Coupling dynamic response calculation method for floating platform and mooring system

Abstract

The invention discloses a coupling dynamic response calculation method for a floating platform and a mooring system, and relates to the technical field of ship and ocean engineering, and the method comprises the steps: determining a water elasticity response estimated value of the floating platform at a (T + 1) th response updating step at a current simulation moment; the dynamic response of the mooring point is obtained through conversion of the water elasticity response estimated value, and the mooring load of the mooring system in the (T + 1) th response updating step is obtained through calculation; solving the hydroelastic response of the floating platform by using the mooring load of the (T + 1) th response updating step; and when the dynamic response iterative coupling calculation reaches a convergence state, obtaining a dynamic response numerical simulation result and entering a next simulation moment. According to the method, the coupling effect of the mooring system and the floating platform under the common influence of rigid body motion and elastic deformation of the floating platform is considered, and the coupling dynamic response of the floating platform and the mooring system of the floating platform can be predicted more accurately.

Description

Technical Field

[0001] The present application relates to the technical field of ship and ocean engineering, and in particular to a calculation method for the coupled dynamic response of a floating platform and a mooring system. Background Art

[0002] Offshore floating structures are important engineering equipment for the utilization of ocean space and the development of ocean resources. Different functional modules of offshore floating structures can be combined into various types of ocean floating platforms, such as large floating platforms like ocean science test platforms, ocean airport runways, offshore tourism platforms, and offshore pastures.

[0003] In the design and application process of a floating platform, it is necessary to calculate and evaluate the dynamic response of the floating platform to ensure the structural integrity and use safety of the floating platform. Currently, conventional methods regard the floating platform as a rigid body to calculate its dynamic response under ocean environmental loads. However, in fact, the floating platform requires a mooring system to constrain and control its spatial movement position to ensure its normal operation and safety and reliability in the ocean environment.

[0004] The motion response of the floating platform is restricted by the mooring system, and the mooring force generated by the mooring system depends on the motion state of the floating platform, resulting in a strong non-linear coupling effect between the dynamic responses of the floating platform and the mooring system. This causes the dynamic response of the floating platform calculated by existing methods to be inaccurate, affecting the hydrodynamic performance analysis and safety and reliability evaluation of the floating platform. Summary of the Invention

[0005] In view of the above problems and technical requirements, the present application proposes a calculation method for the coupled dynamic response of a floating platform and a mooring system. The technical solution of the present application is as follows:

[0006] A calculation method for 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, substitute 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, and solve to obtain the hydroelastic response p(T) of the floating platform at the T-th response update step and use it as the predicted value of the hydroelastic response at the (T + 1)-th response update step When T ≥ 1, use the hydroelastic response p(T) at the T-th response update step as the predicted value of the hydroelastic response at the (T + 1)-th response update step The starting value of the integer parameter N is 1;

[0008] From the predicted value of the hydroelastic response of the floating platform at the (T + 1)-th response update step Convert to obtain the dynamic response X of each mooring line's mooring point 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 use the dynamic response X M (T + 1) of the mooring point as the mooring line boundary condition, and use the lumped mass model of the mooring system to iteratively calculate the mooring load F M (T + 1) generated by the mooring system on the floating platform at the (T + 1)-th response update step;

[0009] Substitute the mooring load F M (T + 1) generated by the mooring system on the floating platform at the (T + 1)-th response update step into the three-dimensional hydroelastic motion equation of the floating platform, and solve to obtain the hydroelastic response p(T + 1) of the floating platform at the (T + 1)-th response update step;

[0010] When it is determined according to the calculation results of each response update step that the iterative coupling calculation of the dynamic responses of the floating platform and the mooring system reaches a convergence state, obtain the numerical simulation results of the dynamic response of the floating platform at the N-th simulation moment, and obtain the numerical simulation results of the mooring load generated by the mooring system on the floating platform at the N-th simulation moment

[0011] Use the numerical simulation results of the mooring load at the N-th simulation moment as the initial mooring load generated by the mooring system on the floating platform at the (N + 1)-th simulation moment and enter the numerical simulation calculation at the (N + 1)-th simulation moment.

