波浪对深海海洋平台作用的时域模拟
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摘要
本文采用高阶边界元方法,在时域内首先研究了绕(辐)射场中具有大尺度结构物和小尺度杆件的复合海洋结构上小尺度杆件的波浪荷载,重点研究了我国南海百年一遇灾害海洋环境下一座Truss Spar平台和一座半潜平台的水动力特性。
本文以三维Laplace方程为基本控制方程建立了线性波浪与任意三维结构物作用的数学模型。通过泰勒级数展开使自由水面边界条件在平均静水面上满足,物面边界条件在平均物面上满足,从而将计算域限制在一个不随时间变化的固定区域内。利用摄动展开并分离入射波浪和散射波浪,建立了线性的边值问题。引入Rankine源和它关于海底的像为格林函数,并利用格林第二定理,建立了关于波浪场中任意点速度势的边界积分方程。
通过一系列复杂的变换,将积分方程离散成以物面单元节点速度势和水面单元节点速度势导数为未知量的矩阵方程。利用三角极坐标变换处理数值计算中的奇异积分问题；固角系数通过采用直接计算得到,保证了各种情况下的计算精度；将物体的对称性应用到求解过程中,从而简化了矩阵方程,大大节约了计算量和计算时间。
在时域计算过程中,利用四阶龙格-库塔法对自由表面上的速度势和瞬时波面进行积分更新；对于物体的运动方程,同样利用四阶龙格-库塔法进行迭代求解。在初始时刻加入缓冲函数；在计算域的边界布置阻尼层,保证了在一个有限的时间域和空间域内得到稳定的计算结果。
本文首先研究了绕(辐)射场中具有大尺度结构物和小尺度杆件的复合海洋结构上小尺度杆件的波浪荷载,给出了绕射势作用下水质点速度和加速度的计算公式,并与解析解进行了对比。对于给定的结构,计算分析了规则波和畸形波作用下小尺度桩柱上波浪荷载的特性,并进一步研究了大尺度结构尺寸变化和小尺度桩柱在绕射场中位置的变化对小尺度桩柱上波浪荷载的影响。最后对运动物体上的小尺度杆件所受的波浪荷载进行了理论推导。
本文重点研究了我国南海百年一遇灾害海洋环境下一座Truss Spar平台和一座半潜平台的水动力特性。通过计算阻尼矩阵研究了阻尼对海洋平台一阶运动响应的影响,得到了平台各自不同位移方向的固有周期。分别对四种荷载组合下Truss Spar平台和半潜平台的运动响应进行了时域模拟,得到了各种荷载组合下两座平台的波浪力、位移和缆绳张力的时间历程曲线,并进行了分析。计算得到两座平台所受风荷载和流荷载,以及在风、流作用下平台的平衡位置,并分析了阻尼矩阵对计算过程的影响。文中还给出了波浪作用下Truss Spar平台波浪爬高和半潜平台最小气隙的计算方法,并分别画出了规则波和不规则波作用下水面的变化及波高的分布。
Based on the high-order boundary element method, the wave force on small-scale members of a composite structure was firstly investigated in diffraction field in time domain. The study is mainly focused on the hydrodynamic characteristics of a Truss Spar and a semi-submersible platform in the South China Sea with 100-year marine environmental disaster.
By taking the 3D Laplace equation as the basic governing equation, a mathematical model with respect to the interaction between linear waves and arbitrary 3D structures was founded. The Taylor series expansion was used to satisfy the free surface boundary condition on the mean static water and the solid-wall boundary conditions on the average body surfaces, respectively. Therefore, the computational domain can be restricted to a fixed time-invariant scope. With the use of perturbation expansion and the seperation of the incident and diffraction (scattering) waves, a linear boundary value problem was set up. By introducing the Rankine source and its image on the sea bottom as the Green function, a boundary integral equation for the velocity potential of an arbitrary point in the wave field was obtained based on the second Green identity.
Through a series of complicated transformation, the integral equation was discretized into matrix equations, with the nodal potential of body elements and the nodal normal derivative of velocity potential of the water surface elements as the unknowns. The singular integral problems emerged in calculations were solved through triangular polar coordinate transformation; the solid angle coefficient was acquired through direct calculation, which guaranteed the calculation precision in different conditions. With the symmetry applied to the solution process, the matrix equations were simplified, and the amount of calculation was reduced greatly.
In the time-domain calculation, the fourth-order Runge-Kutta method was adopted to update the velocity potential and the instantaneous wave elevation on the free surface. As to the motion equations for objects, the fourth-order Runge-Kutta method was employed again for iterative solution. A ramp function was added at the beginning of calculation. A damping layer was arranged at the boundaries of the computational domain to ensure that steady calculation results can be obtained within a finite time and space domain.
Formula for calculating the wave forces on the small-scale members in the diffraction field were firstly derived. The water-particle velocities produced by the diffracting waves were solved using integral equations, and the acceleration was obtained based on the time difference. For some specific examples, the accuracy of the velocity and the acceleration obtained with this method was verified by comparison with the analytical solutions. For a given structure, the characteristics of the wave load on the small-scale members under the action of regular waves and freak waves were analyzed. Then the influence of the size of an upper large-scale structure on the wave load on a small-scale structure was investigated. Finally, the wave load on the medium small-scale member bars at different positions in the diffraction field was analyzed. For oblique members on moving body, the solution procedure was deduced in detail.
The hydrodynamic characteristics of a Truss Spar and a semi-submersible platform in South China Sea with 100-years marine environmental disasters were investigated in emphasis. The viscosity damping effect on first order motion respose was studied by calculating the damping matrix, and the different motion nature period of each platform was obtained by analzing the displacement-time curve. Time domain simulation was carried out for each platform reponse under four kinds of loading combinations, and the time history of wave loadings, replacement, and mooring tension forces were get and analyzed, respectively. The wind and current loads on each platform were calculated and then the equilibrium positions under these loads were obtained. The wave run-up for Truss Spar and minimum air-gap for semi-submersible platform were given under waves. The changing of the wave surface and the wave height distribution for regular waves and irregular waves were described, respectively.
本文以三维Laplace方程为基本控制方程建立了线性波浪与任意三维结构物作用的数学模型。通过泰勒级数展开使自由水面边界条件在平均静水面上满足,物面边界条件在平均物面上满足,从而将计算域限制在一个不随时间变化的固定区域内。利用摄动展开并分离入射波浪和散射波浪,建立了线性的边值问题。引入Rankine源和它关于海底的像为格林函数,并利用格林第二定理,建立了关于波浪场中任意点速度势的边界积分方程。
通过一系列复杂的变换,将积分方程离散成以物面单元节点速度势和水面单元节点速度势导数为未知量的矩阵方程。利用三角极坐标变换处理数值计算中的奇异积分问题；固角系数通过采用直接计算得到,保证了各种情况下的计算精度；将物体的对称性应用到求解过程中,从而简化了矩阵方程,大大节约了计算量和计算时间。
在时域计算过程中,利用四阶龙格-库塔法对自由表面上的速度势和瞬时波面进行积分更新；对于物体的运动方程,同样利用四阶龙格-库塔法进行迭代求解。在初始时刻加入缓冲函数；在计算域的边界布置阻尼层,保证了在一个有限的时间域和空间域内得到稳定的计算结果。
本文首先研究了绕(辐)射场中具有大尺度结构物和小尺度杆件的复合海洋结构上小尺度杆件的波浪荷载,给出了绕射势作用下水质点速度和加速度的计算公式,并与解析解进行了对比。对于给定的结构,计算分析了规则波和畸形波作用下小尺度桩柱上波浪荷载的特性,并进一步研究了大尺度结构尺寸变化和小尺度桩柱在绕射场中位置的变化对小尺度桩柱上波浪荷载的影响。最后对运动物体上的小尺度杆件所受的波浪荷载进行了理论推导。
本文重点研究了我国南海百年一遇灾害海洋环境下一座Truss Spar平台和一座半潜平台的水动力特性。通过计算阻尼矩阵研究了阻尼对海洋平台一阶运动响应的影响,得到了平台各自不同位移方向的固有周期。分别对四种荷载组合下Truss Spar平台和半潜平台的运动响应进行了时域模拟,得到了各种荷载组合下两座平台的波浪力、位移和缆绳张力的时间历程曲线,并进行了分析。计算得到两座平台所受风荷载和流荷载,以及在风、流作用下平台的平衡位置,并分析了阻尼矩阵对计算过程的影响。文中还给出了波浪作用下Truss Spar平台波浪爬高和半潜平台最小气隙的计算方法,并分别画出了规则波和不规则波作用下水面的变化及波高的分布。
Based on the high-order boundary element method, the wave force on small-scale members of a composite structure was firstly investigated in diffraction field in time domain. The study is mainly focused on the hydrodynamic characteristics of a Truss Spar and a semi-submersible platform in the South China Sea with 100-year marine environmental disaster.
