A method for calculating coupled dynamic responses of a floating platform and a mooring system

Abstract

The application discloses a coupling dynamic response calculation method of a floating platform and a mooring system, and relates to the technical field of ships and ocean engineering. The method comprises the following steps: determining a hydroelastic response estimation value of the floating platform at a current simulation moment in a T+1th response updating step; converting the hydroelastic response estimation value to obtain a dynamic response of a mooring point, and calculating a mooring load of the mooring system in the T+1th response updating step; solving the hydroelastic response of the floating platform by using the mooring load in the T+1th response updating step; and obtaining a dynamic response numerical simulation result when the dynamic response iterative coupling calculation reaches a convergence state, and entering a next simulation moment. The method considers the coupling effect of the mooring system and the floating platform under the combined influence of the rigid body motion and the elastic deformation of the floating platform, and can more accurately predict the coupling dynamic response of the floating platform and the mooring system.

Description

A method for calculating the coupled dynamic response of a floating platform and a mooring system Technical Field

[0001] This application relates to the field of shipbuilding and marine engineering technology, and in particular to a method for calculating the coupled dynamic response of a floating platform and a mooring system. Background Technology

[0002] Floating structures are important engineering equipment for marine space utilization and marine resource development. Floating structures with different functional modules can be combined to form various types of marine floating platforms, such as large floating platforms like marine scientific experimental platforms, marine airport runways, marine tourism platforms, and marine ranches.

[0003] In the design and application of floating platforms, it is necessary to calculate and evaluate their dynamic response to ensure structural integrity and operational safety. Current conventional methods treat floating platforms as rigid bodies to calculate their dynamic response under marine environmental loads. However, in reality, floating platforms require mooring systems to constrain and control their spatial movement to ensure normal operation and reliable safety in the marine environment.

[0004] The motion response of a floating platform is constrained by the mooring system, and the mooring force generated by the mooring system depends on the motion state of the floating platform. This results in a strong nonlinear coupling effect between the dynamic response of the floating platform and the mooring system. As a result, the dynamic response of the floating platform calculated by existing methods is not accurate enough, which affects the hydrodynamic performance analysis and safety and reliability assessment of the floating platform. Summary of the Invention

[0005] To address the aforementioned problems and technical requirements, this application proposes a method for calculating the coupled dynamic response of a floating platform and a mooring system. The technical solution of this application is as follows:

[0006] A method for calculating the coupled dynamic response of a floating platform and a mooring system includes the following steps:

[0007] For the T-th response update step at the N-th simulation time, when T=0, the initial mooring load generated by the mooring system on the floating platform at the N-th simulation time is substituted into the three-dimensional hydroelastic motion equation of the floating platform to solve for the hydroelastic response p(T) of the floating platform at the T-th response update step, which is then used as the estimated value of the hydroelastic response at the (T+1)-th response update step. When T≥1, the hydroelastic response p(T) of the Tth response update step is used as the estimated value of the hydroelastic response of the (T+1)th response update step. The initial value of the integer parameter N is 1;

[0008] The estimated water-elastic response of the floating platform from the T+1th response update step The transformation yields the dynamic response X of the mooring points of each mooring line in the mooring system under the influence of the rigid body motion and elastic deformation of the floating platform at the (T+1)th response update step. M (T+1), and the dynamic response X at the mooring point. M Using (T+1) as the mooring line boundary condition, the mooring load F generated by the mooring system on the floating platform at the T+1th response update step is obtained through iterative calculation using the lumped mass model of the mooring system. M (T+1);

[0009] The mooring load F generated by the floating platform is updated by the mooring system at the T+1th response step. M Substituting (T+1) into the three-dimensional hydroelastic motion equation of the floating platform, we can solve for the hydroelastic response p(T+1) of the floating platform at the T+1th response update step.

[0010] When the iterative coupling calculation of the dynamic response of the floating platform and the mooring system reaches convergence based on the calculation results of each response update step, the numerical simulation results of the dynamic response of the floating platform at the Nth simulation time are obtained, as well as the numerical simulation results of the mooring load generated by the mooring system on the floating platform at the Nth simulation time.

[0011] The numerical simulation results of the mooring load at the Nth simulation time. The numerical simulation calculation is performed to calculate the initial mooring load generated by the mooring system on the floating platform at the (N+1)th simulation time.

[0012] A further technical solution is that each response update step includes K iterative calculation steps, where the integer parameter K ≥ 2; the iterative calculation yields the mooring load F generated by the mooring system on the floating platform in the (T+1)th response update step. M (T+1) includes:

[0013] The dynamic response of each mooring point in each iterative calculation step is obtained by interpolating the dynamic response of each mooring point in the most recent multiple response update steps;

[0014] Initialize the integer parameter k=1, and use the dynamic response of each mooring point in the kth iteration calculation step combined with the lumped mass model with the kth iteration parameter to calculate the mooring load generated by the mooring system in the kth iteration calculation step;

[0015] When k < K, the (k+1)th iteration parameter of the lumped mass model is updated based on the calculation result of the kth iteration step, and k = k+1 is set to enter the next iteration step; when k = K, the mooring load generated by the mooring system in the kth iteration step is taken as the mooring load F generated by the mooring system on the floating platform in the (T+1)th response update step. M (T+1).

[0016] A further technical solution involves calculating the mooring load generated by the mooring system in the k-th iteration step, including:

[0017] Based on the lumped mass model, any l-th mooring line is equivalent to multiple mass points, and the displacements of the mass points adjacent to the mooring points on the l-th mooring line are determined.

