基于高阶面元的浮体运动与波浪载荷计算方法
|
摘要
本文以势流理论为基础,应用基于非均匀有理B样条(Non-Uniform Rational B-Spline,简称NURBS)的边界元法,在频域内,对船舶和海洋结构物的线性、二阶运动响应和波浪载荷进行计算；在时域内,结合浮体和系泊缆索的非线性响应计算方法,建立了浮体和系泊系统的耦合分析方法。
首先建立了基于NURBS的边界元方法。对NURBS技术做了多方面的改进,并应用到复杂海洋浮体的构型和湿表面网格划分,结果表明,改进的NURBS技术,能够生成高质量的浮体外形和湿表面网格,而且效率很高。为应用扩展的边界积分方法去除不规则频率,在上述网格生成方法基础上,提出了进一步的网格改进措施。
基于三维线性势流理论,应用基于NURBS的边界元法,在频域内建立了求解浮体线性运动响应和波浪载荷的理论模型,并采用扩展的边界积分方法消除不规则频率现象。对频域内海洋浮体的一阶运动响应、一阶波浪力进行了计算,并与模型试验结果进行了对比分析,验证了基于NURBS的边界元方法是一种计算精度、计算效率都较高的新型数值计算方法。
对边界条件采用泰勒级数展开,通过摄动展开分离级数建立频域二阶边值问题,而且此边值问题的计算域是不随时间变化的。对二阶问题中自由面的积分项进行量阶分析,讨论了该项忽略与否对计算难度、计算结果精度等的影响。将基于NURBS的边界元方法应用到浮体频域二阶运动响应和波浪载荷的计算,并用谱分析法计算海洋浮体的漂移运动,通过与文献中相似计算的比较可以看出,本文二阶问题的计算方法是可靠的。
用三维弹性梁理论将缆索模型化,并采用非线性有限元法对缆索的运动方程进行求解,得到了静态和动态问题中的缆索位移和张力响应,与文献值的对比表明,本文采用的缆索求解方法是有效的。
在浮体和系泊系统的时域耦合分析中,研究并提出了一种预报浮体和系泊系统非线性运动响应和缆索张力的分析技术。考虑瞬时物面变化引起的各种非线性因素,在时域内建立浮体的非线性运动方程并求解。其中,入射波力和静恢复力按瞬时物面条件计算,辐射力和绕射力按浮体在瞬时平均湿表面为平衡位置做简谐振荡运动来计算。以三维弹性梁理论为基础,采用非线性有限元法对缆索进行计算。将浮体的分析方法和系泊缆索的分析方法结合,建立了浮体和系泊系统非线性运动响应和缆索张力的耦合计算方法。对系泊浮体的固有周期、各种工况下大幅非线性运动、缆索张力等进行了计算,并进行对比研究,可以看出,本文的方法既适用于缆索小变形条件下,也适用于缆索大变形条件下浮体与系泊系统的耦合动力分析。
According to potential theory, by use of the boundary element method based on non-uniform rational B-spline (NURBS), the linear and second-order motion responses and wave loads of ship and ocean structure are calculated in frequency domain. By combining the calculating method of the nonlinear responses for floating structures and that for mooring lines, the coupled analysis method of floating body/mooring system is made in time domain:
At first, the boundary element method based on NURBS is made. After developed in several aspects, NURBS technology is applied to construct complex ocean floating body and generate the wetted surface mesh, and the calculating results show that by the developing NURBS method, high quality mesh and floating body constructure can be obtained efficiently. Based on the above method for mesh, the further modifying method for mesh is applied for removing the irregular frequencies by the expanding boundary integral method.
According to 3 dimension potential theory, by use of the boundary element method based on NURBS, the theory model for calculating motion response and wave loads of floating body is built and the irregular frequencies are removed by the expanding boundary integral method, In frequency domain, the linear motion response and wave loads are calculated and the results are compared with that from experiment. According to the comparison, it can be seen that the boundary element method based on NURBS is a new type of numerical method with high efficiency and accuracy.
The boundary conditions are expanded by talor series, and then by perturbation expanding and separating series, the second order boundary value problems are built and the calculating domain for these problems does not change with the increasing time. Free surface integral term exists in the second order problem and by order analysis, it is analyzed that whether the term can be neglected or not and it's influence on the calculating difficulty and the accuracy of the results. In frequency domain, by the boundary element method based on NURBS, the second order motion response and wave loads of floating body are calculated and the spectrum analysis method is applied to calculate the slow drift motion of floating body which is compared with the results from the similar calculation in literatures, and from the comparison, it can be drawn that the calculating methods for second order problem are reliable in this text.
By the 3 dimension elastic beam theory, the calculating model for mooring lines is obtained and then the motion equations of the mooring lines are solved by nonlinear finite element method, so the displacement and tension response of the mooring lines are obtained in static and dynamic problem. The comparison between the results and that from literatures shows that the calculating method used in this text for mooring lines is highly efficient.
In time domain analysis of the coupled floating body/mooring system, a coupled analysis technology is developed for the forecasting of nonlinear motion responses and wave loads of floating body and mooring system. Considering the nonlinear factors resulting from considering the changing of transient body wetted surface, the nonlinear motion equations are built and solved in time domain. The incident wave force and hydrostatic restoring are calculated in transient body surface condition, while the diffraction force and radiation forces are calculated on the assume that the floating body oscillates around the balance situation which is the transient body wetted surface. Based on 3 dimension elastic beam theory, the calculation is carried out for mooring lines by the nonlinear finite element method. Combining the analysis method for floating body and that for mooring lines, the coupled calculating method of nonlinear motion responses and mooring line tension for floating body and mooring lines is made. For the mooring floating body, all kinds of calculations are carried out, such as the natural periods, large amplitude nonlinear motion in all kinds of sea condition, mooring lines tension and so on, and at the same time comparisons among the results show that the analysis methods in this text are fit not only for small amplitude motion but also large amplitude motion in time domain.
首先建立了基于NURBS的边界元方法。对NURBS技术做了多方面的改进,并应用到复杂海洋浮体的构型和湿表面网格划分,结果表明,改进的NURBS技术,能够生成高质量的浮体外形和湿表面网格,而且效率很高。为应用扩展的边界积分方法去除不规则频率,在上述网格生成方法基础上,提出了进一步的网格改进措施。
基于三维线性势流理论,应用基于NURBS的边界元法,在频域内建立了求解浮体线性运动响应和波浪载荷的理论模型,并采用扩展的边界积分方法消除不规则频率现象。对频域内海洋浮体的一阶运动响应、一阶波浪力进行了计算,并与模型试验结果进行了对比分析,验证了基于NURBS的边界元方法是一种计算精度、计算效率都较高的新型数值计算方法。
对边界条件采用泰勒级数展开,通过摄动展开分离级数建立频域二阶边值问题,而且此边值问题的计算域是不随时间变化的。对二阶问题中自由面的积分项进行量阶分析,讨论了该项忽略与否对计算难度、计算结果精度等的影响。将基于NURBS的边界元方法应用到浮体频域二阶运动响应和波浪载荷的计算,并用谱分析法计算海洋浮体的漂移运动,通过与文献中相似计算的比较可以看出,本文二阶问题的计算方法是可靠的。
用三维弹性梁理论将缆索模型化,并采用非线性有限元法对缆索的运动方程进行求解,得到了静态和动态问题中的缆索位移和张力响应,与文献值的对比表明,本文采用的缆索求解方法是有效的。
在浮体和系泊系统的时域耦合分析中,研究并提出了一种预报浮体和系泊系统非线性运动响应和缆索张力的分析技术。考虑瞬时物面变化引起的各种非线性因素,在时域内建立浮体的非线性运动方程并求解。其中,入射波力和静恢复力按瞬时物面条件计算,辐射力和绕射力按浮体在瞬时平均湿表面为平衡位置做简谐振荡运动来计算。以三维弹性梁理论为基础,采用非线性有限元法对缆索进行计算。将浮体的分析方法和系泊缆索的分析方法结合,建立了浮体和系泊系统非线性运动响应和缆索张力的耦合计算方法。对系泊浮体的固有周期、各种工况下大幅非线性运动、缆索张力等进行了计算,并进行对比研究,可以看出,本文的方法既适用于缆索小变形条件下,也适用于缆索大变形条件下浮体与系泊系统的耦合动力分析。
According to potential theory, by use of the boundary element method based on non-uniform rational B-spline (NURBS), the linear and second-order motion responses and wave loads of ship and ocean structure are calculated in frequency domain. By combining the calculating method of the nonlinear responses for floating structures and that for mooring lines, the coupled analysis method of floating body/mooring system is made in time domain:
At first, the boundary element method based on NURBS is made. After developed in several aspects, NURBS technology is applied to construct complex ocean floating body and generate the wetted surface mesh, and the calculating results show that by the developing NURBS method, high quality mesh and floating body constructure can be obtained efficiently. Based on the above method for mesh, the further modifying method for mesh is applied for removing the irregular frequencies by the expanding boundary integral method.
