An underwater sling cable tension solution method based on absolute nodal coordinate method

Abstract

The application provides a method for solving underwater cable tension based on an absolute nodal coordinate method. The method first introduces the absolute nodal coordinate method into underwater cable dynamics analysis, constructs system equations by using node position vectors and gradient vectors in a global coordinate system, and makes the mass matrix constant, thereby eliminating geometric nonlinear errors caused by a small rotation assumption in a traditional finite element method in principle, and avoiding additional calculation burden of updating the mass matrix at each step.

Description

Technical Field

[0001] This invention relates to the field of marine engineering structure dynamics analysis technology, and in particular to a method for solving underwater cable tension based on the absolute nodal coordinate method. Specifically, it relates to a numerical calculation method for solving the dynamic tension of flexible cables in marine lifting operations and underwater towing systems under the combined action of ship motion and wave loads. This method can be directly applied to safety monitoring of deep-sea lifting operations, real-time prediction of cable tension, and dynamic response assessment of flexible marine structures. Background Technology

[0002] In marine engineering lifting operations, the lifting cable connects the surface mother ship to the underwater load, and its dynamic tension directly affects operational safety and equipment lifespan. During operation, the lifting cable is subjected to a combination of complex loads, including ship motion excitation, wave hydrodynamic loads, ocean current forces, and its own weight and buoyancy, exhibiting geometrically nonlinear characteristics of large deformation and large rotation angles. Traditional finite element methods based on the assumption of small deformation are insufficient to accurately describe the real-time spatial configuration and cross-sectional tension distribution of the lifting cable.

[0003] Currently, scholars and engineers both domestically and internationally mainly employ the following technical solutions to address the problem of solving cable tension: (1) Multibody dynamics method based on lumped mass method. This method discretizes the cable into a series of lumped mass points, with adjacent mass points connected by massless spring-damper systems, transforming the dynamics problem of continuous cables into a set of ordinary differential equations for solving a multi-rigid-body system. The lumped mass method has the advantages of simple model and high computational efficiency, and is widely used in preliminary engineering design. However, this method provides a relatively coarse description of the cable bending stiffness, usually ignoring the bending stiffness or simplifying the bending effect to the angle spring between adjacent mass points, which can easily generate spurious high-frequency numerical oscillations under high-frequency wave excitation or rapid speed change conditions. In addition, the lumped mass model is difficult to accurately capture the axial strain distribution of the cable cross-section, and its tension calculation usually depends on the distance change between adjacent mass points, with accuracy limited by the discrete density of the mass points.

[0004] (2) Beam element model based on traditional finite element method. This type of method uses Euler-Bernoulli beam elements or Timoshenko beam elements to spatially discretize the suspension cable, constructs the element stiffness matrix and mass matrix through nodal displacement interpolation functions, and then solves the system dynamic equations. Traditional beam elements have high computational accuracy when describing small rotation and small deformation conditions. However, when the suspension cable undergoes large deformation and large rotation, the small rotation assumption no longer holds, and the high-order geometric nonlinear terms neglected in the element stiffness matrix will introduce significant model errors. To compensate for this deficiency, it is usually necessary to use updated Lagrange schemes or corotation coordinate methods for nonlinear iterative solutions. However, these methods require updating the element coordinate system and stiffness matrix in each iteration, which significantly increases the computational cost. Furthermore, numerical ill-conditioned problems such as shear locking and volume locking may occur in the large curvature bending region, leading to a decrease in computational accuracy or even solution divergence.

[0005] (3) Cable dynamics analysis based on general commercial software. Professional marine engineering cable analysis software, such as OrcaFlex, integrates cable dynamics solution modules using the lumped mass method and the finite element method, enabling coupled time-domain analysis of waves, cables, and hulls. This type of software has been validated by numerous engineering cases, and the calculation results have high engineering reliability. However, its core solution algorithm is usually kept confidential as a trade secret, making it difficult for users to adjust algorithmic parameters and improve models for specific working conditions. At the same time, the setting of the drag force coefficient in commercial software often relies on user experience, which limits the applicability of its built-in models for non-standard cross-section cables or special operating conditions.