By taking the 3D Laplace equation as the basic governing equation, a mathematical model with respect to the interaction between linear waves and arbitrary 3D structures was founded. The Taylor series expansion was used to satisfy the free surface boundary condition on the mean static water and the solid-wall boundary conditions on the average body surfaces, respectively. Therefore, the computational domain can be restricted to a fixed time-invariant scope. With the use of perturbation expansion and the seperation of the incident and diffraction (scattering) waves, a linear boundary value problem was set up. By introducing the Rankine source and its image on the sea bottom as the Green function, a boundary integral equation for the velocity potential of an arbitrary point in the wave field was obtained based on the second Green identity.
Through a series of complicated transformation, the integral equation was discretized into matrix equations, with the nodal potential of body elements and the nodal normal derivative of velocity potential of the water surface elements as the unknowns. The singular integral problems emerged in calculations were solved through triangular polar coordinate transformation; the solid angle coefficient was acquired through direct calculation, which guaranteed the calculation precision in different conditions. With the symmetry applied to the solution process, the matrix equations were simplified, and the amount of calculation was reduced greatly.
In the time-domain calculation, the fourth-order Runge-Kutta method was adopted to update the velocity potential and the instantaneous wave elevation on the free surface. As to the motion equations for objects, the fourth-order Runge-Kutta method was employed again for iterative solution. A ramp function was added at the beginning of calculation. A damping layer was arranged at the boundaries of the computational domain to ensure that steady calculation results can be obtained within a finite time and space domain.
Formula for calculating the wave forces on the small-scale members in the diffraction field were firstly derived. The water-particle velocities produced by the diffracting waves were solved using integral equations, and the acceleration was obtained based on the time difference. For some specific examples, the accuracy of the velocity and the acceleration obtained with this method was verified by comparison with the analytical solutions. For a given structure, the characteristics of the wave load on the small-scale members under the action of regular waves and freak waves were analyzed. Then the influence of the size of an upper large-scale structure on the wave load on a small-scale structure was investigated. Finally, the wave load on the medium small-scale member bars at different positions in the diffraction field was analyzed. For oblique members on moving body, the solution procedure was deduced in detail.
The hydrodynamic characteristics of a Truss Spar and a semi-submersible platform in South China Sea with 100-years marine environmental disasters were investigated in emphasis. The viscosity damping effect on first order motion respose was studied by calculating the damping matrix, and the different motion nature period of each platform was obtained by analzing the displacement-time curve. Time domain simulation was carried out for each platform reponse under four kinds of loading combinations, and the time history of wave loadings, replacement, and mooring tension forces were get and analyzed, respectively. The wind and current loads on each platform were calculated and then the equilibrium positions under these loads were obtained. The wave run-up for Truss Spar and minimum air-gap for semi-submersible platform were given under waves. The changing of the wave surface and the wave height distribution for regular waves and irregular waves were described, respectively.
引文
[1]段梦兰,陈永福,李林斌,等.海洋平台结构的最新研究进展[J].海洋工程,2000,18(1)：86-90.
[2]谢彬,张爱霞,段梦兰.中国南海深水油气田开发工程模式及平台选型[J].石油学报,2007,28(1)：115-118.
[3]李润培,谢永和,舒志.深海平台技术的研究现状与发展趋势[J].中国海洋平台,2003,18(3)：1-5.
[4]黄悦华,任克忍.我国海洋石油钻井平台现状与技术发展分析[J].石油机械,2007,35(9)：157-160.
[5]王立忠.论我国海洋石油工程技术的现状与发展[J].中国海洋平台,2006,35(9)：9-11.
[6]陈新权,深海半潜式平台初步设计中的若干关键问题研究[D].上海：上海交通大学船舶海洋与建筑工程学院,2007.
[7]董艳秋.深海采油平台波浪荷载及响应[M].天津：天津大学出版社,2005.
[8]张帆,深海立柱式平台概念设计及水动力性能研究[D].上海：上海交通大学船舶海洋与建筑工程学院,2008.
[9]张帆,杨建民,李润培.Spar平台的发展趋势及其关键技术[J].中国海洋平台,2005,20(2)：6-11.
[10]吴子全,李怀亮,于文太,等.浅谈海洋平台发展现状[C].第十四届中国海洋(岸)工程学术讨论会论文集,2009：193-198.
[11]刘海霞,深海半潜式钻井平台的发展[J].船舶,2007,3：6-10.
[12]Mei C C. Numerical Methods in Water Wave Diffraction and Radiation [J]. Ann. Rev. Fluid Mech.,10,1978:393-416.
[13]Mei C C. The Applied Dynamics of Ocean Surface Wave [J]. John Wiley and Sons, Inc., New York,1983.
[14]Harlow F H, Welch J E. The MAC Method, a Computing Technique for Solving Viscous, Incompressible, Transient Fluid Problems Involving Free Surface [M]. Los Almos Scientific Lab, Rep. LA-3452,1965.
[15]Wang Y X, Su T C. Computation of Wave Breaking On Sloping Beach by VOF Method [C]. In: Proceedings of the 3rd International Offshore and Polar Engineering Conference. Singapore,1993: 6-11.
[16]邹志利,邱大洪,王永学.VOF法模拟波浪槽中二维非线性波[J].水动力研究与进展,1996A,11(1)：93-103.
[17]Hess J L, Smith A M O. Calculation of Nonlifting Potential Flow about Arbitrary Three-Dimensional Bodies [J]. Journal Ship Research,1964(8):22-24.
[18]Chau F P. The Second Order Velocity Potential for Diffraction of Waves By Fixed Offshore Structure [R]. Report OEG/89/1, University College London,1989.
[19]Monaghan J J. Smoothed Particle Hydrodynamics. Annual Review of Astronomicalan Astrophysics,1992,30:543-574.
[20]Garrison C J. Hydrodynamic Loading of Large Offshore Structures:Three-Dimensional Source Distribution Methods. Numerical Methods in Offshore Engineering. Chichester [M]. A Wiley-Interscience Publication,1978:87-140.
[21]Liu Y H, Kim C H, Kim M H. The Computation of Mean Drift Forces and Wave Run-Up by Higher-Order Boundary Element Method [C]. Proceedings of the 1st International Offshore and Polar Engineering Conference, Edinburgh, United Kingdom,1991.
[22]Eatock Taylor R, Chau F P. Wave Diffraction Theory - Some Developments in Linear and Nonlinear Theory [J]. Journal of offshore mechanics and Arctic engineering.1992,114:185-194.
[23]Teng B, Eatock Taylor R. New Higher-Order Boundary Element Methods for Wave Diffraction/Radiation [J]. Applied Ocean Research.1995, 17:71-78.