According to 3 dimension potential theory, by use of the boundary element method based on NURBS, the theory model for calculating motion response and wave loads of floating body is built and the irregular frequencies are removed by the expanding boundary integral method, In frequency domain, the linear motion response and wave loads are calculated and the results are compared with that from experiment. According to the comparison, it can be seen that the boundary element method based on NURBS is a new type of numerical method with high efficiency and accuracy.
The boundary conditions are expanded by talor series, and then by perturbation expanding and separating series, the second order boundary value problems are built and the calculating domain for these problems does not change with the increasing time. Free surface integral term exists in the second order problem and by order analysis, it is analyzed that whether the term can be neglected or not and it's influence on the calculating difficulty and the accuracy of the results. In frequency domain, by the boundary element method based on NURBS, the second order motion response and wave loads of floating body are calculated and the spectrum analysis method is applied to calculate the slow drift motion of floating body which is compared with the results from the similar calculation in literatures, and from the comparison, it can be drawn that the calculating methods for second order problem are reliable in this text.
By the 3 dimension elastic beam theory, the calculating model for mooring lines is obtained and then the motion equations of the mooring lines are solved by nonlinear finite element method, so the displacement and tension response of the mooring lines are obtained in static and dynamic problem. The comparison between the results and that from literatures shows that the calculating method used in this text for mooring lines is highly efficient.
In time domain analysis of the coupled floating body/mooring system, a coupled analysis technology is developed for the forecasting of nonlinear motion responses and wave loads of floating body and mooring system. Considering the nonlinear factors resulting from considering the changing of transient body wetted surface, the nonlinear motion equations are built and solved in time domain. The incident wave force and hydrostatic restoring are calculated in transient body surface condition, while the diffraction force and radiation forces are calculated on the assume that the floating body oscillates around the balance situation which is the transient body wetted surface. Based on 3 dimension elastic beam theory, the calculation is carried out for mooring lines by the nonlinear finite element method. Combining the analysis method for floating body and that for mooring lines, the coupled calculating method of nonlinear motion responses and mooring line tension for floating body and mooring lines is made. For the mooring floating body, all kinds of calculations are carried out, such as the natural periods, large amplitude nonlinear motion in all kinds of sea condition, mooring lines tension and so on, and at the same time comparisons among the results show that the analysis methods in this text are fit not only for small amplitude motion but also large amplitude motion in time domain.
引文
[1]Wehausen,J. and St. Denis,M. On the motions of ships at sea. Trans. SNAME, Vol.58,1950:184-248P.
[2]St. Denis, M. and Pierson, W. J. Jr. On the Motions of Ships in Confused Seas. Trans. SNAME, Vol.61,1953:280-358P.
[3]Hess, J.L. and Smith, A.M.O. Calculation of nonlifting potential flow about arbitrary three-dimensional bodies. Journal of Ship Research,8(2), 1964:22-44P.
[4]Faltinsen, O.M. and Michelsen, F.C. Motions of large structure in waves at zero Froude number. The Dynamics of Marine Vehicles and Structures in Waves, Editors R.E.D.Bishop and W.G.Price, Mechanical Engineering Publications Limited,1975.
[5]Chang, M.S. and Pien, P.C. Velocity potentials of submerged bodies near a free surface — Application to wave-excited forces and motions.11th SNH, 1976.
[6]Carrison, C.J. Hydrodynamic loading of large offshore structures.Three-dimensional source distribution methods. Numerical Methods in Offshore Engineering, Edited by O.C. Zienkiewicz, A Wiley-Inters cience Publication,1978.
[7]孙伯起,董慎言等.波浪中任意三维零航速物体水动力和运动计算.三维流体动力计算交流讨论会,上海.1985年5月.
[8]刘应中,缪国平.船舶在波浪上的运动理论.上海：上海交通大学出版社,1987年.
[9]戴遗山,贺五洲.简单Green函数法求解三维水动力系数.中国造船,1986年第3期：5-10页.
[10]Maniar, H. A three dimensional higher-order panel method based on
B-splines. Ph.D. Thesis, Department of Ocean Engineering, MIT, Cambridge, Massachusetts,1995.
[11]Beck, R.F. and Loken, K. Three dimensional effects in ship relative motion problems. JSR,Vol.33,1989.
[12]周正全,顾懋祥,缪全明.船舶在波浪中的相对运动的三维预报方法.中国造船,1990增刊.
[13]Beck, R.F. Time-domain computations for floating bodies. Appl. Ocean Res.,16,1994.
[14]Newman, J.N. Algorithms for the free-surface Green function. J.Eng.Maths, 19,1985.
[15]黄德波.时域Green函数及其导数的数值计算.中国造船,1992年第2期.
[16]Beck, R.F. and Liapis, S.J. Transient motions of floating bodies at zero forward speed. Journal of Ship Research, Vol.31, No.3,1987.
[17]Liapis, S.J. and Beck, R.F. Seakeeping computations using time-domain analysis.4th ICNSH, Washington, O.C,1985.
[18]King, B.K., Beck, R.F. and Magee, A.R. Seakeeping calculations with forward speed using time domain analysis,17th ONR, Hague,1988.
[19]张亮,戴遗山.物体近水面航行时绕射问题的时域解.中国造船,1992年第4期.
[20]周正全,张亮和戴遗山.船舶在波浪中航行时绕射问题的线性时域解.中国造船,1993年第3期.
[21]Lin, W.M. and Yue, D.K.P. Numerical solutons for large amplitude ship motions in the time-domain. Proc.18th Symp. On Naval Hydrodynamics, Ann Arbor, MI,1990:41-65P.
[22]段文洋.船舶大幅运动非线性水动力研究.哈尔滨工程大学博士学位论文,1995年.
[23]Shin, Y.S., Chung, J.S., Zhang, S. and Engle, A. Dynamic loadings for
structural analysis of fine form container ship based on a non-linear large amplitude motions and loads method. Trans. SNAME, Vol.105, 1997:127-154P.
[24]Zhang, L. and Taylor, R.E. Time-domain analysis of wave forces on ships with forward speed. Journal of Hydrodynamics, Ser. B,3,1998.
[25]Duan, W.Y. and Dai, Y.S. Time-domain calculation of hydrodynamic forces on ships with large flare. Int. Shipbuild. Progr.,46, No.446,1999:209-221P.
[26]Gadd, G.E. A method of computing the flow and surface wave pattern around full forms. Trans. Roy. Asst. Nav. Archit., Vol.113,1976.
[27]Dawson, C.W. A practical computer method for solving ship-wave problems.2nd International Conference on Numerical Ship Hydrodynamics, USA,1977.
[28]Chapman, R.B. Time-domain method for computing forces and moments acting on 3-D surface piercing hull with forward speed.3rd ICNSH, Paris, 1981.
[29]Nakos, D.E. Ship wave patterns and motions by a three-dimensional Rankine panel method. Ph.D. Thesis, The Department of Ocean Engineering, MIT, USA,1990.
[30]Nakos, D.E. and Sclavounos, P.D. On steady and unsteady ship wave patterns. Journal of Fluid Mechanics, Vol.215,1990:263-288P.
[31]Sclavounos, P.D. and Nakos, D.E. Stability analysis of panel methods for free-surface flows with forward speed. Proceedings,17th Symposium on Naval Hydrodynamics, The Hague, The Netherlands,1988.
[32]Nakos, D.E. and Sclavounos, P.D. Ship motions by a three-dimensional Rankine panel method. Proc.18th Symp. On Naval Hydrodynamics, Ann. Arbor, MI,1990:21-40P.
[33]Sclavounos, P.D., Nakos, D.E. and Huang, Y. Seakeeping and wave induced loads on ship with flare by a Rankine panel method. Proceedings
of the 6th International Conference on Numercial Ship Hydrodynamics, Iowa City, Iowa,1993.
[34]Sclavounos, P.D. Computation of wave ship interactions. Advances in Marine Hydrodynamics, edited by M. Ohkusu, Computational Mechanics Publications,1995.
[35]Nakos, D.E. Kring, D.C. and Sclavounos, P.D. Rankine panel methods for transient free surface flows. Proceedings of the 6th International Conference on Numerical Ship Hydrodynamics, Iowa City, Iowa,1993.
[36]Kring, D.C. Time domain ship motions by a three-dimensional Rankine panel method. Ph.D. Thesis, MIT, Cambridge, MA,1994.