[0012] Its further technical solution is that each response update step includes K iterative calculation steps, and the integer parameter K ≥ 2; the iterative calculation to obtain the mooring load F M (T + 1) generated by the mooring system on the floating platform at the (T + 1)-th response update step includes:

[0013] Interpolate the dynamic responses of each mooring point in the recent multiple response update steps to obtain the dynamic responses of the mooring points at each iterative calculation step;

[0014] Initialize the integer parameter k = 1, and use the dynamic responses of each mooring point at the k-th iterative calculation step and combine with the lumped mass model with the k-th iterative parameter to calculate the mooring load generated by the mooring system at the k-th iterative calculation step;

[0015] When k < K, update to obtain the (k + 1)-th iterative parameter of the lumped mass model according to the calculation results of the k-th iterative calculation step, and let k = k + 1 and enter the next iterative calculation step; when k = K, use the mooring load generated by the mooring system at the K-th iterative calculation step as the mooring load F M (T + 1) generated by the mooring system on the floating platform at the (T + 1)-th response update step.

[0016] Its further technical solution is that the mooring loads generated by the mooring system at the k-th iterative calculation step include:

[0017] According to 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 point on the l-th mooring line are determined;

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

[0019] The mooring line tensions of each mooring line are synthesized by a spatial force system to obtain the mooring load F generated by the mooring system at the k-th iterative calculation step M =[F Mr , r = 1, 2,..., m], the r-th modal component of the mooring load u r is the r-th modal vibration mode 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] Its further technical solution is that the dynamic responses of the mooring points at each iterative calculation step are interpolated based on the dynamic responses of each mooring point at the nearest multiple simulation times, including:

[0021] When N = 1, using the linear interpolation method, based on the dynamic response X M (0) of the mooring point at the 0-th simulation time and the dynamic response X M (T + 1) at the (T + 1)-th response update step at the 1-st simulation time, interpolate to calculate the dynamic response of the mooring point at the k-th iterative calculation step from the T-th to the (T + 1)-th response update step at the 1-st simulation time

[0022] When N ≥ 2, using the second-order Lagrange interpolation method, based on the dynamic response X M (N - 2) of the mooring point at the (N - 2)-th simulation time, the dynamic response X M (N - 1) at the (N - 1)-th simulation time, and the dynamic response X M (T + 1) at the (T + 1)-th response update step, interpolate to calculate the dynamic response of the mooring point at the k-th iterative calculation step from the T-th to the (T + 1)-th response update step at the N-th simulation time

[0023] where, t k is the calculation time of the k-th iterative calculation step, t N-2 is the calculation time of the (N - 2)-th simulation time, t N-1 is the calculation time of the (N - 1)-th simulation time, tN is the calculation time of the Nth simulation time, and the dynamic response X at the 0th simulation time M (0) is the initial dynamic response.

[0024] Its further technical solution is that the dynamic response of the mooring point includes the displacement of the mooring point, and the dynamic response X of each mooring point at any response update step starting from the second response update step is obtained through conversion M including:

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

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

[0027] Perform modal superposition on the modal analysis result and hydroelastic response of the floating platform in the elastic mode and combine 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 at the (T + 1)th response update step M = X M_r + X M_e .

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

[0030]

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

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

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

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

[0035] Its further technical solution is that the rigid-body motion displacement X M_r of the mooring point is:

[0036] X M_r = X G + EX′ M_L

[0037] where X G is the displacement at the center of gravity of the floating platform and X G = [x G , y G , z G , x G is the component of the displacement at the center of gravity of the floating platform in the x direction of the earth coordinate system, y G is the component of the displacement at the center of gravity of the floating platform in the y direction of the earth coordinate system, z G is the component of the displacement at the center of gravity of the floating platform in the z direction of the earth coordinate system, E is the spatial transformation matrix, X' M_L is the coordinate of the mooring point in the floating platform's body-fixed coordinate system and X' M_L = [x' M_L , y' M_L , z' M_L , x′ M_L is the coordinate of the mooring point in the x′ direction of the floating platform's body-fixed coordinate system, y′ M_L is the coordinate of the mooring point in the y′ direction of the floating platform's body-fixed coordinate system, z′ M_L is the coordinate of the mooring point in the z′ direction of the floating platform's body-fixed coordinate system.

[0038] A further technical solution thereof is that the hydroelastic response of the floating platform includes a principal coordinate response matrix. Determining the hydroelastic response of the floating platform at the (T + 1)-th response update step includes:

[0039] According to the three-dimensional hydroelastic theory, the three-dimensional hydroelastic motion equation of the floating platform is determined as:

[0040]

[0041] Using a high-precision numerical discretization method to perform time-domain numerical integration calculation on the three-dimensional hydroelastic motion equation to obtain the principal coordinate response matrix p(T + 1) of the floating platform at the (T + 1)-th response update step;

[0042] wherein, a is the structural generalized mass matrix, A is the generalized added mass matrix at infinite frequency, B is the generalized damping matrix, C is the generalized hydrostatic restoring force matrix, h(t - τ) is the generalized time-delay function matrix determined by the generalized added mass matrix and the added damping matrix, represents the first-order differential of the principal coordinate response matrix, represents the second-order differential of the principal coordinate response matrix, F(t) is the generalized wave excitation force matrix, F d (t) is the generalized wave drift force matrix, F c (t) is the generalized current acting force matrix, F w (t) is the generalized wind acting force matrix, F M (t) is the mooring load generated by the mooring system.

