Floating State Calculation Method of Multi-Convex Structure Considering the Influence of Free Liquid Level

doi:10.12141/j.issn.1000-565X.230192

Abstract

Abstract:

In view of the influence of free surface in tank on floating state and stability, this paper proposed a new floating state algorithm of multi-convex composite structure. The floating body and the liquid tank were decomposed into multiple tetrahedral elements, and then the buoyancy and center of buoyancy of the floating body and the center of gravity of the liquid tank were determined by analyzing the relative position of each tetrahedron and the water surface/liquid surface. An improved double iteration method was also proposed to determine the floating state of multi-convex composite structures: the inner iteration method was used to simulate the heaving motion of the floating body to obtain the water/liquid surface equations outside the floating body and inside the tank; the rotation motion of floating body was simulated by outer iteration. The two iterative methods were carried out alternately until the distance between the gravity action line and the buoyancy action line of the floating body meets the accuracy requirement, and the gravity is equal to the buoyancy force. The study calculated the floating state of a semi-submersible vessel and a semi-submersible offshore platform under various typical working conditions using self-compiled program, and the influence of free surface was also considered. In addition, MAXSURF modeling was used for comparative analysis, and AUTOCAD was used to verify the accuracy. The results show that: (1) the algorithm can take into account the influence of free surface on floating state with clear principle and good convergence; (2) the algorithm is easier to obtain accurate solutions for both traditional single-convex structures (such as single hull vessel) and multi-convex structures (such as multi-hull vessel, floating offshore platform, etc.), and its computational efficiency is higher; (3) the algorithm can realize the “building-block” modeling mode, which can greatly reduce the workload in multi-condition modeling; (4) the algorithm does not need to rely on foreign third-party graphics platform (such as AUTOCAD, CATIA) , which lays a good foundation for the localization of related industrial software in our country.

Key words: free surface, floating state, tetrahedron, double iteration

CLC Number:

U662

LIU Xiao, ZHOU Quan, FAN Tianhui, et al. Floating State Calculation Method of Multi-Convex Structure Considering the Influence of Free Liquid Level[J]. Journal of South China University of Technology(Natural Science Edition), 2024, 52(5): 62-70.

Figures/Tables 23

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 1

Table 2

Table 3

Fig.11

Fig.12

Fig.13

Fig.14

Table 4

Table 5

Table 6

Gravity and buoyancy line distance"

迭代次数	$l / m m$				迭代次数	$l / m m$
迭代次数	工况1（横倾）	工况2（纵倾）	工况3（任意倾）		迭代次数	工况1（横倾）	工况2（纵倾）	工况3（任意倾）
1	8.738 5	9.396 2	13.230 0	7		0.036 4	0.000 0	0.008 3
2	5.544 7	5.642 7	9.740 4	8		0.013 8	0.000 0	0.004 7
3	2.343 3	1.880 9	6.259 6	9		0.011 3	0.000 0	0.002 0
4	0.867 9	0.003 7	2.800 2	10		0.001 2	0.000 0	0.001 5
5	0.739 1	0.000 0	0.688 8	11		0.000 0	0.000 0	0.000 3
6	0.064 0	0.000 0	0.233 2