[37]Kring, D.C. and Sclavounos, P.D. Numerial stability analysis for time-domain ship motion simulations. Journal of Ship Research, Vol.39, No.4, Dec.1995:313-320P.
[38]Kim, Y., Kring, D.C. and Sclavounos, P.D. Linear and nonlinear interactions of surface waves with bodies by a three-dimensional Rankine panel method. Applied Ocean Research,19,1997:235-249P.
[39]Huang, Y.F. Nonlinear ship motions by a Rankine panel method. Ph.D. Thesis, The Department of Ocean Engineering, MIT, USA,1996.
[40]Kring, D.C, Huang, Y.F., Sclavounos, P.D., Vada, T. and Braathen, A. Non-linear ship motions and wave-induced loads by a Rankine panel method. Proceedings of 21th Symposium on Naval Hydrodyn., Trondheim, 1996:16-33P.
[41]Huang, Y.F. and Sclavounos, P.D. Nonlinear ship motions. Journal of Ship Research, Vol.42, No.2, June 1998:120-130P.
[42]Isaacson, M. Nonlinear-wave effects on fixed and floating bodies. Journal of Fluid Mechanics,120,1982:267-281P.
[43]Lin, W.M., Newman, J.N. and Yue, D.K.P. Nonlinear forced motions of floating bodies.15th ONR,1984.
[44]Dommermuth, D.G. and Yue, D.K.P. Numerical simulations of nonlinear axisymmetric flows with a free surface. Journal of Fluid Mechanics,178, 1987:195-219P.
[45]Yang, C. Time domain computation of nonlinear wave forces on 3-D body. Ph.D. thesis, Shanghai Jiao Tong University,1987.
[46]周正全.三维物体与非线性波浪的相互作用.中国船舶科学研究中心博士论文,1988.
[47]Romate, J.E. The numerical simulation of nonlinear gravity waves in three dimensions using a higher order panel method. Ph.D. thesis, University of Twente, The Netherlands,1989.
[48]Broeze, J. Numerical modelling of nonlinear free surface waves with a 3D panel method. Ph.D. thesis, University of Twente, The Netherlands,1993.
[49]van Daalen, E.F.G.. Numerical and theoretical studies of water waves and floting bodies. Ph.D. thesis, University of Twente, The Netherlands,1993.
[50]de Hass, P. Numerical simulation of nonlinear water waves using a panel method:domain decomposition and applications. Ph.D. thesis, University of Twente, The Netherlands,1997.
[51]Kring, D.C., Korsmeyer, F.T., Singer, J., Danmeier, D. and White, J. Accelerated non-linear wave simulations for large structures.7th International Conference on Numerical Ship Hydrodynamics, Nantes, France, July 1999.
[52]Kring, D.C., Korsmeyer, F.T., Singer, J. and White, J. Analyzing mobile offshore bases using accelerated boundary-element methods. Marine Structures,13,200:301-313P.
[53]Skourup, J. and Jonsson, I.G. Computations of forces on, and particle orbits around, horizontal cylinders under steep waves. Ocean Engineering,19(6), 1992:527-553P.
[54]Ferrant, P. Three-dimensional unsteady wave-body interactions by a
Rankine boundary element model. Ship Technology Research,40(4), 1993:165-175P.
[55]Ferrant, P. Simulation of strongly nonlinear wave generation and wave-body interactions using a 3-D MEL model. Proceedings of the 21st ONR Symposium on Naval Hydrodynamics, Trondheim, Norway, 1996:93-109P.
[56]Kim, M.H., Celebi, M.S. and Kim, D.J. Fully non-linear interactions of waves with a three-dimensional body in uniform currents. Applied Ocean Research,20(5),1998:309-321P.
[57]Landrini, M., Gryt Φ yr, G. and Faltinsen, O.M. A B-spline based BEM for unsteady free-surface flows. Journal of Ship Research, Vol.43, No.1, March 1999:13-24P.
[58]Beck, R.F. Time-domain computations for floating bodies. Applied Ocean Research,16,1994.
[59]Beck, R.F., Cao, Y., Scorpio, S.M. and Schultz, W. Non-linear ship motions computations using the desingularized method. Proceedings 20th Symposium on Naval Hydrodynamics, Santa Borbara, Colifornia,1994.
[60]Scorpio, S.M., Beck, R.F. and Korsmeyer, F.T. Non-linear water wave computations using a multipole accelerated, desingularized method. Proceedings 21st Symposium on Naval Hydrodynamics, Trondheim, 1996:34-43P.
[61]Scorpio, S.M. Fully nonlinear ship-wave computations using a multipole accelerated, desingularized method. Ph.D. thesis, Naval Architecture and Marine Engineering in The University of Michigan,1997.
[62]Maniar H. D. A B-spline based higher order method in 3D.10th International Workshop on Water Waves and Floating Bodies, Oxford, UK, 1995:153-I58P.
[63]Teng B, Li Y C. A unique solvable higher order BEM for wave diffraction and radiation. China Ocean Engineering,1996,10(3):333-342P.
[64]柏威.非线性波浪与任意三维物体的相互作用.大连：大连理工大学,2001.
[65]张晓兔.基B样条的三维船体水动力数值计算研究.武汉：武汉理工大学,2002.
[66]钱昆.浮体在大幅波浪中的运动和载荷的计算研究.大连：大连理工大学,2004.
[67]谬国平.挠性部件力学导论.上海交通大学出版社,1995.
[68]Korkutm, M. D. and Hebert, E. J. Some notes on static anchor chain curve. OTC,1971, OTC# 1160:147-155P.
[69]Pedersen, P. T. Equilibrium of offshore cables and pipeline during laying. International Shipbuilding Progress,1975,22:399-408P.
[70]Pangalila, F. V. and Martin, J. P. A method of estimating line tensions and motions of a semi-submersible based on empirical data and model basis results. OTC,1969,2:90-96P.
[71]Gault, A. J. and Cox, W. R. Method for predicting geometry and loading distribution in an anchor chain from a single point mooring buoy to a buried anchorage. OTC,1973,1:309-318P.
[72]马汝建,高学仕.悬链线锚链的非线性恢复系数.中国海洋平台,1994,21：180-183页
[73]马鉴恩,李凤来.锚泊列阵的设计研究.海洋工程,1996,14(2)：52-62页
[74]陈广莲.确定锚泊设备的直接计算法.船舶设备通讯,2004,109(1)：43-50页
[75]Smith, T. M., Chen, M. C. and Radwan, A. M. Systematic data for the preliminary design of mooring systems. Proceedings of the fourth International Offshore Mechanics and Arctic Engineering Symposium, 1985,1:403-407P.
[76]Smith, R. J. and MacFarlane, C. J. Statics of a three component mooring
line. Ocean Engineering,2001,28:899-914P.
[77]Chaff, Y. T., Varyani, K. S. and Barltrop, D. N. P. Semi-analytical quasi-static formulation for three 2 dimensional partially grounded mooring system problems. Ocean Engineering,2002,29:627-649P.
[78]余龙,谭家华.深水多成分悬链线锚泊系统优化设计及应用研究.华东船舶工业学院学报(自然科学版),2004,18(5)：8-13页
[79]余龙,谭家华.基于准静定方法的多成分锚泊线优化.海洋工程,2005,23(1)：69-73页
[80]陈徐均,汤雪峰等.系泊浮体布链方式优劣的理论分析.河海大学学报,2001,29(5)：1-9页
[81]陈徐均,崔维成,沈庆.对称式布置锚链系统的线性化处理.海洋工程,2002,22(1)：75-79页
[82]Hong, S. T. Frequency domain analysis for the tension in a taut mooring line. Technical Report NO.SM72-1, University of Washington,1972.
[83]Hong, S. T. Tension in a taut line mooring:frequency domain analysis. OTC,1974,2:389-400P.
[84]Connell, G. M. Analytical studies of resonance in taut-moored system. OTC, 1974,2:401-416P.
[85]Skop, R. A. and O'Hora, G. J. The static equilibrium configuration of cables arrays by use of the method of imaginary reaction. NRL Report NO.6819, AD68519,1969.
[86]Skop, R. A. and Kaplon, R. E. The static configuration of tri-moored surface, buoy cable array acted on by current-induced force. NRL Report NO.6894,AD65814,1969.
[87]Watson, T. V. and Kuneman, J. E. Determination of the static equilibrium configuration externally redundant submerged cable arrays. OTC,1975, 2:765-776P.
[88]Adams, R. B. Analysis of spread mooring by dimensional function. OTC,
1968,1:77-88P.
[89]Adams, R. B. Accuracy of the taut-tine position indicator for offshore drilling vessels. Trans. ASME J.of Eng. For Industry,1968, 90(1):161-171P.