[0018] The mooring tension F of the l-th mooring line is determined based on the displacement difference between the mooring point and its adjacent mass points. Tl ;

[0019] The mooring load F generated by the mooring system in the k-th iteration calculation step is obtained by combining the mooring tension of each mooring line into a spatial force system. M =[F Mr [r = 1, 2, ..., m], the r-th modal component of the mooring load. u r is the r-th mode shape of the floating platform at the mooring point of the l-th mooring line, m is the total number of modes of the floating platform, and L is the total number of mooring lines.

[0020] A further technical solution involves interpolating the dynamic response of each mooring point at various iterative calculation steps based on the dynamic response at the most recent multiple simulation times, including:

[0021] When N=1, the dynamic response X of the mooring point at the 0th simulation time is used based on the linear interpolation method. M (0) and the dynamic response X at the T+1th response update step of the first simulation time. M (T+1), interpolate to calculate the dynamic response of the mooring point in the k-th iteration of the response update steps from the T-th to the T+1-th time in the first simulation.

[0022] When N≥2, the dynamic response X of the mooring point at the (N-2)th simulation time is calculated using the second-order Lagrange interpolation method. M (N-2), Dynamic response X at the (N-1)th simulation time. M The dynamic response X of (N-1) and the T+1th response update step M (T+1) Interpolation is used to calculate the dynamic response of the mooring point in the k-th iteration of the response update steps from T to T+1 at the Nth simulation time.

[0023] Among them, t k t is the computation time of the k-th iteration step. N-2 It is the calculation time of the (N-2)th simulation time, t N-1It is the calculation time of the (N-1)th simulation time, t N This is the calculation time at the Nth simulation time, and the dynamic response X at the 0th simulation time. M (0) is the initial dynamic response.

[0024] A further technical solution involves converting the dynamic response of the mooring point, including its displacement, into the dynamic response X of each mooring point at any response update step starting from the second response update step. M include:

[0025] Determine the modal analysis results of the floating platform and the coordinates of the mooring point in the body coordinate system; determine the displacement and spatial transformation matrix at the center of gravity of the floating platform based on the modal analysis results and hydroelastic response of the floating platform under rigid body degrees of freedom.

[0026] Based on the displacement at the center of gravity of the floating platform and the spatial transformation matrix, the coordinates of the mooring point in the body coordinate system of the floating platform are transformed by matrix transformation to obtain the rigid body displacement X of the mooring point under the influence of the rigid body motion of the floating platform. M_r ;

[0027] Modal analysis results and hydroelastic response of the floating platform under elastic modal conditions are superimposed modally and combined with the spatial transformation matrix to obtain the elastic deformation displacement X of the mooring point under the influence of the elastic deformation of the floating platform. M_e ;

[0028] Determine the dynamic response X of the mooring point in the T+1 response update step. M =X M_r +X M_e .

[0029] A further technical solution is that the elastic deformation displacement X of the mooring point... M_e for:

[0030]

[0031] Where n is the number of wave frequency components, A i It is the amplitude of the i-th wave frequency component, k i ω is the wave number of the i-th wave frequency component. i θ is the frequency of the i-th wave frequency component. i It is the direction of the i-th wave frequency component. It is the initial phase angle of the i-th wave frequency component, x M_r It is the component of the rigid body displacement at the mooring point in the x-direction, y M_r It is the component of the rigid body displacement at the mooring point in the y direction, and E is the spatial transformation matrix;

[0032] δ(ωi ) is the phase angle of the mooring point displacement caused by elastic deformation, and δ(ω) i )=[δ j (ω i )],

[0033] H(ω i H(ω) is the contribution of elastic deformation to the mooring point displacement per unit amplitude, and H(ω) is the contribution of elastic deformation to the mooring point displacement. i )=[H j (ω i )],

[0034] j = 1, 2, 3 represent the x′, y′, and z′ directions in the body coordinate system of the floating platform, m is the total number of modes of the floating platform, and u rj p is the component of the r-th mode shape of the floating platform in the j-direction. r (ω i ) is the r-th principal coordinate response of the floating platform in the frequency domain calculation, where Re() represents taking the real part of the complex number and Im() represents taking the imaginary part of the complex number.

[0035] A further technical solution is that the rigid body displacement X at the mooring point... M_r for:

[0036] X M_r =X G +EX′ M_L

[0037] Among them, X G It is the displacement at the center of gravity of the floating platform and X G =[x G ,y G ,z G ], x G It is the component of the displacement at the center of gravity of the floating platform in the x-direction in the geodetic coordinate system, and the y-direction component. G It is the component of the displacement at the center of gravity of the floating platform in the y-direction in the geodetic coordinate system, z G X' is the component of the displacement at the center of gravity of the floating platform in the z-direction in the geodetic coordinate system, E is the spatial transformation matrix, and X' is the component of the displacement at the center of gravity of the floating platform in the z-direction. M_L The coordinates of the mooring point in the body coordinate system of the floating platform are X' M_L =[x' M_L ,y' M_L ,z' M_L ],x′ M_L These are the coordinates of the mooring point in the x′ direction and y′ direction in the body coordinate system of the floating platform. M_L It is the coordinate of the mooring point in the y′ direction of the floating platform's body coordinate system, and z′ is the coordinate of the mooring point in the body coordinate system. M_LIt is the coordinate of the mooring point in the z′ direction in the body coordinate system of the floating platform.

[0038] A further technical solution is that the hydroelastic response of the floating platform includes the principal coordinate response matrix, and the hydroelastic response of the floating platform at the T+1th response update step includes:

[0039] Based on the three-dimensional hydroelastic theory, the three-dimensional hydroelastic motion equations of the floating platform are determined as follows:

[0040]

[0041] The principal coordinate response matrix p(T+1) of the floating platform at the T+1th response update step is obtained by time-domain numerical integration of the three-dimensional hydroelastic motion equation using a high-precision numerical discretization method.

