A Multi-Scale Numerical Calculation Method and System for Stress on Deep-Sea Cage Net Structures

Abstract

This invention discloses a multi-scale numerical calculation method and system for the stress on deep-sea cage mesh structures, relating to the field of mechanical simulation technology for marine engineering and aquaculture equipment. The method includes establishing a macroscopic coupled dynamic response analysis model based on rope equivalence, reducing the system's degrees of freedom by eliminating fine mesh entities through hydrodynamic compensation; establishing a high-fidelity microscopic fine mesh finite element sub-model for local high-risk areas; using a dynamic link library for spatial shape function interpolation and time synchronization to accurately map the large-scale displacements of macroscopic rope nodes to the forced boundary conditions of the microscopic sub-model; performing dimensionality reduction and nonlinear iterative solution on the microscopic sub-model, and aggregating and outputting a multi-scale stress response cloud map for all working conditions. This invention, employing the aforementioned multi-scale numerical calculation method and system for the stress on deep-sea cage mesh structures, overcomes the computational bottleneck of ultra-large cages, accurately reconstructs the stress transmission path, and provides a reliable basis for the tear-resistant design and safety early warning of the mesh.

Description

Technical Field

[0001] This invention relates to the field of mechanical simulation technology for marine engineering and aquaculture equipment, and in particular to a multi-scale numerical calculation method and system for the stress on deep-sea cage mesh structures. Background Technology

[0002] With the rapid development of deep-sea aquaculture, the application of large-scale deep-sea aquaculture cages is becoming increasingly widespread. Aquaculture cages typically consist of a main frame, a netting system, and a mooring system (for floating cages). Among these, the netting system is the core component that ensures aquaculture space and prevents fish from escaping. It is also the weakest link in the entire system, experiencing the most intense load response and being most susceptible to fatigue wear and tear damage under complex wave and current environments.

[0003] Numerical calculations and fluid-structure interaction analyses of large, deep-sea net cages present significant challenges due to their vastly different scales. In practical engineering, the macroscopic dimensions (diameter or side length) of net cages often reach tens or even hundreds of meters, while the microscopic mesh size of the netting is typically only about 1 to 5 centimeters. If the finite element method is used to create a solid 3D model of tens or even millions of mesh openings and directly solve for their hydrodynamic response, the system's degrees of freedom would explode exponentially, far exceeding the computing power of current systems.

[0004] To address this computational bottleneck, existing numerical methods typically require significant simplification of the mesh. In hydrodynamic calculations of mesh, the Morrison formula based on mesh grouping theory or a screen model based on the density of porous media are commonly used. While these simplification methods can effectively yield the overall hydrodynamic response of the mesh cage (such as overall drag and macroscopic motion), they geometrically erase the fine mesh structure, failing to provide the overall stress distribution across the entire mesh structure, particularly the stress details of individual mesh fibers. This results in engineers lacking precise local stress data to accurately predict the initiation location of mesh failure and the stress transmission path when designing tear-resistant mesh and assessing local strength. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-scale numerical calculation method and system for the stress on deep-sea cage mesh structures, thereby solving the problems existing in the background art.

[0006] To achieve the above objectives, this invention provides a multi-scale numerical calculation method for the stress on deep-sea cage mesh structures, comprising the following steps: S1. Extract the main supporting skeleton of the deep-sea cage in the global coordinate system, remove the fine netting entity, and discretize the main supporting skeleton using the continuous finite element method to establish a macroscopic coupled dynamic response analysis model of the deep-sea cage based on the equivalent of the steel rope. S2. For high-risk areas of deep-sea cages, establish a high-fidelity micro-fine net finite element sub-model; S3. By using dynamic link library programs, a cross-scale spatial registration and time synchronization mapping mechanism is established to accurately transform macroscopic large-scale loads into forced boundary conditions of microscopic sub-models, thereby realizing the dynamic mapping and nesting of multi-scale boundary constraints and tension data. S4. Drive the underlying finite element solver to perform nonlinear dynamic integration and stress state update on the micro-fine mesh finite element sub-model, and realize the nonlinear finite element solution of the local micro-fine mesh finite element sub-model. S5. By using a spatiotemporal synchronization aggregation algorithm and extreme value envelope evaluation, the multi-scale stress response results under all working conditions are aggregated to generate and output cloud maps and videos.

[0007] Preferably, the main load-bearing skeleton in S1 includes the main frame of the cage, the mooring system, and the macro-rope system.

[0008] Preferably, S1 includes: S11. Discretize the main frame of the cage using three-dimensional spatial beam elements, and discretize the mooring system cables and macro rope system using three-dimensional tension-only cable elements. S2. Calculate the initial density of the removed local mesh. As shown in the following formula: ; In the formula, The diameter of the network cable. The mesh side length; Calculate the equivalent hydrodynamic diameter of the macroscopic wire element. As shown in the following formula: ; In the formula, The physical outer diameter of the rope. The length of the rope unit. This represents the corresponding subordinate area in the topological structure; S13. Calculate the equivalent fluid drag force vector on a macroscopic rope per unit length. and equivalent fluid inertial force vector : ; ; In the formula, The density of seawater; and These are the normal and tangential relative velocity vectors, respectively; and This is the vector of acceleration components of water particles; and The acceleration component vector of the rope element; , , , For hydrodynamic coefficients; Integrating the force vector and transforming it to the global coordinate system yields the equivalent fluid load vector. ; S14. Establish the overall control equations for macroscopic multibody coupled time-domain dynamics, as shown in the following equation: ; In the formula, , , These are the global mass, the added mass, and the damping matrix, respectively. , , These are column vectors for acceleration, velocity, and displacement, respectively. This is the global nonlinear stiffness matrix; For including fluid load The global external load vector; S15. The overall control equations are solved using an implicit integration algorithm combined with the Newton-Raphson iterative method.

