A static analysis method of a multi-point mooring system based on elastic catenary theory

Abstract

This invention provides a static analysis method for multi-point mooring systems based on the elastic catenary theory. This method introduces the axial stiffness of the mooring cables to elastically correct the classical catenary equation, establishing an accurate mechanical model considering the elastic deformation of materials. The displacement of the buoy's center of gravity is calculated using spatial coordinate transformation to obtain new coordinates for each mooring point, which are then transformed to the local coordinate system of each mooring cable to obtain geometric parameters. The elastic catenary equation is solved in the local coordinate system to obtain the tension at the top of each cable, and then transformed to the global coordinate system. The tension of each mooring cable is equivalent to a six-degree-of-freedom force acting on the buoy's center of gravity, and the total restoring force of the mooring system is obtained through vector superposition, establishing the system's static equilibrium equation. This equilibrium equation is solved using a numerical optimization algorithm to obtain the static equilibrium position of the buoy. This invention effectively improves the accuracy of static analysis of mooring systems, the system coupling analysis capability, and the applicability and robustness of the method.

Description

Technical Field

[0001] This invention relates to the field of mooring technology for marine engineering vessels and marine structures, and more specifically, to a static analysis method for multi-point mooring systems based on the elastic catenary theory. Background Technology

[0002] As marine resource development continues to advance into deeper waters, the accuracy of mooring systems, as key facilities for ensuring the safe positioning of floating structures, becomes particularly important. Traditional static analysis methods are mainly based on the classical catenary theory, which assumes that mooring cables are perfectly flexible and inextensible. Although this method is simple to calculate, it has revealed several technical shortcomings that urgently need to be addressed in practical engineering applications.

[0003] In existing technologies, the classical catenary theory suffers from significant limitations in engineering applications due to its neglect of elastic deformation of materials. This method cannot accurately reflect the elastic elongation of mooring cables under tension, especially in deep-water environments where the length of the mooring cable increases significantly, and the proportion of elastic elongation in the total deformation rises. Ignoring this effect leads to systematic biases in the calculation of mooring cable morphology. These biases further affect the accuracy of calculating the tension at the tip of the mooring cable, posing potential risks to the safety assessment of the mooring system.

[0004] Furthermore, traditional methods exhibit significant limitations when dealing with multi-point mooring systems. Existing analytical methods typically treat each mooring cable as an independent force-bearing unit for isolated analysis, failing to fully consider the coupling relationship between float displacement and changes in the morphology of each mooring cable. When the float displaces, the morphology of all mooring cables changes synchronously and interacts with each other through the float structure. Traditional methods cannot accurately describe this system-level coupling effect, leading to errors in the calculation of the overall restoring force of the mooring system and affecting the accuracy of predicting the float's equilibrium position.

[0005] More notably, the classical catenary theory is poorly adapted to complex working conditions. When faced with large deformations, nonlinear material properties, or extreme environmental loads, this theory lacks an effective elastic correction mechanism. Particularly when using elastic materials such as synthetic fiber cables, the constitutive relations of the materials exhibit significant nonlinear characteristics, severely limiting the computational accuracy and applicability of traditional methods, making it difficult to meet the stringent requirements of modern marine engineering for precise design and safety assessment. Summary of the Invention

[0006] The purpose of this invention is to provide a static analysis method for multi-point mooring systems based on the elastic catenary theory, in order to solve the above-mentioned problems existing in the prior art.