Table 6

Fig.15

Table 7

Fig.16

References 18

1	陈彦璋．海洋工程结构物静稳性特性计算方法研究［D］．哈尔滨：哈尔滨工程大学，2017.
2	PARK K P， HAM S H， LEE J B，et al ．Virtual offshore rig experience based on modeling and simulation technology［C］∥ Proceeding of International Conference on Computer Applications in Shipbuilding 2013．［S.l.］：Royal Institution of Naval Architects，2013：77-82.
3	王智洲，李军翼，张伟，等．散货船完整稳性计算综述［J］．中国水运，2016，16（11）：15-17.
	WANG Zhizhou， LI Junyi， ZHANG Wei ．A review of the calculation of bulk carrier integrity stability［J］．China Water Transport，2016，16（11）：15-17.
4	CALABRESE F， MANCARELLA L， ZIZZARI A A，et al ．A FEA-like method for evaluating the ship equilibrium point［J］．IFAC Proceedings Volumes （IFAC-Papers Online），2012，9（1）：115-120.
5	CALABRESE F， CATALDO M， DE PASCALIS A，et al ．A method for evaluating the ship equilibrium point using 3D meshes developed for embedded device［C］∥Proceedings of MTS/IEEE OCEANS 2015-Genova：Discovering Sustainable Ocean Energy for a New World．Genova：IEEE，2015：1-6.
6	ZHANG Z， XIE D ．A mesh insensitive finite element method to compute statical stability curve of floating bodies with arbitrary configurations based on a force-oriented approach［J］．International Journal for Numerical Methods in Engineering，2023，124（7）：1672-1695.
7	SEQUEIRA D， MANN B P ．Static stability analysis of a floating rectangular prism［C］∥Proceedings of the ASME 2016 International Design Engineering Technical Conferences Computers and Information in Engineering Conference．Charlotte：American Society of Mechanical Engineers，2016：1-6.
8	黄晨．模块化浮式海洋结构物静水力性能直接计算方法研究［D］．武汉：华中科技大学，2020.
9	刘梅梅，包胜利，于立伟，等．半潜驳稳性现场快速评估方法研究［J］．水道港口，2021，42（2）：243-251.
	LIU Mei-mei， BAO Sheng-li， YU Li-wei，et al ．Research on rapid on-site assessment method of stability of semi-submersible barge［J］．Journal of Waterway and Harbor，2021，42（2）：243-251.
10	左仔滨，江婷，王明振，等．基于CATIA平台的飞机水上迫降漂浮特性计算方法［J］．航空计算技术，2019，49（4）：95-99.
	ZUO Zai-bin， JIANG Ting， WANG Ming-zhen，et al ．Calculation method of floating characteristics for fixed-wing aircraft base on CATIA secondary development technology［J］．Aeronautical Computing Technique，2019，49（4）：95-99.
11	张明霞，秦帅帅，赵正彬，等．基于CATIA的船体参数化建模和稳性计算［J］．船舶工程，2019，41（1）：48-52.
	ZHANG Mingxia， QING Shuaishuai， ZHAO Zhengbin，et al ．Parametric modeling of hull and calculation of stability based on CATIA［J］．Ship Engineering，2019，41（1）：48-52.
12	马坤，陈德志．自由液面对大倾角稳性的修正计算方法［J］．中国造船，2005，46（1）：3-9.
	MA Kun， CHEN Dezhi ．A correction method on the influence of free surface on great inclining angle stability［J］．Ship Building of China，2005，46（1）：3-9.
13	付田，舒晨晨，汪伟斌，等．一种考虑自由液面的船舶静稳性曲线修正方法［J］．中国水运，2022，22（6）：6-7，78.
	FU Tian， SHU Chenchen， WANG Weibin，et al ．A correction method of ship static stability curve considering free surface［J］．China Water Transport，2022，22（6）：6-7，78.
14	贾清振．基于CATIA的三维船舶建模及破舱稳性计算［D］．大连：大连理工大学，2021.
15	李洛东，刘成名．基于有限元网格的液货体积计算方法［J］．船海工程，2022，51（4）：6-10.
	LI Luo-dong， LIU Cheng-ming ．Method for calculating liquid cargo volume based on finite element mesh［J］．Ship & Ocean Engineering，2022，51（4）：6-10.
16	刘虓，徐磊，樊天慧，等．针对凸多面体组合结构的二重迭代浮态计算方法［J］．华南理工大学学报（自然科学版），2020，48（11）：1-9.
	LIU Xiao， XU Lei， FAN Tianhui，et al ．Double iterative afloat condition calculation method for convex polyhedron composite structure［J］．Journal of South China University of Technology（Natural Science Edition），2020，48（11）：1-9.
17	张宝吉．船舶静力学［M］．上海：上海交通大学出版社，2016.
18	刘虓．基于四面体网格的浮态计算方法_宣传资料［EB/OL］．（2020-12-10）［2022-02-15］．.

三棱柱1	圆柱体2	六面体3
0，-16，7.5//三棱柱顶点1的坐标	35，0，7.5//圆柱体中心1的坐标	95，-16，0//六面体顶点1的坐标
20，-16，0//三棱柱顶点2的坐标	14//圆柱体半径	102.5，-16，1.446//六面体顶点2的坐标
20，-16，7.5//三棱柱顶点3的坐标	35，0，20//圆柱体中心2的坐标	110，-16，7.5//六面体顶点3的坐标
0，16，7.5//三棱柱顶点4的坐标	14//圆柱体半径	95，-16，7.5//六面体顶点4的坐标
20，16，0//三棱柱顶点5的坐标		95，16，0//六面体顶点5的坐标
20，16，7.5//三棱柱顶点6的坐标		102.5，16，1.446//六面体顶点6的坐标
		110，16，7.5//六面体顶点7的坐标
		95，16，7.5//六面体顶点8的坐标

立柱		AutoCAD精确解/m	本文程序解/m	Maxsurf解（200剖面）/m	偏差/% （本文）	偏差/%（Maxsurf）
未加沉箱	1	5.000 9	5.001 1	4.991 0	0.003	0.198
	2	5.000 9	5.001 1	4.991 0	0.003	0.198
	3	4.552 8	4.552 6	4.565 0	0.004	0.268
	4	4.552 8	4.552 6	4.565 0	0.004	0.268
两个沉箱	1	9.022 4	9.029 0	8.974 0	0.073	0.536
	2	9.022 4	9.029 0	8.974 0	0.073	0.536
	3	7.518 4	7.520 6	7.586 0	0.029	0.899
	4	7.518 4	7.520 6	7.586 0	0.029	0.899

工况	0.4 kg压载重心/mm			浮体和压载的合成重心/mm
工况	x	y	z	x	y	z
1	463.0	290.5	319.5	463.0	9.3	185.9
2	152.5	0.0	319.5	453.0	0.0	185.9
3	783.0	300.0	319.5	473.3	9.6	185.9

立柱	工况1（横倾）			工况2（纵倾）			工况3（任意倾）
立柱	程序值/mm	Maxsurf值/mm	偏差/%	程序值/mm	Maxsurf值/mm	偏差/%	程序值/mm	Maxsurf值/mm	偏差/%
1	219.6	218.2	0.620	220.3	216.7	1.661	237.9	238.3	0.187
2	257.7	256.0	0.682	220.3	216.7	1.661	277.2	277.5	0.091
3	257.7	256.0	0.682	257.0	257.6	0.233	239.5	236.0	1.503
4	219.6	218.2	0.620	257.0	257.6	0.233	200.2	196.8	1.704

立柱	AutoCAD精确解/mm	文中程序解/mm	Maxsurf解/mm	偏差/%（本文）	偏差/%（Maxsurf）
1	219.1	219.6	218.2	0.228	0.411
2	257.2	257.7	256.0	0.194	0.467
3	257.2	257.7	256.0	0.194	0.467
4	219.1	219.6	218.2	0.228	0.411