Coupled simulation method for predicting the motion response of a free-floating platform under the action of a solitary wave

Abstract

The present application relates to the technical field of numerical simulation of ocean engineering hydrodynamics, and discloses a method for predicting and coupling simulation of the motion response of an unmoored floating platform under the action of an isolated wave, which models the wave water body as material points (MPM) to solve the large deformation flow of the free surface; and models the unmoored floating platform as a spherical polygon discrete element rigid body (SDEM) with mass, barycenter, floating center, moment of inertia, position and velocity. In each time step, the contact pairs between the water body material points and the platform boundary are identified, and the contact force is calculated according to the geometric overlap and relative velocity. The contact forces are accumulated on the platform barycenter to form the resultant force and the resultant moment; at the same time, the counteracting force is applied to the water body, so that the wave flow field and the free motion of the platform are bidirectionally coupled. The present application can output platform displacement, velocity, attitude angle and other data and stability evaluation indexes, and is suitable for predicting the isolated wave response of a floating platform under the working conditions of temporary release, towing installation, free floating and model test.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology of marine engineering hydrodynamics, and in particular to a coupled simulation method for predicting the motion response of an unmoored floating platform under the action of solitary waves. Background Technology

[0002] With the development of marine resource development, offshore construction, emergency rescue, marine observation, and modular floating facilities, various types of offshore floating platforms are widely used in nearshore and shallow waters. These platforms typically rely on their own buoyancy to support the superstructure or operational loads. Under specific conditions such as temporary release, towing and transfer, pre-installation positioning, and model testing, the platform may be in an unmoored, unanchored, or freely floating state. In this case, the platform's motion response under wave action is mainly determined by the platform's geometry, displacement, center of gravity position, center of buoyancy position, inertial characteristics, and external wave excitation, and is no longer constrained by mooring line tension, anchoring boundaries, or dynamic positioning systems.

[0003] During the superposition of ship-borne waves or the propagation of strong nonlinear waves in shallow waters, isolated waves or quasi-isolated waves with long wavelengths, long periods, and significant nonlinear characteristics may appear in nearshore waters. When isolated waves act on unmoored floating platforms, the platforms may experience significant horizontal drift, heave, and pitch or roll responses, potentially leading to problems such as deck overrun, equipment instability, collisions between platforms, or interference with adjacent marine structures. Therefore, predicting the motion response of unmoored floating platforms under the influence of isolated waves is of practical significance for platform structural design, layout optimization, operational window determination, and safety verification in extreme sea states.

[0004] Existing methods for analyzing the motion response of floating platforms have shortcomings. Potential flow theory and frequency-domain and time-domain hydrodynamic methods typically assume small-amplitude motions and ideal boundaries, making it difficult to handle large deformations of free surfaces and large displacements and rotations of platforms. Furthermore, they often focus on moored floating bodies, lacking adaptability to unconstrained free-drift conditions. Mesh-based computational fluid dynamics methods often require dynamic meshes, overlapping meshes, or submerged boundaries when the platform experiences significant drift or attitude changes; mesh distortion and interpolation errors can affect computational stability and efficiency. When using meshless particle methods alone, there is still room for improvement in boundary particle support domains, neighborhood search efficiency, and the accumulation of contact forces and moments at complex rigid body boundaries. While discrete element methods (DEMs) are convenient for describing the translation, rotation, and contact collisions of rigid bodies, they cannot solve for large-deformation flows on the free surface of continuous media and are difficult to independently perform wave field calculations.

[0005] The material point method employs dual discretization using both material points and a background mesh, combining the advantages of Lagrangian material point methods for describing large deformations with Eulerian background meshes for avoiding mesh distortion. This makes it suitable for simulating large deformations on free surfaces and wave impact processes. The discrete element method (DEM) is suitable for describing the translational, rotational, and contact collision behaviors of rigid bodies with complex boundaries. However, existing wave-structure interaction methods are mostly geared towards fixed or constrained structures such as wave generators, seawalls, and revetments. These structures do not require solving for the platform's free drift, large-angle attitude updates, or the accumulation of the resultant torque of contact forces about the center of mass, nor do they require the platform's motion to be reversed and applied to the wave body within the same time step. Therefore, it is necessary to propose a coupled simulation method of the material point method and the spherical polygon DEM for unmoored, freely floating platforms. Summary of the Invention

