航行船舶的非线性水弹性理论与应用研究
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摘要
船舶在大浪中航行时,其运动和波浪载荷均呈现明显的非线性;航行中船舶所受到的载荷以及由此引起的结构变形和破坏实质上都是一个动态的过程,利用传统的将水动力学问题与结构力学问题分开处理的方法具有一定的局限性,而从流固耦合的角度,建立大浪中航行船舶的非线性水弹性分析方法,深入研究与揭示大浪中航行船舶的安全性,不仅具有理论上的合理性和创新性,而且具有重要的工程应用价值。
在过去的二十多年里,船舶水弹性力学理论和分析方法从二维发展到三维,从线性发展到非线性,并广泛应用到船舶与海洋工程中的流固耦合分析中,如大型船舶,高性能多体船和超大型浮体(VLFS)等的运动、载荷与结构响应评估等,逐渐发展成为一门具有广泛工程应用价值和发展潜力的新兴船舶力学学科分支。
本文在三维船舶水弹性力学领域里开展研究工作,首先着力于继承已有的三维线性船舶水弹性分析方法(Wu,1984;杜双兴,1996),并加以发展和完善,更为严格地考虑了航速与定常兴波流场对船舶水弹性响应的影响;然后在浮体二阶非线性水弹性理论(Wu,Maeda & Kinoshita,1997)基础上,考虑航速和定常兴波流场的影响,并计及大角度刚体运动和瞬时湿表面变化对非线性波浪力的贡献,建立了大浪中航行船舶的三维非线性水弹性分析方法。完成的主要研究工作如下:
(1)简要回顾船舶水弹性理论及相应数值分析方法的历史发展状况。并在Wu,Maeda & Kinoshita(1997)的理论基础上,考虑波浪中航行浮体周围流场的一阶速度势及其一阶响应对二阶水动力的贡献,推导了大浪中航行船舶的广义二阶非线性水弹性理论,并给出了广义三维非线性水弹性运动方程中各二阶波浪作用力水动力系数的表达式。
(2)对耐波性分析中的定常流场处理方法进行了总结,提出了一种去奇虚拟源汇分布法,可以数值求解航行船体非均匀定常兴波流场速度势的高阶偏微分,以潜航椭球体为例进行了计算,经与理论解进行比较,对于没有尖角的光滑曲面,验证了该方法的有效性。另外,利用Kim(2005)给出的边界积分方法,当已知Havelock移动兴波源格林函数及其一阶偏微分量,也可求得定常航行船舶流场速度势的高价偏导数。
(3)考虑定常兴波流场的影响,发展了航行船舶的三维线性水弹性力学分析程序,并以潜航椭球体,水面上航行的可变形半椭球体和SWATH船型为例,探讨了定常兴波流场、叠模流场与均匀流场模型对水弹性响应计算结果的影响。
(4)考虑弹性船舶周围非均匀稳态兴波流场的影响,并计及瞬时湿表面变化与大角度刚体运动引起的非线性水动力,建立了大浪中航行船舶的三维二阶非线性水弹性力学分析方法与程序,并以不规则波中航行的小水线面双体船为例,给出了计及二阶波浪力作用下的航行船体的变形、应力等结果。
(5)基于线性和非线性水弹性分析方法,对波浪中零航速驻留及有航速航行的SWATH外载荷进行了理论预报,并与试验结果进行了比较。
本文的工作,使得采用统一的方法,同时预报大浪中航行船舶(含零航速浮体)的线性和非线性水弹性响应成为可能,不仅在数学上更为接近Bishop,Price & Wu(1986)和Wu,Maeda & Kinoshita(1997)的理论模型,而且在数值上较以前的工作(杜双兴,1996;陈徐均,2001)更为严密地考虑了航速的影响。本文的主要创新点是:
(1)吸收已有的耐波性分析中定常流场处理方法,提出了一种去奇虚拟源汇分布法,能够数值求解航行船体三维非均匀定常兴波流场速度势的高阶偏微分量,对一潜航椭球体的算例表明,数值预报结果与理论解吻合一致;
(2)首次在三维船舶线性水弹性分析中,考虑了定常兴波流场的影响,发展了航行船舶的三维线性水弹性力学分析程序(THAFTS),并利用移动脉动源格林函数,较严格地计及了航速对水弹性响应的影响;
(3)首次建立了计及定常兴波流场影响的航行船舶的二阶非线性水弹性力学分析方法,可同时预报任意形状浮体的兴波流场、在大浪中的运动、结构动载荷与动应力,并首次给出了随机波浪中航行船舶的三维非线性水弹性响应的算例(Tian & Wu,2006a);
(4)首次将三维非线性水弹性理论应用于SWATH的实船计算,并系统分析了其阻力、运动、载荷、变形、应力等结果,得出的结论对高性能双体和多体船舶的工程设计和应用,具有一定的参考价值。
最后,本文发展的非线性水弹性分析方法也同样适用于常规船型,这对我国船舶检验部门发展基于全船直接载荷计算(DLA)的船体结构疲劳分析方法,也具有重要的现实意义。
When a ship is moving in the large amplitude waves, the motions and wave loads shows evident nonlinear character; In addition, the loads of the traveling ship and the structural deflections and damage actually are a dynamic process. The traditional analysis method which deals with the hydrodynamic and structural problems respectively has certain disadvantages. While it has great engineering practical value to establish the nonlinear hydroelastic analysis method for ships moving in large amplitude waves, taking the perspective of the fluid structure interaction. This method which can be used to study the safety performance of the traveling ships in rough sea is also rational and original theoretically.
