A method for solving deepwater riser configuration and hydrodynamic synchronous bidirectional coupling

Abstract

The application relates to the technical field of nonlinear dynamics analysis of an offshore engineering riser, and provides a deepwater riser configuration and hydrodynamic synchronous bidirectional coupling solving method to solve the problems that the method based on a small-angle beam unit in the prior art is poor in precision and large in calculation amount due to insufficient geometric nonlinear description capability, and the ANCF coupling method in the prior art loses the advantage of a constant mass matrix and is low in calculation efficiency due to frequent updating of an additional mass matrix. The method comprises the following steps: S100, establishing a riser nonlinear dynamics model based on an absolute node coordinate method; S200, explicitly expressing nonlinear hydrodynamic loads based on an implicit time domain integral method; and S300, synchronously solving riser nonlinear dynamics response by adopting a Newton-Raphson iteration method.

Description

Technical Field

[0001] This invention relates to the field of nonlinear dynamic analysis technology for marine engineering risers, specifically to a method for synchronously and bidirectionally coupled solution of deep-water riser configuration and hydrodynamics, used to calculate the dynamic response of marine risers under large deformation and their nonlinear hydrodynamic interaction with the surrounding fluid. Background Technology

[0002] Marine risers are critical equipment connecting surface floating structures to underwater oil, gas, and mineral production facilities. Their dynamic response and fatigue life analysis under complex marine environmental loads such as waves and currents are among the core issues in marine engineering structural design. The core challenge of riser dynamic analysis lies in the fact that, as a slender and flexible structure, it undergoes large displacements and large rotations due to geometrical nonlinear deformation. Simultaneously, the fluid loads (i.e., hydrodynamics) it experiences are nonlinear functions strongly correlated with its motion state (including acceleration, velocity, and configuration), forming a complex two-way fluid-structure interaction problem. Accurately and efficiently solving for the synchronously coupled response of the riser configuration and hydrodynamics is crucial for ensuring riser safety.

[0003] Currently, commercial finite element method (FEM) software, such as Orcaflex and ABAQUS, is widely used in the nonlinear dynamic analysis of marine risers. The mainstream solution approach is to discretize the riser structure using beam elements (such as first- or second-order elements like B31, B21, B32, and B22) based on the small rotation angle assumption. These elements describe deformation through the displacement of element nodes and the rotation based on the small rotation angle assumption. Figure 1 As shown, its mass matrix is ​​defined in the element's local coordinate system. When solving fluid-structure interaction problems, hydrodynamic forces are applied to the element as distributed forces. The additional mass effect caused by fluid acceleration contributes an additional mass matrix associated with the riser configuration. This additional mass matrix is ​​coupled with the structure's own mass matrix to form the system's overall mass matrix.

[0004] However, the aforementioned existing technologies have the following inherent defects and limitations:

[0005] 1. Insufficient geometric nonlinearity: Beam elements based on the small rotation angle assumption essentially approximate the bending configuration of a beam by "substituting straight lines for curves," such as... Figure 2 When the riser undergoes large deformations, this approximation introduces significant errors, including in geometric representation and curvilinear coordinate systems. To ensure computational accuracy, the riser must be subdivided into very fine elements (i.e., using a large number of elements), which directly leads to a surge in the system's degrees of freedom and a massive computational scale.

[0006] 2. Low computational efficiency due to the added mass: The root cause of the low computational efficiency lies in the highly nonlinear hydrodynamics and the resulting time-varying characteristics of the system matrix. Specifically, the hydrodynamics is a strongly nonlinear function of the instantaneous riser configuration, requiring the recalculation of the hydrodynamics and updating of the Jacobian matrix at each time step and even at each Newton iteration step in the implicit integration method. More importantly, existing methods directly add the added mass to the system mass matrix, causing the system mass matrix, which should be a constant, to become a variable that changes with the configuration, significantly increasing the computational burden. The aforementioned updates to the Jacobian matrix and the system mass matrix are computationally expensive, constituting the main bottleneck to the solution efficiency.

[0007] In recent years, the absolute nodal coordinate method (ANCF) has emerged as a novel finite element method and has been introduced into multibody dynamics and the analysis of large deformations in flexible structures. The ANCF element uses the coordinates of the nodes in the global coordinate system and the gradient vector as its degrees of freedom. It can accurately describe arbitrarily large displacements and rotations without rotational singularities, and its mass matrix is ​​a constant matrix. Figure 3 and Figure 4As shown. Existing academic studies (such as: CHAI YT, VARYANI K S. An absolute coordinate formulation for three-dimensional flexible pipe analysis [J]. Ocean Engineering, 2006, 33(1): 23-58. ; ZHU X, YOO W S. Suggested new elementreference frame for dynamic analysis of marine cables [J]. NonlinearDynamics, 2017, 87(1): 489-501. ; ZHANG C, KANG Z, MA G, et al. Mechanical modeling of deepwater flexible structures with large deformation based on absolute nodal coordinate formulation [J]. Journal of Marine Science and Technology, 2019, 24(4): 1241-55. etc.) have explored the application of ANCF to marine riser analysis, but these studies usually do not deeply solve the hydrodynamic coupling, especially the computational bottleneck caused by the added mass. When the traditional coupling approach is directly applied to introduce additional mass into the ANCF system, the system matrix still needs to be updated during iteration, thus losing the core advantage that the ANCF mass matrix is ​​constant and failing to achieve efficient computation in a fundamental way.