[0006] To achieve the above objectives, this invention addresses the aforementioned problems by providing a coupled simulation method for predicting the motion response of an unmoored floating platform under the action of isolated waves. This method solves for the wave water body using the material point method and the floating platform using the spherical polygon discrete element method. It can simultaneously describe the large deformation of the free surface and the free motion of the platform under the action of isolated waves or quasi-isolated waves, and can obtain the calculation results of the platform's translation, rotation, resultant force, and resultant moment. This improves the coupling consistency during fluid-structure interaction and is applicable to conditions such as temporary release, towing installation, free floating, and model testing. It can also be used for safety verification and interference risk assessment of floating platforms in extreme sea states.

[0007] To achieve the aforementioned objectives, this invention employs the following technical solution: a coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action, comprising the following steps:

[0008] S1. Discretize the wave water body in the computational water area into material points, establish a background computational grid, and assign mass, position, velocity, volume, density and stress tensor to each material point;

[0009] S2. Discretize the unmoored floating platform into a spherical polygon discrete element rigid body, and define the mass, displacement, center of gravity position, center of buoyancy position, moment of inertia, initial position, initial linear velocity, initial attitude angle and initial angular velocity of the unmoored floating platform.

[0010] S3. Generate or input an isolated wave field to allow the isolated wave to propagate within the calculated water area and act on the unmoored floating platform.

[0011] S4. In each time step, a search region is established with the spherical polygon discrete element rigid body as the center, the background computational grid nodes in the search region are screened, and water body material points that contribute to the background computational grid nodes are backtracked to form potential contact pairs; the contact pairs are determined according to the geometric overlap between the water body material points and the boundary of the spherical polygon.

[0012] S5. Calculate the contact force between the water body material point and the unmoored floating platform based on the geometric overlap, normal unit vector, relative normal velocity, and relative tangential velocity of the contact pair.

[0013] S6. The contact forces are summed over the center of mass of the unmoored floating platform to obtain the resultant force and resultant moment acting on the unmoored floating platform.

[0014] S7. Solve the translational and rotational motion equations of the unmoored floating platform based on the resultant force and resultant moment, and update the position, linear velocity, attitude angle and angular velocity of the unmoored floating platform.

[0015] S8. Apply a force equal in magnitude and opposite in direction to the contact force to the water body material point or background calculation grid node, and update the velocity, position, density, volume and stress state of the wave water body using the material point method.

[0016] In particular, steps S4 to S8 share the same contact detection and contact force calculation results within the same time step, and use explicit time integration to solve the bidirectional coupling between the wave water and the floating platform.

[0017] S9. Reset the background calculation grid and repeat steps S4 to S8 until the set simulation duration or output conditions are reached, and output the horizontal drift, heave, attitude rotation, force time history, torque time history and stability evaluation index of the unmoored floating platform under the action of solitary waves.

[0018] Furthermore, the unmoored floating platform includes a temporary work platform, a floating rescue platform, a floating observation platform, a modular floating island unit, a floating platform during the towing and installation phase, a floating platform during the pre-installation waiting phase, or a free-floating platform in model testing.

[0019] Furthermore, the unmoored floating platform outputs a three-degree-of-freedom motion response of sway, heave, and pitch under two-dimensional calculation conditions; and outputs a six-degree-of-freedom motion response of pitch, sway, heave, roll, yaw, and bow roll under three-dimensional calculation conditions.

[0020] Further, the spherical polygon discrete element rigid body in step S2 is formed in the following way: the geometric boundary of the unmoored floating platform is reduced inward by a set thickness to obtain discrete element primitives, and then the sphere radius equal to the set thickness is swept along the reduced boundary to reconstruct it. The areas occupied by each swept sphere are then combined to form a spherical polygon contact boundary with continuous normals.

[0021] Further, in step S4, the search radius of the search area is determined by the sum of the maximum distance from the centroid of the unmoored floating platform to any point on the boundary of the spherical polygon, the construction radius of the spherical polygon, and the safe extension distance; the geometric overlap is determined by the construction radius of the spherical polygon, the radius of the water body material point, and the shortest distance from the water body material point to the boundary of the spherical polygon; when the geometric overlap is greater than zero, the potential contact pair is determined to be a contact pair.