In the past two decades, the theory and corresponding numerical analysis methods of hydroelasticity of ships have been developed from two dimensional to three dimensional, from linear to nonlinear. The hydroelasticity theory has been extensively applied to a wide range of fluid structure interaction problems in the field of naval architecture and ocean engineering, such as the motions, loads and the structural responses assessment of the large scale ships, high performance multi-hull ships and Very Large Floating Structures (VLFS). The theory of hydroelasticity is now a new rising subject with great importance and potential of further development and engineering application.
The present research works are developed in the field of three dimensional hydroelasticity of ships. Firstly the available three dimensional linear hydroelastic analysis methods(Wu, 1984; Du, 1996) of ships are inherited and are extened to accounting for the influence of the forward speed and the steady wave flow effects to the hydroelastic responses of ships numerically more rigorously; Based on the second order nonlinear hydroelasticity (Wu, Maeda & Kinoshita, 1997) of floating body, including the forward speed and steady wave flow effectrs, taking into account the nonlinear hydrodynamic actions induced by the the large rigid body motions and variation of the instantaneous wetted surface area, the three dimensional nonlinear hydroelastic analysis methods for ships moving in large amplitude waves are established. The following works have been achieved in the present thesis:
(1) A brief review on the development history of the hydroelasticity theory of ships and the corresponding numerical methods has been given. Based on the theoretical foundations of Wu, Maeda & Kinoshita (1997), the generalized second-order nonlinear hydroelastic theory for ships with forward speed in rough seas is deduced, only considering the contribution of the first order velocity potentials responses to the second order hydrodynamic forces. The formulations for each second order hydrodynamic coefficients in the general three dimensional nonlinear hydroelastic motion equations are presented.
(2) The state of the art of the analysis methods dealing with the steady flow fields in seakeeping theory has been summarized. A simple desingularized virtual panel method is proposed which can be used to solve the higher order derivatives of the non-uniform steady wave flow velocity potential. A moving submerged ellipsoid is selected as an example and the computation results are compared with the analytical solutions, showing that this method is useful and effective, particularly for smoothed surfaces without sharp corners. In addition, applying the boundary integral formula derived by Kim (2005), the higher order derivatives of the velocity potential when the ship is moving steadily can also be solved numerically by using the Havelock translating source Green function and the first order partial derivatives.