[0042] Where a is the generalized mass matrix of the structure, A is the generalized additional mass matrix at infinite frequency, B is the generalized damping matrix, C is the generalized hydrostatic restoring force matrix, and h(t-τ) is the generalized time delay function matrix determined by the generalized additional mass matrix and the additional damping matrix. The first derivative of the principal coordinate response matrix is ​​given. Let F(t) be the second derivative of the principal coordinate response matrix, and let F(t) be the generalized wave excitation force matrix. d (t) is the generalized wave drift force matrix, F c (t) is the generalized flow force matrix, F w (t) is the generalized wind force matrix, F M (t) represents the mooring load generated by the mooring system.

[0043] Its further technical solution is that the coupled dynamic response calculation method includes: when the following conditions are met... At that time, it was determined that the iterative coupling calculation of the dynamic response of the floating platform and the mooring system reached a convergence state, where CR R It is the iteration error threshold.

[0044] The beneficial technical effects of this application are:

[0045] This application proposes a method for calculating the coupled dynamic response of a floating platform and a mooring system. By iteratively coupling the calculations to determine the dynamic response of the floating platform and the mooring system, and considering the influence of the rigid body motion and elastic deformation of the floating platform on the dynamic response at the mooring point, this method can more accurately predict the mutual coupling between the floating platform and the mooring system. Compared to traditional numerical simulation methods that only consider the rigid body motion of the floating platform, this method effectively improves the accuracy of the numerical simulation results for the coupled dynamic response of the floating platform and the mooring system.

[0046] Considering that the natural period of the mooring system is much shorter than that of the floating platform, an asynchronous long-iteration calculation of the dynamic response of the mooring system and the mooring load on the floating platform is used to address the inconsistency between the numerical simulation calculation time of the mooring system and the numerical simulation calculation time of the floating platform. Within each response update step, interpolation is used to calculate the dynamic response of the mooring point in each iteration step, and the dynamic response of the mooring system is solved progressively according to each iteration step. This improves computational efficiency while accurately calculating the mooring load on the floating platform at each response update step. Attached Figure Description

[0047] Figure 1 is a flowchart of the coupled dynamic response calculation method.

[0048] Figure 2 is a schematic diagram of the equivalent mass points on the mooring line.

[0049] Figure 3 shows the mooring load time-history curves generated by the mooring system on the floating platform.

[0050] Figure 4 shows the dynamic response time-history curve of the floating platform. Detailed Implementation

[0051] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0052] This application proposes a method for calculating the coupled dynamic response of a floating platform and a mooring system. Please refer to the flowchart in Figure 1. The specific steps are as follows:

[0053] Step 1, for the T-th response update step at the Nth simulation time, can be divided into the following cases:

[0054] When T=0, the initial response update step involves substituting the initial mooring load generated by the mooring system on the floating platform at the Nth simulation time into the three-dimensional hydroelastic motion equation of the floating platform. A high-precision numerical discretization method is then used to solve the three-dimensional hydroelastic motion equation by time-domain numerical integration to obtain the hydroelastic response p(T) of the floating platform at the Tth response update step. This p(T) is then used as the estimated value of the hydroelastic response at the (T+1)th response update step. Where T is an integer parameter and T≥0, and N is an integer parameter and N≥1. For the first simulation time step of N=1, since the inherent properties of the mooring system, such as its geometry and material properties, are deterministic at the initial time step, and the initial state of the mooring line is known, the initial dynamic response and mooring load of the mooring system at N=1 can be determined. The initial mooring load at N≥2 is the numerical simulation result of the mooring load calculated at the previous simulation time step.

[0055] This application takes into account the coupling effect between the mooring system and the floating platform, and adds the mooring load generated by the mooring system on the floating platform to the excitation force of the three-dimensional hydroelastic motion equation of the floating platform. In one embodiment, the three-dimensional hydroelastic motion equation of the floating platform is determined according to the three-dimensional hydroelastic theory as follows:

[0056]

[0057] The hydroelastic response of a floating platform includes the principal coordinate response matrix, where p(t) represents the principal coordinate response matrix and p(t) = [p1(t), p2(t), ..., p m [(t)], where m is the total number of modes of the floating platform. The first derivative of the principal coordinate response matrix is ​​given. Let represent the second-order differential of the principal coordinate response matrix, ... d (t) is the generalized wave drift force matrix, F c (t) is the generalized flow force matrix, F w (t) is the generalized wind force matrix, F M (t) represents the mooring load generated by the mooring system.

[0058] It should be noted that this application mainly studies the mooring load F generated by the mooring system on the floating platform. M The excitation force (t) is used to determine the remaining excitation forces in the three-dimensional hydroelastic motion equation of the floating platform using existing methods, which will not be discussed further in this application.

[0059] The specific solution process for the time-domain numerical integration of the three-dimensional hydroelastic motion equations using a high-precision numerical discretization method is as follows:

[0060] The three-dimensional hydroelastic motion equation of formula (1) can be rewritten in the following form:

[0061]

[0062] Let Y1 = p(t), Substituting into formula (2), the three-dimensional hydroelastic motion equations are rewritten as a set of first-order ordinary differential equations, expressed as:

[0063]

[0064] Where G(t,Y1,Y2) represents the right-hand side of equation (2), the differential equations can be transformed into a linear equation system using the fourth-order Runge-Kutta method, and the principal coordinate response matrix of the floating platform can be solved numerically. The resulting linear equation system is as follows:

[0065]

[0066] Among them, Y 1N Y represents the principal coordinate response matrix of the floating platform at the Nth simulation time. 1T Y represents the principal coordinate response matrix of the floating platform at the T-th response update step. 2N Y represents the first derivative of the principal coordinate response matrix of the floating platform at the Nth simulation time. 2T Let represent the first-order differential of the principal coordinate response matrix of the floating platform at the T-th response update step. K1, K2, K3, K4, L1, L2, L3, and L4 are intermediate variables, and their specific expressions are as follows:

[0067]

[0068] L1=G(t N ,Y 1N ,Y 2N ),

[0069]

[0070] Among them, t N It is the calculation time of the Nth simulation time, where ΔN represents the calculation time step between two adjacent simulation times and ΔN = t. N+1 -t N The initial mooring load at the Nth simulation time is obtained. Substituting the intermediate variables into formula (4) allows for iterative calculation of the hydroelastic response p(T) of the floating platform at the Tth response update step.