[0008] Therefore, the closest existing technologies can be summarized as: (1) the traditional finite element method based on beam elements with small rotation angle assumptions (such as ABAQUS standard elements), or (2) the absolute nodal coordinate method that directly introduces hydrodynamic added mass but fails to effectively maintain its constant mass matrix characteristics. However, both of these methods face the challenge of balancing computational accuracy and computational efficiency when solving the problem of large deformation and strong nonlinear coupling between hydrodynamics of marine risers. Summary of the Invention

[0009] This invention proposes a two-way coupled solution method for deep-water riser configuration and hydrodynamics, which solves the problems of poor accuracy and large computational load of existing methods based on small-angle beam elements due to insufficient geometric nonlinearity description capability, and the low computational efficiency of existing ANCF coupling methods due to the loss of the advantage of constant mass matrix and frequent updates of the additional mass matrix.

[0010] The technical solution of the present invention is as follows:

[0011] A method for synchronously and bidirectionally coupled solution of deep-water riser configuration and hydrodynamics includes the following steps:

[0012] S100: Establish a nonlinear dynamic model for risers based on the absolute nodal coordinate method;

[0013] S200: Explicitizing nonlinear hydrodynamic loads based on implicit time-domain integration method;

[0014] S300: The nonlinear dynamic response of the riser is solved simultaneously using the Newton-Raphson iterative method.

[0015] Furthermore, step S100 includes:

[0016] S110: Riser Discretization: Discretize the continuous marine riser structure into a finite number of absolute node Euler-Bernoulli beam elements.

[0017] S120: Define element nodal coordinates and degrees of freedom: For each absolute nodal Euler-Bernoulli beam element, its nodal coordinates and gradients are directly defined in the global coordinate system as the element's degrees of freedom;

[0018] S130: Overall equations of the assembled riser system: Based on Hamilton's principle or the principle of virtual work, establish the dynamic control equations of the discrete riser system.

[0019] Furthermore, the dynamic control equations in step S130 are in matrix form, specifically:

[0020] ;

[0021] in, , and These represent the generalized acceleration, generalized velocity, and nodal coordinate vectors of the riser system, respectively. The overall quality matrix of the riser system. The overall damping matrix of the riser system is... The elastic force vector, This represents the elemental external force vector corresponding to hydrodynamics.

[0022] Furthermore, step S200 includes:

[0023] S210: Characterizes the elemental external force vector corresponding to hydrodynamic forces: hydrodynamic force per unit length of the riser. Given by the Morison equation:

[0024] ;

[0025] in, It concerns the generalized acceleration of risers. Generalized speed Configuration Pipeline arc length and time Nonlinear functions;

[0026] For normal drag force, it can be written as ;

[0027] For tangential drag force, it can be written as ;

[0028] For normal inertial force, it can be written as ;

[0029] This load includes the additional mass effect caused by fluid acceleration;

[0030] In the above formula, The density of seawater, This is the tangential drag coefficient. This is the normal drag force coefficient. The inertial force coefficient, and These are the velocity and acceleration of the water particles, respectively. and These are the velocity and acceleration of the riser, respectively. The outer diameter of the riser pipe. and Relative speeds Components along the pipeline tangent t and normal n and The accelerations of the water particles and the riser are respectively located on the riser normal. The components on;

[0031] Based on the principle of virtual work, the element external force vector corresponding to hydrodynamics is determined by the element shape function. Hydrodynamic force per unit length of riser Integral, we get:

[0032] ,in, The unit length;

[0033] S220: Introduction of implicit integration method: Discretize the dynamic equations using implicit time-domain integration method;

[0034] Implicit integration methods reduce time steps The generalized velocity to be determined and generalized acceleration Write about the previous time step Given ① generalized acceleration ② Generalized speed ③ Configuration and time step ④ Configuration to be determined The function,

[0035] ;

[0036] ;

[0037] Taking the Newmark-β method as an example, the time steps generalized speed and generalized acceleration Through integral format and configuration Establish explicit relationships:

[0038] ;

[0039] ;

[0040] Among them, coefficient to All are constants, and their specific expressions are as follows: , ;

[0041] Therefore, at the time step to be determined The velocity and acceleration in the integral scheme are approximated using the configuration at the current moment. express;

[0042] S230: Explicit hydrodynamic loads: Substitute approximate relationships into the hydrodynamic expression.

[0043] Furthermore, in step S230, since the motion at the element node can be obtained through interpolation of the shape function and the corresponding generalized motion variable, the element external force vector corresponding to the hydrodynamic force per unit length of the riser can ultimately be characterized as explicitly dependent only on the configuration at the current moment. and time Functions:

[0044] .

[0045] Furthermore, step S300 includes:

[0046] S310: Constructing the residual force equation: Rewrite the discretized riser nonlinear dynamic equation as... Configurations to be sought at any time The nonlinear algebraic equations, namely the residual force equations:

[0047] ;

[0048] Among them, superscript For time step The first in Newton's iteration steps;

[0049] S320: Newton's Iteration Solution: At each time step, Newton's iterations are performed to solve the problem. ;

[0050] S330: Efficiently updating the Jacobian matrix: In each Newton iteration, the Jacobian matrix needs to be calculated and assembled.

[0051] ;

[0052] S340: Convergence Judgment and Time Step Progression: Determines whether the residual force norm is less than the preset tolerance;

[0053] If convergence is achieved, the solution at that time step is accepted, and the process is advanced to the next time step.

[0054] If convergence is not achieved, return to step S320 and continue iterating until convergence is achieved.