[24]Kashiwagi M. A B-Spline Galerkin Scheme for Computing Wave Forces on a Floating Very Large Elastic Plate [C].7th International Offshore and Polar Engineering Conference, Honolulu. 1977:229-236.
[25]Maniar H D. A B-Spline Based Higher Order Method in 3D [C].10th International Workshop on Water Waves and Floating Bodies. Oxford,1995:153-158.
[26]Teng B, Bai W, Xiang, Y. A B-spline Based BEM and Its Application in Predicting Wave Forces on 3D Bodies [J]. China Ocean Engineering,1999,13(3):257-264.
[27]Teng B, Chen B. A muttipole method for current diffraction from bodies [C]. Poceeding of 4th International Conference on Fluid and Mechanics, Dalian China,2004:739-742.
[28]宁德志.快速多极子边界元方法在完全非线性水波问题中的应用[D].大连：大连理工大学土木水利学院,2005.
[29]勾莹.快速多极子方法在多浮体和水弹性问题中的应用[D].大连：大连理工大学土木水利学院,2006.
[30]Korsmeyer F T, Lee C H, Newman, J N, Sclavounos, P D. The Analysis of Wave Effects on Tension-Leg Platforms [C]. Proceeding Conference on Offshore Mechanics and Arctic Engineering, ASME,2, Houston. Texas,1988.
[31]Molin B. Second Order Diffraction Loads up Three Dimensional Bodies [J]. Applied Ocean Research.1979,1:197-202.
[32]Eatock Taylor R, Hung S M. Second Order Diffraction Forces on a Vertical Cylinder in Regular Waves [J]. Applied Ocean Research.1987,1:19-30.
[33]Newman J N. Second-Harmonic Wave Diffraction at Large Depths [J]. Journal of Fluid Mechanics.1990,213:59-70.
[34]Wu G X, Eatock Taylor R. The Second Order Diffraction Force on a Horizontal Cylinder in Finite Water Depth [J]. Applied Ocean Research.1990,12(3):106-111.
[35]邹志利,戴遗山.回转体二阶绕射压力和绕射力[J].中国造船,1992,116.
[36]缪国平,刘应中.大直径圆柱上的二阶波浪力[J].中国造船,1987,98.
[37]Kim M H, Yue D K P. The Complete Second-Order Diffraction Solution for an Axisymmetric Body- Part1 Monochromatic Incident Waves [J]. Journal of Fluid Mechanics.1989,200: 235-264.
[38]Kim M H, Yue D K P. The Complete Second-Order Diffraction Solution for an Axisymmetric Body - Part2 Dichromatic Incident Waves and Body Motions [J]. Journal of Fluid Mechanics. 1990,211:557-593.
[39]滕斌,李玉成,董国海.双色入射波下二阶波浪力响应函数[J].海洋学报,1996,21(2)：115-123.
[40]Malenica S, Molin B. Third-Harmonic Wave Diffraction by a Vertical Cylinder [J]. Journal of Fluid Mechanics.1995,302:203-229.
[41]Teng B, Kato S. Third Order Wave Force on Axisymmetric Bodies [J]. Ocean Engineering,2002, 29:815-843.
[42]Stoker J J. Water Waves, Pure and Applied Mathematics [M]. New York:Interscience Publishers, Inc.,1958.
[43]Finkelstein A. The Initial Value Problem for Transient Water Waves [J]. Communications on Pure and Applied Mathematics,1957,10:511-522.
[44]Adachi H, Ohmatsu S. On the influence of irregular frequencies in the integral equation solutions of the time-dependent free surface problems [J]. The Journal of Engineering Mathematics,1979: 97-119.
[45]Yeung R W. The transient heaving motion of floating cylinders [J]. Journal of Engineering Mathematics,1982,116:97-119.
[46]Zhang L, Dai Y S. Time-domain solutions for hydrodynamics forces and moments acting on a 3-D moving body in waves [J]. Journal of Hydrodynamics,1993B,5(2).
[47]Isaacson M, Cheung K F. Second order wave diffraction around two-dimensional bodies by time-domain method [J]. Applied Ocean Research,1991,13(4):175-186.
[48]Buchmann B, Skourap J, Cheung K F. Run-up on a structure due to second-order waves and a current in a numerical wave tank [J]. Applied Ocean Research,1998,20:297-308.
[49]Cheung K F, Isaacson m, Lee J W. Wave diffraction around three-dimensional bodies in a current [J]. Journal of Offshore Mechanical and Arctic Engineering,1996,118:247-252.
[50]Isaacson M, Cheung K F. Time-domain second-order wave diffraction in three dimensions [J]. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE,1992,118(5):496-516.
[51]Isaacson M, Ng J Y T. Time-domain second-order wave radiation in two dimensions [J]. Journal of Ship Research,1993,37(1):25-33.
[52]Isaacson M, Ng J Y T. Second-order wave radiation of three-dimensional bodies by time-domain method [J]. International Journal of Offshore and Polar Engineering,1993,3(4),264-272.
[53]Bai W, Teng B. Second-order wave diffraction around 3D bodies by a time domain method [J]. China Ocean Engineering,2001,15:73-84.
[54]徐刚,段文洋.不规则波中浮体二阶水动力时域数值模拟[D].哈尔滨工程大学船舶工程学院,2010.
[55]Longuet-Higgins M S, Cokelet C D. The deformation of steep surface waves on water:I. A numerical method of computation [C]. Proc. R. Soc., London,1976, A350:1-26.
[56]杨驰,刘应中.非线性波浪绕射问题的数值计算[J].水动力学研究与进展A辑,1991,6(2)：10-15.
[57]Yang C, Ertekin R C. Numerical simulation of nonlinear wave diffraction by a vertical cylinder [J]. Journal of Offshore Mechanical and Arctic Engineering,1992,114:36-44.
[58]Sangita M, Debabrata S. Nonlinear heave radiation forces on two-dimensional single and twin hulls [J]. Ocean Engineering,2001,28:1031-1052.
[59]Lee C C, Liu Y H and Kim C H. Simulation of nonlinear waves and forces due to transient and steady motion of submerged,sphere [J]. International Journal of Offshore and Polar Engineering, 1994,4(3):174-182.
[60]刘桦,吴卫,王本龙等.完全非线性孤立波的直墙反射[J].海洋工程,2000,18(1)：1-6.
[61]Grilli S T, Sylvia V, Philip W. Development of a 3D numerical wave tank for moeling tsunami generation by underwater landslides [J]. Engineering Analysis with Boundary Elements,2002, 26:301-313.
[62]Beck R F. Time domain computations for floating bodies [J]. Applied Ocean Research,1994,16: 267-282.
[63]Scorpio S M, Beck R F and Korsmeyer F T. Nonlinear water wave computations using a multipole accelerated desingularized method [C]. Proc 21st Int. Sym. On naval Hydro.,1996.
[64]Kim M H, Celebi M S, Kim D J. Fully nonlinear interactions of waves with a threedimensional body in uniform currents [J]. Applied Ocean Research,1998,20:309-321.
[65]Celebi M S. Nonlinear transient wave-body interactions in steady uniform currents [J]. Computer Methods in applied mechanics and engineering,2001,190:5149-5172.
[66]李宗翰,林言弥.含入射波时任意三维浮体之全非线性流场模拟[J].水动力学研究与进展A辑,2003,18(2)：156-162.
[67]Glanvile R S, Paulling J R, Halkyard J E. Analysis of the spar floating drilling production and storage structure [C]. Offshore Technology Conference.1991,6701:57-68.
[68]Mekha B B, Weggel D C, Johnson C P, et al. Effect of second order diffraction forces on the global response of Spars [J]. Proceedings of the 6th International Offshore and Polar Engineering Conference,1996(1):273-280.