[0007] The application is as follows: This invention provides a static analysis method for multi-point mooring systems based on the elastic catenary theory, comprising the following steps: S1. Elastic catenary modeling of a single mooring cable: A static equilibrium model of a single mooring cable is established. The model is elastically modified by introducing the axial stiffness of the mooring cable to correct the classical catenary equation. S2. Motion of floating body and mapping of mooring point coordinates: Based on the displacement dr of the center of gravity of the floating body in the global coordinate system, the new global coordinates of each mooring point after motion are calculated through spatial coordinate transformation, and the new global coordinates and the global coordinates of the corresponding anchor points are transformed to the local coordinate system of the mooring cable to obtain the horizontal projection distance and vertical projection distance of the mooring cable in the local coordinate system. S3. Solving and coordinate transformation of the tension at the top of a single mooring cable: In the local coordinate system of the mooring cable, using the horizontal and vertical projection distances as inputs, the horizontal and vertical components of the tension at the top of the mooring cable are calculated based on the catenary equation, and the tension components are transformed to the global coordinate system. S4. Equivalent force and torque of the mooring cable tip tension on the buoy's center of gravity: The force and torque exerted by the tip tension of each mooring cable on the buoy's center of gravity can be equivalently represented as a six-degree-of-freedom force vector of a single mooring cable on the buoy. ; S5. Establishing System Equilibrium Conditions: This involves establishing the six-degree-of-freedom force vectors generated by all mooring cables acting on the floating body. By performing vector superposition, the total restoring force vector of the mooring system is obtained. ,Right now This establishes its relationship with the force vector of the external environment acting on the floating body. static equilibrium relationship between + =0; S6. System Characteristic Analysis and Equilibrium Position Determination: By providing a series of buoyancy center of gravity displacements... Repeat steps S2 to S5 to calculate the total restoring force vector of the corresponding mooring system. This establishes a mapping relationship F=F(dr) between the displacement of the buoy's center of gravity and the total restoring force vector of the mooring system. Based on this relationship, the static equilibrium equation is solved using a numerical optimization algorithm to obtain the static equilibrium position of the buoy.

[0008] Furthermore, the elastic correction to the classical catenary equation described in step S1 is as follows:

[0009]

[0010] Where X and Z are the horizontal and vertical projected lengths of the mooring cable when it reaches static equilibrium under its own weight and end tension, respectively; H and V are the horizontal and vertical components of the end tension of the mooring cable, respectively; w is the weight per unit length of the mooring cable in water; S is the original length of the mooring cable without stress; E is the elastic modulus of the mooring cable material; A is the cross-sectional area of ​​the mooring cable; and EA is the axial stiffness of the mooring cable.

[0011] Furthermore, in step S2, the displacement dr of the buoyant center of gravity is a six-degree-of-freedom displacement vector, defined as dr=[dx,dy,dz,rx,ry,rz]^T, where dx,dy,dz are the translational displacements of the buoyant center of gravity in the global coordinate system, and rx,ry,rz are the Euler angle rotational displacements of the buoyant body about its own coordinate system.

[0012] Furthermore, step S2 specifically includes the following sub-steps: S201 calculates the new global coordinates of the mooring points after the floating body moves: For the i-th mooring point on the floating body, its initial global coordinates are... The initial global coordinates of the buoyancy center of gravity are When the floating body is displaced, the new global coordinates of the mooring point Calculated using the following formula:

[0013] Where R is the rotation matrix, which is obtained by rotating the Euler rotation displacements rx, ry, rz of the floating body in sequence around the Y-axis, X-axis, and Z-axis of its own coordinate system, i.e., R = Ry(ry)Rx(rx)Rz(rz), where Ry(ry), Rx(rx), and Rz(rz) are the basic rotation matrices around the Y, X, and Z axes, respectively. S202 transforms the new global coordinates of the mooring point to the local coordinate system of the mooring cable: the new global coordinates obtained in step S201 are... Global coordinates fixed to the anchor point of the i-th mooring cable The coordinates are transformed to the local coordinate system of the mooring cable using the following formula:

[0014]

[0015] Obtain the horizontal projection distance and vertical projection distance .

[0016] Furthermore, in step S3, the inverse calculation employs a numerical iterative algorithm, specifically the Newton-Raphson method or the bisection method, to solve for the horizontal and vertical components of the mooring cable. and The nonlinear equation system.