[0055] Furthermore, the iterative formula in step S320 is as follows:

[0056] ;

[0057] Among them, superscript Indicates the number of iterations. Let be the Jacobian matrix of the riser system.

[0058] Furthermore, the Jacobian matrix in step S330 is specifically as follows:

[0059] ;

[0060] The Jacobian matrix contains:

[0061] constant system mass matrix ;

[0062] constant system damping matrix ,in, and The constant coefficients required to introduce implicit integrals;

[0063] Tangent stiffness matrix corresponding to elastic force ;

[0064] The load stiffness matrix corresponding to hydrodynamics .

[0065] The working principle and beneficial effects of this invention are as follows:

[0066] 1. A geometric nonlinear modeling method is provided that can accurately describe the large deformation of risers without rotational singularities, so as to overcome the shortcomings of traditional beam elements based on the small rotation angle assumption in simulating large deformation of risers, such as insufficient accuracy, need for dense mesh generation, and existence of rotational singularities.

[0067] 2. A hydrodynamic coupling processing strategy is provided to avoid updating the overall mass matrix of the system in Newton iteration steps. By explicitly representing the nonlinear hydrodynamic load as a function of riser configuration and time, the additional mass effect does not violate the characteristic that the mass matrix of the absolute nodal coordinate method is constant, thereby fundamentally solving the problem of low computational efficiency caused by reorganizing the mass matrix in each iteration step.

[0068] 3. Ultimately, a highly efficient and accurate synchronous bidirectional coupled solution scheme is achieved. While ensuring the same or even higher accuracy as the reference solution, the number of required elements is significantly reduced, and the calculation time is greatly shortened, providing a reliable calculation tool for the rapid dynamic response analysis and engineering design of marine risers. Attached Figure Description

[0069] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0070] Figure 1 This is a schematic diagram of beam element deformation and rotation characterization based on the traditional finite element method.

[0071] Figure 2 A schematic diagram illustrating the beam element configuration based on the traditional finite element method;

[0072] Figure 3 This is a schematic diagram of the deformation and rotation of a beam element based on the absolute nodal coordinate method of the finite element method.

[0073] Figure 4 This is a schematic diagram illustrating the beam element configuration based on the absolute nodal coordinate method of the finite element method.

[0074] Figure 5 This provides an efficient solution process for the synchronous two-way coupling of marine riser configuration and hydrodynamics based on the absolute node coordinate method.

[0075] Figure 6 for Figure 5 Enlarged view of point A in the image;

[0076] Figure 7 for Figure 5 Enlarged view of point B in the image;

[0077] Figure 8 This is a schematic diagram of the hydrodynamic forces acting on a flexible hose.

[0078] Figure 9 This example compares the convergence characteristics with those of ABAQUS.

[0079] Figure 10 This example compares the computational efficiency of this embodiment with that of ABAQUS.

[0080] Figure 11 This is a comparison diagram of the hose configuration obtained in this embodiment and that obtained by ABAQUS;

[0081] Figure 12 A comparison chart of the X-axis coordinates of the motion time history curves at the tip of the hose;

[0082] Figure 13 This is a comparison chart of the Z-coordinate of the motion time history curve of the tip of the hose. Detailed Implementation

[0083] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0084] Example 1

[0085] like Figure 5-13 As shown, this embodiment proposes a two-way coupled solution method for deep-water riser configuration and hydrodynamics. A high-precision, singularity-free geometric nonlinear model is established through step S100. In step S200, the time-varying, configuration-related additional mass effect is cleverly transformed into the element external force vector. Thus, in the solution of step S300, the superiority of the absolute node Euler-Bernoulli beam element constant mass matrix is ​​fully preserved, and the computational efficiency is improved while ensuring high precision.

[0086] The core idea is to leverage the inherent advantage of the absolute nodal coordinate method in accurately describing large geometric deformations, and to extract time-varying and configuration-related additional mass effects from the system mass matrix by performing special mathematical processing on the hydrodynamic terms, transforming them into element external force vectors. This allows the overall system mass matrix to remain a constant matrix throughout the solution process, thereby achieving efficient solution.

[0087] Includes the following steps:

[0088] S100: Establish a nonlinear dynamic model for risers based on the absolute nodal coordinate method;

[0089] This step aims to address the problem of insufficient geometric nonlinearity in the background art and the avoidance of characterizing the singularity of large rotations.

[0090] Specifically, step S100 includes:

[0091] S110: Riser Discretization: Discretize the continuous marine riser structure into a finite number of absolute node Euler-Bernoulli beam elements.

[0092] S120: Define element nodal coordinates and degrees of freedom: For each absolute nodal Euler-Bernoulli beam element, its nodal coordinates and gradients are directly defined in the global coordinate system as the element's degrees of freedom;

[0093] S130: Overall equations of the assembled riser system: Based on Hamilton's principle or the principle of virtual work, establish the dynamic control equations of the discrete riser system.

[0094] Furthermore, the dynamic control equations in step S130 are in matrix form, specifically:

[0095] ;

[0096] in, , and These represent the generalized acceleration, generalized velocity, and nodal coordinate vectors of the riser system, respectively. The overall quality matrix of the riser system. The overall damping matrix of the riser system is... The elastic force vector, This represents the elemental external force vector corresponding to hydrodynamics.

[0097] The key function of this step is that, since the mass matrix of the absolute node Euler-Bernoulli beam element is constant, the overall mass matrix of the assembled system is thus determined. It is also a constant matrix, which lays the foundation for efficient subsequent solutions.