[0009] Preferably, S2 includes: S21. Select the local mesh region enclosed by the macroscopic wire rope unit as the microscopic solution domain, and take the geometric center line of the macroscopic wire rope as the spatial geometric boundary of the microscopic mesh sub-model. S22. Reconstruct the network knots and wire entities within the microscopic solution domain and discretize them into three-dimensional tension-only nonlinear cable elements; S23. Introduce nonlinear constitutive equations for polymer materials to characterize their uniaxial stress characteristics under tensile stiffening and compressive relaxation. S24. Extract the flow field information at the location of the micro sub-model and calculate the real local fluid drag force and inertial force acting on each micro mesh unit.

[0010] Preferably, the nonlinear constitutive equation of the polymer material in S23 is specifically as follows: For any single element in the micro-network sub-model Its instantaneous engineering strain is The real-time axial tension inside The calculation formula is shown below: ; In the formula, This represents the initial cross-sectional area of ​​the network cable unit. , , It is the nonlinear elastic stiffness coefficient.

[0011] Preferably, S3 includes: S31, in macroscopic time step At the end, the spatial positions, displacement vectors, and axial tensions of the macroscopic rope nodes in the target mesh region of the microscopic sub-model of the package are extracted in real time. S32. For any microscopic boundary node Determine the macroscopic unit to which it belongs and define its dimensionless local coordinates. As shown in the following formula: ; In the formula, This represents the global spatial coordinate vector under the initial stress-free state. and These are the two endpoints of a macroscopic wire rope unit; S33, Using a one-dimensional shape function matrix Calculate the mapped displacement vector inherited by the microscopic boundary nodes. As shown in the following formula: ; In the formula, Represents the dynamic displacement field. Indicates the macroscopic time step. The next macroscopic time step maps the displacement vector. Indicates in Micro-nodes calculated through spatial interpolation at every moment The known displacement, Indicates in Micro-nodes calculated through spatial interpolation at every moment The known displacement, This indicates the time step for solving the microscopic model; The mapped displacement vector is loaded as a Dirichlet boundary condition into the micro-fine mesh finite element sub-model.

[0012] Preferably, S4 includes: S41. Assemble the multi-degree-of-freedom nonlinear dynamic control equations of the micro-net-soil model, as shown in the following equation: ; In the formula, This represents the global quality matrix of the microscopic sub-model. Represents the global damping matrix of the microscopic sub-model. This represents the nonlinear internal force vector of a microscopic system, which is obtained by transforming the axial tension of each microscopic nonlinear cable element to the global coordinate system and assembling nodal forces. This represents the true local fluid load vector directly acting on the microstructure lines, calculated in S24. , , These are the global displacement, velocity, and acceleration vectors for all nodes at the microscopic level, respectively. S42. Rearrange the system's displacement vector as follows: The index of the internal free node is The known node indices of the boundary are The dimensionality-reduced dynamic equations containing only the responses of unknown free nodes are extracted, as shown in the following equation: ; In the formula, This represents the displacement vector of the internal free nodes. This represents the displacement vector of the boundary node. This represents the mass matrix of the internal unknown free nodes themselves. Indicates the internal unknown free node in The acceleration vector at time t. This represents the damping matrix of the internal unknown free nodes themselves. Indicates the internal unknown free node in The unknown velocity vector at time t, This represents the nonlinear elastic internal force vector of a free node. This represents the displacement of an unknown free node within the node. This represents the displacement of the known internal boundary nodes. Indicates direct external load; This represents the coupling quality matrix between free nodes and boundary nodes. This represents the acceleration vector of a known boundary node. This represents the coupling damping matrix between free nodes and boundary nodes. Represents the velocity vector of a known boundary node; S43, at each time step The Newton-Raphson iterative algorithm is introduced to calculate the elastic stiffness matrix. and geometric stiffness matrix Nonlinear tangent stiffness matrix formed by superposition As shown in the following formula: ; In the formula, This represents the nonlinear internal force vector of the internal free nodes. This indicates the axial tension of a single network cable unit; Solve for the displacement increment and update the nodal displacements until the residual force converges; S44. Perform relaxation detection. If a network cable unit shows a relaxation test... Then set its internal force to zero, and assemble the tangent stiffness matrix in the next time step. When this happens, the stiffness contribution of that element is removed.

[0013] Preferably, S5 includes: S51. Set a unified output time series to perform spatiotemporal synchronization and full dataset aggregation of the time history data of macroscopic ropes and microscopic nets. S52. Under the set full-condition environmental load matrix, extract the tension extreme values ​​of macroscopic wire rope elements and microscopic wire mesh elements, and calculate the minimum safety factor for the full-condition load. S53. Based on scalar field color mapping algorithm and multi-detail level rendering technology, generate and output multi-scale force response cloud map and video containing macroscopic overall force of the rope and microscopic local force of a single wire. Specifically, the scalar field color mapping algorithm involves setting a lower limit value for tension. With upper limit Calculate the normalized stress index It is then mapped to three channels of the RGB color space using a multi-segment linear color interpolation function.

[0014] Preferably, S52 includes: Finding physical units under the full set of operating conditions Tension extremes in time-history response As shown in the following formula: ; In the formula, Indicates operating conditions. This represents the full-condition environmental load parameter matrix. Representing the unit Specific working conditions Below, at a specific time The instantaneous axial tension it bears; Calculate the minimum safety factor using tension extreme values. As shown in the following formula: ; In the formula, This represents the allowable breaking tensile strength threshold for the mesh material.

[0015] A system for multi-scale numerical calculation of the stress on deep-sea cage mesh structures includes: Macroscopic dynamics solution module: used to extract the main load-bearing skeleton of deep-sea cages, establish a macroscopic coupled dynamic response analysis model of deep-sea cages containing only the rope system through the hydrodynamic equivalent compensation algorithm, and solve and output the time history displacement and tension data of macroscopic rope nodes; Microscopic Sub-model Construction Module: Used to establish a microscopic fine mesh finite element sub-model of a deep-sea cage in a local high-risk area, with macroscopic ropes as the spatial boundary and containing real microscopic mesh geometry and nonlinear material characteristics; Data mapping nesting module: used for spatial registration and time synchronization between macro and micro models, and to map the displacement of macro framework nodes to the forced boundary conditions of micro sub-models in real time through shape function interpolation; Sub-model finite element solution module: Receives the mapped boundary conditions, performs matrix partitioning dimensionality reduction and nonlinear iterative solution on the micro-fine mesh finite element sub-model, and calculates the nodal displacement and axial tension of a single micro-mesh wire; Multi-scale cloud map output module: Aggregates macroscopic and microscopic force response data, performs extreme value envelope analysis and color mapping under all working conditions, renders and outputs multi-scale axial force cloud maps and nodal displacement cloud maps.