[0022] Further, the contact force in step S5 includes normal spring damping force and tangential damping force; the normal spring damping force is determined by geometric overlap, normal spring stiffness, normal unit vector, relative normal velocity, and normal damping coefficient; the tangential damping force is determined by relative tangential velocity and tangential damping coefficient.

[0023] Furthermore, the resultant torque in step S6 is obtained by multiplying the position vector of each contact point relative to the platform's center of mass with the corresponding contact force and then summing them. The resultant torque is used to update the angular velocity and attitude angle of the unmoored floating platform in step S7.

[0024] Furthermore, the isolated wave field in step S3 is generated by the motion function of the piston-type wave generator; when a piston-type wave generator is used, the motion function is determined by the target wave height, still water depth, wave velocity, and wave generation time.

[0025] Furthermore, the equation of motion in step S7 includes resultant force, resultant torque, gravity, and buoyancy determined by displacement and center of buoyancy; the wave water in step S8 adopts a weakly compressible fluid formula, and the fluid pressure is updated by water density through the equation of state.

[0026] Further, in step S2, the mass, displacement, center of gravity position, center of buoyancy position and moment of inertia are calculated based on the geometry, material density and load distribution of the unmoored floating platform, and the unmoored floating platform is initially in a still water floating state in equilibrium between gravity and buoyancy.

[0027] Furthermore, the time step simultaneously satisfies the stability conditions of both the material point method for water bodies and the discrete element contact method for floating platforms, and is determined based on the characteristic size of the material point, the velocity of sound, the mass of the discrete element, and the contact normal stiffness.

[0028] Furthermore, the stability evaluation indicators include at least one of the following: maximum horizontal drift distance of the platform, maximum heave displacement, maximum attitude angle, attitude angle change rate, peak force, peak torque, and whether the platform has a tendency to overturn.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. The coupled simulation method for predicting the motion response of an unmoored floating platform under the action of isolated waves of the present invention solves the wave water body by means of the material point method and solves the floating platform by means of the spherical polygon discrete element method. It can simultaneously describe the large deformation of the free liquid surface and the free motion of the platform under the action of isolated waves or quasi-isolated waves, avoiding the problem of simplifying the platform as a fixed structure and failing to obtain the drift and attitude response.

[0031] 2. The coupled simulation method for predicting the motion response of an unmoored floating platform under the action of isolated waves of the present invention models the platform as a discrete element rigid body with mass, moment of inertia and attitude variables, and can obtain the calculation results of the platform's translation, rotation, resultant force and resultant moment, without relying on small-amplitude motion or linearized attitude assumptions.

[0032] 3. The method for predicting the motion response of an unmoored floating platform under the action of isolated waves in this invention, by sharing the contact detection and contact force calculation results within the same time step, makes the contact force on the platform and the reverse coupling force of the water body have a consistent source, which is beneficial to improving the coupling consistency in the fluid-structure collision process.

[0033] 4. The method for predicting the motion response of an unmoored floating platform under the action of isolated waves of the present invention is a coupled simulation method that does not introduce mooring tension, anchoring constraints or dynamic positioning control into the platform. It is applicable to working conditions such as temporary release, towing installation, free floating and model testing.

[0034] 5. The coupled simulation method for predicting the motion response of an unmoored floating platform under the action of isolated waves of the present invention outputs indicators such as drift distance, heave displacement, attitude angle, angular velocity, peak force, peak moment and minimum distance between adjacent structures, which can be used for safety verification and interference risk assessment of floating platforms in extreme sea conditions. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the overall workflow of the coupling simulation method for predicting the motion response of an unmoored floating platform under the action of isolated waves, as described in this invention.

[0036] Figure 2 This is a schematic diagram of contact detection and potential contact pair screening in this invention;

[0037] Figure 3 This is a schematic diagram of the contact force calculation in this invention;

[0038] Figure 4 This is a time history curve of the platform motion response in this invention;

[0039] Figure 5 This is a diagram illustrating the interaction process between the solitary wave and the platform in this invention.

[0040] Figure 6 This is a comparison chart of the response of different platform sizes in this invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of this invention.

[0042] Example 1

[0043] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings.

