Dynamic modeling method for parameters of large-flexibility mooring anchor chain

Abstract

The invention belongs to the field of computational mechanics, and discloses a dynamic modeling method for parameters of a large-flexibility mooring anchor chain. On the basis of concentrated mass method modeling, the parameter variation principle is introduced, the nonlinear tension and the nonlinear seabed contact force of the mooring anchor chain are arranged into a unified expression containing parameters in a segmented expression form, and the nonlinear behavior of the anchor chain can be corrected by updating and iterating the parameters. The prediction of the motion state of the anchor chain at the next moment according to the motion state at the current moment in the traditional algorithm is avoided, the dynamic modeling simulation precision of the mooring anchor chain is greatly improved, and a foundation is laid for the subsequent dynamic algorithm solution of the mooring anchor chain.

Description

Technical Field

[0001] The invention belongs to the field of computational mechanics and relates to a method for dynamic modeling of parameters of a large-flexibility mooring anchor chain. Background Art

[0002] The mooring system of the deep-sea platform is a complex, time-varying dynamic system that is subject to the combined effects of complex loads such as wind, waves, and currents. In addition, there is a strong nonlinear effect between the floating body and the mooring system. When the platform has large displacements and large rotations, the geometric nonlinearity of the mooring chain and the nonlinearity of the contact between the chain and the seabed need to be considered. The traditional calculation method is to apply pre-tension according to the breaking strength of the chain to avoid the nonlinear behavior of the chain in tension and compression. Even so, when encountering severe sea conditions, the platform movement amplitude increases, and relaxation-tension changes will still occur, and the nonlinear behavior of the chain is inevitable. Therefore, it is a key issue in the study of mooring systems to carry out research on efficient simulation technology for the strong nonlinear behavior of large-flexibility mooring chains and establish an accurate nonlinear simulation model for mooring chains.

[0003] Current methods, such as Tang Yougang's "Calculation of deep-sea mooring impact tension by lumped mass method" and Hall's "Validation of a lumped-mass mooring line model with DeepCwindsemisubmersible model testdata", mostly use the lumped mass method to assume that the anchor chain is a nonlinear catenary composed of many lumped mass points and massless springs, and the gravity, tension, seabed contact force, damping force, additional mass force and fluid drag force are equivalent to the nodes to establish the calculation model of the anchor chain configuration and dynamics. For the treatment of the nonlinearity of the mooring anchor chain and the nonlinearity of the anchor chain-seabed contact, the traditional method mostly uses the second-order Runge-Kutta method with a constant time step to solve it. According to the tension-relaxation state of the anchor chain at the current moment and the contact with the seabed, the tension of the anchor chain and the seabed contact force are calculated, and the dynamic integration is performed. Since the mooring system is a complex nonlinear system, the motion state at the current moment cannot well predict the motion state of the anchor chain at the next moment, so this simplified calculation method will affect the simulation accuracy of the mooring system.

[0004] In order to solve the above technical problems, the present invention establishes parametric dynamic modeling of mooring anchor chain based on the parametric variation principle. By iterative parameter variable method, the nonlinear behavior of the mooring anchor chain is judged, and a more accurate dynamic simulation of the high-flexibility mooring anchor chain is achieved, which is of great significance to improving the simulation efficiency of the dynamic modeling of the mooring anchor chain. Summary of the invention

[0005] The purpose of the present invention is to provide a more accurate dynamic modeling method for parameters of a large-flexibility mooring anchor chain.

[0006] The technical solution of the present invention:

[0007] A parametric dynamic modeling method for a highly flexible mooring anchor chain, the steps are as follows:

[0008] (1) Dynamic model of mooring chain based on lumped mass method

[0009] Based on the lumped mass method, the dynamic analysis of the mooring chain is carried out, and the mooring chain is equivalent to a nonlinear catenary composed of many lumped mass points and massless springs; the point where the lumped mass is located is called a node, and the nodes are numbered from 0 to N, where node 0 is the fixed end on the seabed and node N is the excitation end connected to the floating platform; considering the gravity, buoyancy, fluid drag force, elastic elongation of the mooring cable, additional water mass and inertia force of the mooring chain, the motion differential equations of each node of the mooring chain are established through Newton's second law; it is assumed that the gravity and buoyancy of the mooring chain act on the lumped mass point, and the drag force on each mooring chain segment is equally divided into two nodes on its left and right, and the equivalent tangential and normal drag forces acting on the node are obtained; since the motion state of the fixed end and the excitation end is known, it is only necessary to establish the motion equations for the middle nodes; the motion equations of the middle nodes of the mooring chain are:

[0010]

[0011] In the formula, m i is the mass of the node, m ai is the additional mass of the node, r i is the state vector of the node, T i+(1 / 2) and C i+(1 / 2) is the tension and internal damping force acting on segment i+1 / 2, D qi and D pi are the tangential and normal drag forces acting on the node, W i and B i is the gravity and buoyancy of the node;

[0012] (2) Establishing a parametric variable model for the tensile and compressive nonlinearity of the mooring chain

[0013] The parametric model of the mooring anchor chain is established based on the parametric variation principle. According to the parametric variation principle, when the mooring anchor chain has tensile and compressive nonlinearity, that is, the tensile stiffness and compressive stiffness coefficients are inconsistent, the segmented constitutive relationship can be organized into a unified expression constrained by corresponding complementary conditions by introducing parameter variables. Since the mooring anchor chain can only bear tensile loads, when the mooring anchor chain is relaxed, the mooring anchor chain is not subjected to stress and has tensile and compressive nonlinear characteristics. The segmented constitutive relationship expression of the mooring anchor chain is:

[0014]

[0015] In the formula, E is the elastic modulus of the mooring anchor chain, d is the equivalent diameter, and l is the unstretched length of the anchor chain segment. Based on the parametric variation principle, the dynamic modeling analysis of the tensile and compressive nonlinear behavior of the mooring anchor chain is carried out, and the parameter λ is introduced

[0016]

[0017] The above formula is equivalent to the complementary condition:

[0018]

[0019] Where, ν i+1 is the constraint relaxation variable of the corresponding equation; then the tension is written as a unified expression:

[0020]

[0021] (3) Establishing a parametric variable model for the seabed contact nonlinearity of the mooring anchor chain

[0022] Similarly, since the existence of the seabed contact force is premised on the contact between the mooring chain and the seabed, the seabed contact force can also be written in segmented form:

[0023]

[0024] In the formula, z bot is the z-direction coordinate of the seabed, z i and are the displacement and velocity of the anchor chain node in the z direction, k b is the stiffness coefficient, which indicates the stiffness per unit area of ​​the seabed; c b is the damping coefficient representing the viscous damping per unit area of ​​the seabed; is a unit direction vector, indicating the z-axis direction; similarly, based on the parametric variation principle, the dynamic modeling analysis of the nonlinear behavior of the mooring anchor chain in seabed contact is carried out, and the parametric variables β and γ are introduced.

[0025]

[0026] The above formula is equivalent to the complementary condition:

[0027]

[0028] In the formula, α i and μ i are the constraint contact variables of the corresponding equations respectively, then the seabed contact force of the node can be written as a unified expression:

[0029]

[0030] (4) Parametric dynamic equations of the entire mooring chain

[0031] Finally, the above node force expressions are summarized and sorted out to obtain the motion equation of the mooring anchor chain node; the motion equation of the mooring anchor chain node is assembled according to the finite element method to establish the parametric dynamic equation of the entire mooring anchor chain:

[0032]

[0033] Where M, C and K are the mass matrix, damping matrix and stiffness matrix of the mooring chain system, respectively; g0 is the linear external force and g1 is the nonlinear external force; the motion state of each node of the mooring chain at the initial moment is taken as the initial condition, and the motion state of the fixed end and the excitation end of the mooring chain at any moment is taken as the boundary condition, and the parametric dynamic equation of the mooring chain is numerically solved:

[0034]

[0035] In the formula, r(0) represents t k = the initial state vector at time 0, r0(t) represents the state vector of the anchor chain fixed end at any time, r N (t) represents the state vector of the anchor chain excitation end at any time, and is the corresponding derivative expression;

[0036] (5) Numerical solution

[0037] The parametric dynamic equations (10) and initial boundary conditions (11) are combined, and the equations are reduced to obtain a complete set of partial differential equations. Finally, the fourth-order Runge-Kutta method is used to integrate and solve the equations in the time domain. When the fourth-order Runge-Kutta explicit algorithm is used for solving, it is known that at the current time t k The motion state at the moment is substituted into the complementary conditions (4) and (8) to obtain t k Substituting the parameter value at time t into the Runge-Kutta method recursive expression, we can get k+1 =t k +Δt is the motion state of the node at time; when the implicit algorithm is used for solution, similarly, each time the motion state is updated, the complementary conditions need to be substituted to update the corresponding parameter values, and the solution is iterated until the accuracy requirements are met.