[0071] When T≥1, the hydroelastic response p(T) of the Tth response update step is used as the estimated value of the hydroelastic response of the (T+1)th response update step.

[0072] Step 2, using the estimated water elastic response of the floating platform from the (T+1)th response update step. The transformation yields the dynamic response X of the mooring points of each mooring line in the mooring system under the influence of the rigid body motion and elastic deformation of the floating platform at the (T+1)th response update step. M (T+1).

[0073] The dynamic response of the mooring point includes its displacement. Since the mooring point is the contact point between the floating platform and the mooring system, and the floating platform experiences both rigid motion and elastic deformation under the constraints of the mooring system, the displacement of the mooring point needs to consider the combined effects of the floating platform's rigid motion and elastic deformation. In one embodiment, the dynamic response X of each mooring point is obtained by transformation at any response update step starting from the second response update step T=1. M The specific method is as follows:

[0074] (1) Modal analysis results of the floating platform are determined by performing modal analysis on the three-dimensional finite element model of the floating platform. The modal analysis results include the mode shape u at any point Q on the floating platform. r The first six rigid body modes (r=1~6) correspond to rigid body modes, and the modes (r=7~m) correspond to elastic modes. The first six rigid body mode shapes can be expressed as follows:

[0075] u1 = {1, 0, 0} T

[0076] u2 = {0, 1, 0} T

[0077] u3 = {0, 0, 1} T

[0078] u4={0,-(z * -z G ),(y * -y G )} T

[0079] u5={(z * -z G ),0,-(x * -x G )} T

[0080] u6={-(y * -y G ),(x * -x G ),0} T

[0081] Among them, (x G ,y G ,z G (x) is the displacement at the center of gravity of the floating platform. * ,y * ,z * ) represents the displacement of point Q caused by the rigid body motion of the floating platform.

[0082] Determine the coordinates of the mooring point in the floating platform's body coordinate system. The floating platform's body coordinate system is defined as follows: when the floating platform is in still water, the origin is the projection point of the center of gravity on the still water surface, the positive direction of the x′ axis points from the stern to the bow of the floating platform, the positive direction of the y′ axis points from the starboard side to the port side of the floating platform, and the positive direction of the z′ axis is vertically upward. The origin position of this coordinate system changes as the floating platform moves, and the direction of the coordinate axes changes as the floating platform rotates.

[0083] The displacement at the center of gravity of the floating platform is calculated based on the rigid body mode shapes and principal coordinate response matrix of the floating platform with rigid body degrees of freedom. Because (x * ,y * ,z * )=(x G ,y G ,z G Since u4~u6=0, the displacement X at the center of gravity of the floating platform is... G = [p1(t),p2(t),p3(t)], which is the displacement X at the center of gravity of the floating platform. G =[x G ,y G ,z G The corresponding principal coordinate response matrix is ​​p(t) = [p1(t), p2(t), ..., p m The first three modal components of [(t)]. G It is the component of the displacement at the center of gravity of the floating platform in the x-direction in the geodetic coordinate system, and the y-direction component. G It is the component of the displacement at the center of gravity of the floating platform in the y-direction in the geodetic coordinate system, z G It is the component of the displacement at the center of gravity of the floating platform in the z-direction in the geodetic coordinate system.

[0084] The spatial transformation matrix E is determined by pre-calibrating the assembly structure of the mooring system and the floating platform. The specific expression is as follows:

[0085]

[0086] Where α is the roll angle of the floating platform, β is the pitch angle of the floating platform, and γ is the yaw angle of the floating platform. The roll, pitch, and yaw angles of the floating platform correspond to the principal coordinate response matrix p(t)=[p1(t),p2(t),...,p m The 4th to 6th modal components of [(t)].

[0087] (2) Based on the displacement at the center of gravity of the floating platform and the spatial transformation matrix, the coordinates of the mooring point in the body coordinate system of the floating platform are transformed by matrix transformation to obtain the rigid body displacement X of the mooring point under the influence of the rigid body motion of the floating platform. M_r .

[0088] In one embodiment, the rigid body displacement X of the mooring point M_r for:

[0089] X M_r =X G +EX′ M_L

[0090] Where X' M_L The coordinates of the mooring point in the body coordinate system of the floating platform are X' M_L =[x' M_L ,y' M_L ,z' M_L ],x′ M_L These are the coordinates of the mooring point in the x′ direction and y′ direction in the body coordinate system of the floating platform. M_L It is the coordinate of the mooring point in the y′ direction of the floating platform's body coordinate system, and z′ is the coordinate of the mooring point in the body coordinate system. M_L It is the coordinate of the mooring point in the z′ direction in the body coordinate system of the floating platform.

[0091] Since the mooring point moves along with the floating platform, its coordinates in the platform's body coordinate system remain unchanged. The rigid body displacement X of the mooring point under the influence of the floating platform's rigid body motion is... M_r The change is only related to the displacement X at the center of gravity of the floating platform. G And it is related to the change in the spatial transformation matrix E.