[0045] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0046] In this embodiment, the computational domain is set as a two-dimensional or three-dimensional numerical flume. The water body is discretized using MPM, and the unmoored floating platform is discretized using SDEM rigid body discretization. A wave-generating boundary is set on one side of the flume to generate isolated waves; the platform is initially positioned at the target location, with its bottom part submerged in the water and its upper part bearing the equivalent operational load.

[0047] The coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action provided in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0048] S1. Discretize the wave water body in the computational water area into material points, establish a background computational grid, and assign mass, position, velocity, volume, density and stress tensor to each material point;

[0049] In this embodiment, establishing the wave water body control equation includes the following steps:

[0050] The wave-laden water body in the computational water area is discretized into a series of material points; each material point carries mass. ,Location ,speed ,volume ,density and stress tensor Physical information such as mass and momentum is collected; simultaneously, a background computational grid is established. The governing equations for the water body include the mass conservation equation and the momentum conservation equation.

[0051] (1)

[0052] (2)

[0053] in Indicates fluid density, Indicates fluid velocity. Represents the Cauchy stress tensor. Represents volume force. Indicates external force. This represents the Lagrange or matter derivative. In the following derivation, the values ​​of matter points and grid nodes are represented by subscripts. and Distinguish them.

[0054] Specifically, S1 includes the following steps:

[0055] S11: Perform data transfer calculations from particles to the mesh.

[0056] The physical parameters of each particle are transmitted to each grid node through a specific mapping relationship, thereby calculating the mass, momentum, external force, and internal force distributed at each node:

[0057] (3)

[0058] (4)

[0059] (5)

[0060] (6)

[0061] in and These represent the mass and velocity vectors of a point mass, respectively. , and Let represent the volume force vector, volume, and Cauchy stress tensor at the material point, respectively. This represents the external force vector, the value of which is calculated by coupling the MPM frame and the SDEM frame. It is a node Regarding its relationship with the position of matter points The weight function is determined by the method described above. To reduce the cross-grid error of the traditional MPM method, this method uses the generalized interpolation material point method instead of the traditional weight function.

[0062] S12: Conduct grid computing

[0063] Using the external and internal forces on the mesh obtained from S11 calculations, and adding necessary boundary conditions, solve the governing equations:

[0064] (7)

[0065] in Indicates the time increment.

[0066] S13: Return calculation results to the material point

[0067] Based on the grid calculation results, the particle position and velocity are updated using the following mapping:

[0068] (8)

[0069] (9)

[0070] S14: Update the calculated constitutive parameters of matter points

[0071] Calculate the strain increment rate tensor based on the updated material point velocity field. Curl Increment Rate Tensor :

[0072] (10)

[0073] (11)

[0074] in It is the gradient vector of the weighting function. Based on the strain increment tensor... Update the density at the material point:

[0075] (12)

[0076] Where tr represents the trace of the strain increment tensor. Due to the point mass of the Lagrange point... Since it is a constant, the volume is updated as follows:

[0077] (13)

[0078] Update the Cauchy stress tensor based on the curl and strain rate tensors:

[0079] (14)

[0080] For a fluid point, the Cauchy stress tensor is expressed as:

[0081] (15)

[0082] in Indicates fluid viscosity. This represents the partial strain rate tensor. It is a unit tensor. This represents fluid pressure. When using a weakly compressible fluid model, fluid pressure is estimated using the equation of state:

[0083] (16)

[0084] in and These are reference density and current density, used for water sampling. , It is the speed of sound, and is generally set to more than ten times the estimated maximum speed of the fluid to ensure that density changes are stable (less than 1%).

[0085] S2. Discretize the unmoored floating platform into a spherical polygon discrete element rigid body, and define the mass, displacement, center of gravity position, center of buoyancy position, moment of inertia, initial position, initial linear velocity, initial attitude angle and initial angular velocity of the unmoored floating platform.