[0016] Therefore, the present invention employs the above-mentioned multi-scale numerical calculation method and system for the stress of deep-sea cage mesh structures, which has the following beneficial effects: (1) This method is the first to combine a macroscopic framework and a microscopic fine sub-model to create a cross-scale nested computational architecture. At the macroscopic level, a large number of mesh nodes are filtered out by density equivalence, which greatly reduces the system degree of freedom of the overall fluid-structure interaction analysis. High-fidelity sub-models are introduced in local key areas to solve the computational disaster of full-size fine modeling of ultra-large aquaculture cages. At the same time, the stress transmission path is accurately restored. By using data communication interface and shape function interpolation algorithm, the large-scale displacement field of macroscopic rope is seamlessly and in real time projected into the forced displacement boundary of microscopic mesh, eliminating the technical blind spot that traditional equivalent grouping model cannot reflect local stress concentration.

[0017] (2) This method has high engineering early warning guidance value. The micro sub-model adopts constitutive equations that reflect the tensile nonlinearity and compressive relaxation characteristics of the netting material, which can accurately solve the real axial force of each netting line. The output full-condition stress cloud map can directly identify the weak units of the netting that are very easy to tear, providing a reliable basis for the tear-resistant structure design, rope arrangement optimization and intelligent damage early warning of deep-sea cages.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating a multi-scale numerical calculation method for the stress on a deep-sea cage mesh structure according to the present invention; Figure 2 This is a system module connection diagram of the present invention; Figure 3 This is a flowchart illustrating the establishment and solution process of the macroscopic model of this invention. Figure 4 This is a flowchart illustrating the construction process of the microscopic sub-model of the present invention; Figure 5 This is a flowchart of the DLL cross-scale dynamic mapping process of the present invention; Figure 6 This is a flowchart of the micro-nonlinear finite element solution process of the present invention; Figure 7 This is a flowchart of the data aggregation and cloud map output process of the present invention. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0022] Example Please see Figures 1-7 This invention provides a multi-scale numerical calculation method for the stress on the netting structure of a deep-sea floating aquaculture cage. Taking a deep-sea floating aquaculture cage as an application scenario, this cage is subjected to the coupled effects of waves, currents, and wind loads in the marine environment. Its netting system is prone to local stress concentration and tearing. The core implementation steps are as follows: like Figure 3 As shown in Figure S1, a macroscopic coupled dynamic response analysis model for deep-sea cages based on the equivalent of steel wire ropes is established. Due to the presence of a massive number of fine mesh openings in large deep-sea cage structures, retaining the true geometric details of the mesh lines in the global fluid-structure interaction analysis would lead to an exponential explosion in the number of system nodes and degrees of freedom in the finite element model, causing the "curse of dimensionality" and making it impossible to complete the time-domain solution within an acceptable engineering timeframe.

[0023] To overcome this computing power bottleneck, this step performs "topology skeleton extraction" and "hydrodynamic equivalent compensation" on the net cage at the macroscopic level, constructing a dimensionality-reduced macroscopic coupled dynamic response analysis model. Specifically, it includes the following steps: S11. Extraction of the macroscopic topology skeleton of the wire mesh cage and discretization of the continuum finite element method. In the global rectangular coordinate system. In this process, the fine mesh structure (i.e., mesh openings and micro-wires) of the deep-sea cages is stripped and removed, extracting only the main load-bearing skeleton. The main load-bearing skeleton includes: the main frame of the cage (such as HDPE buoyancy tube rings, columns, and bottom sinker rings), mooring system cables, and the macroscopic rope system within the mesh structure (including vertical main ropes, horizontal circumferential ropes, and diagonal reinforcing ropes used to bear the tension of the mesh). The extracted main load-bearing skeleton is then discretized using continuum finite element method. 1. For the main frame of the cage with high bending and torsional stiffness, a three-dimensional spatial beam element is used for meshing. This element takes into account the shear deformation effect, and each node has 6 degrees of freedom (3 translational degrees of freedom and 3 rotational degrees of freedom).

[0024] 2. For mooring system cables and macro-line systems that only bear axial tension and not bending moment and pressure, a three-dimensional tension-only element is used for discretization. Each node of this element has 3 translational degrees of freedom.

[0025] By using the aforementioned dimensionality reduction discretization, the original mesh entity with tens of millions of degrees of freedom is transformed into a sparse skeleton model composed of a small number of macroscopic continuous line units, which greatly improves the solution efficiency.

[0026] S12. Based on the principle of equivalence of dependent areas, calculate the equivalent hydrodynamic diameter of the macroscopic wire mesh element and compensate for the fluid resistance characteristics of the fine mesh to calculate the equivalent fluid load of the macroscopic wire mesh element. Since the fine mesh entity was removed in S11, the huge water flow resistance and wave force that the cage system should have been able to withstand would be severely lacking. To address this, this method proposes a hydrodynamic equivalent compensation algorithm based on "dependent area" to accurately map the missing local mesh fluid load to the adjacent macroscopic wire mesh element.

[0027] First, calculate the initial density of the actual local mesh that was removed in the no-flow state. Assume that the local mesh is composed of a diameter of If the mesh is woven from wire and the mesh shape is a square or rhombus with a side length of 1, then the formula for calculating its density is: ; Subsequently, for any segment of the macroscopic wire element after discretization (let its element length be...), The physical outer diameter is The area of ​​the local mesh that it is responsible for constraining and carrying in the topology is defined as the dependent area. To compensate for the water-blocking effect of this local mesh in the hydrodynamic calculations, the equivalent hydrodynamic diameter of this macroscopic wire mesh element is calculated. : ; Using this equivalent algorithm, the macroscopic wire rope element is given a "virtual expansion" diameter in the fluid-structure interaction solver. This diameter is only used to calculate fluid loads and does not change the actual structural mass and axial stiffness of the wire rope. Thus, without increasing the system's degrees of freedom, it physically and equivalently inherits the fluid resistance characteristics of the fine mesh.