[69]Ran Z, Kim M H. Nonlinear coupled response of a tethered Spar platform in waves [J]. Proceedings of the 6th International Offshore and Polar Engineering Conference,1996:281-288.
[70]Halkyard J E. Status of Spar platforms for deepwater production systems [C]. Proceedings of the 6th International Offshore and Polar Engineering Conference,1996:262-272.
[71]Fisher F J, Gopalkrishnan R. Some observations on the heave behavior of Spar platforms [J]. Journal of Offshore Mechanics and Arctic Engineering,1998,120:221-225.
[72]Chitrapu A S, Saha S, Salpekar V Y. Time domain simulation of Spar platform response in random waves and current [C]. Proceedings of the 17th International Conference on Offshore Mechanics and Arctic Engineering, (OMAE98-0380),1998:1-8.
[73]Ye W, Anam I, Zhang J. Effect of wave directionality on wave loads and dynamic response of a Spar [C]. Proceedings of the 17th International Conference on Offshore Mechanics and Arctic Engineering, (OMAE98-0601),1998:1-6.
[74]Datta I, Prislin I, Halkyard J E, et al. Comparison of Truss Spar model test results with numerical predoctions [C]. Proceedings of the 18th International Conference on Offshore Mechanics and Arctic Engineering, (OMAE99/OFT-4231),1999:1-14.
[75]Chitrapu A S, Saha S, Salpekar V Y. Motion response of Spar platform in directional waves and current [C]. Proceedings of the 18th International Conference on Offshore Mechanics and Arctic Engineering, (OMAE99/OFT-4237),1999.
[76]Downie M J, Graham J M R, et al. An experimental investigation of motion control devices for truss spars [J]. Marine Structures,2000,13:75-90.
[77]Ma Q W, Patel M H. On the noe-linear forces acting on a floating spar platform in ocean waves [J]. Applied Ocean Research.2001,23(1):29-40.
[78]Kim M H, Ran Z and Zheng W, Hull/mooring coupled dynamic analysis of a truss spar in time domain [C]. Proceedings of 11th International Offshore and Polar Engineering Conference,2001, 11:42-54.
[79]Anam I, Rosset M, Hon M. Effect of nonlinear wave kinematics on dynamic response of Spars [J]. Jouranl of Engineering Mechanics,2002:925-934.
[80]Bradbury J. Red Hawk showcases first cell spar [J]. Marine Technology,2002,11.
[81]Agarwal A K, Jain A K. Nonlinear coupled dynamic response of offshore Spar platform under regular sea waves [J]. Ocean Engineering,2003,30(4):517-551.
[82]Tao L B, Lim K Y, Thiagarajan K. Heave response of classic Spar with variable geometry [J]. Transactions of the ASME, February,2004:90-95.
[83]Petruska D, Geyer J. Polyester mooring for the Mad Dog Spar-design issues and other considerations [J]. Ocean Engineering,2005,32:767-782.
[84]张帆,杨建民,李润培.新型多柱桁架式Spar平台水动力性能研究[J]．海洋工程,2007,25(2)：1-8.
[85]何景异,尤云祥,石强,魏岗.两层流体中内波作用下Spar平台运动响应[J].海洋工程,2008,26(1)：1-5.
[86]Hooft J P. A mathematical method of determining hydrodynamic induced forces on a semisubmersible [J]. Transactions-Society of Naval Architects and Marine Engineers,1971,79: 28-70.
[87]Haslum K. Design the Trosvik Bingo 3000 [M].The Naval Architect, March 1981.
[88]Minkenberg H L, Sluijs M F V. Motion optimizaion of semi-submersibles [C]. Offshore Technology Conference 1972. Dallas, Texas,1972:131-137.
[89]Horton E E, McCammon L B, et al. Optimization of stable platform characteristics[C]. Offshore Technology Conference, Dallas, Texas,1972.
[90]Takagi M. Arai S I, et al. A Comparison of Methods for Calculating the Motion of a Semisubmersible [J]. Ocean Engineering,1985,12(1):45-97.
[91]杨立军,肖龙飞,杨建民.半潜式平台水动力性能研究[J]．中国海洋平台,2009,24(1)：1-9.
[92]孙复中.半潜船运动的新理论计算方法[J].中国造船,1980,4：64-78.
[93]Soylemez M, Atlar M. A comparative studey of two practical methods for estimating the hydrodynamic loads and motions of a semisubmersible [J]. Journal of Offshore Mechanics and Arctic Engineering,2000,122:57-65.
[94]张威.深海半潜式钻井平台水动力性能分析[D].上海：上海交通大学船舶海洋与建筑工程学院,2006.
[95]Clauss G F, Schmittner C E, Stutz K. Freak wave impact on semisubmersibles time-domain analysisi of motions and forces [C]. Proceedings of the 13th International Offshore and Polar Engineering Conference,2003, JSC-371.
[96]Sen D. Time-domain simulation of motions of large structures in nonlinear waves [C].21st International Conference on Offshore Mechanics and Artic Engineering, Oslo, Norway, OMAE 2002:28033.
[97]Roveri F E. Coupled motion analysis of a semi-submersible platform in campos basin [C].23rd International Conference on Offshore Mechanics and Arctic Engineering. Vancouver, British Columbia, Canada, OMAE2004:51120.
[98]Senra S F, Correa F N, et al. Towards the integration of analysis and design of mooring systems and risers, Part I:studies on a semisubmersible platform [C].21st International Conference on Offshore Mechanics and Artic Engineering. Oslo, Norway, OMAE2002:28046.
[99]黄祥鹿,陈小红,范菊.锚泊浮式结构波浪上运动的频域算法[J].上海交通大学学报,2001,35(10)：1471-1477.
[100]Lowa Y M, Langleyb R S. Time and frequency domain coupled analysis of deepwater floating production systems [J]. Applied Ocean Research 2006,28:371-385.
[101]王彦,尤云祥.黏性波浪场与半潜平台相互作用的数值模拟[J].水动力学研究与进展A,2009,24(6)：793-799.
[102]曹明强,王磊,周利.深水半潜平台风载荷试验分析[J].实验室研究与探索,2009,28(9)：17-19。
[103]曹明强,王磊,周利.深水半潜平台水流载荷试验分析[J].实验室研究与探索,2009,28(6)：26-29.
[104]Cermelli C A, Roddier D G, Busso C C.A novel concept of minimal floating platform for marginal field development [C]. Proceedings of the 14th International Offshore and Polar Engineering Conference, Toulon, France, ISOPE,2004:538-545.
[105]Murray J, Tahar A. Yang C K. Hydrodynamics of dry tree semisubmersibles[C]. Proceedings of the 11th International Offshore and Polar Engineering Conference, Lisbon, Portugal, ISOPE, 2007:JSC-491.
[106]Mansour A M, Huang E W. H-shaped pontoon deepwater floating production semisubmersible [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering, California, USA, OMAE2007:29385.
[107]Stansberg C T. Slow-drif t pitch motions and air-gap observed from model testing with moored semisubmersibles [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering, California, USA, OMAE2007:229536.
[108]Sarkar A, Taylor R E. Low-frequency responses of nonlinearly moored vessels in random waves: coupled surge, pitch and heave motions[J]. Journal of Fluids and Structures,2001,15:133-150.
[109]Chatterjee P K, Jain R, Sengupta S. Reduction of wave-induced surge response of semisubmersible platforms by liquid column vibration absorbers (LCVA) [C]. Proceedings of ETCE/OMAE2000 Joint Conference Energy for the New Millennium, New Orleans, USA, OMAE2000:24160.
[110]Daniels J T. Mooring system and method for deep and ultra deep water, vol.6408781, U.S. Patent, Ed. USA.:Texaco Inc.,2002.