[0086] The spherical polygon discrete element method approximates the complex geometric boundary of the platform using spherical polygons. Specifically, the platform's geometric boundary is first reduced inward in thickness. We obtain discrete element primitives, and then use the radius The sphere is reconstructed by sweeping along the cut boundary, and the union is used to form a spherical polygonal contact boundary with continuous normals. The unmoored floating platform is a rigid body capable of free translation and rotation under wave action; its equation of motion is:

[0087] (17)

[0088] (18)

[0089] in and These represent the platform's mass and acceleration vectors, respectively. and These represent the platform's moment of inertia and angular velocity vectors, respectively. Represents the gravity vector. and These represent the contact force vector and torque vector generated by the interaction of different platforms, respectively; and These are the coupling force and torque vector of the water body, respectively.

[0090] S3. Generate or input an isolated wave field to allow the isolated wave to propagate within the calculated water area and act on the unmoored floating platform.

[0091] An isolated wave field can be generated by the motion of a piston-type wave generator. When using a piston-type wave generator, the wave generator displacement and wave surface elevation can be determined based on KdV theory.

[0092] (19)

[0093] (20)

[0094] in For the target wave height, The depth of still water. For peripheral coefficients, For wave speed, The wave generation time.

[0095] S4. In each time step, a search region is established with the spherical polygon discrete element rigid body as the center, the background computational grid nodes in the search region are screened, and water body material points that contribute to the background computational grid nodes are backtracked to form potential contact pairs; the contact pairs are determined according to the geometric overlap between the water body material points and the boundary of the spherical polygon.

[0096] Specifically, such as Figure 2 As shown, within each time step, a circular or spherical search region is established for the platform spherical polygon discrete element rigid body. In the two-dimensional case, the search radius can be expressed as:

[0097] (twenty one)

[0098] in This represents the maximum distance from the centroid to any point on the edge of an SDEM particle. This indicates the erosion thickness or radius of the enlarged sphere in the SDEM. This is a safety margin distance to ensure that no potential contact or collision is overlooked. Background grid nodes within the search area are identified as potential contact nodes; then, water material points that contribute to these nodes are traced back to form potential contact pairs with the platform.

[0099] (twenty two)

[0100] in This represents the Euclidean distance from the material point to the edge of the SDEM particle. The radius of the material point is defined as the equivalent radius of the original control domain area in GIMP, i.e. .

[0101] like If the potential contact pair is determined, then the definite contact pair that will make contact and collision will be determined, and then all definite contact pairs will be subjected to contact force calculation.

[0102] S5. Calculate the contact force between the water body material point and the unmoored floating platform based on the geometric overlap, normal unit vector, relative normal velocity, and relative tangential velocity of the contact pair.

[0103] Specifically, such as Figure 3As shown, this invention calculates contact forces within the framework of the DEM method. It assumes that the two particles in the contact pair undergo elastic collision, the solid-liquid boundary is a non-slip boundary, and a linear spring-damped model is used for the solution.

[0104] Contact force can be decomposed into normal force and tangential force And calculate according to formulas (23) and (24):

[0105] (twenty three)

[0106] (twenty four)

[0107] in and These are the normal spring stiffness and damping coefficient, Indicates geometric overlap dimensions. Represents the normal unit vector. This represents the relative normal velocity vector. and These represent the tangential damping coefficient and the relative tangential velocity vector at the contact point, respectively. The tangential contact force retains only the viscous component. This satisfies the non-slip boundary conditions. The contact force, as an external force of the platform system, is inverted and becomes a coupled external force of the water system.

[0108] S6. The contact forces described above are summed with respect to the center of mass of the unmoored floating platform to obtain the resultant force and resultant moment acting on the unmoored floating platform.

[0109] S7. Solve the translational and rotational motion equations of the unmoored floating platform based on the resultant force and resultant moment, and update the position, linear velocity, attitude angle and angular velocity of the unmoored floating platform.

[0110] Specifically, the resultant force and resultant moment obtained from S6 are substituted into formulas (17) and (18) to explicitly integrate and update the platform's center of mass acceleration, angular acceleration, linear velocity, angular velocity, position, and attitude angle. Under two-dimensional calculation conditions, the output is the three-degree-of-freedom response of sway, heave, and pitch; under three-dimensional calculation conditions, the output is the six-degree-of-freedom response of pitch, sway, heave, roll, pitch, and bow. The above summation of resultant force and resultant moment is used to describe the drift and rotation of the unmoored platform caused by wave impact, changes in bottom support, and fluid action on the back side of the wave, which is different from constrained structures such as fixed seawalls, revetments, or wavemakers that do not require updating the rigid body attitude.