[0038] Beneficial effects of the present invention: Based on the modeling of the concentrated mass method, the present invention introduces the variational principle of parameters, and organizes the nonlinear tension and nonlinear seabed contact force of the mooring anchor chain from a segmented expression form into a unified expression containing parameters. By updating the iterative parameters, the nonlinear behavior of the anchor chain can be corrected. This avoids the prediction of the motion state of the anchor chain at the next moment based on the motion state at the current moment by the traditional algorithm, greatly improves the accuracy of the dynamic modeling and simulation of the mooring anchor chain, and lays the foundation for the subsequent solution of the dynamic algorithm of the mooring anchor chain. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is the flow chart of dynamic modeling of mooring anchor chain parameters.

[0040] Figure 2 is the anchor chain node number.

[0041] Figure 3 It is the force analysis of anchor chain node.

[0042] Figure 4 is a bar structure with different tensile and compressive stiffness, where (a) is K (+) <K (-) , (b) is K (+) >K (-) .

[0043] Figure 5 is a parametric variational model.

[0044] Figure 6 It is a schematic diagram of the constitutive relationship of the anchor chain, where (a) is the schematic diagram of the relaxation-tension of the anchor chain, and (b) is the constitutive relationship diagram of the anchor chain.

[0045] Figure 7 It is a schematic diagram of anchor chain-seabed contact, where (a) is a schematic diagram of anchor chain-seabed contact, and (b) is a diagram showing the relationship between anchor chain seabed contact force and z coordinate.

[0046] Figure 8 It is the displacement response history diagram of 12 nodes of anchor chain over time, where (a) is the displacement in x direction and (b) is the displacement in z direction.

[0047] Fig. 9 This is the tension response history diagram of the 20th section of the anchor chain over time.

[0048] Fig.10 This is the response history diagram of the seabed contact force at anchor chain node 1 over time. DETAILED DESCRIPTION

[0049] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0050] Based on the parametric variation principle, a parametric dynamic model of a highly flexible mooring anchor chain is established, and efficient modeling and simulation of a highly flexible mooring anchor chain is achieved. The present invention is further described in detail below in conjunction with the accompanying drawings and the accompanying reference numerals. The specific technical solution is as follows:

[0051] (1) Dynamic model of mooring chain based on lumped mass method

[0052] Based on the lumped mass method, the dynamic analysis of the mooring chain is carried out, and the mooring chain is equivalent to a nonlinear catenary composed of many lumped mass points and massless springs; the point where the lumped mass is located is called a node, and the nodes are numbered from 0 to N, where node 0 is the fixed end on the seabed and node N is the excitation end connected to the floating platform; considering the gravity, buoyancy, fluid drag force, elastic elongation of the mooring cable, additional water mass and inertia force of the mooring chain, the motion differential equations of each node of the mooring chain are established through Newton's second law; it is assumed that the gravity and buoyancy of the mooring chain act on the lumped mass point, and the drag force on each mooring chain segment is equally divided into two nodes on its left and right, and the equivalent tangential and normal drag forces acting on the node are obtained; since the motion state of the fixed end and the excitation end is known, it is only necessary to establish the motion equations for the middle nodes; the motion equations of the middle nodes of the mooring chain are:

[0053]

[0054] In the formula, m i is the mass of the node, m ai is the additional mass of the node, r i is the state vector of the node, T i+(1 / 2) and C i+(1 / 2) is the tension and internal damping force acting on segment i+1 / 2, D qi and D pi are the tangential and normal drag forces acting on the node, W i and B i is the gravity and buoyancy of the node;

[0055] (2) Establishing a parametric variable model for the tensile and compressive nonlinearity of the mooring chain

[0056] The parametric model of the mooring anchor chain is established based on the parametric variation principle. According to the parametric variation principle, when the mooring anchor chain has tensile and compressive nonlinearity, that is, the tensile stiffness and compressive stiffness coefficients are inconsistent, the segmented constitutive relationship can be organized into a unified expression constrained by corresponding complementary conditions by introducing parameter variables. Since the mooring anchor chain can only bear tensile loads, when the mooring anchor chain is relaxed, the mooring anchor chain is not subjected to stress and has tensile and compressive nonlinear characteristics. The segmented constitutive relationship expression of the mooring anchor chain is:

[0057]

[0058] In the formula, E is the elastic modulus of the mooring anchor chain, d is the equivalent diameter, and l is the unstretched length of the anchor chain segment. Based on the parametric variation principle, the dynamic modeling analysis of the tensile and compressive nonlinear behavior of the mooring anchor chain is carried out, and the parameter λ is introduced