[0028] Step 13: Vectorized Calculation and Application of Spatial Nonlinear Environmental Loads. Based on the set extreme or conventional marine environmental conditions, the nonlinear Stokes higher-order wave theory is used, and ocean current profile functions are superimposed to calculate the instantaneous velocity vector of water particles at any coordinate point in the global coordinate system. With acceleration vector .

[0029] For the macroscopic wire rope element, the modified Morrison equation is used to calculate the fluid load it experiences. Since the flexible wire rope undergoes large-scale spatial deformation in wave flow, the motion of water particles needs to be decoupled from the motion of the wire rope element itself. The local tangential unit vector of the wire rope element is defined as... The local normal plane is composed of two orthogonal unit normal vectors. and constitute.

[0030] Calculate the relative velocity vector between the water particle and the rope element. ,in This is the velocity vector of the rope element itself.

[0031] Projecting the relative velocity onto the local coordinate system yields the normal relative velocity vector. and tangential relative velocity vector The equivalent fluid drag force vector per unit length of macroscopic wire rope for: ; Equivalent fluid inertial force vector per unit length on a macroscopic wire for: ; In the above formula, The density of seawater; and These are the normal and tangential component vectors of the acceleration of water particles, respectively. and These are the normal and tangential component vectors of the acceleration of the rope element itself, respectively. , , , These are the drag force coefficients and additional mass coefficients in the normal and tangential directions, respectively, and their values ​​are obtained by dynamic interpolation based on the instantaneous Reynolds number and Klegen-Carpenter number.

[0032] Integrate the calculated unit length force vector along the element length and transform it to the global coordinate system to assemble the global equivalent fluid load vector of the macroscopic wire element. .

[0033] Step 14: Taking into account the main frame of the cage, the equivalent rope system, and the mooring system, the macroscopic multibody coupled time-domain dynamics overall control equations of the deep-sea cage system are established using finite element matrix assembly technology, as shown in the following equation: ; in: The global structural quality matrix. Add a global mass matrix; This is the global damping matrix, which includes structural Rayleigh damping and fluid viscous radiation damping; , , These are the global displacement, velocity, and acceleration column vectors for the macroscopic nodes, respectively. This is the global nonlinear stiffness matrix. Due to the large displacement and stress stiffening effects that macroscopic ropes and mooring cables experience under wave and current action, this matrix is ​​derived from the elastic stiffness matrix. and the geometric stiffness matrix that depends on instantaneous displacement and axial force It is built up by stacking, and needs to be updated in real time at each time step; This is the global external load vector, which includes fluid loads. The nonlinear restoring force, gravity, and buoyancy of the mooring system.

[0034] S15. Given that the tension-only element possesses extremely strong geometric nonlinearity and state jump characteristics (such as relaxation failure under compression), explicit integration is highly likely to induce numerical divergence. Therefore, this method preferably employs implicit Newmark-... Integral algorithm or generalized - The algorithm, combining the Newton-Raphson iterative method, performs a time-domain step-by-step solution to the aforementioned nonlinear overall control equations. The time step is set. The dynamic response balance of the system is calculated at each time step.

[0035] After the time-domain solution is completed, the macroscopic rope node data corresponding to the boundary of the subsequent "microscopic fine web sub-model" is extracted through the data post-processing interface program. Specifically, discrete time series data is extracted. Global spatial displacement time-history sequence of relevant macroscopic nodes and unit axial tension time history sequence The extracted time-series data will be permanently written into the system's shared memory or a dedicated cache file as a high-fidelity data source, used in subsequent steps to map boundary constraints to the lower-level micro-scale mesh sub-model via a dynamic link library (DLL).

[0036] like Figure 4 As shown in Figure S2, establish a high-fidelity micro-fine mesh finite element sub-model.

[0037] In S1, due to the adoption of an equivalent hydrodynamic compensation mechanism, the macroscopic dynamic model of the gabion does not include any real mesh nodes. However, fatigue fracture and tearing of the mesh often begin at local nodes with high stress concentration. Therefore, this step aims to establish a high-fidelity microscopic finite element sub-model of the gabion for high-risk areas (such as the center of the upstream face, the corner of the bottom counterweight, etc.). Specifically, it includes the following sub-steps: S21. Select the local mesh region enclosed by macroscopic wire rope units as the microscopic solution domain, and take the geometric center line of the macroscopic wire rope as the spatial geometric boundary of the microscopic mesh sub-model.

[0038] In the overall coordinate system of the macro cage In this process, a local mesh region enclosed by several macroscopic wire rope units is selected as the microscopic solution domain. .

[0039] Extract the geometric centerline of the macroscopic framework enclosing the solution domain and define it as the spatial geometric boundary of the microscopic mesh submodel. This boundary will serve as the physical interface for receiving macroscopic node displacement data in subsequent S3.

[0040] S22. Reconstruct the network knots and wire entities within the microscopic solution domain and discretize them into three-dimensional tension-only nonlinear cable elements.

[0041] In the defined microscopic solution domain Internally, the solid geometry of the fine mesh is reconstructed based on the actual weaving process and geometric specifications of the mesh garment.

[0042] Set the actual mesh shape (e.g., square or rhombus) and mesh side length. And the physical diameter of a single network cable .

[0043] Generate realistic meshes and wires in the geometric model.

[0044] Finite element discretization was performed on the reconstructed fine mesh: the mesh knots were defined as micro-finite element nodes. ( The mesh segments connecting two adjacent mesh knots are discretized into three-dimensional tension-only nonlinear cable elements. Each mesh element... initial cross-sectional area The initial stress-free length is This discretization method directly reflects the microscopic topology of the mesh, completely avoiding the defect of not being able to observe local mesh deformation in macroscopic models.

