浙江舟山桁杆拖虾网的力学计算
|
摘要
随着东海区传统经济鱼类资源的衰退,捕捞虾类的作业逐步发展起来,到目前为止,浙江省海洋捕捞的虾类产量已达到37.9万t,占浙江省海洋捕捞总量的13%,其中桁杆拖虾网已发展成为一种主要作业方式。本文的目的是通过对桁杆拖虾网的力学计算,对桁杆拖虾作业作进一步的分析。
本文根据模型准则制作了模型网,根据实际生产拖曳速度设计模型水槽试验流速,在东京海洋大学动水槽中进行试验,并根据模型试验结果来推算桁杆拖虾网的力学性能。首先,通过对曳纲形状和张力的数值求解,计算出曳纲在拖曳过程中的形状和张力大小;其次,把桁杆等效为一个连续梁,通过求解三矩方程,推出了计算叉纲对桁杆拉力的计算方法,进而计算出桁杆所受到的弯矩和剪力,计算结果显示弯矩是以过桁杆中心点的直线成轴对称,而剪力是以桁杆中心点成点对称;对桁杆拉力最小的叉纲是桁杆两端的叉纲,而以两端到中心的第二根叉纲拉力最大;桁杆所受到的最大拉压应力远小于钢铁的许用应力,因此,我们可以把桁杆改用其他更经济、方便且许用应力允许范围内的材料来制作。最后,对拖虾网的分析,把网片看作充分柔软的薄膜曲面,利用无矩薄壳理论推出网片的形状与张力的基本微分方程,根据网目特殊结构,利用差分法对网片基本微分方程组进行数值求解。从计算拖虾网背网片的第一段网片看,这一段网片基本上呈现为平面网片;形状和受力在z轴方向上没有变化,这也基本符合实际情况。由于网内流态的不确定性,用差分计算方法计算也无法得到精确值,因此利用拖虾网的形状对网身和网囊进行了近似计算。从过网身和网囊的形状近似计算的结果与根据试验计算结果相吻合。
Along with the traditional economic fish resources of the East China Sea declining, beam shrimp trawl gradually developed. So far, the production of the shrimp in Zhejiang province on the East China Sea has reached three hundred and seventy nine thousand t, accounting for 13% of the total marine fish catch in Zhejiang province, the beam shrimp trawl has become a main pattern of fishing operation. The purpose of this Master thesis is to further analysis fishing operation by mechanics calculation of beam shrimp trawl.
This article is based on the model experiment, which was accomplished in the circulating water channel of Tokyo University of Marine Science and Technology, then according to the model experiments results to calculate the beam shrimp trawl mechanics nature. First, through the numerical solution of warp shape and tension, we can work out the warp shape and tension in the process of drag. Second, the beam is equivalent to a continuous beam. Through solving the three moment equation, we can deduce the method to calculate the tension of cross rope acting on the beam. Then figure out the bending moment and shearing force of the beam. The results show that the bending moment is ax symmetric with the line across the beam center, while the shearing force is point symmetry with the center. The cross ropes whose tension acting on the beam is minimum is the cross ropes on the two endpoints of beam, while the maximum tension cross ropes are the second ropes from the beam endpoints to the center, the maximum tension-compression of the beam under the max experiment trawl speed is far lesser then the allowable stress of steel. So the beam can be made of other material whose allowable stress permits. Last, the analysis of the beam shrimp trawl nets. The nets are regarded as full soft curved film surface. Using nonmomental theory of shell, the basic differential equations about shape and tension of nets were deduced. According to the special structure of mesh, the basic differential equations can be solved with finite difference method. From the results of the first section net solution, this section takes on plane net, the shape and tension in z-axis without change. It complies with the actual situation. Because of the uncertainty of the flow in the net, the precise value can’t be obtained with the finite difference method. Therefore, we can get the approximate value by the beam shrimp trawl net shape and the results match the tension of warp from the experiments results.