[0017] Furthermore, in step S3, the tension component conversion is achieved by the following formula:

[0018] in, Let represent the components of the mooring cable tip tension in the global coordinate system. Let be the rotation matrix about the Z-axis of the global coordinate system, and let be the rotation angle. For vectors The angle between the coordinate system and the positive X-axis of the global coordinate system.

[0019] Furthermore, in step S4, the six-degree-of-freedom force vector of the single mooring cable on the floating body... Calculated using the following formula:

[0020] In the formula, These are the coordinates of the mooring point relative to the center of gravity. , , These represent the force components along the x, y, and z axes generated by the tension of the i-th mooring cable on the center of gravity of the buoyancy in the global coordinate system. , , These represent the torque components about the x, y, and z axes generated by the tension of the i-th mooring cable about the center of gravity of the buoyancy.

[0021] Furthermore, in step S6, the numerical optimization algorithm iteratively adjusts the displacement of the buoyancy center of gravity. The trial value is obtained, and steps S2 to S5 are repeated to calculate the system residual R(dr) = F(dr) + =0, until a norm is found that makes the residual equal to 0. Minimum displacement of the center of gravity of buoyancy This is the static equilibrium position.

[0022] The present invention provides a computer-readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, implements a static analysis method for a multi-point mooring system based on the elastic catenary theory.

[0023] The present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes a static analysis method for a multi-point mooring system based on the elastic catenary theory when running the computer program.

[0024] Compared with the prior art, the embodiments of the present invention achieve the following beneficial effects: An elastically modified catenary equation is established, which allows the analytical method to more accurately reflect the constitutive properties of engineering materials. This significantly improves the computational accuracy of static analysis of multi-point mooring systems, especially in deep water, high pretension, or when using highly elastic synthetic fiber cables. It can more realistically reflect the mooring cable morphology and mooring forces, providing a more reliable technical basis for the safety assessment of mooring systems. At the same time, it enhances the applicability and robustness of the analytical method, and can effectively handle complex engineering problems involving large deformations and nonlinear material properties.

[0025] By establishing a complete coordinate mapping system of "floating body motion - mooring point displacement - mooring cable morphology - system restoring force", the method can accurately describe the complex coupling effects in multi-cable systems, realizing the leap from single-cable analysis to system-level analysis, and providing a scientific basis for the overall performance evaluation of mooring systems.

[0026] A systematic numerical solution framework was adopted, achieving efficient and accurate analysis results through innovative computational strategies. The technical solution establishes a complete coordinate mapping system to effectively correlate the motion of the floating body with the morphological changes of the mooring cables, and then solves complex nonlinear equations using a numerical iterative algorithm. This method achieves rapid convergence through optimization algorithms, avoiding the computational difficulties common in traditional methods. This systematic numerical strategy provides a practical and efficient solution for engineering design, capable of meeting the computational needs of complex engineering scenarios. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating a static analysis method for a multi-point mooring system based on the elastic catenary theory provided in an embodiment of the present invention. Figure 2 This is a force analysis diagram of a single mooring cable provided in an embodiment of the present invention. Detailed Implementation

[0028] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments given herein are for illustration and explanation only and are not intended to limit the present invention.

[0029] It should be noted that many specific details are set forth in the following description in order to provide a full understanding of the present invention. However, the present invention may have other embodiments, and therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0030] See attached document Figure 1-2 As shown in the figure, this embodiment provides a static analysis method for a multi-point mooring system based on the elastic catenary theory, including: Modeling of a Single Mooring Cable Using an Elastic Catenary: A static equilibrium model of a single mooring cable is established using the catenary equation. The axial stiffness EA of the mooring cable is introduced to elastically correct the classical catenary equation, which is as follows:

[0031]

[0032] Where X and Z are the horizontal and vertical projected lengths of the mooring cable when it reaches static equilibrium under its own weight and end tension, respectively; H and V are the horizontal and vertical components of the end tension of the mooring cable, respectively; w is the weight per unit length of the mooring cable in water; S is the original length of the mooring cable without stress; E is the elastic modulus of the mooring cable material; and A is the cross-sectional area of ​​the mooring cable.

