A method for hydrodynamic analysis of a floating structure with multi-body multi-coupling characteristics

Abstract

The application discloses a kind of multi-body multi-coupling characteristics of floating structure hydrodynamic analysis method, comprising the following steps: obtaining the geometric characteristics of each floating body, dividing boundary element calculation grid;Calculate each floating body wave exciting force, additional mass and radiation damping, obtain the mass matrix and stiffness matrix of each floating body;Determine the connection mode and coupling factor of floating body;According to the connection mode and coupling characteristics of system, establish the displacement connection condition between each floating body;According to displacement continuous condition and motion constraint relationship, construct motion constraint matrix;According to Lagrange multiplier method, determine the frequency domain motion equation of multi-floater system;Solve motion equation, obtain the motion response of multi-floater system, according to the coupling characteristics of system, further system's analysis wave energy capture power.According to the above analysis method, the present application can solve the problem that the existing simulation method cannot accurately depict the motion response of each degree of freedom when obtaining the hydrodynamic response characteristics of complex multi-body system.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of hydrodynamics of marine engineering structure, and particularly relates to a hydrodynamic analysis method for a floating structure with multi-body and multi-coupling characteristics. BACKGROUND

[0002] The multifunctional floating platform is a kind of marine engineering equipment integrating multiple functions, which mainly uses the principle of buoyancy to complete tasks such as exploration, energy development and observation in the marine environment, and has the characteristics of strong mobility, strong adaptability to complex sea conditions and diversified functions.

[0003] In recent years, the multifunctional floating platform based on the concept of cost sharing and synergistic effect has become a research hotspot. For example, the world's first megawatt floating wave power generation device "Nanqun", the semi-submersible wave energy aquaculture and tourism platform "Penghu", the British wind-wave combined floating aquaculture platform Blue Growth Farm, etc.

[0004] At present, from the perspective of mechanics, such multifunctional floating platforms have similar characteristics, namely the characteristics of multi-body complex connection, which are quite different from traditional marine structures (such as offshore oil and gas platforms). The characteristics of such new multifunctional platforms are as follows: multiple bodies are connected to each other, and the positions of the hinge points are relatively complex; the motion degrees of freedom of the structure are not single relative motion, but often accompanied by motion of other degrees of freedom; the motion of the system is accompanied by additional coupling factors (such as anchoring factors, energy output damping, etc.); therefore, an efficient and accurate hydrodynamic analysis method is the key to the design of such multifunctional marine structures, and therefore, in order to adapt to the development of such new marine structures, a hydrodynamic analysis method suitable for complex multi-body systems on the sea is urgently needed. SUMMARY

[0005] The present application is a hydrodynamic analysis method for a floating structure with multi-body and multi-coupling characteristics, which is provided to solve the problems of the prior art. In order to solve the problem that the existing simulation method cannot accurately depict the motion response of each degree of freedom when obtaining the hydrodynamic response characteristics of a complex multi-body system, an analysis and solution method for the hydrodynamic response of a complex multi-body system is proposed to solve the above problems. The method includes modeling each floating body of the multi-body floating structure and performing boundary element mesh division, determining the connection mode and coupling factors between the floating bodies, establishing displacement connection conditions between the floating bodies, constructing a motion constraint matrix, determining a frequency domain equation according to the Lagrange multiplier method and solving, and systematically analyzing the wave energy capture power.

[0006] The technical scheme adopted by the present application is as follows:

[0007] 1. A hydrodynamic analysis method for a floating structure with multi-body and multi-coupling characteristics, comprising the following steps:

[0008] S1. Obtain the geometric features of each floating body and divide the boundary element computation mesh;

[0009] S2. Calculate the wave excitation force, added mass and radiation damping of each floating body, and obtain the mass matrix and stiffness matrix of each floating body.

[0010] S3. Determine the connection method and coupling factors of the floating body;

[0011] S4. Based on the system's connection method and coupling characteristics, establish the displacement connection conditions between each floating body;

[0012] S5. Construct the motion constraint matrix based on the displacement continuity condition and motion constraint relationship;

[0013] S6. Determine the frequency domain equations of motion for the multi-buoy system using the Lagrange multiplier method;

[0014] S7. Solve the equations of motion to obtain the motion response of the multi-floating body system. Based on the coupling characteristics of the system, further analyze the wave energy capture power.