本文根据模型准则制作了模型网,根据实际生产拖曳速度设计模型水槽试验流速,在东京海洋大学动水槽中进行试验,并根据模型试验结果来推算桁杆拖虾网的力学性能。首先,通过对曳纲形状和张力的数值求解,计算出曳纲在拖曳过程中的形状和张力大小;其次,把桁杆等效为一个连续梁,通过求解三矩方程,推出了计算叉纲对桁杆拉力的计算方法,进而计算出桁杆所受到的弯矩和剪力,计算结果显示弯矩是以过桁杆中心点的直线成轴对称,而剪力是以桁杆中心点成点对称;对桁杆拉力最小的叉纲是桁杆两端的叉纲,而以两端到中心的第二根叉纲拉力最大;桁杆所受到的最大拉压应力远小于钢铁的许用应力,因此,我们可以把桁杆改用其他更经济、方便且许用应力允许范围内的材料来制作。最后,对拖虾网的分析,把网片看作充分柔软的薄膜曲面,利用无矩薄壳理论推出网片的形状与张力的基本微分方程,根据网目特殊结构,利用差分法对网片基本微分方程组进行数值求解。从计算拖虾网背网片的第一段网片看,这一段网片基本上呈现为平面网片;形状和受力在z轴方向上没有变化,这也基本符合实际情况。由于网内流态的不确定性,用差分计算方法计算也无法得到精确值,因此利用拖虾网的形状对网身和网囊进行了近似计算。从过网身和网囊的形状近似计算的结果与根据试验计算结果相吻合。
Along with the traditional economic fish resources of the East China Sea declining, beam shrimp trawl gradually developed. So far, the production of the shrimp in Zhejiang province on the East China Sea has reached three hundred and seventy nine thousand t, accounting for 13% of the total marine fish catch in Zhejiang province, the beam shrimp trawl has become a main pattern of fishing operation. The purpose of this Master thesis is to further analysis fishing operation by mechanics calculation of beam shrimp trawl.
This article is based on the model experiment, which was accomplished in the circulating water channel of Tokyo University of Marine Science and Technology, then according to the model experiments results to calculate the beam shrimp trawl mechanics nature. First, through the numerical solution of warp shape and tension, we can work out the warp shape and tension in the process of drag. Second, the beam is equivalent to a continuous beam. Through solving the three moment equation, we can deduce the method to calculate the tension of cross rope acting on the beam. Then figure out the bending moment and shearing force of the beam. The results show that the bending moment is ax symmetric with the line across the beam center, while the shearing force is point symmetry with the center. The cross ropes whose tension acting on the beam is minimum is the cross ropes on the two endpoints of beam, while the maximum tension cross ropes are the second ropes from the beam endpoints to the center, the maximum tension-compression of the beam under the max experiment trawl speed is far lesser then the allowable stress of steel. So the beam can be made of other material whose allowable stress permits. Last, the analysis of the beam shrimp trawl nets. The nets are regarded as full soft curved film surface. Using nonmomental theory of shell, the basic differential equations about shape and tension of nets were deduced. According to the special structure of mesh, the basic differential equations can be solved with finite difference method. From the results of the first section net solution, this section takes on plane net, the shape and tension in z-axis without change. It complies with the actual situation. Because of the uncertainty of the flow in the net, the precise value can’t be obtained with the finite difference method. Therefore, we can get the approximate value by the beam shrimp trawl net shape and the results match the tension of warp from the experiments results.
引文
[1]江明方,黄传平.舟山拖虾作业现状及其发展意见[J].海洋渔业,1996,18(4):167-169.
[2]宋海棠.东海虾类的生态群落和区系特征[J].海洋科学集刊,2002,44:124-133
[3]宋海棠,丁天明.东海北部拖虾渔业的现状与设立拖虾休渔期的建议[J].浙江水产学院学报,1997,16(4):256-261
[4]宋海棠,丁天明.东海北部海域虾类不同生态类群分布及其渔业[J].台湾海峡,1995,14(1):67-72
[5]杨永麟.脉冲惊虾仪使用意见的讨论[J].海洋水产科技,1996,2.:19-23
[6]浙江海洋水产研究所,中国科学院上海水产研究所.浙江省海洋渔具调查报告(内部资料)[M],1959:55-59
[7]浙江海洋水产研究所,浙江水产学院,舟山地区水产研究所.浙江省海洋渔具调查报告[M],1985:195-202
[8]宋海棠,俞存根,薛利建.东海经济虾蟹类[M],北京:海洋出版社,2006:1
[9]农业部渔业局主编.中国渔业年鉴[M],北京:中国农业出版社,2005:59-60
[10]俞存根.关于调整东海拖虾作业休渔期的建议,舟山市海洋渔业局资料
[11]B.A Christensen.Hydrodynamic modeling of fishing nets[A].IEEE OCEAN’75,New York:484-490
[12]Matt K. Broadhurst,Bottlenose Dolphins.Tursiops truncatus, Removing By-catch from Prawn-trawl Codends During Fishing in New South Wales, Australia Statistical Data Included[J].Marine fishery Review,1998:summer.
