex with standard theoretical results. Orcaflex validation doc 99-105, 24-Sep-07
[54]胡建华.大跨度自锚式悬索桥结构体系及静动力性能研究:[博士学位论文].长沙:湖南大学,2006
[55] Lin Wenjeng. Modelling of submerged cable dynamics using multibody dynamic analyses. PhD Thesis, University of Cincinnati; 1990
[56] Chai, Y.T. and Varyani, K.S. An absolute coordinate formulation for three-dimensional flexible pipe analysis, Ocean Engineering, 2006, 33: 23–58
[57] Liu Y. and Bergdahl L., Frequency-domain dynamic analysis of cables, Engineering Structures, 1997, 19(6): 499-506
[58] Jason I. Gobat and Mark A. Grosenbaugh. A simple model for heave-induced dynamic tension in catenary moorings, Applied Ocean Research, 2001 (23), 159-174
[2] Machado, Z.L., and Dumay, J.M., Dynamic Production Riser on Enchova Field Offshore Brazil. Offshore Brazil Conference, Latin America Oil Show, Rio de Janeiro, June 1980.
[3] R.Chandwani, I.Larsen. Design of Flexible Risers Workshop on Subsea Pipelines, COPPE/UFRJ-Federal University of Brasil, Rio de Janeiro, Brasil, December 8-9 1997
[4] Bai, Y. and Bai. Q., Subsea Pipelines and Risers. Elsevier, Amsterdam, 2005
[5] Jain, A.K. Review of flexible risers and articulated storage systems. Ocean Engineering, 1994, 21: 733–750
[6] Patel, H.M., Seyed, F.B. Review of flexible riser modeling and analysis techniques. Engineering Structures, 1995, 17: 293–304
[7] SINTEF. RIFLEX Theory Manual , 2005
[8] Larsen, C. M. Flexible riser analysis– comparison of results from computer programs, Marine Structures, 1992, 5: 103-119
[9] Patel M. H., Seyed F. B. Internal flow induced behaviour of flexible risers. Engng. Struct. (Flexible risers-special issue) , 1989, 11: 266~280
[10] Seyed F. B., Patel M. H. Mathematics of flexible risers including pressure and internal flow effects. Marine Struct. (flexible riser-special issue), 1992, 5: 121~150
[11]白兴兰.基于惯性耦合的深水钢悬链线立管非线性分析方法研究:[博士学位论文].青岛:中国海洋大学,2009
[12] Stephen A. Hatton, Neil Willis. Steel Catenary Risers for Deepwater Environment. Proceedings-Offshore Technology Conference. Houston, OTC8607, USA, 1998
[13] Egil Giertsen, Richard Verley and Knut Schroder. CARISIMA a Catenary Riser/Soil Interaction Model for Global Riser Analysis. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering. OMAE2004, Vol. 1, 633-640
[14] Ghadimi, R. A simple and efficient algorithm for the static and dynamic analysis of flexible marine risers, Computers and Structures. 1988, 29 (4): 541~544
[15] Boom, H.J.J., Dekker, J.N. and van Elsacker, A.W. Dynamic Aspects of Offshore Riser and Mooring Concepts, 19th Annual OTC, Houston, Texas, 1987
[16] Orcina Ltd. Orcaflex Manual, 2005
[17] Raman-Nair, W. and Baddour, R. E. Three-dimensional dynamics of a flexible marine riser undergoing large elastic deformations, Multibody System Dynamics, 2003, 10 (3): 393~423
[18] Bradley J. Buckham. Dynamics modelling of low-tension tethers for submerged remotely operated vehicles, Ph. D dissertation, University of Victoria, 2003
[19] Low, Y. M. and Langley, R. S. Dynamic analysis of a flexible hanging riser in the time and frequency domain, Proceedings of 25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, 2006
[20] Jason I. Gobat. The Dynamics of Geometrically Compliant Mooring Systems, Ph. D dissertation, S.M., MIT/WHOI Joint Program, 2000
[21] Sophia, T. S. Analysis of the elastica with applications to vibration isolation. Ph. D dissertation, Duke University, 2007
[22] Chatjigeorgiou, I.K. A finite differences formulation for the linear and nonlinear dynamics of 2D catenary risers. Ocean Engineering, 2008, 35: 616~636
[23] Kodaissi, E., Lemerchand, E. and Narzul, P. State of the Art on Dynamic Programs for Flexible Riser Systems, ASME Ninth International Conference on Offshore Mechanics and Arctic Engineering, Houston, 1990
[24] O'Brien, P.J. and McNamara, J.F, Significant Characteristics of Three-Dimensional Flexible Riser Analysis, J. of Engineering Structures, 1989, 11: 223~233.