[0045] S23. Introduce nonlinear constitutive equations for polymer materials to characterize their uniaxial stress characteristics under tensile stiffness and compressive relaxation.

[0046] Deep-sea netting is typically woven from ultra-high molecular weight polyethylene (UHMWPE) or nylon and other high-molecular polymers. Its mechanical properties exhibit high material nonlinearity and a unidirectional stress characteristic of "stiffening under tension and relaxation under compression." To accurately calculate the internal axial tension of a single netting cable, for any single cable element in the microscopic netting sub-model, the instantaneous spatial coordinates of its two end nodes are defined as follows: and .

[0047] Instantaneous spatial length of the unit for: ; Instantaneous engineering strain of this unit for: ; A polynomial constitutive equation describing the nonlinear mechanical characteristics of polymer synthetic fibers is introduced. The real-time axial tension within this cable unit is also introduced. The calculation formula is: in, This is the nonlinear elastic stiffness coefficient obtained through tensile testing of wire mesh materials. This piecewise function not only accurately characterizes the stress-strengthening effect of wire mesh materials, but also mathematically mandates the following: With zero tension, it accurately simulates the physical phenomena of wrinkling and relaxation commonly seen in mesh fabrics in wave currents.

[0048] S24. Extract the flow field information at the location of the micro sub-model and calculate the real local fluid drag force and inertial force acting on each micro mesh unit.

[0049] In the macroscopic model of S1, the fluid load is applied to the wire rope through "density". However, in this microscopic sub-model, since the wire rope entity has been fully reconstructed, the real local hydrodynamic load must be applied directly to each microscopic wire rope element. The instantaneous velocity vector of the water particles at the water depth location of the microscopic sub-model is extracted. and acceleration vector .

[0050] For any microscopic mesh element, let its unit direction vector be... Its own velocity vector is The acceleration vector is Calculate the relative velocity vector between the water particle and the microscopic mesh element. The relative velocity is decomposed into tangential components along the axis of the grid line. and the normal component perpendicular to the grid line As shown in the following formula: ; ; Using the original microscopic Morrison equation, the true local fluid drag force vector acting per unit length of this single microscopic mesh element is calculated. As shown in the following formula: ; The fluid inertial force vector acting per unit length of this unit for: ; in, The density of seawater; and These are the normal components of the acceleration of water particles and the acceleration of the network element, respectively; , , These are the true normal drag force coefficient, tangential drag force coefficient, and additional mass coefficient applicable to slender cylindrical bodies (without any equivalent conversion, and taken according to the standard cylinder flow).

[0051] Will and Integrating along the element length, the local fluid load vector of the microscopic submodel is obtained. .

[0052] Through the above four sub-steps, the physical modeling, material constitutive definition, and application of realistic local hydrodynamics of the microscopic, finely textured mesh sub-model were completed. At this point, the microscopic mesh sub-model is ready to proceed, awaiting only the subsequent "S3" step, which uses a dynamic link library (DLL) to transfer the large-scale displacements of the macroscopic wire rope to its boundaries. Then, time-domain solutions can be performed.

[0053] like Figure 5As shown, after completing the macroscopic coupled dynamic response analysis (S1) and the construction of the microscopic fine mesh sub-model (S2), the macroscopic wire element node distribution is extremely sparse, while the boundary nodes of the microscopic mesh sub-model are extremely dense, making it impossible for the two to directly share data. Therefore, this step establishes a cross-scale spatial registration and temporal synchronization mapping mechanism through a self-developed dynamic link library (DLL) program, accurately transforming macroscopic large-scale loads into forced boundary conditions for the microscopic sub-model.

[0054] S31. Initialize the data communication interface between the macroscopic master solver and the microscopic sub-model solver.

[0055] Initialize the dynamic link library (DLL) communication interface in memory to establish a shared memory area between the macroscopic master solver and the microscopic sub-model solver.

[0056] Let the set of macroscopic rope nodes of the target mesh region in the microscopic sub-model be defined as .

[0057] At each macroscopic time step in the macroscopic dynamics solution At the end, the DLL program uses an API probe to extract and intercept the macroscopic rope node set in real time. Instantaneous spatial position vectors of each macroscopic node in the global coordinate system Global displacement vector and the axial tension of the wire rope unit Then, write the batch of data to the shared memory cache.

[0058] S32. Perform local coordinate parameterization and spatial registration on the boundary nodes of the micro sub-model and the macro-structure elements.

[0059] In the initial configuration without deformation, the boundary of the micro-webbed model The geometry fits onto the axis where the macroscopic wire element is located.

[0060] Let the set of boundary nodes of the microscopic sub-model be... .

[0061] Since the number of micro-nodes is much greater than that of macro-nodes, spatial registration is required in a local coordinate system. For any micro-boundary node... The search algorithm determines the macroscopic rope element to which it belongs (assuming the two endpoints of the element are macroscopic nodes). and ).

[0062] Define this microscopic boundary node Dimensionless local coordinates (natural coordinates) on a macroscopic structural unit : ; in, This represents the global spatial coordinate vector of the corresponding node in the initial stress-free state. This is achieved by extracting the coordinates of all microscopic boundary nodes. The set completes the geometric registration of cross-scale spatial mapping.

[0063] S33. Spatial interpolation is performed using finite element isoparametric functions to convert the time-series sequence of spatial displacement of macroscopic boundary nodes extracted in step S1 into the mapped displacement vector of microscopic boundary nodes.

[0064] To ensure the kinematic coordination of the large macroscopic deformation of the rope when it is transmitted to the microscopic mesh, and to avoid false stress concentration at the microscopic boundary, spatial interpolation is performed using finite element isoparametric functions.

[0065] At any macroscopic time step For micro boundary nodes Its instantaneous mapped displacement vector Interpolation calculations are performed using Lagrange functions or Hermite spline functions.