[13]Matt K. Broadhurst,Paul E. McShine,Roger B.Larsen Effects of twine diameter and mesh size in the body of prawn trawls on bycatch in Gulf St. Vincent, Australia[J].Fishery Bulletin,2000, 98(3):463-473
[14]Matt K. Broadhurst,Steve J. Kennelly,Steve Eayrs.Flow-related effects in Prawn-trawl codends: potential for increasing the escape of unwanted fish through square-mesh panels [J].Fishery Bulletin,1999,97(1):1-8.
[15]Steve Eayrs.Understanding fish and prawn behaviour: potential to reduce by catch in a tropical prawn fishery [J].Fishery Science, 2002,68(sup 1):367-370.
[16]M.Shamim Uddin Khan,Optimal Stock.Harvest and Effort Level of Bangladesh Trawl Shrimp Fishery– A Nonlinear Dynamic [J].Approach Journal of Agriculture & Rural development,2007,5(1&2):143-149
[17]Pingguo He,Vincent Balzano.Reducing the catch of small shrimps in the Gulf of Marine pink shrimp fishing with a size-sorting grid device [J].ICES Journal of Marine Science,2007,64(8):1551-1557
[18]张健,孙满昌,钱卫国.桁拖网不同网目结构网囊对主要鱼类的选择性研究[J].上海水产大学学报,2007,17(4):457-463
[19]张兴国,张英.浅谈桁拖网渔具渔法调整技术[J].中国水产,2003,12:75-76
[20]洪明进.选择性虾拖网渔具渔法研究[J].福建水产,2005,3:14-17
[21]孙满昌,姚来富.桁拖网作业中鱼虾分离的初步试验研究[J].海洋渔业,1998,3:111-115
[22]孙满昌,张健,樊伟.吕四渔场虾桁拖网最小网目尺寸的研究[J].海洋渔业,2002,3:120-124
[23]杨吝编译.澳大利亚减少对虾拖网副渔获物的技术措施[J].现在渔业信息,2001,16(11):16-20
[24]樊伟,孙满昌.桁拖网作业中鱼虾分离效果的试验研究[J].海洋渔业,2000,3:106-109
[25]Matt K. Broadhurst.Modifications to reduce by catch in prawn trawls: A review and framework for development [J].Reviews in fish Biology and fisheries,2000,10(1):27-60
[26]YU Congda,,CHEN Zhihai,CHEN Lianyuan.The rise and fall of electrical beam trawling for shrimp in the East China Sea: technology, fishery, and conservation implications [J].ICES Journal of Marine Science,2007,64(8):1592-1597
[27]A.Hoff,,H.Frost.Modelling combined harvest and effort regulations: the case of the Dutch beam trawl fishery for plaice and sole in the North Sea [J].ICES Journal of Marine Science,2008,65(6): 822-831
[28]HE P,DGOETHEL,T SMITH.Design and Test of a Topless Shrimp Trawl to Reduce Pelagic Fish Bycatch in the Gulf of Marine Pink Shrimp Fishery[J].Journal of Northwest Atlantic Fishery Science,2007,38:13-21
[29]罗炎标,张健,孙满昌[J].大鹏湾捕虾拖网渔获分隔试验的效果分析[J].南方水产,2007,3(1):14-19
[30]张健,孙满昌,罗炎标.广东大鹏湾虾拖网网囊网目选择性研究[J].海洋渔业,2007,29(2):166-173
[31]张兴国.桁拖网捕虾技术推广研究总结[J].海洋渔业,1995,1:11-13
[32]张健,孙满昌.桁拖网不同网目结构的网囊对虾类的选择性[J].中国水产科学,2008,15(4):667-676
[33]李善贞.双联式虾拖网渔具渔法试验报告[J].福建水产,1997,3:7-11
[34]洪明进,叶泉土,郑国富等.网板虾拖作业渔获物种类组成[J].福建水产,2003,4:27-29
[35]洪明进,沈长春,叶泉土等.选择性虾拖网崔广实验报告[J].福建水产,2007 ,4:35-37
[36]佘显炜,虞聪达..渔具力学[M].杭州:浙江科学技术出版社,2004:191
[37]SC/T 4011-1995,拖网模型水池试验方法[S].北京:中国标准出版社,1996
[38]松田皎,漁具物理学[M].东京:成山堂書店，2001:76