[0111] S8. Apply a force equal in magnitude and opposite in direction to the contact force to the water body material point or background calculation grid node, and update the velocity, position, density, volume and stress state of the wave water body using the material point method.

[0112] Specifically, an equal and opposite force to the contact force is applied to the water body material point or the background computational grid node, and this force is used as the coupling force term in formula (2). Subsequently, particle-to-mesh mapping, grid momentum update, mesh-to-particle mapping, and water density, volume, and stress update are completed according to formulas (3) to (16). Thus, the platform motion affects the wave field, and the wave field reacts to the platform, forming a two-way coupling.

[0113] In this process, steps S4 to S8 share the same contact detection and contact force calculation results within the same time step, and use explicit time integration to solve the bidirectional coupling between the wave water and the floating platform.

[0114] S9. Reset the background calculation grid and repeat steps S4 to S8 until the set simulation duration or output conditions are reached, and output the data and stability evaluation index of the unmoored floating platform under the action of solitary waves.

[0115] Specifically, the output data of this invention includes the platform's center of mass displacement time history, linear velocity time history, attitude angle time history, angular velocity time history, resultant force time history, resultant moment time history, maximum horizontal drift distance, maximum heave displacement, maximum attitude angle, attitude angle change rate, peak force, peak moment, whether the platform has a tendency to capsize, and the minimum distance between the platform and adjacent structures or adjacent platforms. These indicators can be used to evaluate the platform's attitude stability, deck wave risk, collision risk, and operational safety risks.

[0116] In the above output, the motion response quantities used to evaluate the platform's attitude stability, capsizing risk, interference with adjacent structures, and operational safety are collectively referred to as stability evaluation indicators. These stability evaluation indicators include at least one of the following: maximum horizontal drift distance, maximum heave displacement, maximum attitude angle, rate of change of attitude angle, peak force, peak moment, and whether the platform exhibits a capsizing tendency; if necessary, the minimum distance between the platform and adjacent structures or adjacent platforms may also be included. Through these stability evaluation indicators, the attitude stability, deck wave risk, collision and interference risk, and operational safety of an unmoored floating platform under the action of solitary waves can be quantitatively evaluated.

[0117] Example 2

[0118] Based on Example 1, in order to ensure numerical stability, the time step Δt in this invention needs to simultaneously satisfy the Courant-Friedrichs-Lewy (CFL) conditions for both MPM fluid and SDEM solid, and is determined according to formula (25):

[0119] (25)

[0120] in The Courant number is a safety factor. Represents the initial dimensions of the material point or background mesh. Indicates the speed of sound. It is the mass of DEM particles. This refers to the contact normal stiffness. In actual calculations, the time step can be further reduced by combining boundary conditions and platform motion velocity.

[0121] Example 3

[0122] In this embodiment, motion response prediction is performed on a single unmoored box-shaped platform under the action of a solitary wave. A long, straight numerical flume is established; exemplarily, the flume length is 15.0 m, the still water depth d is 0.2 m, the left side of the flume is the solitary wave input boundary, and an unmoored box-shaped floating platform is arranged in the middle. The water mass point parameter can be density. Viscosity Platform sphere polygon construction radius normal stiffness Normal damping coefficient Tangential damping coefficient The background grid resolution can be 0.01m × 0.01m, and the particle resolution for each dimension can be 2 material points.

[0123] The platform is initially in a still water floating equilibrium state, with its bottom submerged in the water and its upper part bearing the equivalent operational load. After the calculation begins, the target wave height, still water depth, wave velocity and wave generation time are used as inputs to generate an isolated wave according to formulas (19) and (20), so that the isolated wave propagates from left to right and acts on the wave-facing side of the platform; then, in each time step, the contact pairs between the water material points and the boundary of the spherical polygon platform are determined according to formulas (21) and (22), the normal contact force and tangential contact force are calculated according to formulas (23) and (24), the platform's center of mass position, linear velocity, attitude angle and angular velocity are updated according to formulas (17) and (18), and the water reverse coupling update is completed according to formulas (2) to (16).