[0098] S200: Explicitizing nonlinear hydrodynamic loads based on implicit time-domain integration method;

[0099] This step aims to address the inefficiency caused by frequent updates to the additional mass matrix in the background art.

[0100] Step S200 includes:

[0101] S210: Characterizes the elemental external force vector corresponding to hydrodynamic forces: hydrodynamic force per unit length of the riser. Given by the Morison equation:

[0102] ;

[0103] in, It concerns the generalized acceleration of risers. Generalized speed Configuration Pipeline arc length and time Nonlinear functions;

[0104] For normal drag force, it can be written as ;

[0105] For tangential drag force, it can be written as ;

[0106] For normal inertial force, it can be written as ;

[0107] This load includes the additional mass effect caused by fluid acceleration;

[0108] In the above formula, The density of seawater, This is the tangential drag coefficient. This is the normal drag force coefficient. The inertial force coefficient, and These are the velocity and acceleration of the water particles, respectively. and These are the velocity and acceleration of the riser, respectively. The outer diameter of the riser pipe. and Relative speeds Components along the pipeline tangent t and normal n and The accelerations of the water particles and the riser are respectively located on the riser normal. The components on;

[0109] Based on the principle of virtual work, the element external force vector corresponding to hydrodynamics is determined by the element shape function. Hydrodynamic force per unit length of riser Integral, we get:

[0110] ,in, The unit length;

[0111] S220: Introduction of implicit integration method: Implicit time-domain integration method (such as Newmark-β method, etc., the framework of this embodiment is also compatible with implicit integration methods such as generalized-α method and Wilson-θ method, which has strong algorithmic flexibility) is used to discretize the dynamic equation;

[0112] Implicit integration methods reduce time steps The generalized velocity to be determined and generalized acceleration Write about the previous time step Given ① generalized acceleration ② Generalized speed ③ Configuration and time step ④ Configuration to be determined The function,

[0113] ;

[0114] ;

[0115] Taking the Newmark-β method (parameters β=0.25, γ=0.5, i.e., the average acceleration method) as an example, the time step... generalized speed and generalized acceleration Through integral format and configuration Establish explicit relationships:

[0116] ;

[0117] ;

[0118] Among them, coefficient to All are constants, and their specific expressions are as follows: , It is determined by the integration scheme of the Newmark-β method;

[0119] Therefore, at the time step to be determined The velocity and acceleration in the integral scheme are approximated using the configuration at the current moment. express;

[0120] S230: Explicit hydrodynamic loads: Substitute approximate relationships into the hydrodynamic expression.

[0121] The motion of any point on the riser is expressed through the shape function of a finite beam element (e.g., an absolute node Euler-Bernoulli beam element). And the corresponding generalized motion variables are interpolated, for example .

[0122] The result of implicit integration and Substituting the expression into the Morison equation, taking the normal inertial force term in the Morison equation as an example, the explicit expression of its load is as follows:

[0123] Time step , In It can be rewritten as:

[0124] ;

[0125] After substitution and rearrangement, the normal inertial force in the Morison equation is... Corresponding element external force vector It is completely represented as the configuration to be determined only with respect to the current moment. and time The function, i.e.

[0126] ;

[0127] Special attention should be paid to items that include added mass. It was successfully incorporated into the force expression and no longer affects the mass matrix of the riser system. .

[0128] Similarly, the drag force term can be handled. and Ultimately, this makes the entire hydrodynamic system Only explicitly dependent and This completes the explicit transformation.

[0129] And in step S230,

[0130] Since the motion at the unit node can be obtained by interpolation of the shape function and the corresponding generalized motion variable, the element external force vector corresponding to the hydrodynamic force per unit length of the riser can ultimately be characterized as explicitly dependent only on the configuration at the current moment. and time Functions:

[0131] .

[0132] The core function of this transformation is to: transform the original dependence on the generalized acceleration to be determined. and generalized speed The nonlinear terms are transformed into functions that depend only on the configuration to be determined. This means that the contributions of hydrodynamics (including additional mass effects) are fully incorporated into the element external force vector. Instead of affecting the overall system mass matrix as an added mass, it does not affect the system's mass matrix. Therefore, in the subsequent Newton-Raphson iteration solution process, the overall mass matrix of the system... The matrix remains constant as the one assembled in step S130 and does not require updating.

[0133] S300: The nonlinear dynamic response of the riser is solved simultaneously using the Newton-Raphson iterative method;

[0134] This step enables efficient and high-precision synchronous coupling solution of riser configuration and hydrodynamics.

[0135] The advantage of this approach is that:

[0136] a) It avoids the need for the conversion between the local and global coordinate systems required by traditional beam elements;

[0137] b) Using gradient vectors to represent rotation naturally avoids the singularity problem of describing rotation based on rotation angle parameters;

[0138] c) Due to the use of the initial configuration as a reference and the special definition of the degrees of freedom, the element mass matrix is ​​a constant matrix;

[0139] d) The beam centerline is a parametric curve, which avoids the geometric error of the traditional finite element method of "substituting straight lines for curves" and ensures the accuracy of calculation.

[0140] Specifically, step S300 includes:

[0141] S310: Constructing the residual force equation: Rewrite the discretized riser nonlinear dynamic equation as... Configurations to be sought at any time The nonlinear algebraic equations, namely the residual force equations:

[0142] ;

[0143] Among them, superscript For time step The first in Newton's iteration steps;

[0144] S320: Newton's Iteration Solution: At each time step, Newton's iterations are performed to solve the problem. ;

[0145] The iterative formula is:

[0146] ;

[0147] Among them, superscript Indicates the number of iterations. Let be the Jacobian matrix of the riser system.