[39]Fuxing HU,Tadashi TOKAI,Seiichi TAKEDA.The Performance of the New circulating Water Channel of Tokyo University of Marine Science and Technology[J].Fisheries Engineering,2004,41(2):153-163
[40]宣立强.拖网曳纲形状与张力的计算机模拟[J].湛江海洋大学学报,2005,25(3):90-93
[41]李晓平,王树新,何漫丽等.水下拖曳柔索的动力学理论模型研究[J].中国海洋平台,2003,18(3):31-91
[42]佘显炜.拖网曳纲力学计算的研究[J].浙江水产学报,1994,13(4):225-233
[43]佘显炜.水流和波浪作用下渔具锚链张力和形状计算的研究[J].浙江海洋学院学报(自然科学版),2006,25(3):237-253
[44]Alekseev N.I.Determination of the hydrodynamic characteristics of the warp at sea[J].Rybnoe khozyaistvo Moskva 1964,40(1):56-58
[45]Chubarov S.N.The effect of hydrodynamic forces on wires and the choice of wire for high speed and deep-sea trawling[J].Rybnoe khozyaistvo Moskva,1962,38(5):45-49
[46]Griffin O.M.,Kandiver J.K., Skop R.A.The strumming vibrations of marine cables[J].Ocean Science and Engineer,1982,7(4):461-498
[47]宮崎芳夫,高橋正．網地の流体抵抗に関する基礎的研究——(Ⅱ)[J].Journal of the Tokyo University of Fisheries,1964,50(2):89-94
[48]宮崎芳夫,高橋正．網地の流体抵抗に関する基礎的研究——(Ⅴ)[J].Journal of the Tokyo University of Fisheries,1964,50(2):111-123
[49]佘显炜.计算渔具力学导论[M].上海:上海科学技术文献出版社,2001:9
[50]哈尔滨工业大学理论力学教研室编.理论力学[M].北京:高等教育出版,1988:13
[51]梁治明,邱侃,陆耀洪.材料力学[M].北京:人民教育出版社,1958:260-271
[52]CHUN-WOO.LEE . Dynamic Analysis and Control Technology in a Fishing Gear System[J].FISHERIES SCIENCE,2002,68:1835-1840
[53]BONG-JIN.CHA,CHUN-WOO.LEE.Dynamic Simulation of a Midwater Trawl System’s Behavior [J].FISHERIES SCIENCE,2002,68:1865–1868
[54]万荣,何鑫,王欣欣等.一种适用于网箱耐流特性有限元分析的网目群化方法[J].中国海洋大学学报,2007,37(6):885-888
[55]苏炜,詹杰民.效网面法在模拟网的水动力特性中的应用[J].水动力学研究与进展,2007,22(3):267-272
[56]佘显炜.刺网网片张力和形状的计算[A].佘显炜.计算渔具力学导论[M].上海:上海科学技术文献出版社,2001:260-264
[57]张立英,侯恩淮,张春桂等.用计算机计算拖网网片的减裁与吃扣缝合[J].中国水产科学,1994,1(1):61-65
[58]佘显炜.剪裁网片形状和张力的计算[A].中国水产捕捞学会研讨会论文集,苏州:苏州大学出版社,1997
[59]宮崎芳夫,高橋正．網地の流体抵抗に関する基礎的研究——(Ⅵ)[J].Journal of the Tokyo University of Fisheries,1964,50(2):124-130
[60]T.Kowalski,J.Giawnotti.Calculation of fishing net drag [A].Mar.Tech.Rep.Univ.R.I,1974,15:26
[61]单辉祖,材料力学(Ⅰ)[M].北京:高等教育出版社:2003:303
[62]А.Л.弗里德曼,渔具理论与设计[M].北京:海洋出版社:1988:71
[2]宋海棠.东海虾类的生态群落和区系特征[J].海洋科学集刊,2002,44:124-133
[3]宋海棠,丁天明.东海北部拖虾渔业的现状与设立拖虾休渔期的建议[J].浙江水产学院学报,1997,16(4):256-261
[4]宋海棠,丁天明.东海北部海域虾类不同生态类群分布及其渔业[J].台湾海峡,1995,14(1):67-72
[5]杨永麟.脉冲惊虾仪使用意见的讨论[J].海洋水产科技,1996,2.:19-23
[6]浙江海洋水产研究所,中国科学院上海水产研究所.浙江省海洋渔具调查报告(内部资料)[M],1959:55-59
[7]浙江海洋水产研究所,浙江水产学院,舟山地区水产研究所.浙江省海洋渔具调查报告[M],1985:195-202
[8]宋海棠,俞存根,薛利建.东海经济虾蟹类[M],北京:海洋出版社,2006:1
[9]农业部渔业局主编.中国渔业年鉴[M],北京:中国农业出版社,2005:59-60
[10]俞存根.关于调整东海拖虾作业休渔期的建议,舟山市海洋渔业局资料
[11]B.A Christensen.Hydrodynamic modeling of fishing nets[A].IEEE OCEAN’75,New York:484-490
[12]Matt K. Broadhurst,Bottlenose Dolphins.Tursiops truncatus, Removing By-catch from Prawn-trawl Codends During Fishing in New South Wales, Australia Statistical Data Included[J].Marine fishery Review,1998:summer.