[0015] Furthermore, in S1, the process of dividing the boundary element computation mesh is as follows:

[0016] The floating body is geometrically modeled using modeling software to generate a geometric file, which is then imported into external software for boundary element mesh generation to produce a mesh file.

[0017] Furthermore, in S2, the calculation methods for the wave excitation force, added mass, and radiation damping are as follows:

[0018] Based on linear potential flow theory, for the... A multi-floating body system consisting of several floating bodies, whose respective wetted surfaces are denoted as . ,in Total wet surface area is Total velocity potential It can be decomposed into:

[0019] (1)

[0020] In the formula, For the incident potential, For diffraction, The imaginary unit, , For wave frequency, radiation potential and Spatial coordinate system The Middle The first floating body Radiation potential and motion response amplitude for each degree of freedom, incident potential The specific expression is:

[0021] (2)

[0022] where, is the wave number, is the water depth, is the incident wave amplitude, is the phase angle of the incident wave direction with respect to the positive x-direction, is the acceleration of gravity, is the coordinate of any point in the fixed spatial coordinate system .

[0023] The above velocity potentials satisfy the Laplace equation:

[0024] (3)

[0025] The free surface SF satisfies:

[0026] (4)

[0027] The body surface SB satisfies:

[0028] (5)

[0029] The seabed SD boundary satisfies:

[0030] (6)

[0031] The Sommerfeld condition at infinity:

[0032] (7)

[0033] In equations (3) to (7), is the acceleration of gravity, is the water depth, denotes the horizontal distance between the far-field point and the floating body, denotes the boundary surface normal vector of the th body in the th degree of freedom;

[0034] The radiation and diffraction potentials on the body surface are calculated by the three-dimensional Green function, where for a multi-body system, the number of bodies is The source pair mixed distribution radiation and diffraction equation on the body boundary of a multi-body system is as follows:

[0035] (8)

[0036] (9)

[0037] In equations (8) to (9), , Let be a variable, where The total number of face elements is denoted as , As the source The element in question, Green's function to satisfy the free surface condition, , These are the coordinates of the field point and the source point, respectively.

[0038] Specifically, in solving for the added mass and radiation damping matrix, the following formula can be supplemented, namely, since the first... The first object The motion in the first degree of freedom causes the first The first object The additional mass and radiation damping for each degree of freedom are solved as follows:

[0039] (10)

[0040] Furthermore, the wave excitation force, added mass, and radiation damping are obtained by solving the boundary integral equations through grid discretization to obtain the radiation potential. and diffraction potential This allows us to obtain wave excitation force, added mass, and radiation damping.

[0041] Among them, the additional mass array of the multi-floating body system and radiation damping matrix It can be represented as:

[0042] (11)

[0043] (12)

[0044] In the formula , They respectively represent the reason that the first The first object The motion on the first degree of freedom causes the first The first object Additional mass and radiation damping in each degree of freedom;

[0045] No. The first object The first-order wave excitation force in each degree of freedom includes the Froude-Krylov force and the diffraction force, expressed as follows:

[0046] (13)

[0047] Similarly, wave excitation force It can be represented as:

[0048] (14)

[0049] is the total mass matrix of the multi-floater system, and its specific form is as follows:

[0050] (15)

[0051] is the six-degree-of-freedom mass matrix of the i-th floater, ， and its specific expression form is as follows:

[0052] (16)

[0053] In formula (16), is the mass of the floater , , , are the coordinate components of the center of gravity of the floater on the three coordinate axes, , respectively, represent three directions, and is the moment of inertia of the floater, and its specific form is as follows:

[0054] (17)

[0055] When , = 1, and when , = 0;

[0056] Similarly, is the total hydrostatic restoring moment matrix of the multi-floater system, and its specific form is as follows:

[0057] (18)

[0058] In formula (18), is the six-degree-of-freedom hydrostatic restoring moment matrix of the i-th floater, wherein ， and its specific form is as follows:

[0059] (19)

[0060] In formula (19), , , are the coordinate components of the center of gravity of the floater ​​​The waterline surface area, the distance between the center of buoyancy and the center of gravity, and the volume of water displaced. The density of seawater is 1025 kg / m³. 3 , It is the acceleration due to gravity. Floating body Waterline surface.

[0061] Furthermore, in step S3, the method for determining the connection method and coupling factors of the floating body is as follows:

[0062] The PTO matrix is ​​obtained through the relative motion between the float and the floating carrier, which captures the directional degree of freedom of wave energy. .