[0124] This embodiment outputs the platform's horizontal drift time history, heave time history, pitch angle time history, force time history, torque time history, and the maximum response index extracted from the above time histories. Its typical time history curves and motion process are as follows: Figures 4-5 As shown, this is used to predict the motion response of a single unmoored box platform under solitary wave action.

[0125] Figure 4 In the diagram, black and white lines and curves represent typical time histories of platform horizontal drift, heave displacement, pitch angle, force, and torque changes over time during the action of an isolated wave. The horizontal axis represents time, and the vertical axis represents displacement, angle, force, or torque, respectively. The diagram also marks the period before the isolated wave reaches the platform, the peak value of the wave, and the recovery phase after the wave's action.

[0126] Example 4

[0127] Based on the settings of solitary wave input, water depth, material point parameters, contact parameters, and time step in Example 3, this example sets up at least two unmoored box-shaped platform schemes of different sizes.

[0128] Different size schemes can change the platform's length, width, height, draft, or equivalent cross-sectional dimensions, and the platform's mass, displacement, center of gravity, center of buoyancy, and moment of inertia can be redefined based on the geometric dimensions and load arrangement of each scheme. For each size scheme, the contact pair, contact force, resultant force, and resultant moment are calculated according to formulas (19) to (24), and the platform's translational and rotational states are updated according to formulas (17) and (18). The maximum horizontal drift distance, maximum heave displacement, maximum attitude angle, attitude angle change rate, peak force, and peak moment of each size scheme are compared, and the comparison results are as follows: Figure 6 As shown in the figure, when L=0.10m, 0.30m, and 0.60m, the maximum horizontal drift is approximately 0.36m, 0.35m, and 0.33m, the maximum heave is approximately 0.060m, 0.053m, and 0.040m, and the maximum attitude angle is approximately... , and The rate of change of attitude angle is approximately , and The results show that as the platform size increases, the horizontal drift decreases slightly, while the heave displacement, attitude angle, and rate of change of attitude angle decrease significantly. Specifically, the L=0.60m scheme, compared to the L=0.10m scheme, exhibits approximately a 33% reduction in heave displacement, a 40% reduction in maximum attitude angle, and a 60% reduction in the rate of change of attitude angle, resulting in significantly improved attitude stability. Simultaneously, the peak force increases from approximately 5.9N to 17.3N and 26.1N, and the peak moment increases from approximately 0.05N·m to 0.55N·m and 2.1N·m, respectively. This indicates that while larger platforms reduce motion response, they also bear greater wave forces and moments. Therefore, size optimization should consider both motion stability and structural safety.

[0129] This invention can employ GIMP shape functions to reduce cross-mesh errors, depending on the required accuracy. Platform boundaries can be represented using two-dimensional spherical polygons or three-dimensional spherical polyhedra. For scenarios requiring improved computational efficiency, multi-threaded CPU parallelism can be used to accelerate material point mapping, contact detection, and contact force calculation.

[0130] The embodiments and implementation process of the present invention have been described in detail above with reference to the accompanying drawings and tables, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments, including components, without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action, characterized in that, Includes the following steps: S1. Discretize the wave water body in the computational water area into material points, establish a background computational grid, and assign mass, position, velocity, volume, density and stress tensor to each material point; S2. Discretize the unmoored floating platform into a spherical polygon discrete element rigid body, and define the mass, displacement, center of gravity position, center of buoyancy position, moment of inertia, initial position, initial linear velocity, initial attitude angle and initial angular velocity of the unmoored floating platform. S3. Generate or input an isolated wave field to allow the isolated wave to propagate within the calculated water area and act on the unmoored floating platform. S4. In each time step, a search region is established with the spherical polygon discrete element rigid body as the center, the background computational grid nodes in the search region are screened, and water body material points that contribute to the background computational grid nodes are backtracked to form potential contact pairs; the contact pairs are determined according to the geometric overlap between the water body material points and the boundary of the spherical polygon. S5. Calculate the contact force between the water body material point and the unmoored floating platform based on the geometric overlap, normal unit vector, relative normal velocity, and relative tangential velocity of the contact pair. In step S4, the search radius of the search area is determined by the sum of the maximum distance from the centroid of the unmoored floating platform to any point on the boundary of the spherical polygon, the construction radius of the spherical polygon, and the safe extension distance; the geometric overlap is determined by the construction radius of the spherical polygon, the radius of the water body material point, and the shortest distance from the water body material point to the boundary of the spherical polygon; when the geometric overlap is greater than zero, the potential contact pair is determined to be a contact pair.