[0043] A further technical solution thereof is that the coupled dynamic response calculation method includes: when is satisfied, it is determined that the iterative coupling calculation of the dynamic responses of the floating platform and the mooring system reaches a convergence state, wherein CR R is the iteration error threshold.

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

[0045] A coupled dynamic response calculation method for a floating platform and a mooring system proposed in this application can more accurately predict the mutual coupling effect of the floating platform and the mooring system by iteratively coupling and calculating the dynamic responses 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 of the mooring point. Compared with the traditional numerical simulation method that only considers the rigid body motion of the floating platform, the accuracy of the numerical simulation calculation results of the coupled dynamic response of the floating platform and the mooring system is effectively improved.

[0046] Considering the characteristic that the natural period of the mooring system is much smaller than that of the floating platform, the problem of inconsistent numerical simulation calculation times between the mooring system and the floating platform is solved by asynchronously long iterative calculation of the dynamic response of the mooring system and the mooring loads generated on the floating platform. Within each response update step, the dynamic response of the mooring point at each iterative calculation step is calculated by interpolation, and the dynamic response of the mooring system is solved step by step according to each iterative calculation step, which can improve the calculation efficiency while accurately calculating the mooring loads generated by the mooring system on the floating platform at each response update step. Description of the Drawings

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

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

[0049] Figure 3 is the time history curve of the mooring loads generated by the mooring system on the floating platform.

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

[0051] The following further describes the detailed implementation manner of the present application with reference to the drawings.

[0052] A coupled dynamic response calculation method for a floating platform and a mooring system proposed in the present application, please refer to Figure 1 the flowchart of, and the specific steps are as follows:

[0053] Step 1, for the T-th response update step at the N-th simulation moment, it is divided into the following situations:

[0054] For the initial response update step when T = 0, substitute the initial mooring loads generated by the mooring system on the floating platform at the N-th simulation moment into the three-dimensional hydroelastic motion equation of the floating platform, and use a high-precision numerical discretization method to perform time-domain numerical integration on the three-dimensional hydroelastic motion equation to solve for the hydroelastic response p(T) of the floating platform at the T-th response update step, and use it as the pre-estimated value of the hydroelastic response at the T+1-th response update step Among them, T is an integer parameter and T≥0, and N is an integer parameter and N≥1. For the first simulation moment when N = 1, since the inherent properties such as the geometric dimensions and material properties of the mooring system at the initial moment are determined quantities and the initial state of the mooring line is known, the initial dynamic response and mooring loads of the mooring system when N = 1 can be determined. For the initial mooring loads when N≥2, they are the numerical simulation results of the mooring loads calculated at the previous simulation moment.

[0055] Considering the mutual coupling effect between the mooring system and the floating platform, the mooring load generated by the mooring system on the floating platform is added 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 the floating platform includes the main coordinate response matrix. Among them, p(t) represents the main coordinate response matrix and p(t)=[p 1 (t), p 2 (t),..., p m (t)], m is the total number of modes of the floating platform, represents the first-order differential of the main coordinate response matrix, represents the second-order differential of the main coordinate response matrix, a is the structural generalized mass matrix, A is the generalized added mass matrix at infinite frequency, B is the generalized damping matrix, C is the generalized hydrostatic restoring force matrix, h(t - τ) is the generalized time-delay function matrix determined by the generalized added mass matrix and the added damping matrix, F(t) is the generalized wave excitation force matrix, F d (t) is the generalized wave drift force matrix, F c (t) is the generalized current acting force matrix, F w (t) is the generalized wind acting force matrix, F M (t) is the mooring load generated by the mooring system.

[0058] It should be noted that this application mainly studies the excitation force of the mooring load F M (t) generated by the mooring system on the floating platform. Therefore, the excitation forces of the remaining terms in the three-dimensional hydroelastic motion equation of the floating platform are determined by existing methods, and this application will not introduce them in detail.