[0059]

[0060] The above formula is equivalent to the complementary condition:

[0061]

[0062] Where, ν i+1 is the constraint relaxation variable of the corresponding equation. Then the tension is written as a unified expression:

[0063]

[0064] (3) Establishing a parametric variable model for the seabed contact nonlinearity of the mooring anchor chain

[0065] Similarly, since the existence of the seabed contact force is premised on the contact between the mooring chain and the seabed, the seabed contact force can also be written in segmented form:

[0066]

[0067] In the formula, z bot is the z-direction coordinate of the seabed, z i and are the displacement and velocity of the anchor chain node in the z direction, k b is the stiffness coefficient, which indicates the stiffness per unit area of ​​the seabed; c b is the damping coefficient representing the viscous damping per unit area of ​​the seabed; is a unit direction vector, indicating the z-axis direction; similarly, based on the parametric variation principle, the dynamic modeling analysis of the nonlinear behavior of the mooring anchor chain in seabed contact is carried out, and the parametric variables β and γ are introduced.

[0068]

[0069] The above formula is equivalent to the complementary condition:

[0070]

[0071] In the formula, α i and μ i are the constraint contact variables of the corresponding equations. Then the seabed contact force of the node can be written as a unified expression:

[0072]

[0073] (4) Parametric dynamic equations of the entire mooring chain

[0074] Finally, the above node force expressions are summarized and sorted out to obtain the motion equation of the mooring anchor chain node; the motion equation of the mooring anchor chain node is assembled according to the finite element method to establish the parametric dynamic equation of the entire mooring anchor chain:

[0075]

[0076] Where M, C and K are the mass matrix, damping matrix and stiffness matrix of the mooring chain system, respectively; g0 is the linear external force and g1 is the nonlinear external force; the motion state of each node of the mooring chain at the initial moment is taken as the initial condition, and the motion state of the fixed end and the excitation end of the mooring chain at any moment is taken as the boundary condition, and the parametric dynamic equation of the mooring chain is numerically solved:

[0077]

[0078] In the formula, r(0) represents t k = the initial state vector at time 0, r0(t) represents the state vector of the anchor chain fixed end at any time, r N (t) represents the state vector of the anchor chain excitation end at any time, and is the corresponding derivative expression;

[0079] (5) Numerical solution

[0080] The parametric dynamic equations (21) and initial and boundary conditions (22) are combined, and the equations are reduced to obtain a complete set of partial differential equations. Finally, the fourth-order Runge-Kutta method is used to integrate and solve the equations in the time domain. When the fourth-order Runge-Kutta explicit algorithm is used for solving, it is known that at the current time t k The motion state at the moment is substituted into the complementary conditions (15) and (19) to obtain t k Substituting the parameter value at time t into the Runge-Kutta method recursive expression, we can get k+1 =t k +Δt time node motion state; When using implicit algorithm to solve, similarly, each time the motion state is updated, the complementary conditions need to be substituted to update the corresponding parameter values, and the solution is iterated until the accuracy requirements are met. By updating the parameter variables, the nonlinear behavior of the mooring anchor chain is updated without remodeling, which improves the calculation accuracy and efficiency of the solution;

[0081] The OC3-Hywind 5MW Spar floating wind turbine is used as the simulation object to simulate the dynamic behavior of the wind turbine platform. The displacement excitation of the upper end point of the anchor chain is a horizontal sinusoidal excitation z(t)=10sin(1.1t); the existing open source software MoorDyn is compared with the results of the parametric modeling and simulation in this paper, and the results of the MoorDyn software are used as the reference solution; the anchor chain is divided into twenty sections for analysis, and the motion response, nonlinear tension and seabed contact force response of the mooring anchor chain can be obtained; by comparing with the simulation results of the open source software MoorDyn, the correctness of the modeling and simulation based on the parametric variation principle in this paper is verified.