(3) Including the steady wave flow effects, the three-dimensional hydroelastic analysis program of ships with forward speed is developed. The moving submerged ellipsoid and a water-piecing elastic half-ellipsoid like ship and a SWATH ship is utilized as the numerical models to study the influences of the uniform flow, double body flow and steady wave flow model to the hydroelastic responses.
(4) Taking into account the non-uniform steady wave flow surrounding the elastic ship hull, the nonlinear hydrodynamic actions induced by the rigid body rotations and the variation of the instantaneous wetted surface area are deduced, the three dimensional second order nonlinear hydroelastic analysis methods of ships moving in large amplitude waves are established. The differences of the predicted linear and nonlinear responses (deflections, stresses) are illustrated by the numerical examples of a SWATH ship traveling with forward speed in irregular waves.
(5) Based on the previously linear and nonlinear hydroelastic analysis method, the wave loads of the SWATH ship in waves with and without forward speed are predicted and compared with the model tests data abailable.
The present work provide the possibility of predicting both the linear and nonlinear hydroelastic responses of traveling ships or floating structures in large amplitude waves, mathematically more close to the theoretical formulae presented by Bishop et al (1986) and Wu, Maeda & Kinoshita (1997), and numerically more rigorously accounting for the forward speed effect than the previous work (Du, 1996; Chen, 2001). The main points of originality in this dissertation are as follows:
(1) Based on the available steady flow analysis method in the seakeeping theory, a desingularized virtual panel method is proposed which can be used to solve the higher order derivatives of the non-uniform steady wave flow velocity potential. The numerical example of a submerged moving ellipsoid shows that the computation results correlates well with the analytical results.
(2) The steady wave flow effects is firstly included in the three dimensional hydroelastic analysis of ships, a more rational three dimensional hydroelastic analysis of ships with forward speed is developed (THAFTS). In addition the translating and pulsating source Green function is utilized to accounting for the forward speed effects more rigorously in the hydroelastic responses.
(3) Aaccounting for the steady wave flow effects, the second order nonlinear hydroelastic analysis methods are established firstly, which can be used to predict the steady wave flow, motins and the dynamic wave loads and stresses of arbitrary shape floating structures with forward speed in large amplitude waves. A numerical example (Tian & Wu, 2006a) is given for the first time to illustrate the three dimensional nonlinear hydroelastic responses of ships with forward speed in random waves.
(4) The 3D nonlinear hydroelasticity theory is firstly applied in a real SWATH ship, and the wave resistance, motions, wave loads, deflections and stresses are systematically analyzed. The conclusions drawn here may have some reference value to the practical design and application of the high performance catamaran and multi-hulled ships.