[0148] S330: Efficiently updating the Jacobian matrix: In each Newton iteration, the Jacobian matrix needs to be calculated and assembled. ;

[0149] The Jacobian matrix is ​​specifically as follows:

[0150] ;

[0151] The Jacobian matrix contains:

[0152] constant system mass matrix ;

[0153] constant system damping matrix ,in, and The constant coefficients required to introduce implicit integrals;

[0154] Tangent stiffness matrix corresponding to elastic force ;

[0155] The load stiffness matrix corresponding to hydrodynamics .

[0156] S340: Convergence Judgment and Time Step Progression: Determines whether the residual force norm is less than the preset tolerance;

[0157] If convergence is achieved, the solution at that time step is accepted, and the process is advanced to the next time step.

[0158] If convergence is not achieved, return to step S320 and continue iterating until convergence is achieved.

[0159] Compared to the traditional method in the background technique that requires updating the mass matrix in each Newton iteration step This invention avoids the differentiation and updating of hydrodynamic inertial forces, thus maintaining the system mass matrix. Since it is a constant, it significantly reduces the amount of computation in each iteration, thereby greatly improving computational efficiency.

[0160] The breakthrough of this embodiment lies in its innovative mathematical processing (implicit integral substitution), which cleverly transforms the additional mass effects, traditionally considered essential to the system's mass matrix, into part of the external force vector. This "stripping" operation preserves the strong nonlinear, bidirectional coupling between hydrodynamics and structural motion, while successfully maintaining the core advantage of the ANCF method—the constant mass matrix—at the mathematical solution level.

[0161] This is not simply applying ANCF to riser analysis, but rather creatively resolving the inherent contradiction that ANCF loses its advantage of a constant mass matrix when coupled with strongly nonlinear hydrodynamics. This crucial step makes it possible to avoid updating the enormous system mass matrix in Newton's iterations, thus overcoming the computational efficiency bottleneck of traditional methods and demonstrating significant non-obviousness and technological advancement.

[0162] To clearly demonstrate the comprehensive advantages brought about by the above core ideas, the present invention is compared with the closest prior art from specific dimensions as follows:

[0163] Table 1. Comparison between the present invention and existing technologies (taking ABAQUS traditional beam elements as an example):

[0164]

[0165] Therefore, this embodiment has the following significant technical advancements:

[0166] 1. Significantly improved computational efficiency

[0167] Efficiency improvement is reflected in two aspects:

[0168] The number of units has been greatly reduced: such as Figure 9 Convergence analysis shows that, due to the high-order geometric accuracy of ANCF elements in describing large deformations, only about 30 elements are needed to achieve a relative error of less than 0.01% and stabilize the results. In contrast, traditional ABAQUS B21 elements require about 150 elements to achieve the same accuracy, reducing the number of elements by about 80% and directly reducing the system's degrees of freedom.

[0169] Reduced computational overhead per time step: By explicitly representing the hydrodynamics (including added mass) in step S200, the overall system mass matrix M remains constant throughout the solution process. In each Newton iteration, there is no need to repeatedly calculate and assemble the configuration-dependent system mass matrix and its derivatives; only the tangent stiffness matrix corresponding to the elastic force and the stiffness matrix of the hydrodynamic load need to be updated. This significantly reduces the computational cost per iteration and the total number of iterations required to achieve convergence. Under the same hardware and accuracy requirements, the total computation time of the method of this invention (44.7 seconds) is reduced by approximately 41.3% compared to the traditional method (76.2 seconds).

[0170] 2. High accuracy in geometric nonlinear description, completely avoiding the singularity of large rotations.

[0171] This invention employs the absolute nodal coordinate method to establish the riser model. By directly describing the configuration in the global coordinate system using nodal coordinates and gradient vectors, it can accurately characterize any large displacement and rotation of the riser without relying on small rotation angle assumptions. This fundamentally solves the singularity problem inherent in traditional beam elements based on rotational degrees of freedom in three-dimensional large rotation analysis. Corresponding solution: This effect is directly achieved in step S100.

[0172] 3. Convergence and numerical stability are significantly enhanced.

[0173] The system mass matrix is ​​constant and positive definite, improving the condition number for solving the equations; combined with a precise geometric description, it reduces the error of the physical model, resulting in faster convergence and better numerical stability of the Newton iteration process. Corresponding solution: This effect stems from the combined effect of steps S100 and S200.

[0174] 4. Outstanding engineering application value

[0175] Economic benefits: Improved computational efficiency effectively shortens the design cycle, reduces computational resource consumption, supports rapid evaluation and parametric research under multiple operating conditions, and facilitates the low-cost and rapid development of marine risers.

[0176] Social benefits: The efficient and high-precision analysis tool provided by this invention can more accurately predict the dynamic response and fatigue life of risers under extreme sea conditions, which is of great value to ensuring the safety and reliability of deep-sea oil and gas equipment.

[0177] In summary, this embodiment, by integrating the geometric description advantages of the absolute node coordinate method with the hydrodynamic explicitness strategy, successfully solves the core problem of the difficulty in balancing "accuracy" and "efficiency" in the strong nonlinear fluid-structure interaction analysis of marine risers using traditional methods, achieving a breakthrough in technical performance.