[90]Collipp, B. G. Analyzing mooring line catenaries. Petroleum Engineering, 1968,40(5):72-80P.
[91]Charles, E. N. and Dominguez, R. F. Large displacement mooring dynamics. OTC,1977,1:19-30P.
[92]Orgill G, Wilson J. F. and Schmertmann G R. Static design of mooring arrays for offshore guyed towers. Applied Ocean Research,1985, 7(3):166-174P.
[93]Bliek A. Dynamic analysis of single span cables. Ph.D. thesis, MIT, Cambridge, MA, U.S.A.,1994.
[94]Triantafyllou M. S., Bliek A. & Shin, S. Dynamic analysis as a tool for open-sea mooring system design. Transactions SNAME,1985, 93:303-324P.
[95]Hover F. S., Grosenbaugh M. A. and Triantafyllou M. S. Calculation of dynamic tension in towed underwater cable. IEEE Journal of Oceanic Engineering,1994,19:449-457P.
[96]Thomas D. O. & Hearn G. E. Deepwater mooring line dynamics with emphasis on sea-bed interference effects. Offshore Technology Conference, 1991.
[97]Nakamura N., Koterayama W. and Kyozuka Y. Slow drift damping due to drag forces acting on mooring lines. Ocean Engineering,1991, 18:283-296P.
[98]Huang S. Dynamic analysis of 3-D marine cables. Ocean Engineering,1994, 21:587-605P.
[99]Korterayama W. Motions of moored floating body and dynamic tension of
mooring lines in regular waves. Rep. Res. Inst. Appl. Mech.1978.
[100]Korterayama W. and Nakamura, M. Hydrodynamic forces acting on a vertical circular cylinder oscillating with a very low frequency in waves. Ocean Engineering,1988,15(3):271-287P.
[101]Korterayama W. and Nakamura M. Drag and inertia force coefficients derived from field tests. International Journal of Offshore and Polar Engineering,1992,2(3):162-167P.
[102]李远林,吴家鸣.多锚链系泊浮筒非线性漂移运动的时域模拟.海洋过程,1990,8(1)：25-33页
[103]Toshio Nakajima. A study of the mooring dynamics of various types by lumped mass method. Ph. D. Thesis, University of Tokyo,1991.
[104]Nakajima T., Motors S. and Fujino M. On the dynamic responses of the moored object and the mooring lines in regular waves. Trans. Soc. Of naval arch. Of Japan,1981, No.150.
[105]Toshio Nakajima. On the dynamic analysis of mufti-component mooring lines.1982, OTC#4309:105-110.
[106]Burgess J.J. Equations of motion of a submerged cables with bending stiffness. Int. Offshore Mech. And Artic Eng. Conf., Calgary,1992, Vol.1-A:283-289P.
[107]Webster E.L. Nonlinear static and dynamic response of underwater cables structures using the finite element method. Offshore Technology Conference,1975, OTC#2322,2:754-764P.
[108]Hose E. Surge damping due to mooring lines friction on the seabed. RepN01.11 Research Programme Marine Structures, Mrintek,1985.
[109]Hose E. Influence of mooring line damping upon rig motions. OTC,1986, 2:433-438P.
[110]Hose,E. and Matsumoto,K. Practical estimation of mooring line damping. OTC,1988,2:543-552P.
[111]Hose E. and Matsumoto K. Mooring line damping due to first and second-order vessel motion. OTC,1989,2:135-148P.
[112]Hose E. Resonant heave damping of tension leg platforms. OTC,1990, 2:431-436P.
[113]Hose E. New developments in prediction of mooring system damping. OTC,1991,2:291-298P.
[114]Shashikala A.P. et. al. Dynamics of a moored barge under regular and random waves. Ocean Engineering,1997,24(5):401-430P.
[115]Leonard J.W. and Recker W.W. Nonlinear dynamics of cables with low initial tension. Journal of the Engineering Mechanics, Division,ASCE,1972, 98(2):204-234P.
[116]Leonard J.W. Curved finite element approximation to nonlinear cables. OTC,1972,1:225-233P.
[117]Chatjigeorgion L. K. and Mavrakos S. A. Nonlinear contributions in the prediction of dynamic tension on mooring lines for high and low frequencies of excitation. Proc.7th Int. Offshore and Polar Eng. Conf., Honolulu, ISOPE,1997,2:192-199
[118]Chatjigeorgion L.K. and Mavrakos S. A. Assessment of bottom cable interaction effects on mooring line dynamics. Int. Offshore Mech. And Artic Eng. Conf., Libson,1998, No.335
[119]Chatjigeorgion L. K. and Mavrakos S. A. Comparative study on the efficiency of improved numerical solutions schemes in the prediction of the dynamic behavior of mooring lines. Proc.9th Int. Offshore and Polar Eng. Conf., Brest, France, ISOPE,1999,2:332-339P.
[120]Chatjigeorgion L. K. and Mavrakos, S. A.. Comparative evaluation of numerical schemes for 2D mooring dynamics. International journal of offshore and polar engineering,2000,10(4):301-309 P.
[121]Kwan C. T. and Bruen F. J. Mooring line dynamics:comparison of time domain, frequency domain and quasi-static analysis. OTC,1988,2:513-521 P.
[122]Firewell M. L. Steady-state analysis of underwater cables. Journal of Waterway, Port, Cpastal and Ocean Engineering,1995,121(2):98-104 P.
[123]Wang C. M., Cheong H. F. and Chucheepsakul S. Static analysis of marine cables via shooting-optimization technique. Journal of waterway, port, Coastal and Ocean Engineering,1993,119(1):450-457 P.
[124]De Zoysa A.P.K. Steady-state analysis of under cables. Ocean Engineering, 1978,5:209-223P.
[125]徐兴平.单点系泊系统动力响应计算.中国海洋平台,1994,1：209-302页
[126]徐兴平,童英玉.单点系泊系统动力响应分析.石油大学学报(自然科学版),1994,18(5)：74-78页
[127]马汝建.单点系泊装置的非线性动力分析.石油大学学报(自然科学版),1994,18(5)；65-69P.
[128]谢炜,唐新铭.用于CALM系统分析的修正准静力方法.中国海洋平台.1994,1：243-248页.
[129]黄剑,朱克强.半潜式平台两种锚泊系统的静力分析与比较.华东船舶工业学院学报(自然科学版),2004,18(3)：1-5页.
[130]陈小红,黄祥鹿.单点系泊海洋资料浮标的动力分析.中国造船,1995,130：1-13页
[131]范菊,黄样鹿.锚泊线的动力分析.中国造船,1999,144：13-20P.
[132]范菊,陈小红,黄祥鹿.锚泊线一阶运动响应对二阶锚链阻尼的影响.船舶力学,2000,4：20-27页
[133]范菊,陈小红,黄样鹿,三阶摄动对锚泊线动力分析的影响.船舶力学,2000,4.
[134]黄祥鹿,陈小红,范菊.锚泊浮式结构波浪上运动的频域算法.上海交通大学学报,2001,45：1470-1476页
[135]陈小红,黄祥鹿.随机振荡法测量锚泊线动力的双频率响应函数.上海交
通大学学报,1995,29：13-19页
[136]范菊,纪亨腾,黄祥鹿.浮式塔的动力计算.海洋学报,2001,23：117-123页
[137]陈小红,马巍,黄祥鹿.双频锚泊线动力分析.上海交通大学学报,1993,27,5：1-8页
[138]周崇庆,刘土光和李天匀.风浪中锚泊渔船的锚链系泊张力的分析研究.中国水产科学,1999,6(3)：78-80页
[139]刘应中,缪国平,李谊乐等.系泊系统动力分析的时域方法.上海交通大学学报,1997,31(11)：7-12页
[140]李向群.多点系泊船舶在波浪中的运动及其系泊力.交通部上海船舶运输科学研究所学报,1999,22(1)：9-15页
[141]聂孟喜,王旭升,王晓明,张琳.风、浪、流联合作用下系统系泊力的时域计算方法.清华大学学报(自然科学版),2004,36(17)：1214-1217页
[142]张纬康,杜度.系泊船舶动力学特性的计算机仿真研究.中国造船,2002,45(4)：1-10页
[143]杜度,张宁,马骋,张纬康.系泊系统的时域仿真及其非线性动力学特性分析.船舶力学,2005,9(4)：37-45页
[144]Yeung R W. Numerical methods in free-surface flows. Fluid Mech.,1982,14：395-442页
[145]张廷芳.计算流体力学.大连理工大学出版社,1992.
[146]张景峤.细分曲面生成及其在曲面造型中的应用研究.杭州：浙江大学,2003.
[147]仵大伟.船体曲面表达与三维船舶设计研究.大连：大连理工大学,2002.