[0006] The absolute nodal coordinate method (ANCF), proposed by Shabana in 1996, is a finite element method specifically developed for the dynamic analysis of flexible multibody systems with large deformation and rotation. Unlike traditional methods, ANCF uses nodal position vectors and gradient vectors in a global coordinate system as generalized coordinates, abandoning the concept of rotational degrees of freedom and fundamentally avoiding the singularity problem caused by rotational parameterization. Within this theoretical framework, the system's mass matrix is ​​a constant matrix, with no centrifugal or Coriolis force terms, and the expression of inertial forces in the equations of motion is simple. Simultaneously, the nodal gradient vectors directly describe the tangential direction and tensile state of the cable axis, allowing axial Green's strain and cross-sectional tension to be directly solved through the geometric relationship of the gradient vectors without additional local coordinate system transformations. Therefore, this invention uses the absolute nodal coordinate method to solve the dynamic tension of underwater cables under the combined action of ship motion and wave loads. Summary of the Invention

[0007] The purpose of this invention is to solve the problems in the prior art by proposing a method for solving the tension of underwater cable based on the absolute node coordinate method.

[0008] This invention is achieved through the following technical solution: This invention proposes a method for solving underwater cable tension based on the absolute node coordinate method, the method comprising: Step 1: Spatial discretization of the suspension cable and definition of generalized coordinates; Step 2: Construct a consistent quality matrix for the system; Step 3: Calculate the elastic force vector and tangent stiffness matrix; Step 4: Calculate the generalized external force vector; Step 5: Apply boundary conditions for ship motion; Step Six: Solve for the system dynamic response by time integration; Step 7: Extract the total dynamic tension at any node of the suspension cable.

[0009] Further, in step one, the suspension cable with a total length of L is uniformly discretized into n three-dimensional two-node ANCF cable elements along its axial direction, and the original length of each element is... Each unit contains two nodes, denoted as node I and node J; each node has 6 generalized coordinates: node position vector. and node gradient vector The magnitude of the gradient vector It characterizes the axial tension state at this point, and the direction of the gradient vector represents the tangential direction of the cable axis.

[0010] Furthermore, in step two, the unit-consistent quality matrix... We obtain it from the following formula: ; In the formula, The bulk density of the suspension cable material. Let be the cross-sectional area of ​​the suspension cable. Let be the element cable length. Substituting the shape function expression and integrating, we obtain the analytical form of the element mass matrix, where each block is a scalar multiplied by the identity matrix. for A symmetric positive definite matrix that does not depend on the node coordinates. .

[0011] Furthermore, in step three, the total elastic potential energy of the suspension cable is composed of the axial tensile strain energy. and bending strain energy It consists of two parts; elastic force vector Defined as the gradient of the total potential energy with respect to the system's generalized coordinates: .

[0012] Furthermore, in step four, the generalized external force vector It includes contributions from three parts: effective gravity in water, wave hydrodynamic load, and concentrated load at the end.

[0013] Furthermore, in step five, the boundary conditions include the ship's motion input, the additional translational motion generated by the rotational degrees of freedom, the combined constraint displacement, and the applied constraints.

[0014] Furthermore, in step six, the reduced system motion equations are integrated over time using the explicit central difference method; the time domain is discretized into equally spaced steps. , record the A moment in a time step The corresponding system generalized coordinate vector, velocity vector, and acceleration vector are denoted as follows: , , The system's generalized coordinates are divided into a set of constrained degrees of freedom. and the set of degrees of freedom The displacement, velocity, and acceleration of the constrained degrees of freedom are directly given by the analytical expression of ship motion and do not participate in numerical integration; they are only applied to... To proceed.

[0015] Furthermore, in step seven, the elastic force vector component at any specified node of the suspension cable is extracted from the obtained system response, and the total dynamic tension borne by the node is calculated; the total tension reflects the resultant force contribution of all internal force components of the suspension cable on the node cross section in the degree of freedom of the node position.

[0016] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the underwater cable tension solution method based on the absolute node coordinate method.