[0178] Example 2: Nonlinear dynamic analysis of flexible hoses under hydrodynamic action

[0179] This embodiment simulates a 26-meter-long flexible hose, hinged to the seabed at its bottom (point A) and free at its top (point B). Figure 8 As shown. The hose was completely submerged in water at a depth of 30 meters to analyze its nonlinear dynamic response under hydrodynamic action (structural damping is not considered). The water depth of 30 meters was chosen because the hydrodynamic forces are significant within this depth range, which is sufficient to induce large deformations in the hose. To purely verify the accuracy of the hydrodynamic modeling of this invention, this embodiment intentionally excludes the coupling effects of other real external forces such as gravity and buoyancy, retaining only hydrodynamic force as the only external load, in order to clearly verify the effectiveness of the method. Some modeling parameters in this embodiment are referenced from the literature: ZHU X, YOO W S. Suggested new element reference frame for dynamic analysis of marine cables [J]. Nonlinear Dynamics, 2017, 87(1): 489-501.

[0180] The selection criteria for key calculation parameters are explained below:

[0181] Number of units (preferably 30): based on Figure 9 The convergence analysis results show that when using 30 ANCF elements, the relative error of the calculation results compared to the high-precision reference solution (300 ABAQUS B21 elements) is less than 0.01%, and the curve tends to plateau. Further increasing the number of elements provides only a small improvement in accuracy, but linearly increases the system's degrees of freedom and computational cost. Therefore, choosing 30 elements achieves the optimal balance between accuracy and efficiency.

[0182] Time step (Δt=0.01 s): In this embodiment, the wave period is 12s. Choosing a time step of 0.01s ensures sufficient time resolution (1200 points) within one wave period to capture dynamic response details, while also meeting the numerical stability requirements of the Newmark-β implicit integration method. This value is a typical value in engineering practice that balances computational accuracy and cost.

[0183] Newton's iterative convergence tolerance ( This tolerance is a commonly used standard in nonlinear finite element analysis to ensure the accuracy of iterative solutions. A tolerance of 10 is selected. -4 This ensures that the residual force is small enough to meet engineering accuracy requirements, while avoiding the pursuit of excessively high accuracy (such as 10). -6 This reduces the unnecessary number of iterations, and balances the accuracy of the understanding with computational economy.

[0184] This embodiment incorporates parameter settings into the method based on Embodiment 1, as follows:

[0185] The structural parameters of the solid flexible hose include: length 26 m, hose cross-sectional diameter 0.022 m, material density 1002 kg / m³, and Young's modulus 2.22 × 10⁻⁶. 9 Pa;

[0186] Environmental and load parameters include: gravitational acceleration 9.8 m / s². 2 Seawater density 1025 kg / m³, water depth 30 m, ocean current velocity 0 m / s;

[0187] The hydrodynamic parameters include: propagation direction is the positive X-axis direction, wave height is 3m, wave period is 12s, normal drag coefficient is 1, tangential drag coefficient is 0.05, added mass coefficient is 1, and the wave type is Airy wave;

[0188] The numerical solution parameters include: total simulation time 12s, time step Δt = 0.01s, and Newton iteration convergence tolerance. The implicit integration method used is the Newmark-β method.

[0189] Verify the above parameters by applying them to the following implementation steps:

[0190] Step S1: Establish the riser model based on the absolute node coordinate method

[0191] S1.1: Discretization

[0192] The 26-meter-long riser is discretized into An Euler-Bernoulli beam elements described by absolute nodal coordinates. Each element contains 2 nodes, and each node has 3 position coordinates and 3 gradient coordinates in the global coordinate system, i.e., each node contains 6 degrees of freedom. The number of elements An used in this example includes: 10, 20, 30, 60, 70, 80, 100, 120, and 150.

[0193] S1.2: Assembly System Matrix

[0194] Calculate the mass matrix of each element using the absolute node coordinate method. and the elastic force vector of each unit The specific formula is as follows:

[0195] ;

[0196] ;

[0197] in, The mass per unit length of the riser. The elastic modulus of the riser. The cross-sectional area of ​​the riser is... Let the moment of inertia of the riser section be... The axial strain of the riser is given. The curvature of the material in the riser pipe. The initial material curvature of the riser.

[0198] Due to the characteristics of the absolute node coordinate method It is a constant. It is a constant matrix. Therefore, the mass matrix of all elements is... It is a constant matrix.

[0199] Based on these element matrices, and combined with the damping matrix and the element external force vectors corresponding to the hydrodynamic forces, the preliminary form of the system dynamic equations can be written as:

[0200] ;

[0201] Based on the characteristics of the absolute node coordinate method, the system mass matrix The constant matrix of each unit It was assembled from parts, so it is obvious that... It is a constant matrix.

[0202] Step S2: Explicit processing of hydrodynamic loads

[0203] S2.1 Define hydrodynamics:

[0204] The hydrodynamic forces acting on the riser are calculated using the Morison equation:

[0205] ;

[0206] The definitions of each character in the above formula are explained in step S210 of Example 1, and will not be repeated here. This example uses Airy waves to characterize the velocity and acceleration of water particles.

[0207] S2.2 Introducing the implicit integration scheme:

[0208] The Newmark-β method (with parameters β=0.25, γ=0.5, i.e., the average acceleration method) was used for time-domain discretization. At time step... The following relationship holds:

[0209] ;

[0210] ;

[0211] Among them, coefficient to All are constants, and their specific expressions are as follows:

[0212] , S2.3: Explicitization of hydrodynamic loads:

[0213] The above and Substituting the expression into the Morison equation, the motion at any point on the riser is obtained through the absolute node Euler-Bernoulli beam element shape function. And the corresponding generalized motion variables are interpolated, for example .