[148]林焰,纪卓尚.船体B样条曲面的数学描述及计算机方法.中国造船,1996,11(4)：20-24页
[149]陈绍平,陈宾康.基于NURBS曲线的双艉船型线设计研究.中国造船,2001：42(2)：7-11页
[150]ROGERS D F, SATTERFIELD S G. B-Spline surface for ship hull design. Computer Graphics,1980,14(3):211-217P.
[151]施法中.计算机辅助几何设计与非均匀有理B样条(CAGD & NURBS).高等教育出版社,2001.
[152]孙家广,杨长贵编著.计算机图形学(新版).北京：清华大学出版社,1995.
[153]易大义.数值方法.杭州：浙江科学技术出版社,1984.
[154]赵作智.基于非均匀有理B样条(NURBS)的曲面反求的研究.北京：清华大学,2003.
[155]Maniar H. D. A B-spline based higher order method in 3D.10th International Workshop on Water Waves and Floating Bodies, Oxford, UK, 1995,153-158.
[156]Li H. B., Han G. M., Mang H. A. A new method for evaluating singular integral in stress analysis of solids by the direct boundary element method. Int. Jour, for Num. Math. In Eng.,1985,211,2071-2075P.
[157]戴遗山,段文洋.船舶在在波浪中运动的势流理论.北京：国防工业出版社,2008：90-98页
[158]Wehausen J V, Laitone E V Surface wave. Handbuch der Physik, IX,Berlin, springer-Verlag,1960,468-512P.
[159]Chau F P. The second order velocity potential for diffraction of waves by fixed offshore structures. Department of Mechanical Engineering, University College London, Ph.D. thesis,1989.
[160]Eatock Taylor R, Chau F P. Wave diffraction-some development in linear and non-linear theory. Jour. of Offshore Mech. and Arctic. Eng.,1992, 114,185-194P.
[161]滕斌.波浪力计算中的一个新边界元方法.水动力学研究与进展,1994,9(2)：215-223页
[162]Teng B, Eatock Taylor R. New higher-order wave diffraction/radiation. App. Ocean Res.,1995,17,element methods for 71-77P.
[163]Wu, G. X., Eatock Taylor, R.,1989. The numerical solution of the motions of a ship advancing in waves. Proc.5th Int. Conf. on Numerical Ship Hydrodynamics, Hiroshima, Japan,3:86-94P.
[164]Lamb H. Hydrodynamics.Cambridge University Press,1932.
[165]Ohmatsu S. On the irregular frequencies in the theory of oscillating bodies. Papers, Ship Res. Inst., Japan, No.48,1975P.
[166]Saver P, Ursell F. Integral-equation methods for calculating the virtual mass in water of finite depths. Proc.2nd Int. Symp. Numerical Hydro. University of California,1977.
[167]Ogilvie T F, Shin Y S. Integral equation solutions for time-dependent free surface problems. J. Soc. Nav. Arch. Japan,1978,143.
[168]Kleinman R E. On the mathematical theory of motion of floating bodies[R]. DTNSRDC Report 82/074,1982.
[169]Lee Sclawouns. Removing the irregular frequencies from interval equations in wave-body interactions.J.fluidMech.,1989,207:393-418P.
[170]段文洋,贺五洲.一种消除水动力求解中不规则频率影响的边界元法.水动力学研究与进展,2002,17(2)：156-161 P.
[171]孙亮,腾斌.消除“不规则频率”的非连续高阶元方法.海洋工程,Nov.2004,22(4).
[172]Lee, C.-H., Newman, J. N., Zhu X. An extended boundary integral equation method for the removal of irregular frequency effects. Int. J. of Numerical Methods in Fluids,1996,23:637-660P.
[173]张海彬.FPSO储油轮与半潜式平台波浪载荷三维计算方法研究.哈尔滨工程大学博士论文,2003：32-98页
[174]徐福敏.单点系泊系统低频纵荡二阶力的频域计算.河海大学学报,1997,25(1)：103-106页
[175]陈徐均,吴有生,崔维成,孙芦忠.海洋浮体二阶非线性水弹性力学分析—系泊浮体主坐标响应的频率特征.船舶力学,2002,6(5)：44-57页
[176]Chen, X. B., Duan, W. Y., and Dai Y.S. Accurate computation of second-order low-frequency loads. Proceeding of 7th National Congress on Hydrodynamics and 19th National Conference on Hydrodynamics, Harbin,2005:57-74p.
[177]Chen, X. B. Approximation on the quadratic transfer functions of low-frequency loads.Proceeding of 5th International Conference on Numerical Ship Hydrodynamics, Hiroshima,1989:391-402P.
[178]Lee, C.-H. Wamit theory manual. Massachusetts Institute of Technology Department of Ocean Engineering, Cambridge,1995:1-44P.
[179]Newman, J.N. Process in wave load computation on offshore structure, OMAE 2004,Vancouver.
[180]Kim, M.-H., Yue, D. K. P.. The complete second-order diffraction solution for an axisymetric body—Part Ⅱ. Bichromatic incident waves and body motions. J. Fluid Mechanics,1990,211:557-593P.
[181]滕斌,李玉成,董国海.双色入射波下二阶波浪力响应函数.海洋学报,1999,21(2)：115-123页
[182]ZHIHUANG RAN. Coupled dynamic analysis of floating structures in waves and currents. Ph. D. Thesis, MIT, USA,2000.
[183]Techou C. Non-linear dynamics of mooring lines. Ph. D. Thesis, MIT, USA.1997.
[184]Chatjigeorgiou, IK., Mavrakos, SA. Nonlinear contributions in the prediction of the dynamic tension on mooring lines:for high and low frequencies of excitation. Proc.7th Int Offshore and Polar eng. Coraf.,Honolulu, ISOPE,1997,2:192-199P
[2]St. Denis, M. and Pierson, W. J. Jr. On the Motions of Ships in Confused Seas. Trans. SNAME, Vol.61,1953:280-358P.
[3]Hess, J.L. and Smith, A.M.O. Calculation of nonlifting potential flow about arbitrary three-dimensional bodies. Journal of Ship Research,8(2), 1964:22-44P.
[4]Faltinsen, O.M. and Michelsen, F.C. Motions of large structure in waves at zero Froude number. The Dynamics of Marine Vehicles and Structures in Waves, Editors R.E.D.Bishop and W.G.Price, Mechanical Engineering Publications Limited,1975.
[5]Chang, M.S. and Pien, P.C. Velocity potentials of submerged bodies near a free surface — Application to wave-excited forces and motions.11th SNH, 1976.
[6]Carrison, C.J. Hydrodynamic loading of large offshore structures.Three-dimensional source distribution methods. Numerical Methods in Offshore Engineering, Edited by O.C. Zienkiewicz, A Wiley-Inters cience Publication,1978.
[7]孙伯起,董慎言等.波浪中任意三维零航速物体水动力和运动计算.三维流体动力计算交流讨论会,上海.1985年5月.
[8]刘应中,缪国平.船舶在波浪上的运动理论.上海：上海交通大学出版社,1987年.
[9]戴遗山,贺五洲.简单Green函数法求解三维水动力系数.中国造船,1986年第3期：5-10页.
[10]Maniar, H. A three dimensional higher-order panel method based on
B-splines. Ph.D. Thesis, Department of Ocean Engineering, MIT, Cambridge, Massachusetts,1995.
[11]Beck, R.F. and Loken, K. Three dimensional effects in ship relative motion problems. JSR,Vol.33,1989.
[12]周正全,顾懋祥,缪全明.船舶在波浪中的相对运动的三维预报方法.中国造船,1990增刊.
[13]Beck, R.F. Time-domain computations for floating bodies. Appl. Ocean Res.,16,1994.
[14]Newman, J.N. Algorithms for the free-surface Green function. J.Eng.Maths, 19,1985.
[15]黄德波.时域Green函数及其导数的数值计算.中国造船,1992年第2期.
[16]Beck, R.F. and Liapis, S.J. Transient motions of floating bodies at zero forward speed. Journal of Ship Research, Vol.31, No.3,1987.
[17]Liapis, S.J. and Beck, R.F. Seakeeping computations using time-domain analysis.4th ICNSH, Washington, O.C,1985.
[18]King, B.K., Beck, R.F. and Magee, A.R. Seakeeping calculations with forward speed using time domain analysis,17th ONR, Hague,1988.
[19]张亮,戴遗山.物体近水面航行时绕射问题的时域解.中国造船,1992年第4期.
[20]周正全,张亮和戴遗山.船舶在波浪中航行时绕射问题的线性时域解.中国造船,1993年第3期.