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

[0060] Rewrite the three-dimensional hydroelastic motion equation of formula (1) into the following form:

[0061]

[0062] Let Y 1 =p(t), and substitute it into formula (2) to rewrite the three-dimensional hydroelastic motion equation into a set of first-order ordinary differential equations, and the expression is:

[0063]

[0064] Among them, G(t, Y1 , Y 2 ) represents the right - hand side of Equation (2). Using the fourth - order Runge - Kutta method, the differential equations can be transformed into linear equations, and then the numerical method can be used to solve the main coordinate response matrix of the floating platform. The obtained linear equations are as follows:

[0065]

[0066] where Y 1N represents the main coordinate response matrix of the floating platform at the Nth simulation time, Y 1T represents the main coordinate response matrix of the floating platform at the Tth response update step, Y 2N represents the first - order differential of the main coordinate response matrix of the floating platform at the Nth simulation time, Y 2T represents the first - order differential of the main coordinate response matrix of the floating platform at the Tth response update step. K 1 , K 2 , K 3 , K 4 , L 1 , L 2 , L 3 , L 4 are intermediate variables, and their specific expressions are as follows:

[0067]

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

[0069]

[0070] where t N is the calculation time at the Nth simulation time, ΔN represents the calculation time step between two adjacent simulation times and ΔN = t N+1 - t N . According to the initial mooring load at the Nth simulation time, and each intermediate variable are obtained. Substituting them into Equation (4), the hydro - elastic response p(T) of the floating platform at the Tth response update step can be iteratively calculated.

[0071] When T≥1, the hydro - elastic response p(T) at the Tth response update step is used as the pre - estimate of the hydro - elastic response at the T + 1th response update step

[0072] Step 2, from the pre - estimate of the hydro - elastic response of the floating platform at the T + 1th response update step Convert to obtain the dynamic response X of each mooring point 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 the displacement of the mooring point. Since the mooring point is the contact point between the floating platform and the mooring system, and there are not only rigid body motions but also elastic deformations during the process in which the floating platform is restricted by the mooring system, the displacement of the mooring point needs to consider the combined influence of the rigid body motion and elastic deformation of the floating platform. In one embodiment, convert to obtain the dynamic response X of each mooring point at any response update step starting from the second response update step T = 1 M The specific method is as follows:

[0074] (1) Determine the modal analysis results of the floating platform by performing modal analysis on the three-dimensional finite element model of the floating platform. The modal analysis results include the modal vibration modes u r of any point Q on the floating platform, where the first 6 orders r = 1 - 6 correspond to rigid body modes, and r = 7 - m correspond to elastic modes. The first 6-order rigid body modal vibration modes can be respectively expressed as:

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

[0076] u 2 = {0, 1, 0} T

[0077] u 3 = {0, 0, 1} T

[0078] u 4 = {0, -(z * - z G ), (y * - y G )} T

[0079] u 5 = {(z * - z G ), 0, -(x * - x G )} T

[0080] u 6 = {-(y * - y G ), (x * - x G ), 0} T

[0081] where, (xG , y G , z G ) is the displacement at the center of gravity of the floating platform, (x * , 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 points in the body-fixed coordinate system of the floating platform. The body-fixed coordinate system of the floating platform 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 to the port side of the floating platform, and the positive direction of the z'-axis is vertically upward. This coordinate system changes the origin position as the floating platform moves and changes the coordinate axis directions as the floating platform rotates.

[0083] Calculate the displacement at the center of gravity of the floating platform based on the rigid body mode shapes and the principal coordinate response matrix of the floating platform under the degrees of freedom of the rigid body Since (x * , y * , z * ) = (x G , y G , z G ), u 4 ~u 6 = 0, so the displacement X G at the center of gravity of the floating platform is X 1 = [p 2 (t), p 3 (t), p G (t)], that is, the displacement X G at the center of gravity of the floating platform is X G = [x G , y 1 (t), p 2 (t),..., p m (t)] corresponding to the first 3 modal components of the principal coordinate response matrix p(t) = [p G is the x-direction component of the displacement at the center of gravity of the floating platform in the geodetic coordinate system, y G is the y-direction component of the displacement at the center of gravity of the floating platform in the geodetic coordinate system, z G is the z-direction component of the displacement at the center of gravity of the floating platform in the geodetic coordinate system.

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

[0085]

[0086] Wherein, α is the roll angle of the floating platform, β is the pitch angle of the floating platform, γ is the yaw angle of the floating platform, and the roll angle, pitch angle, and yaw angle of the floating platform respectively correspond to the 4th to 6th order modal components of the main coordinate response matrix p(t) = [p 1 (t), p 2 (t),..., p m (t)].

[0087] (2) Matrix transformation is performed on the coordinates of the mooring point in the body-fixed coordinate system of the floating platform according to the displacement at the center of gravity of the floating platform and the spatial transformation matrix to obtain the rigid body motion displacement X M_r of the mooring point under the influence of the rigid body motion of the floating platform.