[111]Johnsen J M, Oritsland. Design and optimisation of taut-leg mooring systems [C]. Offshore Technology Conference, Houston, Texas,1999.
[112]李玉成,滕斌.波浪对海上建筑物的作用[M].北京,海洋出版社,2002.
[113]Ohyama T, nadaoka K. Development of a numerical wave tank for analysis of nonlinear and irregular wave field [J]. Fluid Dynamics Research,1991,8:231-251.
[114]Chan R K C, Chan F W K. Numerical solution of transient and steady free surface flows about a ship of general hull shape [C]. Proceedings of the 13th Symposium Naval Hydrodynamics, Tokyo, Japan,1980.
[115]Kantha L H, Blumberg A F, Mellor G L. Computing phase speeds at open boundary conditions [J]. Journal of Hydraulic Engineering Proc. ASCE,1990,116:592-597.
[116]Tanaka Y, Nakamura T. Numerical generation of gravity waves and open boundary scheme [C]. Proceedings of the 10th Offshore Mechanics and Arctic Engineering Conference, Stavanger, Norway,1991.
[117]Bushby F H, Timpson M S. A 10-level atmospheric model and frontal rain [J]. Quarterly Journal of the Royal Meteorological Society,1967,93(395):1-17.
[118]Ferrant P. Three-dimensional unsteady wave-body interactions by a Rankine boundary element method [J]. Ship Technology Research,1993:165-175.
[119]Ogilvie T F. Second-order hydrodynamic effects on ocean platforms [C]. Proceedings of International Workshop on Ship and Platform Motions, Berkeley California,1983:205-265.
[120]Li H B, Han G M, Mang H A. A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method [J]. International Journal for Numerical Methend in Engineering,1985,211:2071-2075.
[121]Brebbia C A. The boundary element method for engineers [M]. Wley:New York,1978.
[122]Wu G X, Eatock Taylor R. The numerical solution of the motions of a ship advancing in waves [C]. Proceedings of the 5th international conference on numerical ship hudrodynamics,1989: 386-394.
[123]Montic V. A new formula for the C-matrix in the somigliana identity [J]. Journal of Elasticity, 1993,33:191-201.
[124]Morison J R, M P O'Brien, et al. Forces exerted by surface waves on piles. Petro. Trans., Am. Inst. of Mining Eng.,1950:189.
[125]MacCamy R C, R A Fuchs. Wave forces on piles:a diffraction theory. Beach Erosion Board Tech. Memo.,1954:69.
[126]Kurian V J, Montasir A A, Narayanan, S P. Numerical and model test results for truss spar platform [C] Proceedings of 19th International Offshore and Polar Engineering Conference, 2009(11):99-104.
[127]陈耀鹏,薛鸿祥.Truss Spar平台桁架管节点疲劳分析[J].海洋工程,2007,25(2)：15-20.
[128]Luo Y H, Lu R, et al. Time-domain fatigue analysis for critical Connections of truss spar [C]. Proceedings of 11th International Offshore and Polar Engineering Conference,2001(1):362-368.
[129]Garret C J R. Wave forces on a circular dock [J]. Fluid Mech.,1971,46:129-139.
[130]Tromans P S, Anaturk A R, Hagameijer P.A New model for kinematics of large ocean waves-application as a design wave [C]. ISOPE, Edinburgh,1991:11-16.
[131]Rozario J B, Tromans P S, et al. Comparison of loads predicted using newwave and other wave models with measurements on the turn structure.Wave Kinematics and Environmental Forces [J]. Society for Underwater Technology,1993,1(29):143-159.
[132]Elzinga T, Tromans P S. Validation of new wave theory and RDWF predictions against measured global loading on a North Sea jacket [C]. Proceedings of the 6th International Conference on the Behavior of Off-shore Structure (BOSS). University of London,1992:495-505.
[133]Bateman W J D, Swan C, Taylor P H. On the efficient numerical simulation of directionally spread surface water waves [J]. Journal of Computational Physics,2001,174:277-305.
[134]Swan C, Taylor P H, Van Langen H. Observations of wave-structure interaction for a multi-legged concrete platform [J]. Applied Ocean Research,1997,19:309-327.
[135]俞聿修.随机波浪及其工程应用[M],大连,大连理工大学出版社,1992,1
[136]中国船级社,海上移动平台入级与建造规范[S],北京,人民交通出版社,2005,7.
[137]Muga B J, Wilson J F. Dynamic analysis of ocean structures [M]. Plenum, New York,1970.
[138]Graff W J. Introduction of offshore structures [M]. Gulf Publishing Co., Houston, Texas,1981.
[139]Sweetman B, Winterstein S R, Cornell C A. Airgap analysis of floating st ructures:first-and second-order transfer functions from system identification [J]. Applied Ocean Research,2002,24: 107-118.
[140]Sweetman B, Winterstein S R, Meling T S. Airgap prediction from second-order diffraction and stokes theory [J]. International Journal of Offshore and Polar Engineering, Palo Alto, United State. ISOPE2002,12:184-188.
[141]Simos A N, Fujarra A L C, Sparano J V, Umeda C H. Experimental evaluation of the dynamic air gap of a large-volume semi-submersible platform [C].25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, OMAE2006:92352.
[142]Manuel L, Winterstein S R. Reliability-based predictions of a design air gap for floating offshore structures[C].8th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, PMC2000:343.
[143]Manuel L, Winterstein S R. Air gap response of floating structures under random waves: analytical predictions based on linear and nonlinear diffraction [C]. Proceedings of the 18th International Conference on Offshore Mechanics and Arctic Engineering, Newfoundland, Canada, OMAE1999:6041.
[144]Kazemi S, Incecik A. Experimental study of air gap response and wave impact forces of a semi-submersible drilling unit [C].25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, OMAE2006:92083.
[145]李玉成,滕斌.波浪对海上建筑物的作用[M].北京,海洋出版社,2002.
[2]谢彬,张爱霞,段梦兰.中国南海深水油气田开发工程模式及平台选型[J].石油学报,2007,28(1)：115-118.
[3]李润培,谢永和,舒志.深海平台技术的研究现状与发展趋势[J].中国海洋平台,2003,18(3)：1-5.
[4]黄悦华,任克忍.我国海洋石油钻井平台现状与技术发展分析[J].石油机械,2007,35(9)：157-160.
[5]王立忠.论我国海洋石油工程技术的现状与发展[J].中国海洋平台,2006,35(9)：9-11.
[6]陈新权,深海半潜式平台初步设计中的若干关键问题研究[D].上海：上海交通大学船舶海洋与建筑工程学院,2007.
[7]董艳秋.深海采油平台波浪荷载及响应[M].天津：天津大学出版社,2005.
[8]张帆,深海立柱式平台概念设计及水动力性能研究[D].上海：上海交通大学船舶海洋与建筑工程学院,2008.
[9]张帆,杨建民,李润培.Spar平台的发展趋势及其关键技术[J].中国海洋平台,2005,20(2)：6-11.
[10]吴子全,李怀亮,于文太,等.浅谈海洋平台发展现状[C].第十四届中国海洋(岸)工程学术讨论会论文集,2009：193-198.
[11]刘海霞,深海半潜式钻井平台的发展[J].船舶,2007,3：6-10.
[12]Mei C C. Numerical Methods in Water Wave Diffraction and Radiation [J]. Ann. Rev. Fluid Mech.,10,1978:393-416.
[13]Mei C C. The Applied Dynamics of Ocean Surface Wave [J]. John Wiley and Sons, Inc., New York,1983.
[14]Harlow F H, Welch J E. The MAC Method, a Computing Technique for Solving Viscous, Incompressible, Transient Fluid Problems Involving Free Surface [M]. Los Almos Scientific Lab, Rep. LA-3452,1965.