[0033] The first half of the right-hand side of the catenary equation is consistent with the classical catenary formula, describing the ideal catenary shape of the mooring cable under its own weight; while the second half, namely (HS) / (EA) and [V²-(V-wS)²] / (2wEA), are introduced elastic correction terms. They quantitatively describe the additional effects on the horizontal and vertical projected lengths of the mooring cable after elastic elongation under axial tension.

[0034] S2 Floating Body Motion and Mooring Point Coordinate Mapping: Based on the displacement dr of the floating body's center of gravity in the global coordinate system, the new global coordinates of each mooring point after motion are calculated through spatial coordinate transformation. The new global coordinates and the global coordinates of the corresponding anchor points are then transformed to the local coordinate system of the mooring cable to obtain the horizontal and vertical projection distances of the mooring cable in the local coordinate system.

[0035] First, it is necessary to accurately describe the motion of the floating body. The displacement dr of the center of mass of the floating body is a six-degree-of-freedom displacement vector, defined as dr=[dx,dy,dz,rx,ry,rz]^T, where dx,dy,dz are the translational displacements of the center of mass of the floating body in the global coordinate system, and rx,ry,rz are the rotational displacements of the floating body about its own coordinate system using Euler angles.

[0036] When the floating body undergoes this displacement, the spatial position of any mooring point i on it will change. Calculate the new global coordinates of this mooring point. The calculation principle is based on rigid body coordinate transformation in three-dimensional space, specifically implemented through the following formula:

[0037] in, The initial global coordinates of the i-th mooring point are: The initial global coordinates of the buoyancy center of gravity are, R is the new global coordinate of the mooring point after the floating body has been displaced; R is the rotation matrix, which is obtained by rotating the floating body's Euler rotation displacements rx, ry, rz in sequence around the Y-axis, X-axis, and Z-axis of its own coordinate system, i.e., R = Ry(ry)Rx(rx)Rz(rz), where Ry(ry), Rx(rx), and Rz(rz) are the basic rotation matrices around the Y, X, and Z axes, respectively.

[0038] After obtaining the new global coordinates of the mooring point, it is necessary to calculate the morphology of each individual mooring cable. Morphological analysis of each mooring cable is most easily performed within its own two-dimensional plane (i.e., the local coordinate system of the mooring cable). This plane is determined by the mooring point, the anchor point, and the direction of gravity (Z-axis). The obtained new global coordinates... Global coordinates fixed to the anchor point of the i-th mooring cable The coordinates are transformed to the local coordinate system of the mooring cable using the following formula:

[0039]

[0040] Through spatial coordinate transformation, the complex six-degree-of-freedom rigid body motion of the floating body (displacement of the floating body's center of gravity, dr) was successfully converted into two key geometric parameters of each mooring cable in the local coordinate system: horizontal projection distance. and vertical projection distance These two parameters accurately describe the suspension profile of the mooring cable under the current displacement of the floating body.

[0041] S3 Single Mooring Cable Top Tensile Tension Solution and Coordinate Transformation: In the local coordinate system of the mooring cable, using the horizontal and vertical projection distances as inputs, and based on the catenary equation, the horizontal and vertical components of the mooring cable top tension are calculated inversely, and the tension components are transformed to the global coordinate system; The output of S2 is the horizontal projected distance of the mooring cable. and vertical projection distance Furthermore, the equation for the elastic catenary establishes the relationship between the shape (X,Z) and the tension (H,V):

[0042]

[0043] in, and It is the right half of the equation for the elastic catenary established by S1.

[0044] and The horizontal tension component H and the vertical tension component V at the tip of the mooring cable are known quantities (target values), while these are unknowns to be determined. This constitutes a system of nonlinear equations with two equations and two unknowns:

[0045]

[0046] Since this system of equations has no analytical solution, a numerical iterative algorithm must be used to solve it. This embodiment preferably uses the Newton-Raphson method because it has a quadratic convergence speed and high efficiency. Through this numerical process, the equations under the current mooring cable configuration can be accurately solved. , Under these conditions, the tip tension borne by the mooring cable ( , ).