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

[0089] X M_r = X G + EX′ M_L

[0090] Wherein, X' M_L is the coordinate of the mooring point in the body-fixed coordinate system of the floating platform and X' M_L = [x' M_L , y' M_L , z' M_L , x′ M_L is the coordinate of the mooring point in the x′ direction in the body-fixed coordinate system of the floating platform, y′ M_L is the coordinate of the mooring point in the y′ direction in the body-fixed coordinate system of the floating platform, and z′ M_L is the coordinate of the mooring point in the z′ direction in the body-fixed coordinate system of the floating platform.

[0091] Since the mooring point moves together with the floating platform, the coordinate of the mooring point in the body-fixed coordinate system of the floating platform does not change. The change in the rigid body motion displacement X M_r of the mooring point is only related to the displacement X G at the center of gravity of the floating platform and the change in the spatial transformation matrix E.

[0092] (3) Modal superposition is performed on the modal analysis results and hydroelastic responses of the floating platform in the elastic mode and combined with the spatial transformation matrix to obtain the elastic deformation displacement X M_e of the mooring point under the influence of the elastic deformation of the floating platform.

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

[0094]

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

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

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

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

[0099] (4) Determine the dynamic response X of the mooring point at the (T + 1)-th 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. Usually, only the influence of the rigid body motion of the floating platform is considered for the velocity of the mooring point. The velocity v M = v M_r = v G + ω × (EX' M_L ), where v M_r is the contribution of the rigid body motion of the floating platform to the velocity of the mooring point, ω is the rotational angular velocity at the center of gravity of the floating platform, which corresponds to the 4th to 6th modal components of the first-order differential of the principal coordinate response matrix.

[0101] Step 3: Using the dynamic response X of the mooring point M (T + 1) as the boundary condition of the mooring line, the mooring load F generated by the mooring system on the floating platform at the (T + 1)-th response update step is iteratively calculated 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 specific steps for iteratively calculating the mooring load F generated by the mooring system on the floating platform at the (T + 1)-th response update step are as follows: M (T + 1) are:

[0103] (1) Interpolate the dynamic response of the mooring point at each iterative calculation step based on the dynamic responses of each mooring point at multiple recent simulation times.

[0104] According to the method in Step 2, the dynamic response of the mooring point at each response update step during the coupled interaction between the floating platform and the mooring system can be calculated. Since the natural period of the mooring system is much smaller than that of the floating platform, the calculation time step between two adjacent iterative calculation steps of the mooring system is much smaller than the calculation time step between two adjacent response update steps of the floating platform. Therefore, the dynamic response of the mooring point at each iterative calculation step cannot be directly obtained and needs to be determined by interpolation.

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

[0106] When N = 1, use the linear interpolation method to interpolate the dynamic response X of the mooring point at the 0-th simulation time M (0) and the dynamic response X of the (T + 1)-th response update step at the 1-st simulation time M (T + 1) to interpolate and calculate the dynamic response of the mooring point at the k-th iterative calculation step of the T-th to (T + 1)-th response update steps at the 1-st simulation time

[0107] When N ≥ 2, use the second-order Lagrange interpolation method to interpolate the dynamic response X of the mooring point at the (N - 2)-th simulation time M (N - 2), the dynamic response X of the mooring point at the (N - 1)-th simulation time M (N - 1) and the dynamic response X of the (T + 1)-th response update step M (T + 1) to interpolate and calculate the dynamic response of the mooring point at the k-th iterative calculation step of the T-th to (T + 1)-th response update steps at the N-th simulation time

[0108] where, t kis the calculation time of the k-th iterative calculation step, t N-2 is the calculation time of the (N - 2)-th simulation time step, t N-1 is the calculation time of the (N - 1)-th simulation time step, t N is the calculation time of the N-th simulation time step. When T = 1, t N-1 ≤t k ≤t N and when T ≥ 2, t N-2 <t N-1 ≤t k ≤t N The dynamic response X M (0) is the initial dynamic response, and the initial dynamic response of the mooring point at the initial time is known.

[0109] (2) Initialize the integer parameter k = 1. Using the dynamic response of each mooring point at the k-th iterative calculation step and combining with the lumped mass model with the k-th iteration parameters, calculate the mooring loads generated by the mooring system at the k-th iterative calculation step.

[0110] In one embodiment, the specific method for calculating the mooring loads generated by the mooring system at the k-th iterative 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 Figure 2 shown. The mass point g = 1 represents the mooring line anchor point, g = G + 1 represents the mooring point, and g = G represents the mass point adjacent to the mooring point on the mooring line.