[0017] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the underwater cable tension solution method based on the absolute node coordinate method.

[0018] The beneficial effects of this invention are: This invention addresses the challenging problem of solving the dynamic tension of flexible cables under large deformation in deep-sea cable deployment operations. For the first time, it fully introduces the absolute nodal coordinate method into the dynamic analysis of underwater cables. By constructing system equations using nodal position vectors and gradient vectors in a global coordinate system, the mass matrix remains constant, fundamentally eliminating the geometric nonlinearity errors caused by the small rotation assumption in traditional finite element methods, while also avoiding the additional computational burden of updating the mass matrix at each step. Based on this, an elastic force model coupling axial tension and bending deformation is established, using Green's law... Lagrange strain and spatial curvature scalars describe two deformation modes respectively, and numerical differentiation techniques are used to calculate the tangent stiffness matrix, ensuring strict consistency between the elastic force vector and the stiffness matrix at the numerical discretization level. For the boundary conditions of the ship's six degrees of freedom motion, a constraint application strategy of linear superposition of translational and rotational forces is proposed. The rotational components such as roll, pitch, and yaw are directly converted into equivalent additional translational forces through the lever arm of the lifting point relative to the center of gravity, and algebraically superimposed with the three translational degrees of freedom. This eliminates the need to construct rotational matrices or perform complex angular velocity synthesis, significantly simplifying the boundary processing procedure. At the same time, the displacement, velocity, and acceleration of the constraint points are all given analytically and forcibly updated at each step, ensuring a high degree of coordination of the three kinematic elements at the boundary and greatly improving the numerical stability of long-term simulations. In the wave hydrodynamic calculation, a smooth transition processing is applied to the towing force in the low relative velocity range, further enhancing the computational robustness. Furthermore, the total tensile force of the cross section can be directly extracted based on the components of the elastic force vector. This tensile force includes multiple contributions such as axial tension, bending deformation and its associated shear force, which can truly reflect the comprehensive bearing state of any cross section of the cable and overcome the limitation of traditional methods that it is difficult to separate tension information from nodal reaction forces.

[0019] Compared with existing technologies, the method described in this invention has the following advantages: high computational accuracy, capable of accurately capturing the large deformation nonlinear response of the cable under the combined excitation of ship motion and waves; good numerical stability, suitable for long-term, multi-condition continuous simulation, effectively suppressing numerical oscillations caused by boundary inconsistencies and load mutations; all six degrees of freedom motion parameters can be independently and flexibly configured, covering a variety of operational scenarios from simple heave to fully coupled ship motion, with strong adaptability; the linear superposition processing of boundary conditions is simple to implement, lowering the threshold for engineering applications; the extracted total tension has a clear physical meaning, and can be directly used for strength verification and operational safety assessment without additional post-processing; the entire solution framework has good versatility and scalability for cable length, cross-sectional dimensions, material properties, wave parameters, and ship motion patterns, and can be easily extended to the dynamic analysis of various flexible marine structures such as mooring cables, towing cables, and risers. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of the motion curve of a ship facing the waves under the action of regular waves.

[0022] Figure 2This is a time-history diagram of the tension of the first node cable under the action of a regular wave, based on the ship's motion input at the first end.

[0023] Figure 3 This is a time-history diagram of the tension at the end node of the suspending cable, based on the ship's motion input at the forward end under the action of a regular wave.

[0024] Figure 4 This is a schematic diagram of the displacement of the suspended object in the X direction under the condition of being subjected to a thrust of 690 kgf in the X direction.

[0025] Figure 5 This is a schematic diagram of the displacement of the suspended object in the Z direction under the condition of being subjected to a thrust of 690 kgf in the X direction.

[0026] Figure 6 This is a diagram showing the shape of the cable at a certain moment.

[0027] Figure 7 The simulation and experimental comparison diagram shows the application of the method of the present invention to the scaled-down experiment. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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.