[0047] The tension components obtained by solving ( , The tension vectors of each mooring cable are defined in the local coordinate system of the mooring cable. To perform subsequent force calculations for the entire mooring system, the tension vectors of each mooring cable must be uniformly transformed to the global coordinate system. This transformation is achieved through a rotational transformation:

[0048] in, Let represent the components of the mooring cable tip tension in the global coordinate system. Let be the rotation matrix about the Z-axis of the global coordinate system, and let be the rotation angle. For vectors The angle between the coordinate system and the positive X-axis of the global coordinate system.

[0049] This transformation converts the tension components (axial horizontal force H, vertical downward force V) in the local coordinate system to the global coordinate system, based on the actual orientation of the mooring cable on the horizontal plane, thereby obtaining its components in the global X, Y, Z directions. .

[0050] S4. Equivalent force and torque of the mooring cable tip tension on the buoy's center of gravity: The force and torque exerted by the tip tension of each mooring cable on the buoy's center of gravity can be equivalently represented as a six-degree-of-freedom force vector of a single mooring cable on the buoy. ; The tension of the mooring cables acting at a single mooring point can be equivalently represented as the resultant force and resultant moment acting on the center of gravity of the floating body, which directly affects its motion. Through this equivalent transformation, the complex force system dispersed at each mooring point of the floating body can be simplified into a single principal vector and principal moment acting on the center of gravity, thereby greatly simplifying the subsequent calculation and equilibrium analysis of the system's resultant force.

[0051] When the tension at the tip of a mooring cable is applied to the mooring point on the float... At that time, its effect on the motion of the floating body can be completely equivalent to: a force of magnitude and direction that is related to the motion of the floating body. The force is exactly the same, but its point of application is shifted to the center of gravity of the buoyancy; and an additional couple generated due to the force shift, the moment of which is equal to The torque about the center of gravity of the buoyant body.

[0052] Therefore, the total effect of a single mooring cable on the floating body can be fully described by a six-degree-of-freedom vector:

[0053] In the formula, These are the coordinates of the mooring point relative to the center of gravity. , , These represent the force components along the x, y, and z axes generated by the tension of the i-th mooring cable on the center of gravity of the buoyancy in the global coordinate system. , , These represent the torque components about the x, y, and z axes generated by the tension of the i-th mooring cable about the center of gravity of the buoyancy.

[0054] S5. Establishing System Equilibrium Conditions: This involves establishing the six-degree-of-freedom force vectors generated by all mooring cables acting on the floating body. By performing vector superposition, the total restoring force vector F of the mooring system is obtained, i.e. This establishes its relationship with the force vector of the external environment acting on the floating body. Static equilibrium relationships between (such as the resultant forces and moments exerted on the buoyant body by wind, waves, and currents) + =0; S6. System Characteristic Analysis and Equilibrium Position Determination: Steps S2-S5 established the total restoring force vector. It is an implicit function of the displacement dr of the floating body's center of gravity (F=F(dr)), completing all the theoretical work from single-cable modeling to establishing the system equilibrium conditions. This step transforms the theoretical model into a practically feasible numerical algorithm, ultimately achieving an accurate solution for the floating body's equilibrium position.

[0055] F(dr) is a complex implicit function whose relationship cannot be described by an explicit expression. Solving this equation cannot be done directly and must be done using numerical iteration methods.

[0056] To gain a comprehensive understanding of the mooring system's performance, this embodiment first establishes a global relationship between the system's restoring force and the displacement of the buoyant center of gravity through parameter scanning. The specific steps are as follows: For the degree of freedom of motion of the floating body of interest (e.g., sway dx), within its possible range of motion, a series of discrete trial values ​​of the floating body's center of gravity displacement are generated with a certain step size k. For each trial value, the displacements of the other five degrees of freedom are kept to zero.