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

[0113]

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

[0115] The added mass, fluid resistance, inertial force caused by fluid acceleration, gravity and buoyancy acting on the mass point g, damping force caused by structural damping, and seabed soil forces can be determined according to the environmental parameters such as wind, waves, and ocean currents in the target sea area to be simulated and the inherent properties of the mooring system according to existing methods, which will not be elaborated in this application.

[0116] Substituting the various environmental forces acting on the mass point g into Equation (5) can calculate the acceleration of the mass point g, and then the dynamic responses such as the velocity and displacement of the mass point g can be determined. The specific method for solving Equation (5) can adopt existing technologies. In this application, a high-precision numerical discretization method is used to perform time-domain numerical integration on this motion equation to obtain 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] Rewrite the dynamic equation of Equation (5) into the following form:

[0118]

[0119] Let y 1gJ = x sgJ (t), and substitute it into Equation (6) to rewrite the dynamic equation into a set of first-order ordinary differential equations:

[0120]

[0121] where f(t, y 1gJ , y 2gJ ) represents the right-hand side term of Equation (6). Using the fourth-order Runge-Kutta method, the differential equation can be converted into a linear equation, so as to solve the dynamic equation of Equation (5) using numerical methods. The converted linear equations are:

[0122]

[0123] where y 1gJk represents the displacement of the mass point g at the k-th iterative calculation step, y 1gJ(k+1) represents the displacement of the mass point g at the (k + 1)-th iterative calculation step, y 2gJk represents the velocity of the mass point g at the k-th iterative calculation step, y 2gJ(k+1) represents the velocity of the mass point g at the (k + 1)-th iterative calculation step, and Δt represents the calculation time step between two adjacent iterative calculation steps. β 1 , β 2 , β 3 , β 4 , γ 1 , γ 2 , γ 3 , γ 4 are intermediate variables, and their specific expressions are:

[0124] β 1 = y 2gJk , β 4 = y 2gJk + Δt × γ 3 ,

[0125] γ 1 = f(t n , y 1gJk , y 2gJk ),

[0126]

[0127] γ 4 = f(t n + Δt, y 1gJk + Δt × β 3 , y 2gJk + Δt × β 3 )

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

[0129] When g = G, the displacement of the mass point adjacent to the mooring point on the l-th mooring line at the k-th iterative calculation step can be determined according to the displacement of the (k - 1)-th iterative calculation step and the k-th iterative parameter. Among them, the iterative parameters include the mooring line tension in the dynamic equation.

[0130] After determining the mooring point of the l-th mooring line and the displacements of its adjacent mass points, the mooring line tension F Tl = [F TlJ of the l-th mooring line can be determined according to the displacement difference between the mooring point and its adjacent mass points, and at the same time, the mooring line tension of the (k + 1)-th iterative parameter at the (k + 1)-th iterative calculation step is updated. The mooring line tension F Tl in the J direction component F TlJ The specific calculation formula is:

[0131]

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

[0133] The mooring line tensions of each mooring line are synthesized in a spatial force system to obtain the mooring load F generated by the mooring system at the k-th iterative calculation step. M =[F Mr , r = 1, 2,..., m], the r-th mode 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, update the (k + 1)-th iterative parameters of the lumped mass model according to the calculation results of the k-th iterative calculation step, and let k = k + 1 to enter the next iterative calculation step, and continue to iteratively calculate the mooring load generated by the mooring system on the floating platform until the calculation time of the mooring system reaches the calculation time of the floating platform. When k = K, use the mooring load generated by the mooring system at the K-th iterative calculation step as the mooring load F M (T + 1) generated by the mooring system on the floating platform at the (T + 1)-th response update step.

[0135] Step 4, Substitute the mooring load F M (T + 1) generated by the mooring system on the floating platform at the (T + 1)-th response update step into the three-dimensional hydroelastic motion equation of the floating platform, and use the updated mooring load as the excitation force to re-solve the three-dimensional hydroelastic motion equation to obtain the hydroelastic response p(T + 1) of the floating platform at the (T + 1)-th 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 will affect the mooring load of the mooring system, and the mooring load will in turn affect the hydroelastic response of the floating platform. Therefore, continuous iterative coupling calculations are required within each simulation time to update the dynamic responses of the floating platform and the mooring system.

[0137] When it is determined that the iterative coupling calculation of the dynamic responses of the floating platform and the mooring system reaches the convergence state according to the calculation results of each response update step, the numerical simulation results of the dynamic responses of the floating platform and the mooring system at the N-th simulation time are obtained, and the numerical simulation results of the mooring load generated by the mooring system on the floating platform at the N-th simulation time are obtained.