[0063] Furthermore, in S4, the displacement connection conditions between the various floating bodies are established as follows:

[0064] Based on the kinematic relationship between the float and the floating carrier, the relative motion direction degree of freedom is released, and the other degrees of freedom satisfy the displacement continuity condition at the hinge point. The displacement continuity condition and the corresponding displacement constraint matrix are then determined. .

[0065] The present invention has the following beneficial effects:

[0066] This invention, after confirming the complex connection and coupling factors between floating bodies, calculates the wave energy capture efficiency based on solving the motion response, thereby evaluating the wave power generation performance of multiple systems; it features high computational efficiency and high accuracy. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the structure of Embodiment 1 of the present invention.

[0068] In the diagram: 1. Floating carrier; 2. Hemispherical float; 3. Connecting rod; 4. Hinge joint. Detailed Implementation

[0069] The technical solution of the present invention will be clearly and completely described below through embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] Example 1

[0071] In this embodiment, as Figure 1The structure shown is a floating structure with multi-body and multi-coupling characteristics, which is composed of multiple floating bodies hinged together. The floating bodies are divided into floating body carriers 1 and hemispherical floats 2. The two floating bodies 1 are hinged together by hinge parts 4, and the floating bodies 1 can rotate relative to each other. Each floating body 1 is provided with a hemispherical float 2, which is hinged to the floating body 1 by connecting rods 3, so that the hemispherical float 2 and the floating body 1 can rotate relative to each other. That is, there is also a relative roll motion between the hemispherical float 2 and the floating body 1. Wave energy capture is achieved by using the relative roll motion between the hemispherical float 2 and the floating body 1, while releasing the roll motion between the hemispherical float 2 and the floating body 1 as well as the pitch motion between the floating bodies 1.

[0072] The geometric parameters of many floating bodies in the ocean are complex and diverse, with common shapes including box-shaped, cylindrical, and spherical. Due to the diverse types of floating structures in complex multibody systems, this embodiment focuses on... Figure 1 The multi-floating body system structure shown is composed of an oscillating float and a floating carrier. An example is given using the hydrodynamic analysis method for floating structures with multi-body, multi-coupling characteristics disclosed in this invention. The method includes the following steps:

[0073] S1. Obtain the geometric features of each floating body and divide the boundary element computation mesh, specifically:

[0074] Using modeling software Figure 1 The oscillating float and floating carrier in the multi-floating body system structure shown are geometrically modeled, and after generating the geometric file, they are imported into external software for boundary element mesh generation to generate the mesh file.

[0075] S2. Calculate the wave excitation force, added mass, and radiation damping of each floating body, and obtain the mass matrix and stiffness matrix of each floating body. The algorithm is as follows:

[0076] Based on linear potential flow theory, for the... A multi-floating body system consisting of several floating bodies, whose respective wetted surfaces are denoted as . ,in Total wet surface area is The total velocity potential can be decomposed into:

[0077] (1)

[0078] In the formula, For the incident potential, For diffraction, The imaginary unit, , For wave frequency, radiation potential and Spatial coordinate system The Middle The first floating body incident potential The specific expression is:

[0079] (2)

[0080] where, is the wave number, is the water depth, is the incident wave amplitude, is the phase angle of the incident wave direction with respect to the positive incident direction, is the gravitational acceleration, is the coordinate of any point in the fixed spatial coordinate system

[0081] The above velocity potential satisfies the Laplace equation:

[0082] (3)

[0083] The free water surface SF satisfies:

[0084] (4)

[0085] The body surface SB satisfies:

[0086] (5)

[0087] The seabed SD boundary satisfies:

[0088] (6)

[0089] The Sommerfeld condition at infinity:

[0090] (7)

[0091] In equations (3) to (7), is the gravitational acceleration, is the water depth, denotes the horizontal distance between the far-field point and the floating body, denotes the boundary surface normal vector of the th body in the th degree of freedom;

[0092] The radiation potential and diffraction potential of the floating body surface are calculated by three-dimensional Green's function, where the number of floating bodies in the multi-floating body system is The source pair mixed distribution radiation and diffraction equation of the multi-floating body system body boundary is as follows:

[0093] (8) ​

[0094] (9)

[0095] In formula (8) to formula (9), is a variable, wherein the total number of surface elements is denoted as , is a surface element where a source point is located, is a Green function satisfying the free surface condition, respectively, are coordinates of a field point and a source point;