[0029] This invention proposes an underwater cable tension solution method based on the absolute node coordinate method. By discretizing the cable into multiple three-dimensional two-node ANCF cable elements, an accurate finite element model including axial tensile stiffness and bending stiffness is established. A dynamic equation framework with a constant consistent mass matrix and nonlinear elastic force vector is adopted. The wave hydrodynamic load is calculated by combining the Morison equation, and the dynamic total tension of the cross section is directly extracted through the elastic force vector.

[0030] Specifically, in combination Figures 1-7 This invention proposes a method for solving underwater cable tension based on the absolute nodal coordinate method, the method comprising: Step 1: Spatial discretization of the suspension cable and definition of generalized coordinates; Further, in step one, the suspension cable with a total length of L is uniformly discretized into n three-dimensional two-node ANCF cable elements along its axial direction, and the original length of each element is... Each unit contains two nodes, denoted as node I and node J; each node has 6 generalized coordinates: node position vector. (The spatial coordinates of the node in the global coordinate system O-XYZ) and the node gradient vector (The partial derivative of the position vector at this node with respect to the material coordinate x); the magnitude of the gradient vector It characterizes the axial tension state at this point, and the direction of the gradient vector represents the tangential direction of the cable axis.

[0031] The node coordinate vector of a cell for Column vectors:

[0032] The total degrees of freedom of the entire cable system is The system's generalized coordinate vector The coordinates of all nodes are arranged in order.

[0033] Any point within the unit (material coordinates) The position in the global coordinate system is obtained through cubic Hermite interpolation: .

[0034] In the formula: for The shape function matrix, in block form, is:

[0035] for Identity matrix, scalar form function to From dimensionless coordinates Provided.

[0036]

[0037]

[0038]

[0039]

[0040] The first and second derivatives of position with respect to the material coordinates are expressed as follows: , .

[0041] The derivatives of the shape functions are: , , ,

[0042] , , , .

[0043] Step 2: Construct a consistent quality matrix for the system; Furthermore, in step two, one of the core advantages of the ANCF unit is the system's mass matrix. This is a constant matrix, unchanging with system configuration, and does not need to be recalculated at every time step. (Element-consistent mass matrix) We obtain it from the following formula: ; In the formula, The bulk density of the suspension cable material , The cross-sectional area of ​​the suspension cable , Unit cable length Substituting the shape function expression and integrating, we obtain the analytical form of the element mass matrix, where each block is a scalar multiplied by the identity matrix. for A symmetric positive definite matrix that does not depend on the node coordinates. .

[0044] Step 3: Calculate the elastic force vector and tangent stiffness matrix; Furthermore, in step three, the total elastic potential energy of the suspension cable is composed of the axial tensile strain energy. and bending strain energy It consists of two parts; elastic force vector Defined as the gradient of the total potential energy with respect to the system's generalized coordinates: .

[0045] (1) Axial tensile strain energy and elastic force Using the Green-Lagrange strain metric, the axial strain at any point within the element is:

[0046] The axial strain energy of the element is

[0047] In the formula elastic modulus axial elastic force contribution Depend on Generalized coordinates of unit Taking the partial derivative, we get:

[0048] in: .

[0049] (2) Bending strain energy and elastic force Bending deformation is measured using a curvature scalar, and the bending curvature at any point within the element is:

[0050] In the formula The symbol × represents the cross product of three-dimensional vectors, | | represents the Euclidean norm.

[0051] The element bending strain energy is:

[0052] in Let be the moment of inertia of the cross section.

[0053] Flexural elastic force contribution Depend on right Taking the partial derivative, we get:

[0054] For calculation Let the auxiliary vector be:

[0055] but Apply the chain rule: ,in:

[0056] cross product right The partial derivatives can be given by the following formula:

[0057] in Represents the vector The resulting antisymmetric matrix satisfies:

[0058] The total elastic force vector of the element is the sum of its axial and bending contributions: .

[0059] Step 4: Calculate the generalized external force vector; Furthermore, in step four, the generalized external force vector It includes contributions from three parts: effective gravity in water, wave hydrodynamic load, and concentrated load at the end.