[15]Wang Y X, Su T C. Computation of Wave Breaking On Sloping Beach by VOF Method [C]. In: Proceedings of the 3rd International Offshore and Polar Engineering Conference. Singapore,1993: 6-11.
[16]邹志利,邱大洪,王永学.VOF法模拟波浪槽中二维非线性波[J].水动力研究与进展,1996A,11(1)：93-103.
[17]Hess J L, Smith A M O. Calculation of Nonlifting Potential Flow about Arbitrary Three-Dimensional Bodies [J]. Journal Ship Research,1964(8):22-24.
[18]Chau F P. The Second Order Velocity Potential for Diffraction of Waves By Fixed Offshore Structure [R]. Report OEG/89/1, University College London,1989.
[19]Monaghan J J. Smoothed Particle Hydrodynamics. Annual Review of Astronomicalan Astrophysics,1992,30:543-574.
[20]Garrison C J. Hydrodynamic Loading of Large Offshore Structures:Three-Dimensional Source Distribution Methods. Numerical Methods in Offshore Engineering. Chichester [M]. A Wiley-Interscience Publication,1978:87-140.
[21]Liu Y H, Kim C H, Kim M H. The Computation of Mean Drift Forces and Wave Run-Up by Higher-Order Boundary Element Method [C]. Proceedings of the 1st International Offshore and Polar Engineering Conference, Edinburgh, United Kingdom,1991.
[22]Eatock Taylor R, Chau F P. Wave Diffraction Theory - Some Developments in Linear and Nonlinear Theory [J]. Journal of offshore mechanics and Arctic engineering.1992,114:185-194.
[23]Teng B, Eatock Taylor R. New Higher-Order Boundary Element Methods for Wave Diffraction/Radiation [J]. Applied Ocean Research.1995, 17:71-78.
[24]Kashiwagi M. A B-Spline Galerkin Scheme for Computing Wave Forces on a Floating Very Large Elastic Plate [C].7th International Offshore and Polar Engineering Conference, Honolulu. 1977:229-236.
[25]Maniar H D. A B-Spline Based Higher Order Method in 3D [C].10th International Workshop on Water Waves and Floating Bodies. Oxford,1995:153-158.
[26]Teng B, Bai W, Xiang, Y. A B-spline Based BEM and Its Application in Predicting Wave Forces on 3D Bodies [J]. China Ocean Engineering,1999,13(3):257-264.
[27]Teng B, Chen B. A muttipole method for current diffraction from bodies [C]. Poceeding of 4th International Conference on Fluid and Mechanics, Dalian China,2004:739-742.
[28]宁德志.快速多极子边界元方法在完全非线性水波问题中的应用[D].大连：大连理工大学土木水利学院,2005.
[29]勾莹.快速多极子方法在多浮体和水弹性问题中的应用[D].大连：大连理工大学土木水利学院,2006.
[30]Korsmeyer F T, Lee C H, Newman, J N, Sclavounos, P D. The Analysis of Wave Effects on Tension-Leg Platforms [C]. Proceeding Conference on Offshore Mechanics and Arctic Engineering, ASME,2, Houston. Texas,1988.
[31]Molin B. Second Order Diffraction Loads up Three Dimensional Bodies [J]. Applied Ocean Research.1979,1:197-202.
[32]Eatock Taylor R, Hung S M. Second Order Diffraction Forces on a Vertical Cylinder in Regular Waves [J]. Applied Ocean Research.1987,1:19-30.
[33]Newman J N. Second-Harmonic Wave Diffraction at Large Depths [J]. Journal of Fluid Mechanics.1990,213:59-70.
[34]Wu G X, Eatock Taylor R. The Second Order Diffraction Force on a Horizontal Cylinder in Finite Water Depth [J]. Applied Ocean Research.1990,12(3):106-111.
[35]邹志利,戴遗山.回转体二阶绕射压力和绕射力[J].中国造船,1992,116.
[36]缪国平,刘应中.大直径圆柱上的二阶波浪力[J].中国造船,1987,98.
[37]Kim M H, Yue D K P. The Complete Second-Order Diffraction Solution for an Axisymmetric Body- Part1 Monochromatic Incident Waves [J]. Journal of Fluid Mechanics.1989,200: 235-264.
[38]Kim M H, Yue D K P. The Complete Second-Order Diffraction Solution for an Axisymmetric Body - Part2 Dichromatic Incident Waves and Body Motions [J]. Journal of Fluid Mechanics. 1990,211:557-593.
[39]滕斌,李玉成,董国海.双色入射波下二阶波浪力响应函数[J].海洋学报,1996,21(2)：115-123.
[40]Malenica S, Molin B. Third-Harmonic Wave Diffraction by a Vertical Cylinder [J]. Journal of Fluid Mechanics.1995,302:203-229.
[41]Teng B, Kato S. Third Order Wave Force on Axisymmetric Bodies [J]. Ocean Engineering,2002, 29:815-843.
[42]Stoker J J. Water Waves, Pure and Applied Mathematics [M]. New York:Interscience Publishers, Inc.,1958.
[43]Finkelstein A. The Initial Value Problem for Transient Water Waves [J]. Communications on Pure and Applied Mathematics,1957,10:511-522.
[44]Adachi H, Ohmatsu S. On the influence of irregular frequencies in the integral equation solutions of the time-dependent free surface problems [J]. The Journal of Engineering Mathematics,1979: 97-119.
[45]Yeung R W. The transient heaving motion of floating cylinders [J]. Journal of Engineering Mathematics,1982,116:97-119.
[46]Zhang L, Dai Y S. Time-domain solutions for hydrodynamics forces and moments acting on a 3-D moving body in waves [J]. Journal of Hydrodynamics,1993B,5(2).
[47]Isaacson M, Cheung K F. Second order wave diffraction around two-dimensional bodies by time-domain method [J]. Applied Ocean Research,1991,13(4):175-186.
[48]Buchmann B, Skourap J, Cheung K F. Run-up on a structure due to second-order waves and a current in a numerical wave tank [J]. Applied Ocean Research,1998,20:297-308.
[49]Cheung K F, Isaacson m, Lee J W. Wave diffraction around three-dimensional bodies in a current [J]. Journal of Offshore Mechanical and Arctic Engineering,1996,118:247-252.
[50]Isaacson M, Cheung K F. Time-domain second-order wave diffraction in three dimensions [J]. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE,1992,118(5):496-516.
[51]Isaacson M, Ng J Y T. Time-domain second-order wave radiation in two dimensions [J]. Journal of Ship Research,1993,37(1):25-33.
[52]Isaacson M, Ng J Y T. Second-order wave radiation of three-dimensional bodies by time-domain method [J]. International Journal of Offshore and Polar Engineering,1993,3(4),264-272.
[53]Bai W, Teng B. Second-order wave diffraction around 3D bodies by a time domain method [J]. China Ocean Engineering,2001,15:73-84.
[54]徐刚,段文洋.不规则波中浮体二阶水动力时域数值模拟[D].哈尔滨工程大学船舶工程学院,2010.
[55]Longuet-Higgins M S, Cokelet C D. The deformation of steep surface waves on water:I. A numerical method of computation [C]. Proc. R. Soc., London,1976, A350:1-26.
[56]杨驰,刘应中.非线性波浪绕射问题的数值计算[J].水动力学研究与进展A辑,1991,6(2)：10-15.
[57]Yang C, Ertekin R C. Numerical simulation of nonlinear wave diffraction by a vertical cylinder [J]. Journal of Offshore Mechanical and Arctic Engineering,1992,114:36-44.
[58]Sangita M, Debabrata S. Nonlinear heave radiation forces on two-dimensional single and twin hulls [J]. Ocean Engineering,2001,28:1031-1052.