[0214] After substitution and rearrangement, the element external force vector corresponding to hydrodynamics is... It is completely represented as the configuration to be determined only with respect to the current moment. and time function Special attention should be paid to items that include added mass. It was successfully incorporated into the force expression and no longer affects the mass matrix of the riser system. .

[0215] Step S3: Solve using Newton's iterative method

[0216] S3.1: Constructing the residual equations:

[0217] exist At time t, the residual force equation of the system is:

[0218] ;

[0219] S3.2 Newton's Iteration:

[0220] From the initial guess Start iterating;

[0221] S3.2.1: Calculation and assembly of residual forces:

[0222] Based on current estimates Calculate the elastic force vector and Then calculate and assemble the residual force. .

[0223] S3.2.2 Calculate the Jacobian matrix:

[0224] Based on current estimates ,calculate and And combined with the constant matrix and Assemble to obtain the Jacobian matrix ,for:

[0225] .

[0226] It can be seen that the system mass matrix in the Jacobian matrix It is a constant matrix. This differs from traditional methods that require updating the system mass matrix at each iteration step. In stark contrast, among them The mass matrix is ​​the mass added due to hydrodynamic forces.

[0227] S3.2.3 Update the solution and number of iterations: , .

[0228] S3.2.4 Loop Check: Repeat iterations until... Then proceed to the next time step.

[0229] Comparative test cases

[0230] To objectively evaluate the technical effects of this invention, the same marine riser model was solved using the commercial software ABAQUS / Standard on the same hardware platform (Intel i7-12700H CPU, 64GB RAM) as a benchmark for comparison.

[0231] A finite element model of the riser was established using B21 elements (first-order linear shear deformation beam elements) in ABAQUS. This element is based on the small rotation angle assumption, with each node containing three degrees of freedom (two translational and one rotational). To meet the accuracy requirement of a relative error of less than 0.01% with the high-precision reference solution (using 300 B21 elements), mesh independence verification was performed. The results show that the riser needs to be discretized into 150 B21 elements to achieve the required accuracy. The Morison hydrodynamic load, consistent with that of this invention, was applied using the AQUA module of ABAQUS. The key difference is that ABAQUS requires recalculating and assembling the overall system matrix including the added mass in each Newton iteration step at each time step, based on the instantaneous configuration of the riser. Combined with the larger number of elements, this significantly increases the computational overhead.

[0232] Results Comparison and Analysis

[0233] To objectively evaluate the effectiveness of the method of this invention, under the condition of ensuring the same computational accuracy (relative error < 0.01%), the present invention was compared with the traditional ABAQUS-based method in terms of both convergence characteristics and computational efficiency. The results are as follows:

[0234] Regarding convergence properties, the results are as follows: Figure 9 As shown, the absolute node coordinate element method used in this study achieves a relative error of less than 0.01% and stabilizes when the number of elements is 30; while the traditional ABAQUS element method requires approximately 150 elements to achieve the same level of accuracy. Furthermore, under any given number of elements, the computational error of this method is significantly lower than that of the traditional element method, indicating that the absolute node coordinate method has significant advantages in both convergence speed and numerical accuracy.

[0235] In terms of computational efficiency, under the same convergence accuracy (relative error < 0.01%), the method of this invention using absolute node coordinate elements completes the simulation in 44.7 seconds, while the traditional ABAQUS elements take 76.2 seconds. Figure 10 As shown, the computation time of the method of this invention is reduced by 41.3%, effectively verifying its significant improvement in efficiency. Furthermore, to accurately capture the large deformation dynamics of the hose, this method requires only 30 elements to achieve the accuracy required by ABAQUS software using 300 traditional B21 elements, a number of elements only one-tenth of the latter, greatly improving computational economy. Figures 11 to 13 As shown.

[0236] In summary, the results of this specific implementation fully demonstrate that the proposed method for simultaneous two-way coupling of marine riser configuration and hydrodynamics based on the absolute node coordinate method effectively unifies computational accuracy and efficiency by organically combining explicit hydrodynamic processing with the absolute node coordinate method. This method significantly reduces computational resource requirements while ensuring high-precision solutions, providing a more efficient solution than existing commercial software for the nonlinear dynamic analysis of marine risers.

[0237] In addition, regarding the explanation of terminology:

[0238] Absolute Nodal Coordinate Formulation (ANCF) is a finite element method that uses the position coordinates and gradients of nodes in the global coordinate system as element node coordinate vectors. It is particularly suitable for analyzing flexible multibody systems with large displacements and rotations.

[0239] ABAQUS: A commercial nonlinear finite element analysis software widely used in the engineering field.

[0240] Jacobian matrix: refers to the tangent stiffness matrix of nonlinear system equations in the Newton-Raphson iteration method, whose elements are the partial derivatives of residual forces with respect to degrees of freedom.

[0241] Scalability:

[0242] (1) Wide applicability of wave theory: Although the above embodiments are based on Airy linear waves, the method framework has good theoretical inclusiveness and extensibility, and can be compatible with various nonlinear wave models such as Stokes waves, elliptical cosine waves (Cnoidal waves) and even solitary waves. In addition, this method can be combined with different forms of ocean current velocity profiles to accurately characterize the velocity and acceleration of water particles in the wave-current coupled field, thereby more realistically simulating hydrodynamic loads in complex marine environments.

[0243] (2) Versatility of structural types: The above embodiments are aimed at general flexible and slender structures, which are not only applicable to marine risers, but can also be extended to similar engineering structures such as submarine pipelines and transport hoses.