[13]Matt K. Broadhurst,Paul E. McShine,Roger B.Larsen Effects of twine diameter and mesh size in the body of prawn trawls on bycatch in Gulf St. Vincent, Australia[J].Fishery Bulletin,2000, 98(3):463-473
[14]Matt K. Broadhurst,Steve J. Kennelly,Steve Eayrs.Flow-related effects in Prawn-trawl codends: potential for increasing the escape of unwanted fish through square-mesh panels [J].Fishery Bulletin,1999,97(1):1-8.
[15]Steve Eayrs.Understanding fish and prawn behaviour: potential to reduce by catch in a tropical prawn fishery [J].Fishery Science, 2002,68(sup 1):367-370.
[16]M.Shamim Uddin Khan,Optimal Stock.Harvest and Effort Level of Bangladesh Trawl Shrimp Fishery– A Nonlinear Dynamic [J].Approach Journal of Agriculture & Rural development,2007,5(1&2):143-149
[17]Pingguo He,Vincent Balzano.Reducing the catch of small shrimps in the Gulf of Marine pink shrimp fishing with a size-sorting grid device [J].ICES Journal of Marine Science,2007,64(8):1551-1557
[18]张健,孙满昌,钱卫国.桁拖网不同网目结构网囊对主要鱼类的选择性研究[J].上海水产大学学报,2007,17(4):457-463
[19]张兴国,张英.浅谈桁拖网渔具渔法调整技术[J].中国水产,2003,12:75-76
[20]洪明进.选择性虾拖网渔具渔法研究[J].福建水产,2005,3:14-17
[21]孙满昌,姚来富.桁拖网作业中鱼虾分离的初步试验研究[J].海洋渔业,1998,3:111-115
[22]孙满昌,张健,樊伟.吕四渔场虾桁拖网最小网目尺寸的研究[J].海洋渔业,2002,3:120-124
[23]杨吝编译.澳大利亚减少对虾拖网副渔获物的技术措施[J].现在渔业信息,2001,16(11):16-20
[24]樊伟,孙满昌.桁拖网作业中鱼虾分离效果的试验研究[J].海洋渔业,2000,3:106-109
[25]Matt K. Broadhurst.Modifications to reduce by catch in prawn trawls: A review and framework for development [J].Reviews in fish Biology and fisheries,2000,10(1):27-60
[26]YU Congda,,CHEN Zhihai,CHEN Lianyuan.The rise and fall of electrical beam trawling for shrimp in the East China Sea: technology, fishery, and conservation implications [J].ICES Journal of Marine Science,2007,64(8):1592-1597
[27]A.Hoff,,H.Frost.Modelling combined harvest and effort regulations: the case of the Dutch beam trawl fishery for plaice and sole in the North Sea [J].ICES Journal of Marine Science,2008,65(6): 822-831
[28]HE P,DGOETHEL,T SMITH.Design and Test of a Topless Shrimp Trawl to Reduce Pelagic Fish Bycatch in the Gulf of Marine Pink Shrimp Fishery[J].Journal of Northwest Atlantic Fishery Science,2007,38:13-21
[29]罗炎标,张健,孙满昌[J].大鹏湾捕虾拖网渔获分隔试验的效果分析[J].南方水产,2007,3(1):14-19
[30]张健,孙满昌,罗炎标.广东大鹏湾虾拖网网囊网目选择性研究[J].海洋渔业,2007,29(2):166-173
[31]张兴国.桁拖网捕虾技术推广研究总结[J].海洋渔业,1995,1:11-13