[0066] Taking a two-node linear macroscopic cable element as an example, its one-dimensional shape function matrix Defined as: ; The exact forced displacement vector inherited by the microscopic boundary node from the macroscopic model is then: ; If the macroscopic wire element adopts a beam element that considers bending stiffness, then a cubic Hermite shape function with rotational degree of freedom needs to be introduced to ensure the continuity of the derivative (i.e., the tangent direction) of the mapped displacement field, and further improve the mapping accuracy under local large deformation conditions.

[0067] By combining the time sub-cycle interpolation algorithm, the mapped displacement vector is loaded as a Dirichlet boundary condition into the micro-network sub-model.

[0068] Since the mesh size of the micro-mesh sub-model is much smaller than that of the macro-model, a smaller time step is usually required to satisfy the Courant-Friedrich-Lyuvi conditions for numerical integration or to ensure the convergence of implicit computation. That is, macroscopic time step (in (The sub-cycle ratio is an integer greater than 1).

[0069] Therefore, the DLL interface performs a sub-loop interpolation algorithm in the time domain. Let the current microscopic solution time be... Located in two adjacent macroscopic time steps Between them, the microscopic boundary nodes At any moment instantaneous displacement Update using linear interpolation over time: ; In the formula, Represents the dynamic displacement field. Indicates the macroscopic time step. The next macroscopic time step maps the displacement vector. Indicates in Micro-nodes calculated through spatial interpolation at every moment The known displacement, Indicates in Micro-nodes calculated through spatial interpolation at every moment The known displacement, This indicates the time step for solving the microscopic model.

[0070] Finally, the dynamic displacement field obtained after the above spatial and temporal dual interpolation is... The Dirichlet boundary conditions are forcibly applied to the stiffness matrix equation of the microstructure mesh model: ; Thus, the global environmental load and large-scale geometric deformation absorbed by the macroscopic wire rope are precisely and seamlessly injected into the physical boundary of the local fine mesh, successfully opening up the technical path for the transmission of macroscopic forces to microscopic local areas. This provides an absolutely accurate boundary driving source for the subsequent S4 solution of the high-precision force of a single micro-mesh wire.

[0071] S4. Nonlinear finite element solution of local micro-network model.

[0072] like Figure 6 As shown, after obtaining the forced displacement sequence of the microscopic boundary nodes in real time through the S3 dynamic link library (DLL), this step aims to drive the underlying finite element solver to perform nonlinear dynamic integration and stress state updates on the microscopic fine mesh sub-model. Due to the extremely strong flexibility, large deformation, and "compression relaxation" characteristics of the mesh, this step establishes a high-precision solution process that includes matrix partitioning and nonlinear tangent stiffness updates. Specifically, it includes the following sub-steps: S41. Assemble the multi-degree-of-freedom nonlinear dynamic control equations of the micro-net model.

[0073] In the global coordinate system, the multi-degree-of-freedom nonlinear dynamic control equations of the micro-network model are assembled according to the finite element theory: ; in, This represents the global quality matrix of the microscopic sub-model; This represents the global damping matrix of the microscopic sub-model; This is the real local fluid load vector that directly acts on the micro-network lines, calculated in S24. It is the nonlinear internal force vector of the microscopic system, which is obtained by transforming the axial tension of each microscopic nonlinear cable element to the global coordinate system and assembling the nodal forces. , , These are the global displacement, velocity, and acceleration vectors for all nodes at the microscopic level.

[0074] S42. Based on the Dirichlet boundary conditions imported in S3, the equations are reduced in dimension by matrix partitioning, and the internal unknown free node equations are separated.

[0075] Since S3 has explicitly given the forced displacements of the microscopic boundary nodes (i.e., nodes attached to the macroscopic framework) through cross-scale mapping, .

[0076] To solve for the response of the unknown internal nodes, the above governing equations need to be matrix partitioned.

[0077] All nodes in the microscopic submodel are divided into two categories: internal free nodes (subscript...) ) and known boundary nodes (subscripts) The system's displacement vector is rearranged as follows: ,in .

[0078] The corresponding governing equations are expanded in blocks as follows: ; In the formula, This represents the mass matrix of the internal free nodes themselves. This represents the mass matrix of the boundary nodes themselves. and This represents the coupling quality matrix between free nodes and boundary nodes. This represents the unknown acceleration of an internal, unknown, free node. Represents the known acceleration of the boundary nodes; This represents the damping matrix of the internal free nodes themselves. and This represents the coupling damping matrix between nodes. This represents the unknown velocity of the internal free nodes. Represents the known velocity of the boundary node; This represents the sum of the internal forces borne by all internal free nodes. This represents the sum of internal forces borne by all boundary nodes; This indicates the external force acting directly on the internal nodes. This represents the external force acting on the boundary node.

[0079] Extracting the first row of the above block matrix yields a reduced-dimensional dynamic equation containing only the responses of unknown free nodes: ; In the formula, This represents the displacement vector of the internal free nodes. This represents the displacement vector of the boundary node. This represents the mass matrix of the internal unknown free nodes themselves. Indicates the internal unknown free node in The acceleration vector at time t. This represents the damping matrix of the internal unknown free nodes themselves. Indicates the internal unknown free node in The unknown velocity vector at time t, This represents the nonlinear elastic internal force vector of a free node. This represents the displacement of an unknown free node within the node. This represents the displacement of the known internal boundary nodes. Indicates direct external load; This represents the coupling quality matrix between free nodes and boundary nodes. This represents the acceleration vector of a known boundary node. This represents the coupling damping matrix between free nodes and boundary nodes. This represents the velocity vector of a known boundary node.

[0080] The right side of the equation includes the inertial and damping coupling forces generated by the external fluid load and the motion of the known boundary nodes (driven by macroscopic deformation). This dimension-reduced equation will serve as the core equation for the time-domain solution, greatly reducing the amount of unnecessary computation.

[0081] S43. Use a nonlinear iterative algorithm to solve the dimensionality-reduced dynamic equations and update the coordinates of the microscopic nodes.

[0082] For micro time steps Using Newmark- The implicit time integration algorithm transforms the aforementioned dimension-reduced differential equation into an algebraic equation. This is due to the internal force vector... The displacement exhibits a highly nonlinear relationship at each time step. Therefore, the Newton-Raphson iterative algorithm must be introduced.

