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本文采用比例边界有限元方法(SBFEM), 获得了三维短峰波对带双层开孔外筒的圆筒新型结构水动力相互作用的半解析解. SBFEM综合了有限元(FEM)和边界元(BEM)法的优点, 使问题降阶一维, 而又不需要基本解, 不出现奇异性问题, 自动满足无穷远边界条件. SBFEM将整个计算域分成两个有限子域和一个无限子域, 利用变分原理推导出各个子域波浪速度势沿径向变化所应满足的二阶常微分方程组(SBFEM控制方程), 针对有限子域和无限子域分别采用贝塞尔函数和汉克尔函数作为基函数进行解析求解. 数值算例表明, 本文所推荐的方法只需对最外筒边界进行离散, 采用少数节点便能得到高度精确的结果. 与单层开孔圆筒结构波动场的比较, 发现双层开孔结构对降低内筒所受波浪力效果更好. 进一步分析了短峰波的波浪参数、结构的形状参数及材料参数对整个结构所受波浪荷载及计算域波浪爬升的影响, 这为带双层开孔外筒的圆筒结构的水动力分析和结构设计提供了有价值的参考.Porous structure can effectively reduce the loads caused by the water wave, which results in lowering the cost of engineering project. The double porous shelter performs even better. Therefore, it receives much attention from researches. However, most of the previous studies dealing with the analysis of the interaction between water wave are porous structure were based on two-dimensional plane wave assumption. This can hardly reflect the real phenomena of complex wave action. In this paper, a semi-analytical solution to the hydrodynamic interaction between the three-dimensional short-crested wave and the cylindrical structure with double porous shelters is performed by employing the scaled boundary finite element method (SBFEM). The SBFEM possesses the advantages of finite element method (FEM) and boundary element method (BEM): the spatial dimension of the problem is reduced by one, no fundamental solution is needed and no singularity occurs. Meanwhile, this method can meet the infinity of the boundary condition automatically. In the SBFEM, the total computational domain is divided into three sub-domains, two ring-shaped finite sub-domains and one outer infinite sub-domain. A variational principle approach is proposed to establish the SBFE governing equations, which describe the variation of the velocity potential of wave motion in the radial direction. Bessel functions and Hankel functions are chosen as the basis functions for the solution of bounded and unbounded sub-domain problems, respectively. Numerical examples show that the proposed approach achieves very high accuracy and converges rapidly with quite few discretized nodes at the outer boundary. In comparison with the cylindrical structure with single porous shelter, the former performs better for the reduction of the water wave force. In addition, The influences of the wave parameters and the configuration of the structure on the system hydrodynamics, including the wave force, wave and diffracted wave contour are extensively examined. This research provides a valuable insight into the hydrodynamic analysis of cylindrical structure with double porous shelters and their structural design.
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Keywords:
- scaled boundary finite-element method /
- short-crested wave /
- Wave diffraction /
- double-layered porous cylindrical structure
[1] Jarlan G E 1961 Dock and Harbour Authority 486 394
[2] Huang Z H, Li Y, Liu Y 2011 Ocean Engineering 10 1031
[3] Chwang A T, Chan A T 1998 Annual Review of Fluid Mechanics 30 53
[4] Ojima R, Owaki T, Yamagata N, Komoto Y 1994 Proceedings of International conference on Hydro-Technical engineering for port and harbour construction Yokosuka Japan, October 19---21 1994 p 691
[5] Wang K H, Ren X. 1994 Ocean Engineering 21 343
[6] Zhu D T 2011 Chinese Ocean Engineering 25 201
[7] Darwiche M K M, Williams A N, Wang K H 1994 Journal of Waterway, Port, Coastal and Ocean Engineering 120 382
[8] Williams A N, Li W 1998 Ocean Engineering 25 195
[9] Williams A N, Li W, Wang K H 2000 Ocean Engineering 27 1
[10] Teng B,Han L, Li Y C. 2000 Chinese Ocean Engineering 14(3) 297
[11] Teng B, Han L, Li Y C 2001 Ocean Engineering 19 32 (in Chinese) [滕斌, 韩凌,李 玉成 2001 海洋工程 19 32]
[12] Teng B, Zhao M, Li Y C 2001 Acta Oceanologica Sinica 23 133 (in Chinese) [滕斌, 赵明, 李玉成 2001 海洋工程 23 133]
[13] Williams A N, Li W 2000 Ocean Engineering 27 841
[14] Sun L 2005 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese) [孙路 2005 博士学位论文 (大连: 大连理工大学)]