[0096] In the specific representation of the added mass and radiation damping matrix solution, the following formula can be supplemented, that is, the added mass and radiation damping of the first object on the first freedom degree caused by the motion of the first object on the first motion freedom degree is solved as follows:

[0097] (10)

[0098] The wave exciting force, the added mass and the radiation damping are solved by grid discretization of the boundary integral equation to obtain the radiation potential and the diffraction potential , and further to obtain the wave exciting force, the added mass and the radiation damping,

[0099] wherein the added mass matrix and the radiation damping matrix of the multi-float system can be expressed as:

[0100] (11)

[0101] (12)

[0102] In the formula, , respectively, are the added mass and the radiation damping of the first object on the first freedom degree caused by the motion of the first object on the first motion freedom degree; The first-order wave exciting force on the first freedom degree of the first object includes the Froude-Krylov force and the diffraction force, and the expression is as follows:

[0103]

[0104] (13)

[0105] Similarly, the wave exciting force​​​​​​​​​​ It can be represented as:

[0106] (14)

[0107] The total mass matrix of the multi-floating body system is shown in the following form:

[0108] (15)

[0109] For the first The six-degree-of-freedom mass matrix of a floating body ， Its specific form of expression is as follows:

[0110] (16)

[0111] In equation (16), Floating body quality , , Floating bodies The coordinate components of the center of gravity on the three coordinate axes. middle , respectively represent The three directions represent the moment of inertia of the floating body, and their specific forms are as follows:

[0112] (17)

[0113] when hour, = 1, when hour, =0;

[0114] Similarly, The total hydrostatic restoring force matrix of the multi-floating body system is shown in the following form:

[0115] (18)

[0116] In equation (18), For the first The six-degree-of-freedom still water restoring force matrix of a floating body, where ， The specific format is as follows:

[0117] (19)

[0118] In equation (19), , , Floating bodies waterplane area, distance between center of buoyancy and center of gravity, displacement volume, sea water density, 1025 kg / m 3 , gravity acceleration, floating body waterplane.

[0119] S3, determine the connection mode and coupling factors of the floating body;

[0120] Obtain the PTO matrix by the relative motion between the floater and the floating carrier in the direction of capturing wave energy , in the multi-floater system structure shown in Figure 1 , for two floating bodies and Wave energy capture is carried out by relative roll, and the corresponding relative roll displacement can be expressed as , The expressions are as follows:

[0121] (20)

[0122] The local force at the constraint position can be expressed as: , PTO damping.

[0123] Convert the local force to the force column vector acting on the coordinate system of each floating body , so its PTO matrix The expression form is as follows:

[0124] (21)

[0125] S4, according to the connection mode and coupling characteristics of the system, establish the displacement connection conditions between each floating body;

[0126] According to the motion relationship between the floater and the floating carrier, only the relative motion direction freedom is released, and other freedom directions satisfy the displacement continuity condition at the hinge point to determine the displacement continuity condition and the corresponding displacement restriction matrix .

[0127] In the structure shown in Figure 1 , there are two displacement constraint relationships. On the one hand, there is relative pitch motion between the floating carriers, and on the other hand, the floater and the floating carrier drive the PTO damping system to realize wave energy capture through relative roll motion;

[0128] The floating carrier is only allowed to rotate in the pitch direction at the hinge point, and the freedom motion in other directions is limited, so the floating carrier and the floating carrier The displacement continuity condition at the hinge point is expressed as follows:

[0129] (22)

[0130] In formula (22), , and are the coordinates of the floating carrier , the hinge point and the center of rotation of the floating carrier respectively, and are the motion responses of the floating body and the floating body respectively in the respective constrained degrees of freedom, corresponding to the surge, sway, heave, roll and yaw respectively;

[0131] In addition, since the PTO damping is driven by the relative roll motion between the roll float and the floating carrier (or ), there is relative motion between the hemispherical float and the floating carrier in the roll direction, and the other degrees of freedom are constrained at the hinge point, which is expressed as follows:

[0132] (23)

[0133] In formula (23), , and are the coordinates of the roll float , the hinge point and the center of rotation of the floating carrier respectively, and are the motion responses of the hemispherical float and the floating carrier respectively in the respective constrained degrees of freedom, corresponding to the surge, sway, heave, roll and yaw respectively;

[0134] S5, according to the displacement continuity condition and the motion constraint relationship, a motion constraint matrix is constructed;

[0135] The right side of the above formula (22) is transferred to the left side, and it is converted into a matrix form, so that the constraint matrix of the floating carrier and the floating carrier releasing the roll is obtained:

[0136] (24)

[0137] (25)

[0138] Similarly, moving the right side of equation (23) to the left side and converting it to matrix form, the semi-submersible floater and the floating carrier The constraint matrix of releasing roll is:

[0139] (26)

[0140] (27)

[0141] According to the actual hinge relationship, the matrixes , , , are combined to obtain the displacement restriction matrix ;

[0142] S6, determining the frequency domain motion equation of the multi-floater system according to the Lagrange multiplier method;

[0143] When regular waves are incident, for the multi-floater system, each floater is regarded as a rigid body, the total external force is assumed to be applied at the center of gravity of each sub-module, each floater is simplified as a generalized concentrated mass acting at the center of gravity, in addition to considering the interaction between the floater due to wave radiation and diffraction, the influence of the connecting force between the floater must also be considered, then the motion equation of the articulated multi-floater system can be written as:

[0144] (28)

[0145] The motion equation of the complex multi-floater system is:

[0146] (29)

[0147] In equation (29): is the number of hinge points, is the number of floater, is the overall stiffness matrix of the multi-floater system, and its specific expression form is:

[0148] , , , , , and correspond to the mass matrix (equation (15)), the added mass matrix and the radiation damping matrix (equations (11), (12)), the PTO damping matrix (equation (21)), the still water stiffness matrix (equation (18)), and the mooring stiffness matrix, respectively, represents the connection force between the floating bodies, is the displacement restriction matrix;

[0149] displacement vector is respectively as follows:

[0150] (30)

[0151] wherein: represents the motion response of the i-th floating body in the j-th degree of freedom;

[0152] S7, solving the motion equation to obtain the motion response of the multi-floating body system, and further analyzing the wave energy capture power of the system according to the coupling characteristics of the system.

[0153] The motion response of each floating body of the multi-floating body system can be obtained by solving formula (29). Taking the case shown in FIG. 1 as an example, the power of the floating body Figure 1 and the power generated by the i-th floating body may be expressed as:

[0154] (31)

[0155] The corresponding relative roll displacement is expressed as .

[0156] The above description is not a limitation of the present application, and the present application is not limited to the above examples. By modifying the displacement conditions and correcting the PTO matrix , it can also be applied to other complex multi-body articulated cases, such as coupling of super-large floating bodies and array floating bodies, array type floating breakwater, offshore installation ship, crane ship hoisting, etc. Changes, modifications, additions or replacements made by ordinary skilled in the technical field within the essential scope of the present application also belong to the protection scope of the present application.​​​​

Claims

1. A method for hydrodynamic analysis of a floating structure having a multi-body multi-coupling feature, characterized by: The method comprises the following steps: S1, obtaining the geometric characteristics of each floating body, and dividing a boundary element calculation grid; S2, calculating wave exciting force, added mass and radiation damping of each floating body, and obtaining mass matrix and stiffness matrix of each floating body; S3, determining the connection mode of the floating body, and obtaining PTO damping and coupling factors; PTO matrix obtained by relative motion between floater and floating carrier in the direction of freedom of wave energy capture In a multi-floater system configuration, for two floater and Wave energy capture by relative roll, corresponding relative roll displacement may be expressed as , with the corresponding displacement matrix, The expressions for , respectively, are as follows: ; The local force in the constrained position can be expressed as: , is the derivative of the displacement matrix , i.e. the velocity matrix, is the PTO damping; Convert the local forces to a force column vector acting on each body coordinate system Thus the PTO matrix is expressed as follows: ; S4, establishing displacement connection conditions between the floating bodies according to the connection mode and coupling characteristics of the system; S5, constructing a motion constraint matrix according to the displacement continuity conditions and motion constraint relationships; S6, determining a frequency domain motion equation of the multi-floating body system according to the Lagrange multiplier method; the frequency domain motion equation is as follows: ； In the formula, M is the number of hinged points, N is the number of floating bodies, [K] is the overall stiffness matrix of the multi-floating body system, and the specific expression form is as follows: ; wherein, and correspond to the mass matrix, the added mass matrix and the radiation damping matrix, the PTO damping matrix, the still water stiffness matrix and the mooring stiffness matrix, respectively, denotes the connection forces between the floating bodies, is the displacement restriction matrix; S7, solving the motion equation to obtain the motion response of the multi-floating body system, and further obtaining the wave energy capture power of the system according to the coupling characteristics of the system. The wave exciting force, the added mass and the radiation damping are solved by discretizing the boundary integral equation through a mesh to obtain a radiation potential and a diffraction potential , and further to obtain the wave exciting force, the added mass and the radiation damping; where the added mass matrix of the multi-floater system and the radiation damping matrix may be expressed as: ; In the formula They respectively represent the reason that the first The first object The motion on the first degree of freedom causes the first The first object Additional mass and radiation damping in each degree of freedom; No. The first object The first-order wave excitation force in each degree of freedom includes the Froude-Krylov force and the diffraction force, expressed as follows: ； Similarly, the wave exciting force may be represented as: ; The total mass matrix for the multi-floater system is given in detail as follows: ; The sixth order mass matrix for the first body, which is expressed as follows: ; wherein the mass of the floating body , the coordinates of the center of gravity of the floating body i in the three coordinate axes, wherein , respectively, represent the moments of inertia of the floating body in the three directions, which have the following specific forms: ； When time, When time, ; The same applies to the following equations. The total hydrostatic restoring matrix for the multi-body system is given by the following expression: ； wherein is the 6x6 hydrostatic restoring matrix for the th body, where is given by the following expression: ； In the formula, Floating bodies The waterline surface area, the distance between the center of buoyancy and the center of gravity, and the volume of water displaced. The density of seawater is 1025 kg / m³. 3 , It is the acceleration due to gravity. Floating body Waterline surface.