[0244] (3) Compatibility with load conditions: The above embodiments are verified using a hose model subjected only to hydrodynamic forces. The proposed method framework is not only applicable to single hydrodynamic scenarios, but can also effectively handle complex working conditions where multiple external forces (such as gravity, buoyancy, internal flow forces, etc.) are coupled with hydrodynamic forces.

[0245] The above-described operating methods can be arbitrarily adjusted according to the design, provided that the hardware module supports them; this embodiment will not elaborate further. The above are merely preferred embodiments of the present invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for solving the deepwater riser configuration and hydrodynamic synchronous bidirectional coupling, characterized in that, Includes the following steps: S100: Establish a nonlinear dynamic model for risers based on the absolute nodal coordinate method; Step S100 includes: S110: Riser Discretization: Discretize the continuous marine riser structure into a finite number of absolute node Euler-Bernoulli beam elements; S120: Define element nodal coordinates and degrees of freedom: For each absolute nodal Euler-Bernoulli beam element, its nodal coordinates and gradients are directly defined in the global coordinate system as the element's degrees of freedom; S130: Overall equations of the assembled riser system: Based on Hamilton's principle or the principle of virtual work, establish the dynamic control equations of the discrete riser system; The dynamic control equations in step S130 are in matrix form, specifically: ； wherein, , and are the generalized acceleration, generalized velocity and nodal coordinate vectors of the riser system respectively, is the global mass matrix of the riser system, is the global damping matrix of the riser system, is the elastic force vector, is the element external force vector corresponding to the hydrodynamic force; S200: Explicitizing nonlinear hydrodynamic loads based on implicit time-domain integration method; S300: The nonlinear dynamic response of the riser is solved simultaneously using the Newton-Raphson iterative method.

2. The method for synchronous bidirectional coupling solution of deep-water riser configuration and hydrodynamics according to claim 1, characterized in that, Step S200 includes: S210: Characterizes the elemental external force vector corresponding to hydrodynamic forces: hydrodynamic force per unit length of the riser. Given by the Morison equation: ； in, It concerns the generalized acceleration of risers. Generalized speed Configuration Pipeline arc length and time Nonlinear functions; For normal drag force, it can be written as ; For tangential drag force, it can be written as ; For normal inertial force, it can be written as ; This load includes the additional mass effect caused by fluid acceleration; In the above formula, The density of seawater, This is the tangential drag coefficient. This is the normal drag force coefficient. The inertial force coefficient, and These are the velocity and acceleration of the water particles, respectively. and These are the velocity and acceleration of the riser, respectively. The outer diameter of the riser pipe. and Relative velocities Components along the pipeline tangent t and normal n and The accelerations of the water particles and the riser are respectively located on the riser normal. The components on; Based on the principle of virtual work, the element external force vector corresponding to hydrodynamics is determined by the element shape function. Hydrodynamic forces per unit length of riser Integral, we get: ,in, The unit length; S220: Introduction of implicit integration method: Discretize the dynamic equations using implicit time-domain integration method; Implicit integration methods reduce time steps The generalized velocity to be determined and generalized acceleration Write about the previous time step Given ① generalized acceleration ② Generalized speed ③ Configuration and time step ④ Configuration to be determined The function, ； ； Taking the Newmark-β method as an example, the time steps generalized speed and generalized acceleration Through integral format and configuration Establish explicit relationships: ； ； Among them, coefficient to All are constants, and their specific expressions are as follows: , ; Therefore, at the time step to be determined The velocity and acceleration in the integral scheme are approximated using the configuration at the current moment. express; S230: Explicit hydrodynamic loads: Substitute approximate relationships into the hydrodynamic expression.

3. The method for synchronous bidirectional coupling solution of deep-water riser configuration and hydrodynamics according to claim 2, characterized in that, In step S230, Since the motion at the unit node can be obtained by interpolation of the shape function and the corresponding generalized motion variable, the element external force vector corresponding to the hydrodynamic force per unit length of the riser can ultimately be characterized as explicitly dependent only on the configuration at the current moment. and time Functions: 。 4. The method for synchronous two-way coupling solution of deep-water riser configuration and hydrodynamics according to claim 3, characterized in that, Step S300 includes: S310: Constructing the residual force equation: Rewrite the discretized riser nonlinear dynamic equation as... Configurations to be sought at any time The nonlinear algebraic equations, namely the residual force equations: ； Among them, superscript For time step The first in Newton's iteration steps; S320: Newton's Iteration Solution: At each time step, Newton's iterations are performed to solve the problem. ; S330: Efficiently updating the Jacobian matrix: In each Newton iteration, the Jacobian matrix needs to be calculated and assembled. ； S340: Convergence Judgment and Time Step Progression: Determines whether the residual force norm is less than the preset tolerance; If convergence is achieved, the solution at that time step is accepted, and the process is advanced to the next time step. If convergence is not achieved, return to step S320 and continue iterating until convergence is achieved.

5. The method for synchronous bidirectional coupling solution of deep-water riser configuration and hydrodynamics according to claim 4, characterized in that, The iterative formula in step S320 is: ； Among them, superscript Indicates the number of iterations. Let be the Jacobian matrix of the riser system.

6. The method for synchronous two-way coupling solution of deep-water riser configuration and hydrodynamics according to claim 5, characterized in that, The Jacobian matrix in step S330 is specifically as follows: ； The Jacobian matrix contains: constant system mass matrix ; constant system damping matrix ,in, and The constant coefficients required to introduce implicit integrals; Tangent stiffness matrix corresponding to elastic force ; The load stiffness matrix corresponding to hydrodynamics .

Images