[0092] (3) Modal superposition of the modal analysis results and hydroelastic response of the floating platform under elastic modes, combined with the spatial transformation matrix, yields the elastic deformation displacement X of the mooring point under the influence of the elastic deformation of the floating platform. M_e .

[0093] In one embodiment, the elastic deformation displacement X of the mooring point M_e for:

[0094]

[0095] Where n is the number of wave frequency components, A i It is the amplitude of the i-th wave frequency component, k i ω is the wave number of the i-th wave frequency component. i θ is the frequency of the i-th wave frequency component. i It is the direction of the i-th wave frequency component. It is the initial phase angle of the i-th wave frequency component, x M_r It is the component of the rigid body displacement at the mooring point in the x-direction, y M_r It is the component of the rigid body displacement at the mooring point in the y direction, and E is the spatial transformation matrix;

[0096] δ(ω i ) is the phase angle of the mooring point displacement caused by elastic deformation, and δ(ω) i )=[δ j (ω i )],

[0097] H(ω i H(ω) is the contribution of elastic deformation to the mooring point displacement per unit amplitude, and H(ω) is the contribution of elastic deformation to the mooring point displacement. i )=[H j (ω i )],

[0098] j = 1, 2, 3 represent the x′, y′, and z′ directions in the body coordinate system of the floating platform, m is the total number of modes of the floating platform, and u rj p is the component of the r-th mode shape of the floating platform in the j-direction. r (ω i ) is the r-th principal coordinate response of the floating platform in the frequency domain calculation, where Re() represents taking the real part of the complex number and Im() represents taking the imaginary part of the complex number.

[0099] (4) Determine the dynamic response X of the mooring point in the T+1 response update step. M =X M_r +X M_e .

[0100] The dynamic response of the mooring point also includes the velocity of the mooring point. Typically, the velocity of the mooring point only considers the effects of the rigid body motion of the floating platform. The velocity v of the mooring point... M =v M_r =v G +ω×(EX' M_L ), where v M_r ω is the contribution of the rigid body motion of the floating platform to the velocity at the mooring point, and ω is the rotational angular velocity at the center of gravity of the floating platform, which corresponds to the first derivative of the principal coordinate response matrix. The 4th to 6th modal components.

[0101] Step 3, using the dynamic response X at the mooring point M Using (T+1) as the mooring line boundary condition, the mooring load F generated by the mooring system on the floating platform at the T+1th response update step is obtained through iterative calculation using the lumped mass model of the mooring system. M (T+1).

[0102] In one embodiment, each response update step includes K iterative calculation steps, where the integer parameter K ≥ 2; the iterative calculation yields the mooring load F generated by the mooring system on the floating platform in the (T+1)th response update step.M The specific steps for (T+1) are as follows:

[0103] (1) The dynamic response of each mooring point in each iterative calculation step is obtained by interpolating the dynamic response of each mooring point at the most recent simulation times.

[0104] The dynamic response of the mooring point in each response update step can be calculated using the method in step 2 during the coupling interaction between the floating platform and the mooring system. Since the natural period of the mooring system is much smaller than that of the floating platform, the computation time step between two adjacent iterations of the mooring system is much smaller than that between two adjacent response update steps of the floating platform. Therefore, the dynamic response of the mooring point in each iteration cannot be directly obtained and needs to be determined through interpolation.

[0105] In one embodiment, the specific method for interpolating the dynamic response of the mooring point in each iterative calculation step between the T-th and T+1-th response update steps is as follows:

[0106] When N=1, the dynamic response X of the mooring point at the 0th simulation time is used as the basis for the linear interpolation method. M (0) and the dynamic response X at the T+1th response update step of the first simulation time. M (T+1), interpolate to calculate the dynamic response of the mooring point in the k-th iteration of the response update steps from the T-th to the T+1-th time in the first simulation.

[0107] When N≥2, the second-order Lagrange interpolation method is used to calculate the dynamic response X of the mooring point at the (N-2)th simulation time. M (N-2), Dynamic response X at the (N-1)th simulation time. M The dynamic response X of (N-1) and the T+1th response update step M (T+1) Interpolation is used to calculate the dynamic response at the k-th iteration of the response update step from the T-th to the T+1-th time of the Nth simulation time at the mooring point.

[0108] Among them, t k t is the computation time of the k-th iteration step. N-2 It is the calculation time of the (N-2)th simulation time, t N-1 It is the calculation time of the (N-1)th simulation time, t N This is the calculation time of the Nth simulation time. When T=1, t N-1 ≤t k ≤t N When T≥2, t N-2 <t N-1≤t k ≤t N The dynamic response X at simulation time 0 M (0) is the initial dynamic response, and the initial dynamic response of the mooring point at the initial moment is known.

[0109] (2) Initialize integer parameter k=1, and use the dynamic response of each mooring point in the kth iteration calculation step combined with the lumped mass model with the kth iteration parameter to calculate the mooring load generated by the mooring system in the kth iteration calculation step.

[0110] In one embodiment, the specific method for calculating the mooring load generated by the mooring system in the k-th iteration calculation step using the lumped mass model is as follows:

[0111] According to the lumped mass model, any l-th mooring line is equivalent to multiple mass points, as shown in Figure 2. Mass point g=1 represents the anchor point of the mooring line, g=G+1 represents the mooring point, and g=G represents the mass point on the mooring line adjacent to the mooring point.

[0112] The dynamic response of any mass point g on the mooring line can be calculated from the dynamic equation of that mass point. The dynamic equation of any mass point g on the mooring line is:

[0113]

[0114] Where, m g It is the mass of mass point g, A SgJ It is the additional mass of mass point g in the J direction. It is the acceleration of mass g in the J direction, F TgJ Yes, it is the mooring line tension caused by the axial deformation of the mooring line, F. DgJ It is the fluid resistance caused by wave-current action, F IgJ It is the inertial force caused by fluid acceleration, F GBgJ F is the gravitational force and buoyancy acting on the mass point g. DPgJ It is the damping force caused by structural damping, F SDgJ It is the force of the sea and soil, and J = 1, 2, 3 are the x, y, and z directions of the geodetic coordinate system.