[32]张健,孙满昌.桁拖网不同网目结构的网囊对虾类的选择性[J].中国水产科学,2008,15(4):667-676
[33]李善贞.双联式虾拖网渔具渔法试验报告[J].福建水产,1997,3:7-11
[34]洪明进,叶泉土,郑国富等.网板虾拖作业渔获物种类组成[J].福建水产,2003,4:27-29
[35]洪明进,沈长春,叶泉土等.选择性虾拖网崔广实验报告[J].福建水产,2007 ,4:35-37
[36]佘显炜,虞聪达..渔具力学[M].杭州:浙江科学技术出版社,2004:191
[37]SC/T 4011-1995,拖网模型水池试验方法[S].北京:中国标准出版社,1996
[38]松田皎,漁具物理学[M].东京:成山堂書店，2001:76
[39]Fuxing HU,Tadashi TOKAI,Seiichi TAKEDA.The Performance of the New circulating Water Channel of Tokyo University of Marine Science and Technology[J].Fisheries Engineering,2004,41(2):153-163
[40]宣立强.拖网曳纲形状与张力的计算机模拟[J].湛江海洋大学学报,2005,25(3):90-93
[41]李晓平,王树新,何漫丽等.水下拖曳柔索的动力学理论模型研究[J].中国海洋平台,2003,18(3):31-91
[42]佘显炜.拖网曳纲力学计算的研究[J].浙江水产学报,1994,13(4):225-233
[43]佘显炜.水流和波浪作用下渔具锚链张力和形状计算的研究[J].浙江海洋学院学报(自然科学版),2006,25(3):237-253
[44]Alekseev N.I.Determination of the hydrodynamic characteristics of the warp at sea[J].Rybnoe khozyaistvo Moskva 1964,40(1):56-58
[45]Chubarov S.N.The effect of hydrodynamic forces on wires and the choice of wire for high speed and deep-sea trawling[J].Rybnoe khozyaistvo Moskva,1962,38(5):45-49
[46]Griffin O.M.,Kandiver J.K., Skop R.A.The strumming vibrations of marine cables[J].Ocean Science and Engineer,1982,7(4):461-498
[47]宮崎芳夫,高橋正．網地の流体抵抗に関する基礎的研究——(Ⅱ)[J].Journal of the Tokyo University of Fisheries,1964,50(2):89-94
[48]宮崎芳夫,高橋正．網地の流体抵抗に関する基礎的研究——(Ⅴ)[J].Journal of the Tokyo University of Fisheries,1964,50(2):111-123
[49]佘显炜.计算渔具力学导论[M].上海:上海科学技术文献出版社,2001:9
[50]哈尔滨工业大学理论力学教研室编.理论力学[M].北京:高等教育出版,1988:13
[51]梁治明,邱侃,陆耀洪.材料力学[M].北京:人民教育出版社,1958:260-271
[52]CHUN-WOO.LEE . Dynamic Analysis and Control Technology in a Fishing Gear System[J].FISHERIES SCIENCE,2002,68:1835-1840
[53]BONG-JIN.CHA,CHUN-WOO.LEE.Dynamic Simulation of a Midwater Trawl System’s Behavior [J].FISHERIES SCIENCE,2002,68:1865–1868
[54]万荣,何鑫,王欣欣等.一种适用于网箱耐流特性有限元分析的网目群化方法[J].中国海洋大学学报,2007,37(6):885-888
[55]苏炜,詹杰民.效网面法在模拟网的水动力特性中的应用[J].水动力学研究与进展,2007,22(3):267-272
[56]佘显炜.刺网网片张力和形状的计算[A].佘显炜.计算渔具力学导论[M].上海:上海科学技术文献出版社,2001:260-264
[57]张立英,侯恩淮,张春桂等.用计算机计算拖网网片的减裁与吃扣缝合[J].中国水产科学,1994,1(1):61-65
[58]佘显炜.剪裁网片形状和张力的计算[A].中国水产捕捞学会研讨会论文集,苏州:苏州大学出版社,1997
[59]宮崎芳夫,高橋正．網地の流体抵抗に関する基礎的研究——(Ⅵ)[J].Journal of the Tokyo University of Fisheries,1964,50(2):124-130
[60]T.Kowalski,J.Giawnotti.Calculation of fishing net drag [A].Mar.Tech.Rep.Univ.R.I,1974,15:26
[61]单辉祖,材料力学(Ⅰ)[M].北京:高等教育出版社:2003:303
[62]А.Л.弗里德曼,渔具理论与设计[M].北京:海洋出版社:1988:71