[0057] For each Execute the entire process from S2 to S5 once. That is: according to Calculate the new coordinates and mooring cable configurations for each mooring point (S2); solve for the tension in each mooring cable (S3) and represent it as equivalent to the center of gravity (S4); synthesize the contributions of all mooring cables to obtain the total restoring force of the system under the displacement of the buoyancy center of gravity. (S5).

[0058] Record each and its corresponding Taking oscillation as an example, a set of data points can be obtained { , ( The restoring force-displacement curve of the system in the oscillation direction is plotted. This curve intuitively reflects the static stiffness characteristics of the system, and its slope is the stiffness coefficient of the system in that degree of freedom.

[0059] This process no longer involves solving for a single equilibrium point, but rather, through a systematic "hypothesis-calculation" process, fully reveals the static response behavior of the mooring system. This provides engineers with a crucial data foundation for evaluating the system's performance under different offsets and identifying nonlinear characteristics.

[0060] Based on a global understanding of the system's characteristics, the ultimate goal is to precisely find the equilibrium condition R(dr) = F(dr) + The displacement dr of the center of gravity of the buoyancy is equal to 0. This is a standard unconstrained optimization problem, and the objective function is to minimize the norm of the residual R:

[0061] This invention preferably uses a quasi-Newton method (such as the BFGS algorithm) for solving the problem because it has advantages in convergence speed and computational efficiency.

[0062] Through step S6, this embodiment can obtain the force of the buoyant body under a given external environment. The precise static equilibrium position (displacement of the buoyant center of gravity, dr) is obtained. This is the direct objective of mooring system design; at the same time, the static response characteristics of the mooring system (such as the "restoring force-displacement" curve), i.e., the static stiffness of the system, are obtained.

[0063] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0064] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. Any of the claimed embodiments can be used in any combination.

Claims

1. A static analysis method for a multi-point mooring system based on the elastic catenary theory, characterized in that, Includes the following steps: S1. Elastic catenary modeling of a single mooring cable: A static equilibrium model of a single mooring cable is established. The model is elastically modified by introducing the axial stiffness of the mooring cable to correct the classical catenary equation. S2. Motion of floating body and mapping of mooring point coordinates: Based on the displacement dr of the center of gravity of the floating body in the global coordinate system, the new global coordinates of each mooring point after motion are calculated through spatial coordinate transformation, and the new global coordinates and the global coordinates of the corresponding anchor points are transformed to the local coordinate system of the mooring cable to obtain the horizontal projection distance and vertical projection distance of the mooring cable in the local coordinate system. S3. Solving and coordinate transformation of the tension at the top of a single mooring cable: In the local coordinate system of the mooring cable, using the horizontal and vertical projection distances as inputs, the horizontal and vertical components of the tension at the top of the mooring cable are calculated based on the catenary equation, and the tension components are transformed to the global coordinate system. S4. Equivalent force and torque of the mooring cable tip tension on the buoy's center of gravity: The force and torque exerted by the tip tension of each mooring cable on the buoy's center of gravity can be equivalently represented as a six-degree-of-freedom force vector of a single mooring cable on the buoy. ; S5. Establishing System Equilibrium Conditions: This involves establishing the six-degree-of-freedom force vectors generated by all mooring cables acting on the floating body. By performing vector superposition, the total restoring force vector of the mooring system is obtained. ,Right now This establishes its relationship with the force vector of the external environment acting on the floating body. static equilibrium relationship between + =0; S6. System Characteristic Analysis and Equilibrium Position Determination: By providing a series of buoyancy center of gravity displacements... Repeat steps S2 to S5 to calculate the total restoring force vector of the corresponding mooring system. This establishes a mapping relationship F=F(dr) between the displacement of the buoy's center of gravity and the total restoring force vector of the mooring system. Based on this relationship, the static equilibrium equation is solved using a numerical optimization algorithm to obtain the static equilibrium position of the buoy.