[0115] The additional mass, fluid resistance, inertial force caused by fluid acceleration, gravity and buoyancy on mass point g, damping force caused by structural damping, and sea-soil interaction force can be determined according to existing methods based on environmental parameters such as wind, waves, and ocean currents of the target sea area to be simulated, combined with the inherent properties of the mooring system. This application will not elaborate further.

[0116] Substituting the various environmental forces acting on mass point g into formula (5) allows us to calculate the acceleration of mass point g, and thus determine its velocity and displacement, among other dynamic responses. Existing technologies can be used to solve formula (5). This application employs a high-precision numerical discretization method to perform time-domain numerical integration of the motion equation, obtaining the dynamic responses of each mass point on the mooring line, thereby obtaining the dynamic response of the mooring system. The specific solution process is as follows:

[0117] The dynamic equation of formula (5) can be rewritten in the following form:

[0118]

[0119] Let y 1gJ =x sgJ (t), Substituting into formula (6), the dynamic equations are rewritten as a set of first-order ordinary differential equations:

[0120]

[0121] Where, f(t,y) 1gJ ,y 2gJ ) represents the right-hand side of equation (6). Using the fourth-order Rogon-Kutta method, the differential equation can be transformed into a linear equation, thus enabling the numerical solution of the dynamic equation of equation (5). The resulting linear equation system is as follows:

[0122]

[0123] Among them, y 1gJk Let y represent the displacement of mass point g in the k-th iteration calculation step. 1gJ(k+1) Let y represent the displacement of mass point g in the (k+1)th iteration calculation step. 2gJk y represents the velocity of mass point g in the k-th iteration calculation step. 2gJ(k+1) Let represent the velocity of mass point g in the (k+1)th iteration calculation step, and Δt represent the calculation time step between two adjacent iteration calculation steps. β1, β2, β3, β4, γ1, γ2, γ3, and γ4 are intermediate variables, and their specific expressions are as follows:

[0124] β1=y 2gJk , β4=y 2gJk +Δt×γ3,

[0125] γ1=f(t n ,y 1gJk ,y 2gJk ),

[0126]

[0127] γ4=f(t n +Δt,y 1gJk +Δt×β3,y 2gJk +Δt×β3)

[0128] Among them, t k It is the calculation time of the k-th iteration calculation step. According to formula (8), the calculation time of the iteration calculation can be gradually advanced according to the calculation time step of the iteration calculation step, so as to obtain the displacement of the mass point g in each iteration calculation step.

[0129] When g = G, the displacement of the mass point adjacent to the mooring point on the l-th mooring line in the k-th iteration can be determined using the displacement in the (k-1)-th iteration and the k-th iteration parameters through the above calculation process. The iteration parameters include the mooring line tension in the dynamic equations.

[0130] After determining the displacement of the mooring point of the l-th mooring line and its adjacent mass points, the mooring tension F of the l-th mooring line can be determined based on the displacement difference between the mooring point and its adjacent mass points. Tl =[F TlJ Simultaneously, the mooring line tension is updated to the (k+1)th iteration parameter obtained in the (k+1)th iteration calculation step. Mooring line tension F Tl Component F in the J direction TlJ The specific calculation formula is as follows:

[0131]

[0132] Among them, K G It is the stiffness of the mooring line between the mooring point and its adjacent mass points, x S(G+1)k It is the displacement of the mooring point in the J direction, x SGk L is the displacement of the mass point adjacent to the mooring point on the mooring line in the J direction. N0 n is the length between the mooring point and its adjacent mass points before the mooring line undergoes elastic deformation. GJ It is the direction cosine of the mooring line in the J direction between the mooring point and its adjacent mass points.

[0133] The mooring load F generated by the mooring system in the k-th iteration calculation step is obtained by combining the mooring tension of each mooring line into a spatial force system. M =[F Mr [r = 1, 2, ..., m], the r-th modal component of the mooring load. u r is the r-th mode shape of the floating platform at the mooring point of the l-th mooring line, m is the total number of modes of the floating platform, and L is the total number of mooring lines.

[0134] (3) When k < K, the k+1th iteration parameter of the lumped mass model is updated based on the calculation result of the kth iteration calculation step, and k = k+1 is set to enter the next iteration calculation step. The iteration calculation of the mooring load generated by the mooring system on the floating platform continues until the calculation time of the mooring system reaches the calculation time of the floating platform. When k = K, the mooring load generated by the mooring system in the kth iteration calculation step is taken as the mooring load F generated by the mooring system on the floating platform in the T+1th response update step. M (T+1).

[0135] Step 4: Update the mooring system in the T+1th response step to the mooring load F generated by the floating platform. M Substituting (T+1) into the three-dimensional hydroelastic motion equation of the floating platform, and using the updated mooring load as the excitation force, the three-dimensional hydroelastic motion equation is solved again to obtain the hydroelastic response p(T+1) of the floating platform in the T+1 response update step.

[0136] Due to the strong nonlinear coupling effect between the floating platform and the mooring system, the hydroelastic response of the floating platform affects the mooring load on the mooring system, and the mooring load, in turn, affects the hydroelastic response of the floating platform. Therefore, iterative coupling calculations are required at each simulation time step to update the dynamic responses of the floating platform and the mooring system.