[25] Felippa, C. A. and Haugen, B. Unified Formulation of Small-Strain Co-rotational Finite Elements: I. Theory, Computer Methods in Applied Mechanics and Engineering, Special Issue on Shells, 2005
[26] Yazdchi, M. and Crisfield, M.A. Buoyancy forces and the 2D finite element analysis of flexible offshore pipes and risers. International Journal for Numerical Methods in Engineering, 2002, 54: 61~88
[27] O’Brien P.J., Lane M., McNamara J.F. Improvements to the Convected Co-Ordinates Method for Predicting Large Deflection Extreme Riser Response. OMAE2002-28237, Oslo, 2002
[28] Romero, I. A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations, Multibody Syst Dyn, 2008, 20: 51~68
[29] Berzeri, M. and Shabana, A. A. Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation, Journal of Sound and vibration, 2000, 235(4): 539~565
[30] Nordgren RP. On computation of the motion of elastic rods. J Appl Mech 1974, 41:777–80.
[31] Garrett, D.L. Dynamic analysis of slender rods. Journal of Energy Resources Technology, 1982, 104: 302~306
[32] Paulling, J.R., Webster, W.C. A consistent large amplitude analysis of the coupled response of a TLP and Tendon System, Proceedings of the 5th OMAE Symposium, Japan, 1986 vol. III, 126~133
[33] Ran, Z. Coupled Dynamic Analysis of Floating Structures in Wave and Current. Ph. D Dissertation, Texas A&M University, College Station, TX, 2000
[34] Garrett, D.L. Coupled analysis of floating production system. Ocean Engineering, 2005, 32: 802–816
[35]宋儒鑫.深水开发中的海底管道和海洋立管.船舶工业技术经济信息,2003,218(8): 31-42
[36]黄维平,李华军.深水开发的新型立管系统——钢悬链线立管(SCR).中国海洋大学学报,2006(5): 775-780
[37]黄维平,白兴兰,李华军.国外深水钢悬链线立管研究发展现状中国海洋大学学报2009(2): 290-294
[38] LIANG Hui, Review of research on interactions between deepwater steel catenary risers and soft clay seabeds, J. Marine. Sci. Appl. (2009) 8: 163-167
[39]李凌.大尺度深水立管非线性振动特性研究:[硕士学位论文].天津:天津大学,2004
[40]李传凯.钢悬链线立管静力及波激疲劳分析:[硕士学位论文].大连:大连理工大学,2008
[41]傅俊杰,杨和振,深海钢悬链立管触地点动力响应分析.海洋工程, 2009(2): 36-40
[42] Sparks, C.P. The Influence of tension, pressure and weight on pipe and riser deformationsand stresses. Journal of Energy Resources Technology, 1984, 106: 46–54
[43] Roger Chang, STRAIGHT TALK ABOUT RISER TENSION AND MORE, Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, Hawaii, USA, OMAE2009-79759
[44]竺艳蓉.海洋工程波浪力学.天津:天津大学出版社,1991
[45]李效民.顶张力立管动力响应数值模拟及其疲劳寿命预测:[博士学位论文].青岛:中国海洋大学,2010
[46] DNV-OS-F201 Dynamic Risers, 2001
[47] William C. Webster. Mooring induced damping. Ocean Engineering, 1995, 22:571–591
[48] Arcandra. Hull/mooring/riser coupled dynamic analysis of a deepwater floating platform with polyester lines. PhD Thesis, Texas A and M University; 2001
[49] Chen X.H. Studies on dynamic interaction between deep-water floating structures and their mooring/tendon system. PhD Thesis, Texas A&M University, College Station, Texas, 2002
[50] Michael P. Paidoussis, Fluid-Structure Interactions, Volume 1. Slender Structures and Axial Flow, academic press
[51] Persio Leister de Almeida Barros, Renato Pavanello, Euclides Mesquita, and Celso Kazuyuki Morooka, SCR-Seafloor Interaction Modeling With Winkler, Pasternak and Kerr Beam-On-Elastic-Foundation Theories, OMAE2009-79459
[52] Liu Y. and Bergdahl L., Influence of current and seabed friction on mooring cable response-comparison between time-domain and frequency-domain analysis, Engineering Structures, 1997, 19(11): 945-953
[53] Orcina, Comparison of Orcaflex with standard theoretical results. Orcaflex validation doc 99-105, 24-Sep-07
[54]胡建华.大跨度自锚式悬索桥结构体系及静动力性能研究:[博士学位论文].长沙:湖南大学,2006
[55] Lin Wenjeng. Modelling of submerged cable dynamics using multibody dynamic analyses. PhD Thesis, University of Cincinnati; 1990
[56] Chai, Y.T. and Varyani, K.S. An absolute coordinate formulation for three-dimensional flexible pipe analysis, Ocean Engineering, 2006, 33: 23–58
[57] Liu Y. and Bergdahl L., Frequency-domain dynamic analysis of cables, Engineering Structures, 1997, 19(6): 499-506
[58] Jason I. Gobat and Mark A. Grosenbaugh. A simple model for heave-induced dynamic tension in catenary moorings, Applied Ocean Research, 2001 (23), 159-174