Claims

1. A parametric dynamic modeling method for high-flexibility mooring anchor chains, characterized in that: Here are the steps: (1) Dynamic model of mooring chain based on lumped mass method The dynamic analysis of the mooring chain is carried out based on the concentrated mass method, and the mooring chain is equivalent to a nonlinear catenary composed of many concentrated mass points and massless springs. The point where the concentrated mass is located is called a node. The nodes are numbered from 0 to N, where node 0 is the fixed end on the seabed and node N is the excitation end connected to the floating platform. Considering the gravity, buoyancy, fluid drag force, elastic elongation of the mooring cable, additional water mass and inertia force of the mooring chain, the motion differential equations of each node of the mooring chain are established through Newton's second law. Assuming that the gravity and buoyancy of the mooring chain act on the concentrated mass point, the drag force on each mooring chain segment is equally divided into two nodes on its left and right, and the equivalent tangential and normal drag forces acting on the node are obtained. Since the motion state of the fixed end and the excitation end is known, it is only necessary to establish the motion equations for the middle nodes. The motion equations of the middle nodes of the mooring chain are: In the formula, m i is the mass of the node, m ai is the additional mass of the node, r i is the state vector of the node, T i+(1 / 2) and C i+(1 / 2) is the tension and internal damping force acting on segment i+1 / 2, D qi and D pi are the tangential and normal drag forces acting on the node, W i and B i is the gravity and buoyancy of the node; (2) Establishing a parametric variable model for the tensile and compressive nonlinearity of the mooring chain The parametric model of the mooring anchor chain is established based on the parametric variation principle. According to the parametric variation principle, when the mooring anchor chain has tensile and compressive nonlinearity, that is, the tensile stiffness and compressive stiffness coefficients are inconsistent, the segmented constitutive relationship can be organized into a unified expression constrained by corresponding complementary conditions by introducing parameter variables. Since the mooring anchor chain can only bear tensile loads, when the mooring anchor chain is relaxed, the mooring anchor chain is not subjected to stress and has tensile and compressive nonlinear characteristics. The segmented constitutive relationship expression of the mooring anchor chain is: In the formula, E is the elastic modulus of the mooring anchor chain, d is the equivalent diameter, and l is the unstretched length of the anchor chain segment. Based on the parametric variation principle, the dynamic modeling analysis of the tensile and compressive nonlinear behavior of the mooring anchor chain is carried out, and the parameter λ is introduced The above formula is equivalent to the complementary condition: Where, ν i+1 is the constraint relaxation variable of the corresponding equation; then the tension is written as a unified expression: (3) Establishing a parametric variable model for the seabed contact nonlinearity of the mooring anchor chain Similarly, since the existence of the seabed contact force is premised on the contact between the mooring chain and the seabed, the seabed contact force can also be written in segmented form: In the formula, z bot is the z-direction coordinate of the seabed, i and are the displacement and velocity of the anchor chain node in the z direction, k b is the stiffness coefficient, which indicates the stiffness per unit area of ​​the seabed; c b is the damping coefficient representing the viscous damping per unit area of ​​the seabed; is a unit direction vector, indicating the z-axis direction; similarly, based on the parametric variation principle, the dynamic modeling analysis of the nonlinear behavior of the mooring anchor chain in seabed contact is carried out, and the parametric variables β and γ are introduced. The above formula is equivalent to the complementary condition: In the formula, α i and μ i are the constraint contact variables of the corresponding equations respectively, then the seabed contact force of the node can be written as a unified expression: (4) Parametric dynamic equations of the entire mooring chain Finally, the above node force expressions are summarized and sorted out to obtain the motion equation of the mooring anchor chain node; the motion equation of the mooring anchor chain node is assembled according to the finite element method to establish the parametric dynamic equation of the entire mooring anchor chain: Where M, C and K are the mass matrix, damping matrix and stiffness matrix of the mooring chain system, respectively; g0 is the linear external force and g1 is the nonlinear external force; the motion state of each node of the mooring chain at the initial moment is taken as the initial condition, and the motion state of the fixed end and the excitation end of the mooring chain at any moment is taken as the boundary condition, and the parametric dynamic equation of the mooring chain is numerically solved: In the formula, r(0) represents t k = the initial state vector at time 0, r0(t) represents the state vector of the anchor chain fixed end at any time, r N (t) represents the state vector of the anchor chain excitation end at any time, and is the corresponding derivative expression; (5) Numerical solution The parametric dynamic equations (10) and initial boundary conditions (11) are combined, and the equations are reduced to obtain a complete set of partial differential equations. Finally, the fourth-order Runge-Kutta method is used to integrate and solve the equations in the time domain. When the fourth-order Runge-Kutta explicit algorithm is used for solving, it is known that at the current time t k The motion state at the moment is substituted into the complementary conditions (4) and (8) to obtain t k Substituting the parameter value at time t into the Runge-Kutta method recursive expression, we can get k+1 =t k +Δt is the motion state of the node at time; when the implicit algorithm is used for solution, similarly, each time the motion state is updated, the complementary conditions need to be substituted to update the corresponding parameter values, and the solution is iterated until the accuracy requirements are met.

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