[0137] When the iterative coupled calculation of the dynamic response of the floating platform and the mooring system reaches convergence based on the calculation results of each response update step, the numerical simulation results of the dynamic response of the floating platform and the mooring system at the Nth simulation time are obtained, as well as the numerical simulation results of the mooring load generated by the mooring system on the floating platform at the Nth simulation time.

[0138] In one embodiment, the convergence state is determined based on the hydroelastic response of the floating platform in two adjacent response update steps. When the condition is met... At that time, the iterative coupling calculation of the dynamic response of the floating platform and the mooring system is determined to have reached convergence, where p(T) is the hydroelastic response of the floating platform at the T-th response update step, p(T+1) is the hydroelastic response of the floating platform at the T+1-th response update step, and CR R It is the iteration error threshold, which can be customized based on experience.

[0139] Step 5: Calculate the numerical simulation results of the mooring load at the Nth simulation time. The numerical simulation calculation is performed to calculate the initial mooring load generated by the mooring system on the floating platform at the (N+1)th simulation time.

[0140] The iterative coupling calculation method for the dynamic response of the floating platform and mooring system disclosed in this application can accurately calculate the dynamic response of the mooring system and the floating platform at each simulation moment. By plotting the dynamic response curves according to the simulation time, the numerical simulation results of the dynamic response of the floating platform and its mooring system can be obtained. The mooring load generated by the mooring system on the floating platform has its x-direction component in the geodetic coordinate system. The time-history curve is shown in Figure 3, and the dynamic response time-history curve of the floating platform is shown in Figure 4.

[0141] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.

Claims

1. A method for calculating the coupled dynamic response of a floating platform and a mooring system, characterized in that, The coupled dynamic response calculation method includes: for the T-th response update step at the N-th simulation time, when T=0, substituting the initial mooring load generated by the mooring system on the floating platform at the N-th simulation time into the three-dimensional hydroelastic motion equation of the floating platform, solving for the hydroelastic response p(T) of the floating platform at the T-th response update step, and using it as the estimated value of the hydroelastic response at the T+1-th response update step. When T≥1, the hydroelastic response p(T) of the Tth response update step is used as the estimated value of the hydroelastic response of the (T+1)th response update step. The initial value of the integer parameter N is 1; the estimated value of the hydroelastic response of the floating platform is obtained from the (T+1)th response update step. The transformation yields the dynamic response X of the mooring points of each mooring line in the mooring system under the influence of the rigid body motion and elastic deformation of the floating platform at the (T+1)th response update step. M (T+1), and the dynamic response X at the mooring point. M Using (T+1) as the mooring line boundary condition, the mooring load F generated by the mooring system on the floating platform at the T+1th response update step is obtained through iterative calculation using the lumped mass model of the mooring system. M (T+1); The mooring load F generated by the floating platform in the T+1th response update step of the mooring system. M Substituting (T+1) into the three-dimensional hydroelastic motion equations of the floating platform, the hydroelastic response p(T+1) of the floating platform at the (T+1)th response update step is obtained. When the iterative coupling calculation of the dynamic response of the floating platform and the mooring system reaches convergence based on the calculation results of each response update step, the numerical simulation results of the dynamic response of the floating platform at the Nth simulation time are obtained, as well as the numerical simulation results of the mooring load generated by the mooring system on the floating platform at the Nth simulation time. The numerical simulation results of the mooring load at the Nth simulation time. The numerical simulation calculation is performed to calculate the initial mooring load generated by the mooring system on the floating platform at the (N+1)th simulation time.

2. The coupled dynamic response calculation method according to claim 1, characterized in that, Each response update step includes K iterative calculation steps, where the integer parameter K ≥ 2; the iterative calculation yields the mooring load F generated by the mooring system on the floating platform in the (T+1)th response update step. M (T+1) includes: interpolating the dynamic response of each mooring point at each of the most recent simulation times to obtain the dynamic response of the mooring point in each iterative calculation step; initializing the integer parameter k=1, and using the dynamic response of each mooring point in the kth iterative calculation step combined with the lumped mass model with the kth iterative parameter to calculate the mooring load generated by the mooring system in the kth iterative calculation step; when k<K, updating the k+1th iterative parameter of the lumped mass model according to the calculation result of the kth iterative calculation step, and setting k=k+1 to enter the next iterative calculation step; when k=K, using the mooring load generated by the mooring system in the kth iterative calculation step as the mooring load F generated by the mooring system on the floating platform in the T+1 response update step. M (T+1).

3. The coupled dynamic response calculation method according to claim 2, characterized in that, The mooring load calculated by the mooring system in the k-th iteration includes: representing any l-th mooring line as multiple mass points according to the lumped mass model, and determining the displacements of the mass points adjacent to the mooring point on the l-th mooring line; determining the mooring line tension F of the l-th mooring line based on the displacement difference between the mooring point and its adjacent mass points. Tl The mooring load F generated by the mooring system in the k-th iteration calculation step is obtained by combining the mooring line tension of each mooring line into a spatial force system. M =[F Mr [r = 1, 2, ..., m], the r-th modal component of the mooring load. u r is the r-th mode shape of the floating platform at the mooring point of the l-th mooring line, m is the total number of modes of the floating platform, and L is the total number of mooring lines.