[0083] Definition of the first The residual force vector (unbalanced force) of the system in the next iteration. for: ; in, Let be the effective external force vector on the right side of the equation.

[0084] Calculate the nonlinear tangent stiffness matrix of a microscopic subsystem The tangent stiffness matrix is ​​derived from the elastic stiffness matrix. and geometric stiffness matrix (stress stiffening matrix) Composed of multiple layers: ; In the formula, This represents the nonlinear internal force vector of the internal free nodes. This indicates the axial tension of a single network cable unit.

[0085] Geometric stiffness matrix Precisely reflects the tension of the network cable The enhanced effect on its resistance to lateral deformation.

[0086] Assemble the effective tangent stiffness matrix And solve for the displacement increment As shown in the following formula: ; ; In the formula, This represents the proportionality factor used to convert mass force into equivalent stiffness. This represents the proportionality factor used to convert damping force into equivalent stiffness.

[0087] Update node displacement Repeat the above iterations until the displacement increment norm is reached. and residual norm All are less than the set convergence tolerance threshold (e.g.) If the solution converges at that time step, then the solution is considered to have converged.

[0088] S44. Calculate the actual engineering strain of the micro-mesh element, extract the instantaneous axial tension of a single mesh by combining the nonlinear constitutive equation, and eliminate the stiffness contribution of the compressed mesh element.

[0089] Once the microscopic time-step solution converges, extract the updated node space coordinate matrix of the full quantum model. .

[0090] For any micro-mesh unit within the sub-model (Connecting network nodes) and The actual spatial length is calculated based on its instantaneous node coordinates. and real engineering strain .

[0091] Calling the polynomial nonlinear constitutive equation for polymer materials defined in S23: Calculate the precise axial tension of each wire at the current moment. .

[0092] At the same time, the program automatically performs "relaxation detection": if a certain network cable unit shows... (i.e., the element is under compression), then its internal forces are immediately set to zero, and the tangent stiffness matrix is ​​assembled in the next time step. At that time, the stiffness contribution of that element is eliminated. This underlying logic perfectly replicates the real physical wrinkling behavior of flexible mesh under non-uniform hydrodynamic forces.

[0093] Finally, the instantaneous axial tension data and node displacement data of each network line are saved to the microscopic results database for S5 to aggregate the multi-scale stress response results under all working conditions and render cloud maps.

[0094] like Figure 7 As shown, S5 is a nonlinear finite element solution for the local micro-network model.

[0095] After completing the macroscopic dynamic solution (S1) and the local microscopic fine mesh submodel solution (S4), the system has acquired massive amounts of structural response data at different time steps and spatial grids. This step aims to transform the multi-scale pure digital results into tensor field distribution cloud maps with intuitive engineering guidance through spatiotemporal synchronous aggregation algorithms and extreme value envelope evaluation. Specifically, it includes the following sub-steps: S51. Set a unified output time series to perform spatiotemporal synchronization and full dataset aggregation of the time history data of macroscopic ropes and microscopic nets.

[0096] Because macroeconomic models use macroeconomic time steps The micro-sub-model uses a sub-cycle time step. Data alignment needs to be performed on a unified timeline.

[0097] Set a unified output time series Using the Lagrange time-domain interpolation algorithm, the macroscopic wire rope nodal displacement field at each output time point is extracted. Macroscopic axial tension of the wire rope and the displacement field of the microscopic sub-model network axial tension of a single micro-wire .

[0098] In the global coordinate system, the local coordinates of the microscopic sub-models are precisely superimposed onto the macroscopic deformation skeleton to construct a full multi-scale response dataset. This enables absolute synchronization of macro and micro data in both physical space and time dimensions.

[0099] in, It represents the global spatial displacement of each node on the macroscopic framework. This represents the axial tension of a macroscopic wire element. This represents the instantaneous displacement of thousands of nodes in the micro-mesh model. This indicates the axial tension within each fine mesh unit.

[0100] S52. Under the set full-condition environmental load matrix, extract the tension extreme values ​​of macroscopic wire rope elements and microscopic wire mesh elements, and calculate the minimum safety factor for the full-condition environment.

[0101] A full-condition environmental load parameter matrix is ​​defined for the actual operating environment of deep-sea aquaculture cages. (This includes combinations of wave height, wave period, current velocity, and wind speed with different return periods).

[0102] Iterate through all the set working conditions. Call S1 to S4 to perform batch calculations.

[0103] For any entity unit ( (These can be macroscopic wire elements or microscopic mesh elements), and the tension extrema are sought in the entire time-history response under the full set of working conditions. : ; In the formula, Indicates operating conditions. This represents the full-condition environmental load parameter matrix. Representing the unit Specific working conditions Below, at a specific time The instantaneous axial tension it bears.

[0104] Furthermore, an allowable tensile strength threshold for mesh materials is introduced. Calculate the minimum safety factor for the unit under all operating conditions. : ; This extreme value envelope analysis extracts the limit stress boundary of the cage under the worst working conditions, providing envelope surface data for tear-resistant design.

[0105] S53. To transform the abstract tension scalar into a visual contour plot, a scalar field color mapping algorithm is introduced. A lower limit value for the tension displayed in the contour plot is set. With upper limit For any unit Instantaneous tension or extreme tension Calculate its normalized stress index : ; Using a multi-segment linear color interpolation function (such as the classic Jet or Rainbow color spectrum), the normalized stress index is... Mapped to the three channels of the RGB color space For example, the four-segment mapping function for red-yellow-green-blue is: ; ; ; Using the mapping function described above, low-stress areas are presented in a cool color (blue), while high-stress danger areas are presented in a warm color (red).