Finally, the nonlinear hydroelastic analysis method developed in the present thesis can also be applied to the conventional ships. It has significant practical value in develping the ship structure fatigue analysis method based on the direct loads calculation (DLA) for the classification societies.
在过去的二十多年里,船舶水弹性力学理论和分析方法从二维发展到三维,从线性发展到非线性,并广泛应用到船舶与海洋工程中的流固耦合分析中,如大型船舶,高性能多体船和超大型浮体(VLFS)等的运动、载荷与结构响应评估等,逐渐发展成为一门具有广泛工程应用价值和发展潜力的新兴船舶力学学科分支。
本文在三维船舶水弹性力学领域里开展研究工作,首先着力于继承已有的三维线性船舶水弹性分析方法(Wu,1984;杜双兴,1996),并加以发展和完善,更为严格地考虑了航速与定常兴波流场对船舶水弹性响应的影响;然后在浮体二阶非线性水弹性理论(Wu,Maeda & Kinoshita,1997)基础上,考虑航速和定常兴波流场的影响,并计及大角度刚体运动和瞬时湿表面变化对非线性波浪力的贡献,建立了大浪中航行船舶的三维非线性水弹性分析方法。完成的主要研究工作如下:
(1)简要回顾船舶水弹性理论及相应数值分析方法的历史发展状况。并在Wu,Maeda & Kinoshita(1997)的理论基础上,考虑波浪中航行浮体周围流场的一阶速度势及其一阶响应对二阶水动力的贡献,推导了大浪中航行船舶的广义二阶非线性水弹性理论,并给出了广义三维非线性水弹性运动方程中各二阶波浪作用力水动力系数的表达式。
(2)对耐波性分析中的定常流场处理方法进行了总结,提出了一种去奇虚拟源汇分布法,可以数值求解航行船体非均匀定常兴波流场速度势的高阶偏微分,以潜航椭球体为例进行了计算,经与理论解进行比较,对于没有尖角的光滑曲面,验证了该方法的有效性。另外,利用Kim(2005)给出的边界积分方法,当已知Havelock移动兴波源格林函数及其一阶偏微分量,也可求得定常航行船舶流场速度势的高价偏导数。
(3)考虑定常兴波流场的影响,发展了航行船舶的三维线性水弹性力学分析程序,并以潜航椭球体,水面上航行的可变形半椭球体和SWATH船型为例,探讨了定常兴波流场、叠模流场与均匀流场模型对水弹性响应计算结果的影响。
(4)考虑弹性船舶周围非均匀稳态兴波流场的影响,并计及瞬时湿表面变化与大角度刚体运动引起的非线性水动力,建立了大浪中航行船舶的三维二阶非线性水弹性力学分析方法与程序,并以不规则波中航行的小水线面双体船为例,给出了计及二阶波浪力作用下的航行船体的变形、应力等结果。
(5)基于线性和非线性水弹性分析方法,对波浪中零航速驻留及有航速航行的SWATH外载荷进行了理论预报,并与试验结果进行了比较。
本文的工作,使得采用统一的方法,同时预报大浪中航行船舶(含零航速浮体)的线性和非线性水弹性响应成为可能,不仅在数学上更为接近Bishop,Price & Wu(1986)和Wu,Maeda & Kinoshita(1997)的理论模型,而且在数值上较以前的工作(杜双兴,1996;陈徐均,2001)更为严密地考虑了航速的影响。本文的主要创新点是:
(1)吸收已有的耐波性分析中定常流场处理方法,提出了一种去奇虚拟源汇分布法,能够数值求解航行船体三维非均匀定常兴波流场速度势的高阶偏微分量,对一潜航椭球体的算例表明,数值预报结果与理论解吻合一致;
(2)首次在三维船舶线性水弹性分析中,考虑了定常兴波流场的影响,发展了航行船舶的三维线性水弹性力学分析程序(THAFTS),并利用移动脉动源格林函数,较严格地计及了航速对水弹性响应的影响;
(3)首次建立了计及定常兴波流场影响的航行船舶的二阶非线性水弹性力学分析方法,可同时预报任意形状浮体的兴波流场、在大浪中的运动、结构动载荷与动应力,并首次给出了随机波浪中航行船舶的三维非线性水弹性响应的算例(Tian & Wu,2006a);
(4)首次将三维非线性水弹性理论应用于SWATH的实船计算,并系统分析了其阻力、运动、载荷、变形、应力等结果,得出的结论对高性能双体和多体船舶的工程设计和应用,具有一定的参考价值。
最后,本文发展的非线性水弹性分析方法也同样适用于常规船型,这对我国船舶检验部门发展基于全船直接载荷计算(DLA)的船体结构疲劳分析方法,也具有重要的现实意义。
When a ship is moving in the large amplitude waves, the motions and wave loads shows evident nonlinear character; In addition, the loads of the traveling ship and the structural deflections and damage actually are a dynamic process. The traditional analysis method which deals with the hydrodynamic and structural problems respectively has certain disadvantages. While it has great engineering practical value to establish the nonlinear hydroelastic analysis method for ships moving in large amplitude waves, taking the perspective of the fluid structure interaction. This method which can be used to study the safety performance of the traveling ships in rough sea is also rational and original theoretically.
In the past two decades, the theory and corresponding numerical analysis methods of hydroelasticity of ships have been developed from two dimensional to three dimensional, from linear to nonlinear. The hydroelasticity theory has been extensively applied to a wide range of fluid structure interaction problems in the field of naval architecture and ocean engineering, such as the motions, loads and the structural responses assessment of the large scale ships, high performance multi-hull ships and Very Large Floating Structures (VLFS). The theory of hydroelasticity is now a new rising subject with great importance and potential of further development and engineering application.