4. The coupled dynamic response calculation method according to claim 2, characterized in that, The dynamic response of each mooring point in each iterative calculation step is obtained by interpolating the dynamic response of each mooring point at the most recent multiple simulation times, including: when N=1, using a linear interpolation method based on the dynamic response X of the mooring point at the 0th simulation time. M (0) and the dynamic response X at the T+1th response update step of the first simulation time. M (T+1), interpolate to calculate the dynamic response of the mooring point in the k-th iteration of the response update steps from the T-th to the T+1-th time of the first simulation time. When N≥2, the dynamic response X of the mooring point at the (N-2)th simulation time is calculated using the second-order Lagrange interpolation method. M (N-2), Dynamic response X at the (N-1)th simulation time. M The dynamic response X of (N-1) and the T+1th response update step M (T+1) Interpolation is used to calculate the dynamic response of the mooring point in the k-th iteration of the response update steps from T to T+1 at the Nth simulation time. Among them, t k t is the computation time of the k-th iteration step. N-2 It is the calculation time of the (N-2)th simulation time, t N-1 It is the calculation time of the (N-1)th simulation time, t N This is the calculation time at the Nth simulation time, and the dynamic response X at the 0th simulation time. M (0) is the initial dynamic response.

5. The coupled dynamic response calculation method according to claim 1, characterized in that, The dynamic response of a mooring point includes its displacement, which is transformed to obtain the dynamic response X of each mooring point at any response update step starting from the second response update step. M This includes: determining the modal analysis results of the floating platform and the coordinates of the mooring point in the body coordinate system; determining the displacement and spatial transformation matrix at the center of gravity of the floating platform based on the modal analysis results and hydroelastic response of the floating platform under rigid body degrees of freedom; and performing a matrix transformation on the coordinates of the mooring point in the body coordinate system of the floating platform based on the displacement and spatial transformation matrix at the center of gravity of the floating platform to obtain the rigid body displacement X of the mooring point under the influence of the rigid body motion of the floating platform. M_r Modal analysis results and hydroelastic response of the floating platform under elastic modal conditions are superimposed and combined with the spatial transformation matrix to obtain the elastic deformation displacement X of the mooring point under the influence of the elastic deformation of the floating platform. M_e Determine the dynamic response X of the mooring point in the (T+1)th response update step. M =X M_r +X M_e .

6. The coupled dynamic response calculation method according to claim 5, characterized in that, The elastic deformation displacement X of the mooring point M_e for: Where n is the number of wave frequency components, A i It is the amplitude of the i-th wave frequency component, k i ω is the wave number of the i-th wave frequency component. i θ is the frequency of the i-th wave frequency component. i It is the direction of the i-th wave frequency component. It is the initial phase angle of the i-th wave frequency component, x M_r It is the component of the rigid body displacement at the mooring point in the x-direction, y M_r δ(ω) represents the component of the rigid body displacement at the mooring point in the y-direction, and E is the spatial transformation matrix; i ) is the phase angle of the mooring point displacement caused by elastic deformation, and δ(ω) i )=[δ j (ω i )], H(ω i H(ω) is the contribution of elastic deformation to the mooring point displacement per unit amplitude, and H(ω) is the contribution of elastic deformation to the mooring point displacement. i )=[H j (ω i )], j = 1, 2, 3 represent the x′, y′, and z′ directions in the body coordinate system of the floating platform, m is the total number of modes of the floating platform, and u rj p is the component of the r-th mode shape of the floating platform in the j-direction. r (ω i ) is the r-th principal coordinate response of the floating platform in the frequency domain calculation, where Re() represents taking the real part of the complex number and Im() represents taking the imaginary part of the complex number.

7. The coupled dynamic response calculation method according to claim 5, characterized in that, The rigid body motion displacement X of the mooring point M_r For: X M_r =X G +EX′ M_L Among them, X G It is the displacement at the center of gravity of the floating platform and X G =[x G ,y G ,z G ], x G It is the component of the displacement at the center of gravity of the floating platform in the x-direction in the geodetic coordinate system, and the y-direction component. G It is the component of the displacement at the center of gravity of the floating platform in the y-direction in the geodetic coordinate system, z G X' is the component of the displacement at the center of gravity of the floating platform in the z-direction in the geodetic coordinate system, E is the spatial transformation matrix, and X' is the component of the displacement at the center of gravity of the floating platform in the z-direction. M_L The coordinates of the mooring point in the body coordinate system of the floating platform are X' M_L =[x' M_L ,y' M_L ,z' M_L ],x′ M_L These are the coordinates of the mooring point in the x′ direction and y′ direction in the body coordinate system of the floating platform. M_L It is the coordinate of the mooring point in the y′ direction of the floating platform's body coordinate system, and z′ is the coordinate of the mooring point in the body coordinate system. M_L It is the coordinate of the mooring point in the z′ direction in the body coordinate system of the floating platform.

8. The coupled dynamic response calculation method according to claim 1, characterized in that, The hydroelastic response of a floating platform includes the principal coordinate response matrix. Determining the hydroelastic response of the floating platform at the (T+1)th response update step involves: Based on three-dimensional hydroelastic theory, the three-dimensional hydroelastic motion equations of the floating platform are determined as follows: The principal coordinate response matrix p(T+1) of the floating platform at the T+1th response update step is obtained by time-domain numerical integration of the three-dimensional hydroelastic motion equations using a high-precision numerical discretization method; where a is the generalized mass matrix of the structure, A is the generalized additional mass matrix at infinite frequency, B is the generalized damping matrix, C is the generalized hydrostatic restoring force matrix, and h(t-τ) is the generalized time delay function matrix determined by the generalized additional mass matrix and the additional damping matrix. The first derivative of the principal coordinate response matrix is ​​given. Let F(t) be the second derivative of the principal coordinate response matrix, and let F(t) be the generalized wave excitation force matrix. d (t) is the generalized wave drift force matrix, F c (t) is the generalized flow force matrix, F w (t) is the generalized wind force matrix, F M (t) represents the mooring load generated by the mooring system.

9. The coupled dynamic response calculation method according to claim 1, characterized in that, The coupled dynamic response calculation method includes: when the following conditions are met... At that time, it was determined that the iterative coupling calculation of the dynamic response of the floating platform and the mooring system reached a convergence state, where CR R It is the iteration error threshold.

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