[0138] In one embodiment, the convergence state is judged according to the hydroelastic responses of the floating platform at two adjacent response update steps. When When , it is determined that the iterative coupling calculation of the dynamic response of the floating platform and the mooring system reaches a convergence state, where p(T) is the hydroelastic response of the floating platform in the Tth response update step, p(T+1) is the hydroelastic response of the floating platform in the T+1th response update step, and CR R It is the iteration error threshold, which can be set based on experience.

[0139] Step 5: The numerical simulation results of the mooring load at the Nth simulation time are The initial mooring load generated by the mooring system on the floating platform at the N+1th simulation moment and the numerical simulation calculation at the N+1th simulation moment are entered.

[0140] The dynamic response iterative coupling calculation method of the floating platform and the mooring system disclosed in this application can accurately calculate the dynamic response of the mooring system and the floating platform at each simulation time, and the dynamic response curve can be drawn according to the simulation time to obtain the numerical simulation results of the dynamic response of the floating platform and its mooring system. The time history curve is as follows Figure 3 As shown in the figure, the dynamic response time history curve of the floating platform is as follows: Figure 4 shown.

[0141] The above is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the protection scope of the present 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 comprises: For the Tth response update step at the Nth simulation time, when T = 0, the initial mooring load generated by the mooring system on the floating platform at the Nth simulation time is substituted into the three-dimensional hydroelastic motion equation of the floating platform, and the hydroelastic response p(T) of the floating platform at the Tth response update step is obtained and used as the estimated hydroelastic response of the T+1th response update step. When T ≥ 1, the hydroelastic response p(T) of the Tth response update step is used as the estimated hydroelastic response of the T+1th response update step. The starting value of the integer parameter N is 1; Estimated hydroelastic response of the floating platform from the T+1th response update step The conversion results in 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+1th response update step. M (T+1), and the dynamic response of the mooring point is X M (T+1) is used as the boundary condition of the mooring line. The lumped mass model of the mooring system is used to iteratively calculate the mooring load F generated by the mooring system on the floating platform in the T+1 response update step. M (T+1); The mooring load F generated by the mooring system on the floating platform in the T+1th response update step is M (T+1) is substituted into the three-dimensional hydroelastic motion equation of the floating platform, and the hydroelastic response p(T+1) of the floating platform at the T+1th response update step is obtained; When it is determined that the iterative coupling calculation of the dynamic response of the floating platform and the mooring system has reached a convergence state according to 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, and the numerical simulation results of the mooring load generated by the mooring system on the floating platform at the Nth simulation time are obtained. The numerical simulation results of the mooring load at the Nth simulation time are The initial mooring load generated by the mooring system on the floating platform at the N+1th simulation moment and the numerical simulation calculation at the N+1th simulation moment are entered.

2. The coupled dynamic response calculation method according to claim 1, characterized in that: Each response update step includes K iterative calculation steps, with an integer parameter K ≥ 2. The iterative calculation obtains the mooring load F generated by the mooring system on the floating platform in the T+1th response update step. M (T+1) includes: The dynamic response of each mooring point at each iterative calculation step is obtained by interpolating the dynamic response of each mooring point at the latest multiple simulation moments; Initialize the integer parameter k=1, use the dynamic response of each mooring point in the kth iteration calculation step combined with the lumped mass model with the kth iteration parameters to calculate the mooring load generated by the mooring system in the kth iteration calculation step; When k<K, the k+1th iteration parameter of the lumped mass model is updated according to the calculation result of the kth iteration calculation step, and k=k+1 is set to enter the next iteration calculation step; when k=K, the mooring load generated by the mooring system in the Kth iteration calculation step is used as the mooring load F generated by the mooring system on the floating platform in the T+1th response update step. M (T+1).