The present research works are developed in the field of three dimensional hydroelasticity of ships. Firstly the available three dimensional linear hydroelastic analysis methods(Wu, 1984; Du, 1996) of ships are inherited and are extened to accounting for the influence of the forward speed and the steady wave flow effects to the hydroelastic responses of ships numerically more rigorously; Based on the second order nonlinear hydroelasticity (Wu, Maeda & Kinoshita, 1997) of floating body, including the forward speed and steady wave flow effectrs, taking into account the nonlinear hydrodynamic actions induced by the the large rigid body motions and variation of the instantaneous wetted surface area, the three dimensional nonlinear hydroelastic analysis methods for ships moving in large amplitude waves are established. The following works have been achieved in the present thesis:
(1) A brief review on the development history of the hydroelasticity theory of ships and the corresponding numerical methods has been given. Based on the theoretical foundations of Wu, Maeda & Kinoshita (1997), the generalized second-order nonlinear hydroelastic theory for ships with forward speed in rough seas is deduced, only considering the contribution of the first order velocity potentials responses to the second order hydrodynamic forces. The formulations for each second order hydrodynamic coefficients in the general three dimensional nonlinear hydroelastic motion equations are presented.
(2) The state of the art of the analysis methods dealing with the steady flow fields in seakeeping theory has been summarized. A simple desingularized virtual panel method is proposed which can be used to solve the higher order derivatives of the non-uniform steady wave flow velocity potential. A moving submerged ellipsoid is selected as an example and the computation results are compared with the analytical solutions, showing that this method is useful and effective, particularly for smoothed surfaces without sharp corners. In addition, applying the boundary integral formula derived by Kim (2005), the higher order derivatives of the velocity potential when the ship is moving steadily can also be solved numerically by using the Havelock translating source Green function and the first order partial derivatives.
(3) Including the steady wave flow effects, the three-dimensional hydroelastic analysis program of ships with forward speed is developed. The moving submerged ellipsoid and a water-piecing elastic half-ellipsoid like ship and a SWATH ship is utilized as the numerical models to study the influences of the uniform flow, double body flow and steady wave flow model to the hydroelastic responses.
(4) Taking into account the non-uniform steady wave flow surrounding the elastic ship hull, the nonlinear hydrodynamic actions induced by the rigid body rotations and the variation of the instantaneous wetted surface area are deduced, the three dimensional second order nonlinear hydroelastic analysis methods of ships moving in large amplitude waves are established. The differences of the predicted linear and nonlinear responses (deflections, stresses) are illustrated by the numerical examples of a SWATH ship traveling with forward speed in irregular waves.
(5) Based on the previously linear and nonlinear hydroelastic analysis method, the wave loads of the SWATH ship in waves with and without forward speed are predicted and compared with the model tests data abailable.
The present work provide the possibility of predicting both the linear and nonlinear hydroelastic responses of traveling ships or floating structures in large amplitude waves, mathematically more close to the theoretical formulae presented by Bishop et al (1986) and Wu, Maeda & Kinoshita (1997), and numerically more rigorously accounting for the forward speed effect than the previous work (Du, 1996; Chen, 2001). The main points of originality in this dissertation are as follows:
(1) Based on the available steady flow analysis method in the seakeeping theory, a desingularized virtual panel method is proposed which can be used to solve the higher order derivatives of the non-uniform steady wave flow velocity potential. The numerical example of a submerged moving ellipsoid shows that the computation results correlates well with the analytical results.
(2) The steady wave flow effects is firstly included in the three dimensional hydroelastic analysis of ships, a more rational three dimensional hydroelastic analysis of ships with forward speed is developed (THAFTS). In addition the translating and pulsating source Green function is utilized to accounting for the forward speed effects more rigorously in the hydroelastic responses.