[21]Lin, W.M. and Yue, D.K.P. Numerical solutons for large amplitude ship motions in the time-domain. Proc.18th Symp. On Naval Hydrodynamics, Ann Arbor, MI,1990:41-65P.
[22]段文洋.船舶大幅运动非线性水动力研究.哈尔滨工程大学博士学位论文,1995年.
[23]Shin, Y.S., Chung, J.S., Zhang, S. and Engle, A. Dynamic loadings for
structural analysis of fine form container ship based on a non-linear large amplitude motions and loads method. Trans. SNAME, Vol.105, 1997:127-154P.
[24]Zhang, L. and Taylor, R.E. Time-domain analysis of wave forces on ships with forward speed. Journal of Hydrodynamics, Ser. B,3,1998.
[25]Duan, W.Y. and Dai, Y.S. Time-domain calculation of hydrodynamic forces on ships with large flare. Int. Shipbuild. Progr.,46, No.446,1999:209-221P.
[26]Gadd, G.E. A method of computing the flow and surface wave pattern around full forms. Trans. Roy. Asst. Nav. Archit., Vol.113,1976.
[27]Dawson, C.W. A practical computer method for solving ship-wave problems.2nd International Conference on Numerical Ship Hydrodynamics, USA,1977.
[28]Chapman, R.B. Time-domain method for computing forces and moments acting on 3-D surface piercing hull with forward speed.3rd ICNSH, Paris, 1981.
[29]Nakos, D.E. Ship wave patterns and motions by a three-dimensional Rankine panel method. Ph.D. Thesis, The Department of Ocean Engineering, MIT, USA,1990.
[30]Nakos, D.E. and Sclavounos, P.D. On steady and unsteady ship wave patterns. Journal of Fluid Mechanics, Vol.215,1990:263-288P.
[31]Sclavounos, P.D. and Nakos, D.E. Stability analysis of panel methods for free-surface flows with forward speed. Proceedings,17th Symposium on Naval Hydrodynamics, The Hague, The Netherlands,1988.
[32]Nakos, D.E. and Sclavounos, P.D. Ship motions by a three-dimensional Rankine panel method. Proc.18th Symp. On Naval Hydrodynamics, Ann. Arbor, MI,1990:21-40P.
[33]Sclavounos, P.D., Nakos, D.E. and Huang, Y. Seakeeping and wave induced loads on ship with flare by a Rankine panel method. Proceedings
of the 6th International Conference on Numercial Ship Hydrodynamics, Iowa City, Iowa,1993.
[34]Sclavounos, P.D. Computation of wave ship interactions. Advances in Marine Hydrodynamics, edited by M. Ohkusu, Computational Mechanics Publications,1995.
[35]Nakos, D.E. Kring, D.C. and Sclavounos, P.D. Rankine panel methods for transient free surface flows. Proceedings of the 6th International Conference on Numerical Ship Hydrodynamics, Iowa City, Iowa,1993.
[36]Kring, D.C. Time domain ship motions by a three-dimensional Rankine panel method. Ph.D. Thesis, MIT, Cambridge, MA,1994.
[37]Kring, D.C. and Sclavounos, P.D. Numerial stability analysis for time-domain ship motion simulations. Journal of Ship Research, Vol.39, No.4, Dec.1995:313-320P.
[38]Kim, Y., Kring, D.C. and Sclavounos, P.D. Linear and nonlinear interactions of surface waves with bodies by a three-dimensional Rankine panel method. Applied Ocean Research,19,1997:235-249P.
[39]Huang, Y.F. Nonlinear ship motions by a Rankine panel method. Ph.D. Thesis, The Department of Ocean Engineering, MIT, USA,1996.
[40]Kring, D.C, Huang, Y.F., Sclavounos, P.D., Vada, T. and Braathen, A. Non-linear ship motions and wave-induced loads by a Rankine panel method. Proceedings of 21th Symposium on Naval Hydrodyn., Trondheim, 1996:16-33P.
[41]Huang, Y.F. and Sclavounos, P.D. Nonlinear ship motions. Journal of Ship Research, Vol.42, No.2, June 1998:120-130P.
[42]Isaacson, M. Nonlinear-wave effects on fixed and floating bodies. Journal of Fluid Mechanics,120,1982:267-281P.
[43]Lin, W.M., Newman, J.N. and Yue, D.K.P. Nonlinear forced motions of floating bodies.15th ONR,1984.
[44]Dommermuth, D.G. and Yue, D.K.P. Numerical simulations of nonlinear axisymmetric flows with a free surface. Journal of Fluid Mechanics,178, 1987:195-219P.
[45]Yang, C. Time domain computation of nonlinear wave forces on 3-D body. Ph.D. thesis, Shanghai Jiao Tong University,1987.
[46]周正全.三维物体与非线性波浪的相互作用.中国船舶科学研究中心博士论文,1988.
[47]Romate, J.E. The numerical simulation of nonlinear gravity waves in three dimensions using a higher order panel method. Ph.D. thesis, University of Twente, The Netherlands,1989.
[48]Broeze, J. Numerical modelling of nonlinear free surface waves with a 3D panel method. Ph.D. thesis, University of Twente, The Netherlands,1993.
[49]van Daalen, E.F.G.. Numerical and theoretical studies of water waves and floting bodies. Ph.D. thesis, University of Twente, The Netherlands,1993.
[50]de Hass, P. Numerical simulation of nonlinear water waves using a panel method:domain decomposition and applications. Ph.D. thesis, University of Twente, The Netherlands,1997.
[51]Kring, D.C., Korsmeyer, F.T., Singer, J., Danmeier, D. and White, J. Accelerated non-linear wave simulations for large structures.7th International Conference on Numerical Ship Hydrodynamics, Nantes, France, July 1999.
[52]Kring, D.C., Korsmeyer, F.T., Singer, J. and White, J. Analyzing mobile offshore bases using accelerated boundary-element methods. Marine Structures,13,200:301-313P.
[53]Skourup, J. and Jonsson, I.G. Computations of forces on, and particle orbits around, horizontal cylinders under steep waves. Ocean Engineering,19(6), 1992:527-553P.
[54]Ferrant, P. Three-dimensional unsteady wave-body interactions by a
Rankine boundary element model. Ship Technology Research,40(4), 1993:165-175P.
[55]Ferrant, P. Simulation of strongly nonlinear wave generation and wave-body interactions using a 3-D MEL model. Proceedings of the 21st ONR Symposium on Naval Hydrodynamics, Trondheim, Norway, 1996:93-109P.
[56]Kim, M.H., Celebi, M.S. and Kim, D.J. Fully non-linear interactions of waves with a three-dimensional body in uniform currents. Applied Ocean Research,20(5),1998:309-321P.
[57]Landrini, M., Gryt Φ yr, G. and Faltinsen, O.M. A B-spline based BEM for unsteady free-surface flows. Journal of Ship Research, Vol.43, No.1, March 1999:13-24P.
[58]Beck, R.F. Time-domain computations for floating bodies. Applied Ocean Research,16,1994.
[59]Beck, R.F., Cao, Y., Scorpio, S.M. and Schultz, W. Non-linear ship motions computations using the desingularized method. Proceedings 20th Symposium on Naval Hydrodynamics, Santa Borbara, Colifornia,1994.
[60]Scorpio, S.M., Beck, R.F. and Korsmeyer, F.T. Non-linear water wave computations using a multipole accelerated, desingularized method. Proceedings 21st Symposium on Naval Hydrodynamics, Trondheim, 1996:34-43P.
[61]Scorpio, S.M. Fully nonlinear ship-wave computations using a multipole accelerated, desingularized method. Ph.D. thesis, Naval Architecture and Marine Engineering in The University of Michigan,1997.
[62]Maniar H. D. A B-spline based higher order method in 3D.10th International Workshop on Water Waves and Floating Bodies, Oxford, UK, 1995:153-I58P.
[63]Teng B, Li Y C. A unique solvable higher order BEM for wave diffraction and radiation. China Ocean Engineering,1996,10(3):333-342P.
[64]柏威.非线性波浪与任意三维物体的相互作用.大连：大连理工大学,2001.
[65]张晓兔.基B样条的三维船体水动力数值计算研究.武汉：武汉理工大学,2002.
[66]钱昆.浮体在大幅波浪中的运动和载荷的计算研究.大连：大连理工大学,2004.
[67]谬国平.挠性部件力学导论.上海交通大学出版社,1995.
[68]Korkutm, M. D. and Hebert, E. J. Some notes on static anchor chain curve. OTC,1971, OTC# 1160:147-155P.
[69]Pedersen, P. T. Equilibrium of offshore cables and pipeline during laying. International Shipbuilding Progress,1975,22:399-408P.
[70]Pangalila, F. V. and Martin, J. P. A method of estimating line tensions and motions of a semi-submersible based on empirical data and model basis results. OTC,1969,2:90-96P.