2. The coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action according to claim 1, characterized in that, It also includes the following steps: S6. The contact forces are summed over the center of mass of the unmoored floating platform to obtain the resultant force and resultant moment acting on the unmoored floating platform. S7. Solve the translational and rotational motion equations of the unmoored floating platform based on the resultant force and resultant moment, and update the position, linear velocity, attitude angle and angular velocity of the unmoored floating platform. S8. Apply a force equal in magnitude and opposite in direction to the contact force to the water body material point or background calculation grid node, and update the velocity, position, density, volume and stress state of the wave water body using the material point method. S9. Reset the background calculation grid and repeat steps S4 to S8 until the set simulation duration or output conditions are reached, and output the horizontal drift, heave, attitude rotation, force time history, torque time history and stability evaluation index of the unmoored floating platform under the action of solitary waves.

3. The coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action according to claim 2, characterized in that: Steps S4 to S8 share the same contact detection and contact force calculation results within the same time step, and use explicit time integration to perform a two-way coupled solution for the wave water body and the floating platform. The time step simultaneously satisfies the stability conditions of the material point method solution for the water body and the discrete element contact solution for the floating platform, and is determined based on the characteristic size of the material point, sound velocity, discrete element mass, and contact normal stiffness.

4. The coupled simulation method for predicting the motion response of an unmoored floating platform under isolated wave action according to any one of claims 1 to 3, characterized in that: The unmoored floating platform includes temporary work platforms, floating rescue platforms, floating observation platforms, modular floating island units, floating platforms during the towing and installation phase, floating platforms during the pre-installation waiting phase, or free-floating platforms in model tests. The unmoored floating platform outputs a three-degree-of-freedom motion response of sway, heave, and pitch under two-dimensional calculation conditions; the unmoored floating platform outputs a six-degree-of-freedom motion response of pitch, sway, heave, roll, yaw, and bow roll under three-dimensional calculation conditions.

5. The coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action according to claim 3, characterized in that, The spherical polygon discrete element rigid body in step S2 is formed in the following way: the geometric boundary of the unmoored floating platform is reduced inward by a set thickness to obtain discrete element primitives, and then the sphere radius equal to the set thickness is swept along the reduced boundary to reconstruct it. The area occupied by each swept sphere is then combined to form a spherical polygon contact boundary with continuous normals. In step S2, the mass, displacement, center of gravity, center of buoyancy, and moment of inertia of the unmoored floating platform are calculated based on its geometry, material density, and load distribution, and the unmoored floating platform is initially placed in a still water floating state in equilibrium between gravity and buoyancy.

6. The coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action according to claim 3, characterized in that: The contact force in step S5 includes normal spring damping force and tangential damping force; the normal spring damping force is determined by geometric overlap, normal spring stiffness, normal unit vector, relative normal velocity, and normal damping coefficient; the tangential damping force is determined by relative tangential velocity and tangential damping coefficient.

7. The coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action according to claim 3, characterized in that: The resultant torque in step S6 is obtained by multiplying the position vector of each contact point relative to the center of mass of the platform with the corresponding contact force and then summing them. The resultant torque is used to update the angular velocity and attitude angle of the unmoored floating platform in step S7.

8. The coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action according to claim 3, characterized in that: The isolated wave field in step S3 is generated by the motion function of the piston wave generator; when the piston wave generator is used, the motion function is determined by the target wave height, still water depth, wave velocity and wave generation time.

9. The coupled simulation method for predicting the motion response of an unmoored floating platform under solitary wave action according to claim 3, characterized in that: The motion equations described in step S7 include resultant force, resultant torque, gravity, and buoyancy determined by displacement and center of buoyancy position; the wave water body described in step S8 adopts a weakly compressible fluid formula, and the fluid pressure is updated by water density through the equation of state; the stability evaluation indicators described in step S9 include at least one of the following: maximum horizontal drift distance of the platform, maximum heave displacement, maximum attitude angle, attitude angle change rate, peak force, peak torque, and whether the platform has a tendency to capsize.

Images