(3) Aaccounting for the steady wave flow effects, the second order nonlinear hydroelastic analysis methods are established firstly, which can be used to predict the steady wave flow, motins and the dynamic wave loads and stresses of arbitrary shape floating structures with forward speed in large amplitude waves. A numerical example (Tian & Wu, 2006a) is given for the first time to illustrate the three dimensional nonlinear hydroelastic responses of ships with forward speed in random waves.
(4) The 3D nonlinear hydroelasticity theory is firstly applied in a real SWATH ship, and the wave resistance, motions, wave loads, deflections and stresses are systematically analyzed. The conclusions drawn here may have some reference value to the practical design and application of the high performance catamaran and multi-hulled ships.
Finally, the nonlinear hydroelastic analysis method developed in the present thesis can also be applied to the conventional ships. It has significant practical value in develping the ship structure fatigue analysis method based on the direct loads calculation (DLA) for the classification societies.
引文
[1] Ahmed, T. M., Hudson, D.A. and Temarel P., 2004, Incorporation of steady flow effects in linear three-dimensional seakeeping predictions for high speed hulls, Proceedings of 9th PRADS, Luebeck Travemuende, Germany, 496-503
[2] Akita, Y. and Ochi, K., 1954, Investigations on the strength of ships going in waves by model experiments, J. of the Soc. of Naval Arch. of Japan, 95
[3] Akita, Y. and Ochi, K., 1955, Model experiment on the strength of ships moving in waves, Trans. SNAME, 63, 203-236
[4] Aksu, S., Bishop, R.E.D., Price, W.G., et al., 1990, On the behavior of a product carrier in ballast traveling in a seaway, Trans. RINA, W2
[5] Aksu, S., Price, W.G. and Suhrbier, K.R., et al., 1993, A comparative study of the dynamic behavior of fast patrol boat traveling in rough sea, Marine Structure, 6(5~6), 421-441
[6] Aksu, S., Price, W.G. and Temarel, P., 1991, A comparison of two-dimensional and three-dimensional hydroelasticity theories including the effect of slamming, Journal of Mechanical Engineering Science, 205, 3-15
[7] Baar, J.J.M. and Price, W.G., 1988, Evaluation of the wavelike disturbance in the Kelvin wave source potential, 32(1), 44-53
[8] Bai, K.J., Kim, S.E., Kim, J.W., 1988, The cross flow effect on the force and moment acting on a SWATH ship, 17th Symposium on Naval Hydrodynamics, The Hague, the Netherlands,
[9] Belik, O., Bishop, R.E.D. and Price, W.D., 1980, On the slamming response of ships to regular head waves, Trans. RINA, 122, 325-337
[10] Bertram, V., 1998, Numerical investigation of steady flow effects in three-dimensional seakeeping computations. 22th Symposinum on Naval Hydrodynamics, 417-431
[11] Bertram, V., 2002, Practical Ship Hydrodynamics, Butterworth-Heinemann
[12] Bessho, M., 1964, On the fundamental function in the theory of the wave-making resistance of ships, Memoirs of the Defense Academy of Japan, 4(2), 99-119
[13] Bessho, M., 1977, On the fundamental singularity in the theory of ship motion in a seaway, Memoirs of the Defense Academy Japan, 17(8), 95-105
[14] Betts, C.V., Bishop, R.E.D. and Price, W.G., 1977, The symmetric generalized fluid forces applied to a ship in a seaway, Trans. RINA, 199, 265-278
[15] Bingham, A.E., Hampshire, J.K., Miao, S.H., et al., 2001, Motions and loads of a trimaran traveling in waves. Proc. 6th International Conference on Fast Sea Transportations FAST’01, II, 167-176
[16] Bingham, H.B. and Maniar H.D., 1996, Computing the double-body m-terms using aBspline based panel method, 11th Int. Workshop on Water Waves and Floating Bodies. Hamburg, German
[17] Bishop, R.E.D. and Price, W.G., 1977, The generalized antisymmetric fluid forces applied to a ship in a seaway, International Shipbuilding Progress, 24, 3-14
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