[0060] (1) Effective gravity in water (self-weight minus buoyancy) The effective weight per unit length of cable in water (vertically downward) is: In the formula: seawater density Unit gravity equivalent nodal force We obtain this through integration of the shape function:

[0061] (2) Wave hydrodynamic loads (Morison equation) The wave hydrodynamic force per unit length of cable is calculated using the Morison semi-empirical formula, which is determined by the drag force. and inertial force The result of superposition is:

[0062] First, calculate the local tangential unit vector of the cable:

[0063] Let the velocity of the water particles be... The structural velocity is relative speed .Will It is decomposed into normal components and tangential components.

[0064]

[0065]

[0066] The drag force is proportional to the square of the relative velocity, and its direction is the same as the relative velocity.

[0067] The normal drag force and the tangential drag force are respectively

[0068]

[0069] In the formula: and These are the normal and tangential drag coefficients, respectively, which are 0.8~1.2 and 0.05~0.15 for cylindrical cables.

[0070] The total drag force is the sum of the normal and tangential contributions:

[0071] The inertial force consists of two parts: the Froude-Krylov force (the pressure gradient force caused by the acceleration of water particles) and the additional mass force (the reaction force generated by the acceleration of the cable causing the surrounding fluid to accelerate). Its complete expression is:

[0072] In the formula, For the acceleration of water particles, superscript n and t These represent the normal and tangential components, respectively. This refers to structural acceleration. and The inertial force coefficient is recommended as 2.0 for the normal direction and 1.0 to 1.2 for the tangential direction.

[0073] The kinematic quantities of the water particles are given by the deep-water Airy wave theory. Let the angle between the wave propagation direction and the X-axis be θ. wave number is angular frequency Then the velocity of water particles and acceleration The analytical formula is:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] In the formula For wave height, Global vertical coordinates (positive for upward, water surface) underwater ), wave number Satisfying the deep-water dispersion relation: .

[0080] The hydrodynamic equivalent nodal force is obtained by integrating the shape functions:

[0081] (3) Concentrated load of the end-lifted object The quality of the cable end connection is The underwater suspended object. The effective gravity vector of the suspended object in the water is:

[0082] in The volume of water discharged from the suspended object is given. Furthermore, the hydrodynamic damping force experienced by the suspended object during its movement can be modeled using a piecewise linear or quadratic damping model, and after smoothing, applied as a concentrated force to the positional degrees of freedom of the system's end nodes.

[0083] Assemble the three external forces according to their degrees of freedom to obtain the generalized external force vector of the system. .

[0084] Step 5: Apply boundary conditions for ship motion; Furthermore, in step five, the boundary conditions include the ship's motion input, the additional translational motion generated by the rotational degrees of freedom, the combined constraint displacement, and the applied constraints.

[0085] (1) Ship motion input The first node of the rigging cable (the first node of the system) is subject to forced displacement constraints due to the ship's motion. The ship's motion is described by rigid body motion with six degrees of freedom, each of which is input as an independent function and is a known function of time t.

[0086] (2) Additional translational motion and combined constrained displacements generated by rotational degrees of freedom The fixed position of the lifting point P in the ship's coordinate system is denoted as: .

[0087] in This is a longitudinal offset (positive towards the bow). This is a lateral offset (positive to port). This is the vertical offset (positive for upward).

[0088] The rotation of the ship causes an additional translational displacement of the sling point P fixed to the hull in the global coordinate system. This additional translational displacement caused by the rotation can be approximated by a linearization method, which directly obtains the result by multiplying the angle (in radians) by the coordinates of the sling point relative to the center of gravity. Additional translation in the X direction (caused by pitch and roll):

[0089] Additional translation in the Y direction (caused by roll and pitch):

[0090] Additional translational motion in the Z direction (caused by roll and pitch):

[0091] The additional translational motion generated by the rotation is superimposed with the translational motion of the center of gravity to obtain the combined constrained displacement of the lifting point in the global coordinate system:

[0092]

[0093]

[0094] The corresponding composite constraint velocity and composite constraint acceleration are obtained by taking the first and second derivatives of the above displacement expression with respect to time, respectively.