2. The method of hydrodynamic analysis of a floating structure with multi-body multi-coupling characteristics according to claim 1, characterized in that: In the S1, the process of dividing the boundary element calculation grid is as follows: Geometric modeling of the floating body is performed through a modeling software to generate a geometric file, and the geometric file is imported into an external software to divide the boundary element grid and generate a grid file.

3. The method of hydrodynamic analysis of a floating structure with multi-body multi-coupling characteristics according to claim 1, characterized in that: In the S2, the calculation method of the wave exciting force, the added mass and the radiation damping is as follows: Based on linear potential flow theory, for a multi-body system consisting of N individual floating bodies, their respective wet surfaces are denoted by where The total wet surface is and the total velocity potential is decomposed into: ; wherein, is the incident potential, is the diffraction potential, is the imaginary unit, , is the wave frequency, and are the radiation potential and the motion response amplitude of the th floating body in the th degree of freedom, respectively, the incident potential is given by: is given by: ; wherein is the wave number, is the water depth, is the incident wave amplitude, is the phase angle of the incident wave direction with respect to the normal incidence, is the acceleration of gravity, is the fixed spatial coordinate system of any point within. The above velocity potential satisfies the Laplace equation: ； The free water surface SF satisfies: ； The object surface SB satisfies: ； The sea bottom SD boundary satisfies: ; The infinite distance Sommerfeld condition: ; wherein, g is the gravitational acceleration, h is the water depth, denotes the horizontal distance between the far field point and the floating body, denotes the position of the th object in the th degree of freedom; The radiating and diffracting potentials of the floating body surface are calculated by three-dimensional Green's functions, where the number of floating bodies in the multi-floating body system is N The source-pair mixed distribution radiation and diffraction equation of the multi-floating body system object boundary is as follows: , ， wherein, is a variable, wherein the total number of facets is denoted by , is the facet where the source point is located, is the Green function satisfying the free surface condition, are the coordinates of the field point and the source point, respectively; The following formula is added to the additional mass and radiation damping matrix solution, i.e. the additional mass and radiation damping of the first object in the first degree of freedom of motion caused by the motion of the first object in the first degree of freedom of motion is solved as follows: ; The grid data is input as an initial condition into a boundary element calculation program to obtain the wave exciting force, the added mass and the radiation damping.

4. The method of hydrodynamic analysis of a floating structure with multi-body multi-coupling characteristics according to claim 1, characterized in that: In the S3, the method for determining the connection mode of the floating body and the coupling factors is as follows: Obtaining pto matrix by relative motion between floater and floating carrier in the direction of wave energy capture freedom .

5. The method of hydrodynamic analysis of a floating structure with multi-body multi-coupling characteristics according to claim 1, characterized in that: In the S4, the displacement connection conditions between the floating bodies are established as follows: According to the motion relationship between the float and the floating carrier, the relative motion direction freedom is released, other freedom direction satisfies the displacement continuity condition at the hinge point to determine the displacement continuity condition and the corresponding displacement restriction matrix .

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