[59]Lee C C, Liu Y H and Kim C H. Simulation of nonlinear waves and forces due to transient and steady motion of submerged,sphere [J]. International Journal of Offshore and Polar Engineering, 1994,4(3):174-182.
[60]刘桦,吴卫,王本龙等.完全非线性孤立波的直墙反射[J].海洋工程,2000,18(1)：1-6.
[61]Grilli S T, Sylvia V, Philip W. Development of a 3D numerical wave tank for moeling tsunami generation by underwater landslides [J]. Engineering Analysis with Boundary Elements,2002, 26:301-313.
[62]Beck R F. Time domain computations for floating bodies [J]. Applied Ocean Research,1994,16: 267-282.
[63]Scorpio S M, Beck R F and Korsmeyer F T. Nonlinear water wave computations using a multipole accelerated desingularized method [C]. Proc 21st Int. Sym. On naval Hydro.,1996.
[64]Kim M H, Celebi M S, Kim D J. Fully nonlinear interactions of waves with a threedimensional body in uniform currents [J]. Applied Ocean Research,1998,20:309-321.
[65]Celebi M S. Nonlinear transient wave-body interactions in steady uniform currents [J]. Computer Methods in applied mechanics and engineering,2001,190:5149-5172.
[66]李宗翰,林言弥.含入射波时任意三维浮体之全非线性流场模拟[J].水动力学研究与进展A辑,2003,18(2)：156-162.
[67]Glanvile R S, Paulling J R, Halkyard J E. Analysis of the spar floating drilling production and storage structure [C]. Offshore Technology Conference.1991,6701:57-68.
[68]Mekha B B, Weggel D C, Johnson C P, et al. Effect of second order diffraction forces on the global response of Spars [J]. Proceedings of the 6th International Offshore and Polar Engineering Conference,1996(1):273-280.
[69]Ran Z, Kim M H. Nonlinear coupled response of a tethered Spar platform in waves [J]. Proceedings of the 6th International Offshore and Polar Engineering Conference,1996:281-288.
[70]Halkyard J E. Status of Spar platforms for deepwater production systems [C]. Proceedings of the 6th International Offshore and Polar Engineering Conference,1996:262-272.
[71]Fisher F J, Gopalkrishnan R. Some observations on the heave behavior of Spar platforms [J]. Journal of Offshore Mechanics and Arctic Engineering,1998,120:221-225.
[72]Chitrapu A S, Saha S, Salpekar V Y. Time domain simulation of Spar platform response in random waves and current [C]. Proceedings of the 17th International Conference on Offshore Mechanics and Arctic Engineering, (OMAE98-0380),1998:1-8.
[73]Ye W, Anam I, Zhang J. Effect of wave directionality on wave loads and dynamic response of a Spar [C]. Proceedings of the 17th International Conference on Offshore Mechanics and Arctic Engineering, (OMAE98-0601),1998:1-6.
[74]Datta I, Prislin I, Halkyard J E, et al. Comparison of Truss Spar model test results with numerical predoctions [C]. Proceedings of the 18th International Conference on Offshore Mechanics and Arctic Engineering, (OMAE99/OFT-4231),1999:1-14.
[75]Chitrapu A S, Saha S, Salpekar V Y. Motion response of Spar platform in directional waves and current [C]. Proceedings of the 18th International Conference on Offshore Mechanics and Arctic Engineering, (OMAE99/OFT-4237),1999.
[76]Downie M J, Graham J M R, et al. An experimental investigation of motion control devices for truss spars [J]. Marine Structures,2000,13:75-90.
[77]Ma Q W, Patel M H. On the noe-linear forces acting on a floating spar platform in ocean waves [J]. Applied Ocean Research.2001,23(1):29-40.
[78]Kim M H, Ran Z and Zheng W, Hull/mooring coupled dynamic analysis of a truss spar in time domain [C]. Proceedings of 11th International Offshore and Polar Engineering Conference,2001, 11:42-54.
[79]Anam I, Rosset M, Hon M. Effect of nonlinear wave kinematics on dynamic response of Spars [J]. Jouranl of Engineering Mechanics,2002:925-934.
[80]Bradbury J. Red Hawk showcases first cell spar [J]. Marine Technology,2002,11.
[81]Agarwal A K, Jain A K. Nonlinear coupled dynamic response of offshore Spar platform under regular sea waves [J]. Ocean Engineering,2003,30(4):517-551.
[82]Tao L B, Lim K Y, Thiagarajan K. Heave response of classic Spar with variable geometry [J]. Transactions of the ASME, February,2004:90-95.
[83]Petruska D, Geyer J. Polyester mooring for the Mad Dog Spar-design issues and other considerations [J]. Ocean Engineering,2005,32:767-782.
[84]张帆,杨建民,李润培.新型多柱桁架式Spar平台水动力性能研究[J]．海洋工程,2007,25(2)：1-8.
[85]何景异,尤云祥,石强,魏岗.两层流体中内波作用下Spar平台运动响应[J].海洋工程,2008,26(1)：1-5.
[86]Hooft J P. A mathematical method of determining hydrodynamic induced forces on a semisubmersible [J]. Transactions-Society of Naval Architects and Marine Engineers,1971,79: 28-70.
[87]Haslum K. Design the Trosvik Bingo 3000 [M].The Naval Architect, March 1981.
[88]Minkenberg H L, Sluijs M F V. Motion optimizaion of semi-submersibles [C]. Offshore Technology Conference 1972. Dallas, Texas,1972:131-137.
[89]Horton E E, McCammon L B, et al. Optimization of stable platform characteristics[C]. Offshore Technology Conference, Dallas, Texas,1972.
[90]Takagi M. Arai S I, et al. A Comparison of Methods for Calculating the Motion of a Semisubmersible [J]. Ocean Engineering,1985,12(1):45-97.
[91]杨立军,肖龙飞,杨建民.半潜式平台水动力性能研究[J]．中国海洋平台,2009,24(1)：1-9.
[92]孙复中.半潜船运动的新理论计算方法[J].中国造船,1980,4：64-78.
[93]Soylemez M, Atlar M. A comparative studey of two practical methods for estimating the hydrodynamic loads and motions of a semisubmersible [J]. Journal of Offshore Mechanics and Arctic Engineering,2000,122:57-65.
[94]张威.深海半潜式钻井平台水动力性能分析[D].上海：上海交通大学船舶海洋与建筑工程学院,2006.
[95]Clauss G F, Schmittner C E, Stutz K. Freak wave impact on semisubmersibles time-domain analysisi of motions and forces [C]. Proceedings of the 13th International Offshore and Polar Engineering Conference,2003, JSC-371.
[96]Sen D. Time-domain simulation of motions of large structures in nonlinear waves [C].21st International Conference on Offshore Mechanics and Artic Engineering, Oslo, Norway, OMAE 2002:28033.
[97]Roveri F E. Coupled motion analysis of a semi-submersible platform in campos basin [C].23rd International Conference on Offshore Mechanics and Arctic Engineering. Vancouver, British Columbia, Canada, OMAE2004:51120.
[98]Senra S F, Correa F N, et al. Towards the integration of analysis and design of mooring systems and risers, Part I:studies on a semisubmersible platform [C].21st International Conference on Offshore Mechanics and Artic Engineering. Oslo, Norway, OMAE2002:28046.
[99]黄祥鹿,陈小红,范菊.锚泊浮式结构波浪上运动的频域算法[J].上海交通大学学报,2001,35(10)：1471-1477.
[100]Lowa Y M, Langleyb R S. Time and frequency domain coupled analysis of deepwater floating production systems [J]. Applied Ocean Research 2006,28:371-385.
[101]王彦,尤云祥.黏性波浪场与半潜平台相互作用的数值模拟[J].水动力学研究与进展A,2009,24(6)：793-799.