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] (3) Apply constraints The synthesized constraint displacement, constraint velocity, and constraint acceleration are directly assigned to the three positional degrees of freedom of the first node (the first to third components of the system's generalized coordinates):

[0101]

[0102]

[0103] in This represents the constraint degree-of-freedom vector (degrees of freedom 1-3 of the first node). The gradient degree-of-freedom of the first node (degrees of freedom 4-6) remains free and evolves naturally from the system dynamics equations without any mandatory constraints.

[0104] The solution process for this constraint at each time step is as follows: 1. Perform dynamic solution on the entire system to obtain intermediate solutions for all degrees of freedom, including the first node. 2. The intermediate solution Replace the first node position degree of freedom value with the current composite constraint displacement. 3. Forcibly update the velocity and acceleration of the first node's position degree of freedom to the current composite constraint velocity. and combined constrained acceleration .

[0105] Step Six: Solve for the system dynamic response by time integration; Furthermore, in step six, the reduced system motion equations are integrated over time using the explicit central difference method; the time domain is discretized into equally spaced steps. , record the A moment in a time step The corresponding system generalized coordinate vector, velocity vector, and acceleration vector are denoted as follows: , , The system's generalized coordinates are divided into a set of constrained degrees of freedom. and the set of degrees of freedom The displacement, velocity, and acceleration of the constrained degrees of freedom are directly given by the analytical expression of ship motion and do not participate in numerical integration; they are only applied to... To proceed.

[0106] The discrete equations of motion for each degree of freedom are derived using a central difference scheme. At any given moment, the relationship between acceleration, displacement, and velocity in each degree of freedom is approximated using a second-order central difference:

[0107]

[0108] Substituting the above approximation into the equation of motion for the degrees of freedom, and rearranging, we obtain the following about... The explicit recurrence formula:

[0109] In the formula This is an optional damping matrix sub-block. This invention employs the stiffness proportional damping form of Rayleigh damping. ,in This is the stiffness proportionality factor. This represents the linear stiffness matrix under the current configuration. This damping effectively absorbs high-frequency numerical oscillations while having minimal impact on the low-frequency physical response.

[0110] Start the first step At this time, it is necessary to construct a virtual "previous step" displacement. Using initial acceleration and initial velocity It is derived by inversely from the central difference relation.

[0111]

[0112] Within each time step, first calculate the elastic force vector under the current configuration. and external force vector Assemble the tangent stiffness matrix And form a damping matrix Then, extract the free degree-of-freedom sub-blocks and solve them according to the above recursive formula. Then, the displacement, velocity, and acceleration of the constrained and free degrees of freedom are updated to complete one time step.

[0113] Through the above explicit recursive process, all generalized coordinates, velocities, and accelerations of the system at each discrete moment can be obtained sequentially, thus completing the solution of the dynamic response of the system throughout the entire simulation period.

[0114] Step 7: Extract the total dynamic tension at any node of the suspension cable.

[0115] Furthermore, in step seven, the elastic force vector component at any specified node of the suspension cable is extracted from the obtained system response, and the dynamic total tension borne by the node is calculated; the total tension reflects the resultant force contribution of all internal force components (axial tension, bending, shear) of the suspension cable on the node cross section in the degree of freedom of the node position.

[0116] Let the first The global elastic force vector at each time step is For any specified first Each node has a corresponding elastic force vector located at [node number]. The arrive Line, denoted as:

[0117] According to the definition of elastic force vector: , It is the total strain energy of the system. The partial derivative with respect to the coordinates of the k-th node has the physical meaning of the elastic restoring force acting on the degree of freedom of that node.

[0118] According to the principle of action and reaction, the first The internal force vector borne by the cable section at each node and Equal in size, opposite in direction:

[0119] The total dynamic tension (scalar) at this node is taken as the Euclidean norm of the vector:

[0120] , , The first The total tension vector at each node is globally , , The directional component.