[71]Gault, A. J. and Cox, W. R. Method for predicting geometry and loading distribution in an anchor chain from a single point mooring buoy to a buried anchorage. OTC,1973,1:309-318P.
[72]马汝建,高学仕.悬链线锚链的非线性恢复系数.中国海洋平台,1994,21：180-183页
[73]马鉴恩,李凤来.锚泊列阵的设计研究.海洋工程,1996,14(2)：52-62页
[74]陈广莲.确定锚泊设备的直接计算法.船舶设备通讯,2004,109(1)：43-50页
[75]Smith, T. M., Chen, M. C. and Radwan, A. M. Systematic data for the preliminary design of mooring systems. Proceedings of the fourth International Offshore Mechanics and Arctic Engineering Symposium, 1985,1:403-407P.
[76]Smith, R. J. and MacFarlane, C. J. Statics of a three component mooring
line. Ocean Engineering,2001,28:899-914P.
[77]Chaff, Y. T., Varyani, K. S. and Barltrop, D. N. P. Semi-analytical quasi-static formulation for three 2 dimensional partially grounded mooring system problems. Ocean Engineering,2002,29:627-649P.
[78]余龙,谭家华.深水多成分悬链线锚泊系统优化设计及应用研究.华东船舶工业学院学报(自然科学版),2004,18(5)：8-13页
[79]余龙,谭家华.基于准静定方法的多成分锚泊线优化.海洋工程,2005,23(1)：69-73页
[80]陈徐均,汤雪峰等.系泊浮体布链方式优劣的理论分析.河海大学学报,2001,29(5)：1-9页
[81]陈徐均,崔维成,沈庆.对称式布置锚链系统的线性化处理.海洋工程,2002,22(1)：75-79页
[82]Hong, S. T. Frequency domain analysis for the tension in a taut mooring line. Technical Report NO.SM72-1, University of Washington,1972.
[83]Hong, S. T. Tension in a taut line mooring:frequency domain analysis. OTC,1974,2:389-400P.
[84]Connell, G. M. Analytical studies of resonance in taut-moored system. OTC, 1974,2:401-416P.
[85]Skop, R. A. and O'Hora, G. J. The static equilibrium configuration of cables arrays by use of the method of imaginary reaction. NRL Report NO.6819, AD68519,1969.
[86]Skop, R. A. and Kaplon, R. E. The static configuration of tri-moored surface, buoy cable array acted on by current-induced force. NRL Report NO.6894,AD65814,1969.
[87]Watson, T. V. and Kuneman, J. E. Determination of the static equilibrium configuration externally redundant submerged cable arrays. OTC,1975, 2:765-776P.
[88]Adams, R. B. Analysis of spread mooring by dimensional function. OTC,
1968,1:77-88P.
[89]Adams, R. B. Accuracy of the taut-tine position indicator for offshore drilling vessels. Trans. ASME J.of Eng. For Industry,1968, 90(1):161-171P.
[90]Collipp, B. G. Analyzing mooring line catenaries. Petroleum Engineering, 1968,40(5):72-80P.
[91]Charles, E. N. and Dominguez, R. F. Large displacement mooring dynamics. OTC,1977,1:19-30P.
[92]Orgill G, Wilson J. F. and Schmertmann G R. Static design of mooring arrays for offshore guyed towers. Applied Ocean Research,1985, 7(3):166-174P.
[93]Bliek A. Dynamic analysis of single span cables. Ph.D. thesis, MIT, Cambridge, MA, U.S.A.,1994.
[94]Triantafyllou M. S., Bliek A. & Shin, S. Dynamic analysis as a tool for open-sea mooring system design. Transactions SNAME,1985, 93:303-324P.
[95]Hover F. S., Grosenbaugh M. A. and Triantafyllou M. S. Calculation of dynamic tension in towed underwater cable. IEEE Journal of Oceanic Engineering,1994,19:449-457P.
[96]Thomas D. O. & Hearn G. E. Deepwater mooring line dynamics with emphasis on sea-bed interference effects. Offshore Technology Conference, 1991.
[97]Nakamura N., Koterayama W. and Kyozuka Y. Slow drift damping due to drag forces acting on mooring lines. Ocean Engineering,1991, 18:283-296P.
[98]Huang S. Dynamic analysis of 3-D marine cables. Ocean Engineering,1994, 21:587-605P.
[99]Korterayama W. Motions of moored floating body and dynamic tension of
mooring lines in regular waves. Rep. Res. Inst. Appl. Mech.1978.
[100]Korterayama W. and Nakamura, M. Hydrodynamic forces acting on a vertical circular cylinder oscillating with a very low frequency in waves. Ocean Engineering,1988,15(3):271-287P.
[101]Korterayama W. and Nakamura M. Drag and inertia force coefficients derived from field tests. International Journal of Offshore and Polar Engineering,1992,2(3):162-167P.
[102]李远林,吴家鸣.多锚链系泊浮筒非线性漂移运动的时域模拟.海洋过程,1990,8(1)：25-33页
[103]Toshio Nakajima. A study of the mooring dynamics of various types by lumped mass method. Ph. D. Thesis, University of Tokyo,1991.
[104]Nakajima T., Motors S. and Fujino M. On the dynamic responses of the moored object and the mooring lines in regular waves. Trans. Soc. Of naval arch. Of Japan,1981, No.150.
[105]Toshio Nakajima. On the dynamic analysis of mufti-component mooring lines.1982, OTC#4309:105-110.
[106]Burgess J.J. Equations of motion of a submerged cables with bending stiffness. Int. Offshore Mech. And Artic Eng. Conf., Calgary,1992, Vol.1-A:283-289P.
[107]Webster E.L. Nonlinear static and dynamic response of underwater cables structures using the finite element method. Offshore Technology Conference,1975, OTC#2322,2:754-764P.
[108]Hose E. Surge damping due to mooring lines friction on the seabed. RepN01.11 Research Programme Marine Structures, Mrintek,1985.
[109]Hose E. Influence of mooring line damping upon rig motions. OTC,1986, 2:433-438P.
[110]Hose,E. and Matsumoto,K. Practical estimation of mooring line damping. OTC,1988,2:543-552P.
[111]Hose E. and Matsumoto K. Mooring line damping due to first and second-order vessel motion. OTC,1989,2:135-148P.
[112]Hose E. Resonant heave damping of tension leg platforms. OTC,1990, 2:431-436P.
[113]Hose E. New developments in prediction of mooring system damping. OTC,1991,2:291-298P.
[114]Shashikala A.P. et. al. Dynamics of a moored barge under regular and random waves. Ocean Engineering,1997,24(5):401-430P.
[115]Leonard J.W. and Recker W.W. Nonlinear dynamics of cables with low initial tension. Journal of the Engineering Mechanics, Division,ASCE,1972, 98(2):204-234P.
[116]Leonard J.W. Curved finite element approximation to nonlinear cables. OTC,1972,1:225-233P.
[117]Chatjigeorgion L. K. and Mavrakos S. A. Nonlinear contributions in the prediction of dynamic tension on mooring lines for high and low frequencies of excitation. Proc.7th Int. Offshore and Polar Eng. Conf., Honolulu, ISOPE,1997,2:192-199
[118]Chatjigeorgion L.K. and Mavrakos S. A. Assessment of bottom cable interaction effects on mooring line dynamics. Int. Offshore Mech. And Artic Eng. Conf., Libson,1998, No.335
[119]Chatjigeorgion L. K. and Mavrakos S. A. Comparative study on the efficiency of improved numerical solutions schemes in the prediction of the dynamic behavior of mooring lines. Proc.9th Int. Offshore and Polar Eng. Conf., Brest, France, ISOPE,1999,2:332-339P.
[120]Chatjigeorgion L. K. and Mavrakos, S. A.. Comparative evaluation of numerical schemes for 2D mooring dynamics. International journal of offshore and polar engineering,2000,10(4):301-309 P.
[121]Kwan C. T. and Bruen F. J. Mooring line dynamics:comparison of time domain, frequency domain and quasi-static analysis. OTC,1988,2:513-521 P.
[122]Firewell M. L. Steady-state analysis of underwater cables. Journal of Waterway, Port, Cpastal and Ocean Engineering,1995,121(2):98-104 P.
[123]Wang C. M., Cheong H. F. and Chucheepsakul S. Static analysis of marine cables via shooting-optimization technique. Journal of waterway, port, Coastal and Ocean Engineering,1993,119(1):450-457 P.
[124]De Zoysa A.P.K. Steady-state analysis of under cables. Ocean Engineering, 1978,5:209-223P.