[15] Vijayalakshmi K, Neelamani S, Sundaravadivelu R 2007 Ocean Engineering 34 327
[16] Sankarbabu K, Sannasiraj S A, Sundar V 2008 Ocean Engineering 55 431
[17] Zhong Z, Wang K H 2008 Ocean Engineering 33 927
[18] Li Y C, Liu H J, Teng B 2005 Ocean Engineering 1 18 (in Chinese)[李玉成,刘洪杰,滕斌. 2005 海洋工程 1 18]
[19] Sawaragi T, Iwata K 1978 Coastal Engineering in Japan 21 63
[20] Kondo H Proceedings of Coastal Structures '79 ASCE, Virginia, March 14---16 1979 p962
[21] Wang H, Shen L Y, Wang Y 2011 Port & Waterway Engineering 2 (in Chinese) [汪宏, 沈丽玉, 王勇 2011 水运工程 2 21]
[22] Liu Y, · Li Y C, Teng B 2011 Journal of Engineering Mathematics DOI 10.1007/s10665-011-9484-2
[23] Tsai C P, Jeng D S, Hsu J R C 1994 Applied Ocean Research 6 317
[24] Deng Z G, Huang H 2010 Acta Physica Sinica 59 735 (in Chinese) [邓争光, 黄虎 2010 物理学报 59 735]
[25] Huang H, Yang L, Xia Y B 2010 Acta Physica Sinica 59 2182 (in Chinese) [黄虎, 杨丽, 夏应波 2010 物理学报 59 2182]
[26] Huang H, Xia Y B 2010 Acta Physica Sinica 59 3663 (in Chinese) [黄虎, 夏应波 2010 物理学报 59 3663]
[27] Huang H 2011 Acta Physica Sinica 60 074701 (in Chinese) [黄虎 2011 物理学报 60 074701]
[28] Wolf J P, Song C M 1996 International Journal for Numerical Methods in Engineering 13 2189
[29] Lin G, Liu J, Li J B 2011 IET Microwaves, Antennas& Propagation 12 1508
[30] Tao L B, Song H 2009 Journal of Waterway, Port, Coastal and Ocean Engineering 5 200
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[1] Jarlan G E 1961 Dock and Harbour Authority 486 394
[2] Huang Z H, Li Y, Liu Y 2011 Ocean Engineering 10 1031
[3] Chwang A T, Chan A T 1998 Annual Review of Fluid Mechanics 30 53
[4] Ojima R, Owaki T, Yamagata N, Komoto Y 1994 Proceedings of International conference on Hydro-Technical engineering for port and harbour construction Yokosuka Japan, October 19---21 1994 p 691
[5] Wang K H, Ren X. 1994 Ocean Engineering 21 343
[6] Zhu D T 2011 Chinese Ocean Engineering 25 201
[7] Darwiche M K M, Williams A N, Wang K H 1994 Journal of Waterway, Port, Coastal and Ocean Engineering 120 382
[8] Williams A N, Li W 1998 Ocean Engineering 25 195
[9] Williams A N, Li W, Wang K H 2000 Ocean Engineering 27 1
[10] Teng B,Han L, Li Y C. 2000 Chinese Ocean Engineering 14(3) 297
[11] Teng B, Han L, Li Y C 2001 Ocean Engineering 19 32 (in Chinese) [滕斌, 韩凌,李 玉成 2001 海洋工程 19 32]
[12] Teng B, Zhao M, Li Y C 2001 Acta Oceanologica Sinica 23 133 (in Chinese) [滕斌, 赵明, 李玉成 2001 海洋工程 23 133]
[13] Williams A N, Li W 2000 Ocean Engineering 27 841
[14] Sun L 2005 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese) [孙路 2005 博士学位论文 (大连: 大连理工大学)]
[15] Vijayalakshmi K, Neelamani S, Sundaravadivelu R 2007 Ocean Engineering 34 327
[16] Sankarbabu K, Sannasiraj S A, Sundar V 2008 Ocean Engineering 55 431
[17] Zhong Z, Wang K H 2008 Ocean Engineering 33 927
[18] Li Y C, Liu H J, Teng B 2005 Ocean Engineering 1 18 (in Chinese)[李玉成,刘洪杰,滕斌. 2005 海洋工程 1 18]
[19] Sawaragi T, Iwata K 1978 Coastal Engineering in Japan 21 63
[20] Kondo H Proceedings of Coastal Structures '79 ASCE, Virginia, March 14---16 1979 p962
[21] Wang H, Shen L Y, Wang Y 2011 Port & Waterway Engineering 2 (in Chinese) [汪宏, 沈丽玉, 王勇 2011 水运工程 2 21]
[22] Liu Y, · Li Y C, Teng B 2011 Journal of Engineering Mathematics DOI 10.1007/s10665-011-9484-2
[23] Tsai C P, Jeng D S, Hsu J R C 1994 Applied Ocean Research 6 317
[24] Deng Z G, Huang H 2010 Acta Physica Sinica 59 735 (in Chinese) [邓争光, 黄虎 2010 物理学报 59 735]
[25] Huang H, Yang L, Xia Y B 2010 Acta Physica Sinica 59 2182 (in Chinese) [黄虎, 杨丽, 夏应波 2010 物理学报 59 2182]
[26] Huang H, Xia Y B 2010 Acta Physica Sinica 59 3663 (in Chinese) [黄虎, 夏应波 2010 物理学报 59 3663]
[27] Huang H 2011 Acta Physica Sinica 60 074701 (in Chinese) [黄虎 2011 物理学报 60 074701]
[28] Wolf J P, Song C M 1996 International Journal for Numerical Methods in Engineering 13 2189
[29] Lin G, Liu J, Li J B 2011 IET Microwaves, Antennas& Propagation 12 1508
[30] Tao L B, Song H 2009 Journal of Waterway, Port, Coastal and Ocean Engineering 5 200
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