[0121] This refers to the program sequence output by the method of this invention for the dynamic total tension at any specified node of the suspension cable. This value is strictly equal to the resultant projection of all stress components of the suspension cable on the cross-section of that node in the normal direction of the cross-section. It includes the comprehensive contribution of axial tension, bending deformation, and bending deformation and its associated cross-sectional shear force (i.e., the lateral force caused by bending), and is an engineering mechanics index that truly reflects the bearing state of any cross-section of the suspension cable. First node This refers to the total dynamic tensile force at the lifting point, and the final node. This refers to the total dynamic tensile force at the connection point of the suspended load. (Intermediate node) This reflects the internal force transmission in each section of the suspension cable.

[0122] Through the seven steps described above in this invention, a high-precision solution for the dynamic tension of any node of an underwater cable under the combined action of ship motion and wave load can be achieved, and the total tension time history of each node and the complete kinematic response of the system can be output completely.

[0123] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the underwater cable tension solution method based on the absolute node coordinate method.

[0124] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the underwater cable tension solution method based on the absolute node coordinate method.

[0125] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0126] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0127] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0128] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as execution by a hardware decoding processor, or as a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0129] The above provides a detailed description of the underwater cable tension calculation method based on the absolute node coordinate method proposed in this invention. Specific examples are used to illustrate the principle and implementation of this invention. The above description of the embodiments is only for the purpose of helping to understand the method and core idea of ​​this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for solving underwater cable tension based on the absolute nodal coordinate method, characterized in that, The method includes: Step 1: Spatial discretization of the suspension cable and definition of generalized coordinates; Step 2: Construct a consistent quality matrix for the system; Step 3: Calculate the elastic force vector and tangent stiffness matrix; Step 4: Calculate the generalized external force vector; Step 5: Apply boundary conditions for ship motion; Step Six: Solve for the system dynamic response by time integration; Step 7: Extract the total dynamic tension at any node of the suspension cable.

2. The method according to claim 1, characterized in that, In step one, the suspension cable with a total length of L is uniformly discretized into n three-dimensional two-node ANCF cable elements along its axial direction, and the original length of each element is... Each unit contains two nodes, denoted as node I and node J; each node has 6 generalized coordinates: node position vector. and node gradient vector The magnitude of the gradient vector It characterizes the axial tension state at this point, and the direction of the gradient vector represents the tangential direction of the cable axis.

3. The method according to claim 2, characterized in that, In step two, the unit uniformity mass matrix We obtain it from the following formula: ； In the formula, The bulk density of the suspension cable material. Let be the cross-sectional area of ​​the suspension cable. Let be the element cable length. Substituting the shape function expression and integrating, we obtain the analytical form of the element mass matrix, where each block is a scalar multiplied by the identity matrix. for A symmetric positive definite matrix that does not depend on the node coordinates. .

4. The method according to claim 3, characterized in that, In step three, the total elastic potential energy of the suspension cable is composed of axial tensile strain energy. and bending strain energy It consists of two parts; elastic force vector Defined as the gradient of the total potential energy with respect to the system's generalized coordinates: 。 5. The method according to claim 4, characterized in that, In step four, the generalized external force vector It includes contributions from three parts: effective gravity in water, wave hydrodynamic load, and concentrated load at the end.

6. The method according to claim 5, characterized in that, In step five, the boundary conditions include the ship's motion input, the additional translational motion generated by the rotational degrees of freedom, the combined constraint displacement, and the applied constraints.

7. The method according to claim 6, characterized in that, In step six, the reduced system equations of motion are integrated over time using the explicit central difference method; the time domain is discretized into equally spaced steps. , record the A moment in a time step The corresponding system generalized coordinate vector, velocity vector, and acceleration vector are denoted as follows: , , The system's generalized coordinates are divided into a set of constrained degrees of freedom. and the set of degrees of freedom The displacement, velocity, and acceleration of the constrained degrees of freedom are directly given by the analytical expression of ship motion and do not participate in numerical integration; they are only applied to... To proceed.

8. The method according to claim 7, characterized in that, In step seven, the elastic force vector component at any specified node of the suspension cable is extracted from the obtained system response, and the total dynamic tension borne by the node is calculated. This total tension reflects the resultant force contribution of all internal force components of the suspension cable on the node cross section in the degree of freedom of the node position.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-8.

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