[125]徐兴平.单点系泊系统动力响应计算.中国海洋平台,1994,1：209-302页
[126]徐兴平,童英玉.单点系泊系统动力响应分析.石油大学学报(自然科学版),1994,18(5)：74-78页
[127]马汝建.单点系泊装置的非线性动力分析.石油大学学报(自然科学版),1994,18(5)；65-69P.
[128]谢炜,唐新铭.用于CALM系统分析的修正准静力方法.中国海洋平台.1994,1：243-248页.
[129]黄剑,朱克强.半潜式平台两种锚泊系统的静力分析与比较.华东船舶工业学院学报(自然科学版),2004,18(3)：1-5页.
[130]陈小红,黄祥鹿.单点系泊海洋资料浮标的动力分析.中国造船,1995,130：1-13页
[131]范菊,黄样鹿.锚泊线的动力分析.中国造船,1999,144：13-20P.
[132]范菊,陈小红,黄祥鹿.锚泊线一阶运动响应对二阶锚链阻尼的影响.船舶力学,2000,4：20-27页
[133]范菊,陈小红,黄样鹿,三阶摄动对锚泊线动力分析的影响.船舶力学,2000,4.
[134]黄祥鹿,陈小红,范菊.锚泊浮式结构波浪上运动的频域算法.上海交通大学学报,2001,45：1470-1476页
[135]陈小红,黄祥鹿.随机振荡法测量锚泊线动力的双频率响应函数.上海交
通大学学报,1995,29：13-19页
[136]范菊,纪亨腾,黄祥鹿.浮式塔的动力计算.海洋学报,2001,23：117-123页
[137]陈小红,马巍,黄祥鹿.双频锚泊线动力分析.上海交通大学学报,1993,27,5：1-8页
[138]周崇庆,刘土光和李天匀.风浪中锚泊渔船的锚链系泊张力的分析研究.中国水产科学,1999,6(3)：78-80页
[139]刘应中,缪国平,李谊乐等.系泊系统动力分析的时域方法.上海交通大学学报,1997,31(11)：7-12页
[140]李向群.多点系泊船舶在波浪中的运动及其系泊力.交通部上海船舶运输科学研究所学报,1999,22(1)：9-15页
[141]聂孟喜,王旭升,王晓明,张琳.风、浪、流联合作用下系统系泊力的时域计算方法.清华大学学报(自然科学版),2004,36(17)：1214-1217页
[142]张纬康,杜度.系泊船舶动力学特性的计算机仿真研究.中国造船,2002,45(4)：1-10页
[143]杜度,张宁,马骋,张纬康.系泊系统的时域仿真及其非线性动力学特性分析.船舶力学,2005,9(4)：37-45页
[144]Yeung R W. Numerical methods in free-surface flows. Fluid Mech.,1982,14：395-442页
[145]张廷芳.计算流体力学.大连理工大学出版社,1992.
[146]张景峤.细分曲面生成及其在曲面造型中的应用研究.杭州：浙江大学,2003.
[147]仵大伟.船体曲面表达与三维船舶设计研究.大连：大连理工大学,2002.
[148]林焰,纪卓尚.船体B样条曲面的数学描述及计算机方法.中国造船,1996,11(4)：20-24页
[149]陈绍平,陈宾康.基于NURBS曲线的双艉船型线设计研究.中国造船,2001：42(2)：7-11页
[150]ROGERS D F, SATTERFIELD S G. B-Spline surface for ship hull design. Computer Graphics,1980,14(3):211-217P.
[151]施法中.计算机辅助几何设计与非均匀有理B样条(CAGD & NURBS).高等教育出版社,2001.
[152]孙家广,杨长贵编著.计算机图形学(新版).北京：清华大学出版社,1995.
[153]易大义.数值方法.杭州：浙江科学技术出版社,1984.
[154]赵作智.基于非均匀有理B样条(NURBS)的曲面反求的研究.北京：清华大学,2003.
[155]Maniar H. D. A B-spline based higher order method in 3D.10th International Workshop on Water Waves and Floating Bodies, Oxford, UK, 1995,153-158.
[156]Li H. B., Han G. M., Mang H. A. A new method for evaluating singular integral in stress analysis of solids by the direct boundary element method. Int. Jour, for Num. Math. In Eng.,1985,211,2071-2075P.
[157]戴遗山,段文洋.船舶在在波浪中运动的势流理论.北京：国防工业出版社,2008：90-98页
[158]Wehausen J V, Laitone E V Surface wave. Handbuch der Physik, IX,Berlin, springer-Verlag,1960,468-512P.
[159]Chau F P. The second order velocity potential for diffraction of waves by fixed offshore structures. Department of Mechanical Engineering, University College London, Ph.D. thesis,1989.
[160]Eatock Taylor R, Chau F P. Wave diffraction-some development in linear and non-linear theory. Jour. of Offshore Mech. and Arctic. Eng.,1992, 114,185-194P.
[161]滕斌.波浪力计算中的一个新边界元方法.水动力学研究与进展,1994,9(2)：215-223页
[162]Teng B, Eatock Taylor R. New higher-order wave diffraction/radiation. App. Ocean Res.,1995,17,element methods for 71-77P.
[163]Wu, G. X., Eatock Taylor, R.,1989. The numerical solution of the motions of a ship advancing in waves. Proc.5th Int. Conf. on Numerical Ship Hydrodynamics, Hiroshima, Japan,3:86-94P.
[164]Lamb H. Hydrodynamics.Cambridge University Press,1932.
[165]Ohmatsu S. On the irregular frequencies in the theory of oscillating bodies. Papers, Ship Res. Inst., Japan, No.48,1975P.
[166]Saver P, Ursell F. Integral-equation methods for calculating the virtual mass in water of finite depths. Proc.2nd Int. Symp. Numerical Hydro. University of California,1977.
[167]Ogilvie T F, Shin Y S. Integral equation solutions for time-dependent free surface problems. J. Soc. Nav. Arch. Japan,1978,143.
[168]Kleinman R E. On the mathematical theory of motion of floating bodies[R]. DTNSRDC Report 82/074,1982.
[169]Lee Sclawouns. Removing the irregular frequencies from interval equations in wave-body interactions.J.fluidMech.,1989,207:393-418P.
[170]段文洋,贺五洲.一种消除水动力求解中不规则频率影响的边界元法.水动力学研究与进展,2002,17(2)：156-161 P.
[171]孙亮,腾斌.消除“不规则频率”的非连续高阶元方法.海洋工程,Nov.2004,22(4).
[172]Lee, C.-H., Newman, J. N., Zhu X. An extended boundary integral equation method for the removal of irregular frequency effects. Int. J. of Numerical Methods in Fluids,1996,23:637-660P.
[173]张海彬.FPSO储油轮与半潜式平台波浪载荷三维计算方法研究.哈尔滨工程大学博士论文,2003：32-98页
[174]徐福敏.单点系泊系统低频纵荡二阶力的频域计算.河海大学学报,1997,25(1)：103-106页
[175]陈徐均,吴有生,崔维成,孙芦忠.海洋浮体二阶非线性水弹性力学分析—系泊浮体主坐标响应的频率特征.船舶力学,2002,6(5)：44-57页
[176]Chen, X. B., Duan, W. Y., and Dai Y.S. Accurate computation of second-order low-frequency loads. Proceeding of 7th National Congress on Hydrodynamics and 19th National Conference on Hydrodynamics, Harbin,2005:57-74p.
[177]Chen, X. B. Approximation on the quadratic transfer functions of low-frequency loads.Proceeding of 5th International Conference on Numerical Ship Hydrodynamics, Hiroshima,1989:391-402P.
[178]Lee, C.-H. Wamit theory manual. Massachusetts Institute of Technology Department of Ocean Engineering, Cambridge,1995:1-44P.
[179]Newman, J.N. Process in wave load computation on offshore structure, OMAE 2004,Vancouver.
[180]Kim, M.-H., Yue, D. K. P.. The complete second-order diffraction solution for an axisymetric body—Part Ⅱ. Bichromatic incident waves and body motions. J. Fluid Mechanics,1990,211:557-593P.
[181]滕斌,李玉成,董国海.双色入射波下二阶波浪力响应函数.海洋学报,1999,21(2)：115-123页
[182]ZHIHUANG RAN. Coupled dynamic analysis of floating structures in waves and currents. Ph. D. Thesis, MIT, USA,2000.
[183]Techou C. Non-linear dynamics of mooring lines. Ph. D. Thesis, MIT, USA.1997.
[184]Chatjigeorgiou, IK., Mavrakos, SA. Nonlinear contributions in the prediction of the dynamic tension on mooring lines:for high and low frequencies of excitation. Proc.7th Int Offshore and Polar eng. Coraf.,Honolulu, ISOPE,1997,2:192-199P