[102]曹明强,王磊,周利.深水半潜平台风载荷试验分析[J].实验室研究与探索,2009,28(9)：17-19。
[103]曹明强,王磊,周利.深水半潜平台水流载荷试验分析[J].实验室研究与探索,2009,28(6)：26-29.
[104]Cermelli C A, Roddier D G, Busso C C.A novel concept of minimal floating platform for marginal field development [C]. Proceedings of the 14th International Offshore and Polar Engineering Conference, Toulon, France, ISOPE,2004:538-545.
[105]Murray J, Tahar A. Yang C K. Hydrodynamics of dry tree semisubmersibles[C]. Proceedings of the 11th International Offshore and Polar Engineering Conference, Lisbon, Portugal, ISOPE, 2007:JSC-491.
[106]Mansour A M, Huang E W. H-shaped pontoon deepwater floating production semisubmersible [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering, California, USA, OMAE2007:29385.
[107]Stansberg C T. Slow-drif t pitch motions and air-gap observed from model testing with moored semisubmersibles [C]. Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering, California, USA, OMAE2007:229536.
[108]Sarkar A, Taylor R E. Low-frequency responses of nonlinearly moored vessels in random waves: coupled surge, pitch and heave motions[J]. Journal of Fluids and Structures,2001,15:133-150.
[109]Chatterjee P K, Jain R, Sengupta S. Reduction of wave-induced surge response of semisubmersible platforms by liquid column vibration absorbers (LCVA) [C]. Proceedings of ETCE/OMAE2000 Joint Conference Energy for the New Millennium, New Orleans, USA, OMAE2000:24160.
[110]Daniels J T. Mooring system and method for deep and ultra deep water, vol.6408781, U.S. Patent, Ed. USA.:Texaco Inc.,2002.
[111]Johnsen J M, Oritsland. Design and optimisation of taut-leg mooring systems [C]. Offshore Technology Conference, Houston, Texas,1999.
[112]李玉成,滕斌.波浪对海上建筑物的作用[M].北京,海洋出版社,2002.
[113]Ohyama T, nadaoka K. Development of a numerical wave tank for analysis of nonlinear and irregular wave field [J]. Fluid Dynamics Research,1991,8:231-251.
[114]Chan R K C, Chan F W K. Numerical solution of transient and steady free surface flows about a ship of general hull shape [C]. Proceedings of the 13th Symposium Naval Hydrodynamics, Tokyo, Japan,1980.
[115]Kantha L H, Blumberg A F, Mellor G L. Computing phase speeds at open boundary conditions [J]. Journal of Hydraulic Engineering Proc. ASCE,1990,116:592-597.
[116]Tanaka Y, Nakamura T. Numerical generation of gravity waves and open boundary scheme [C]. Proceedings of the 10th Offshore Mechanics and Arctic Engineering Conference, Stavanger, Norway,1991.
[117]Bushby F H, Timpson M S. A 10-level atmospheric model and frontal rain [J]. Quarterly Journal of the Royal Meteorological Society,1967,93(395):1-17.
[118]Ferrant P. Three-dimensional unsteady wave-body interactions by a Rankine boundary element method [J]. Ship Technology Research,1993:165-175.
[119]Ogilvie T F. Second-order hydrodynamic effects on ocean platforms [C]. Proceedings of International Workshop on Ship and Platform Motions, Berkeley California,1983:205-265.
[120]Li H B, Han G M, Mang H A. A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method [J]. International Journal for Numerical Methend in Engineering,1985,211:2071-2075.
[121]Brebbia C A. The boundary element method for engineers [M]. Wley:New York,1978.
[122]Wu G X, Eatock Taylor R. The numerical solution of the motions of a ship advancing in waves [C]. Proceedings of the 5th international conference on numerical ship hudrodynamics,1989: 386-394.
[123]Montic V. A new formula for the C-matrix in the somigliana identity [J]. Journal of Elasticity, 1993,33:191-201.
[124]Morison J R, M P O'Brien, et al. Forces exerted by surface waves on piles. Petro. Trans., Am. Inst. of Mining Eng.,1950:189.
[125]MacCamy R C, R A Fuchs. Wave forces on piles:a diffraction theory. Beach Erosion Board Tech. Memo.,1954:69.
[126]Kurian V J, Montasir A A, Narayanan, S P. Numerical and model test results for truss spar platform [C] Proceedings of 19th International Offshore and Polar Engineering Conference, 2009(11):99-104.
[127]陈耀鹏,薛鸿祥.Truss Spar平台桁架管节点疲劳分析[J].海洋工程,2007,25(2)：15-20.
[128]Luo Y H, Lu R, et al. Time-domain fatigue analysis for critical Connections of truss spar [C]. Proceedings of 11th International Offshore and Polar Engineering Conference,2001(1):362-368.
[129]Garret C J R. Wave forces on a circular dock [J]. Fluid Mech.,1971,46:129-139.
[130]Tromans P S, Anaturk A R, Hagameijer P.A New model for kinematics of large ocean waves-application as a design wave [C]. ISOPE, Edinburgh,1991:11-16.
[131]Rozario J B, Tromans P S, et al. Comparison of loads predicted using newwave and other wave models with measurements on the turn structure.Wave Kinematics and Environmental Forces [J]. Society for Underwater Technology,1993,1(29):143-159.
[132]Elzinga T, Tromans P S. Validation of new wave theory and RDWF predictions against measured global loading on a North Sea jacket [C]. Proceedings of the 6th International Conference on the Behavior of Off-shore Structure (BOSS). University of London,1992:495-505.
[133]Bateman W J D, Swan C, Taylor P H. On the efficient numerical simulation of directionally spread surface water waves [J]. Journal of Computational Physics,2001,174:277-305.
[134]Swan C, Taylor P H, Van Langen H. Observations of wave-structure interaction for a multi-legged concrete platform [J]. Applied Ocean Research,1997,19:309-327.
[135]俞聿修.随机波浪及其工程应用[M],大连,大连理工大学出版社,1992,1
[136]中国船级社,海上移动平台入级与建造规范[S],北京,人民交通出版社,2005,7.
[137]Muga B J, Wilson J F. Dynamic analysis of ocean structures [M]. Plenum, New York,1970.
[138]Graff W J. Introduction of offshore structures [M]. Gulf Publishing Co., Houston, Texas,1981.
[139]Sweetman B, Winterstein S R, Cornell C A. Airgap analysis of floating st ructures:first-and second-order transfer functions from system identification [J]. Applied Ocean Research,2002,24: 107-118.
[140]Sweetman B, Winterstein S R, Meling T S. Airgap prediction from second-order diffraction and stokes theory [J]. International Journal of Offshore and Polar Engineering, Palo Alto, United State. ISOPE2002,12:184-188.
[141]Simos A N, Fujarra A L C, Sparano J V, Umeda C H. Experimental evaluation of the dynamic air gap of a large-volume semi-submersible platform [C].25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, OMAE2006:92352.
[142]Manuel L, Winterstein S R. Reliability-based predictions of a design air gap for floating offshore structures[C].8th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, PMC2000:343.
[143]Manuel L, Winterstein S R. Air gap response of floating structures under random waves: analytical predictions based on linear and nonlinear diffraction [C]. Proceedings of the 18th International Conference on Offshore Mechanics and Arctic Engineering, Newfoundland, Canada, OMAE1999:6041.
[144]Kazemi S, Incecik A. Experimental study of air gap response and wave impact forces of a semi-submersible drilling unit [C].25th International Conference on Offshore Mechanics and Arctic Engineering, Hamburg, Germany, OMAE2006:92083.
[145]李玉成,滕斌.波浪对海上建筑物的作用[M].北京,海洋出版社,2002.