2. The static analysis method for multi-point mooring systems based on the elastic catenary theory according to claim 1, characterized in that, The elastic correction to the classical catenary equation mentioned in step S1 is as follows: Where X and Z are the horizontal and vertical projected lengths of the mooring cable when it reaches static equilibrium under its own weight and end tension, respectively; H and V are the horizontal and vertical components of the end tension of the mooring cable, respectively; w is the weight per unit length of the mooring cable in water; S is the original length of the mooring cable without stress; E is the elastic modulus of the mooring cable material; A is the cross-sectional area of ​​the mooring cable; and EA is the axial stiffness of the mooring cable.

3. The static analysis method for multi-point mooring systems based on the elastic catenary theory according to claim 1, characterized in that, In step S2, the displacement dr of the buoyancy center of gravity is a six-degree-of-freedom displacement vector, defined as dr=[dx,dy,dz,rx,ry,rz]^T, where dx,dy,dz are the translational displacements of the buoyancy center of gravity in the global coordinate system, and rx,ry,rz are the Euler angle rotational displacements of the buoyancy body about its own coordinate system.

4. The static analysis method for multi-point mooring systems based on the elastic catenary theory according to claim 3, characterized in that, Step S2 specifically includes the following sub-steps: S201 calculates the new global coordinates of the mooring points after the floating body moves: For the i-th mooring point on the floating body, its initial global coordinates are... The initial global coordinates of the buoyancy center of gravity are When the floating body is displaced, the new global coordinates of the mooring point Calculated using the following formula: Where R is the rotation matrix, which is obtained by rotating the Euler rotation displacements rx, ry, rz of the floating body in sequence around the Y-axis, X-axis, and Z-axis of its own coordinate system, i.e., R = Ry(ry)Rx(rx)Rz(rz), where Ry(ry), Rx(rx), and Rz(rz) are the basic rotation matrices around the Y, X, and Z axes, respectively. S202 transforms the new global coordinates of the mooring point to the local coordinate system of the mooring cable: the new global coordinates obtained in step S201 are... Global coordinates fixed to the anchor point of the i-th mooring cable The coordinates are transformed to the local coordinate system of the mooring cable using the following formula: Obtain the horizontal projection distance and vertical projection distance .

5. The static analysis method for multi-point mooring systems based on the elastic catenary theory according to claim 1, characterized in that, In step S3, the inverse calculation uses a numerical iterative algorithm, specifically the Newton-Raphson method or the bisection method, to solve for the horizontal and vertical components of the mooring cable. and The nonlinear equation system.

6. The static analysis method for multi-point mooring systems based on the elastic catenary theory according to claim 1, characterized in that, In step S3, the tension component conversion is achieved by the following formula: in, Let represent the components of the mooring cable tip tension in the global coordinate system. Let be the rotation matrix about the Z-axis of the global coordinate system, and let be the rotation angle. For vectors The angle between the coordinate system and the positive X-axis of the global coordinate system.

7. The static analysis method for multi-point mooring systems based on the elastic catenary theory according to claim 1, characterized in that, In step S4, the six-degree-of-freedom force vector of the single mooring cable on the floating body Calculated using the following formula: In the formula, These are the coordinates of the mooring point relative to the center of gravity. , , These represent the force components along the x, y, and z axes generated by the tension of the i-th mooring cable on the center of gravity of the buoyancy in the global coordinate system. , , These represent the torque components about the x, y, and z axes generated by the tension of the i-th mooring cable about the center of gravity of the buoyancy.

8. The static analysis method for multi-point mooring systems based on the elastic catenary theory according to claim 1, characterized in that, In step S6, the numerical optimization algorithm iteratively adjusts the displacement of the buoyancy center of gravity. The trial value is obtained, and steps S2 to S5 are repeated to calculate the system residual R(dr) = F(dr) + =0, until a norm is found that makes the residual equal to 0. Minimum displacement of the center of gravity of buoyancy This is the static equilibrium position.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor runs the computer program, it performs the method as described in any one of claims 1 to 8.

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