3. The coupled dynamic response calculation method according to claim 2, characterized in that: The mooring loads generated by the mooring system in the kth iteration calculation step are calculated to include: According to the lumped mass model, any l-th mooring line is equivalent to multiple mass points, and the displacement of the mass points adjacent to the mooring point on the l-th mooring line is determined; Determine the mooring line tension F of the lth mooring line according to the displacement difference between the mooring point of the lth mooring line and its adjacent mass points Tl ; The mooring line tension of each mooring line is synthesized by a spatial force system to obtain the mooring load F generated by the mooring system in the kth iteration calculation step. M =[F Mr ,r=1,2,...,m], the rth modal component of the mooring load u r is the rth mode vibration shape of the floating platform at the mooring point of the lth 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 at each iterative calculation step is obtained by interpolating the dynamic response of each mooring point at the most recent multiple simulation moments, including: When N=1, the linear interpolation method is used according to the dynamic response X of the mooring point at the 0th simulation time. M (0) and the dynamic response X of the T+1th response update step at the first simulation time M (T+1), interpolation calculation of the dynamic response of the mooring point in the kth iteration calculation step from the Tth to the T+1th response update step at the first simulation time When N ≥ 2, the second-order Lagrange interpolation method is used according to the dynamic response X of the mooring point at the N-2th simulation time. M (N-2), the dynamic response X at the N-1th simulation moment M The dynamic response X of the (N-1) and T+1th response update steps M (T+1) Interpolation calculation of the dynamic response of the mooring point at the kth iteration calculation step from the Tth to the T+1th response update step at the Nth simulation time Among them, t k is the calculation time of the kth iteration step, t N-2 is the calculation time of the N-2th simulation time, t N-1 is the calculation time of the N-1th simulation time, t N is the calculation time of 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 the mooring point includes the displacement of the mooring point, which is converted to obtain the dynamic response X of each mooring point in any response update step starting from the second response update step M include: Determine the modal analysis results of the floating platform and the coordinates of the mooring point of the floating platform in the body coordinate system; determine the displacement and space transformation matrix at the center of gravity of the floating platform based on the modal analysis results of the floating platform under the rigid body freedom and the hydroelastic response; According to the displacement at the center of gravity of the floating platform and the space transformation matrix, the coordinates of the mooring point in the floating platform body coordinate system are transformed by matrix to obtain the rigid body motion displacement X of the mooring point under the influence of the rigid body motion of the floating platform. M_r ; The modal analysis results of the floating platform under elastic mode and the hydroelastic response are modally superimposed and combined with the space 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 at the T+1th 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 is the amplitude of the frequency component of the ith wave, k i is the wave number of the ith wave frequency component, ω i is the frequency of the ith wave frequency component, θ i is the direction of the ith wave frequency component, is the initial phase angle of the ith wave frequency component, x M_r is the component of the rigid body motion displacement of the mooring point in the x direction, and y M_r is the component of the rigid body motion displacement of the mooring point in the y direction, and E is the space transformation matrix; δ(ω i ) is the phase angle of the displacement of the mooring point caused by elastic deformation and δ(ω i )=[δ j (ω i )], H(ω i ) is the contribution of elastic deformation to the displacement of the mooring point under unit amplitude and H(ω i )=[H j (ω i )], j = 1, 2, 3 are the x′, y′, z′ directions of the floating platform body coordinate system, m is the total number of modes of the floating platform, u rj is the component of the rth mode shape of the floating platform in the j direction, p r (ω i ) is the rth order principal coordinate response of the floating platform in the frequency domain calculation, Re() represents the real part of the complex number, and Im() represents 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 is the displacement of the floating platform's center of gravity and X G =[x G ,y G ,z G ], x G is the displacement of the floating platform at the center of gravity in the x-direction in the geodetic coordinate system, and y G is the displacement of the floating platform at the center of gravity in the y direction in the geodetic coordinate system, z G is the displacement component of the floating platform's center of gravity in the z direction in the geodetic coordinate system, E is the space transformation matrix, X' M_L is the coordinate of the mooring point in the floating platform body coordinate system and X' M_L =[x' M_L ,y' M_L ,z' M_L ],x′ M_L is the coordinate of the mooring point in the x′ direction in the floating platform body coordinate system, y′ M_L is the coordinate of the mooring point in the y′ direction in the floating platform body coordinate system, z′ M_L It is the coordinate of the mooring point in the z′ direction in the floating platform body coordinate system.

8. The coupled dynamic response calculation method according to claim 1, characterized in that: The hydroelastic response of the floating platform includes the principal coordinate response matrix, and determining the hydroelastic response of the floating platform at the T+1th response update step includes: According to the three-dimensional hydroelastic theory, the three-dimensional hydroelastic motion equation of the floating platform is determined as follows: The high-precision numerical discretization method is used to perform time-domain numerical integration calculations on the three-dimensional hydroelastic motion equations to obtain the principal coordinate response matrix p(T+1) of the floating platform at the T+1th response update step. Where a is the structural generalized mass matrix, 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. represents the first-order differential of the principal coordinate response matrix, represents the second-order differential of the principal coordinate response matrix, F(t) is the generalized wave excitation force matrix, and F 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) is 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 comprises: When satisfied When , it is determined that the iterative coupling calculation of the dynamic response of the floating platform and the mooring system has reached a convergence state, where CR R is the iteration error threshold.

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