[0106] S54. Based on multi-level detail rendering technology in computer graphics, generate and output multi-scale stress response cloud maps. In the global view, hide the micro-mesh, and only render the deformation posture and tension color distribution of the main frame of the cage and the macro-level ropes, so that engineers can grasp the overall motion state of the cage and the load transfer direction of the main load-bearing frame. In the local magnified view, activate the rendering layer of the micro-fine mesh sub-model, based on the sub-S53 generated. A color matrix accurately depicts the axial stress color of each tiny mesh line within a local mesh area. Ultimately, the system outputs a dynamic deformation cloud map video including a time dimension, as well as a static cloud map report showing the extreme value envelope under all operating conditions. The microscopic mesh lines highlighted in red in the charts represent the "stress hotspots" in the entire system that are highly susceptible to fatigue, wear, or initial tearing, providing intuitive and precise spatial positioning for the reinforcement design and damage warning of the mesh.

[0107] The aforementioned system for multi-scale numerical calculation of stress on deep-sea cage mesh structures includes: Macroscopic dynamics solution module: used to extract the main load-bearing skeleton of deep-sea cages, and establish a macroscopic coupled dynamic response analysis model of deep-sea cages containing only the rope system through the hydrodynamic equivalent compensation algorithm, and solve and output the time history displacement and tension data of macroscopic rope nodes.

[0108] Microscopic Sub-model Construction Module: Used to establish a microscopic fine mesh finite element sub-model of a deep-sea cage in a local high-risk area, with macroscopic ropes as the spatial boundary and containing the geometric and nonlinear material characteristics of a real microscopic mesh.

[0109] Data mapping nesting module: used for spatial registration and time synchronization between macro and micro models, and to map the displacement of macro framework nodes to the forced boundary conditions of micro sub-models in real time through shape function interpolation.

[0110] Sub-model finite element solution module: Receives the mapped boundary conditions, performs matrix partitioning dimensionality reduction and nonlinear iterative solution on the micro-fine mesh finite element sub-model, and calculates the nodal displacement and axial tension of a single micro-mesh wire.

[0111] Multi-scale cloud map output module: Aggregates macroscopic and microscopic force response data, performs extreme value envelope analysis and color mapping under all working conditions, renders and outputs multi-scale axial force cloud maps and nodal displacement cloud maps.

[0112] This embodiment also includes a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above method.

[0113] This embodiment also includes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above method.

[0114] Therefore, this invention adopts the above-mentioned multi-scale numerical calculation method and system for the stress of deep-sea cage mesh structure. By establishing a nested mechanism of macroscopic rope model and microscopic fine mesh sub-model, and using dynamic data mapping technology, it accurately calculates the local axial force and nodal displacement of the mesh wire under all working conditions, providing a high-precision analysis means for mesh structure optimization, vulnerability assessment and safety early warning.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-scale numerical calculation method for the stress on deep-sea cage mesh structures, characterized in that, Includes the following steps: S1. Extract the main supporting skeleton of the deep-sea cage in the global coordinate system, remove the fine netting entity, and discretize the main supporting skeleton using the continuous finite element method to establish a macroscopic coupled dynamic response analysis model of the deep-sea cage based on the equivalent of the steel rope. S2. For high-risk areas of deep-sea cages, establish a high-fidelity micro-fine net finite element sub-model; S3. By using dynamic link library programs, a cross-scale spatial registration and time synchronization mapping mechanism is established to accurately transform macroscopic large-scale loads into forced boundary conditions of microscopic sub-models, thereby realizing the dynamic mapping and nesting of multi-scale boundary constraints and tension data. S4. Drive the underlying finite element solver to perform nonlinear dynamic integration and stress state update on the micro-fine mesh finite element sub-model, and realize the nonlinear finite element solution of the local micro-fine mesh finite element sub-model. S5. By using the spatiotemporal synchronization aggregation algorithm and extreme value envelope evaluation, the multi-scale stress response results under all working conditions are aggregated to generate and output cloud maps and videos. The main load-bearing skeleton in S1 includes the main frame of the cage, the mooring system, and the macro rope system; S1 includes: S11. Discretize the main frame of the cage using three-dimensional spatial beam elements, and discretize the mooring system cables and macro rope system using three-dimensional tension-only cable elements. S12. Calculate the initial density of the removed local mesh. As shown in the following formula: ； In the formula, The diameter of the network cable. The mesh side length; Calculate the equivalent hydrodynamic diameter of the macroscopic wire element. As shown in the following formula: ； In the formula, The physical outer diameter of the rope. The length of the rope unit. This represents the corresponding subordinate area in the topological structure; S13. Calculate the equivalent fluid drag force vector on a macroscopic rope per unit length. and equivalent fluid inertial force vector : ； ； In the formula, The density of seawater; and These are the normal and tangential relative velocity vectors, respectively; and This is the vector of acceleration components of water particles; and The acceleration component vector of the rope element; , , , For hydrodynamic coefficients; Integrating the force vector and transforming it to the global coordinate system yields the equivalent fluid load vector. ; S14. Establish the overall control equations for macroscopic multibody coupled time-domain dynamics, as shown in the following equation: ； In the formula, , , These are the global mass, the added mass, and the damping matrix, respectively. , , These are column vectors for acceleration, velocity, and displacement, respectively. This is the global nonlinear stiffness matrix; For including fluid load The global external load vector; S15. The overall control equations are solved using an implicit integration algorithm combined with the Newton-Raphson iterative method.

2. The multi-scale numerical calculation method for the stress of deep-sea cage mesh structure according to claim 1, characterized in that, S2 includes: S21. Select the local mesh region enclosed by the macroscopic wire rope unit as the microscopic solution domain, and take the geometric center line of the macroscopic wire rope as the spatial geometric boundary of the microscopic mesh sub-model. S22. Reconstruct the network knots and wire entities within the microscopic solution domain and discretize them into three-dimensional tension-only nonlinear cable elements; S23. Introduce nonlinear constitutive equations for polymer materials to characterize their uniaxial stress characteristics under tensile stiffening and compressive relaxation. S24. Extract the flow field information at the location of the micro sub-model and calculate the real local fluid drag force and inertial force acting on each micro mesh unit.

3. The multi-scale numerical calculation method for the stress of deep-sea cage mesh structure according to claim 2, characterized in that, The nonlinear constitutive equation for the polymer material in S23 is specifically as follows: For any single element in the micro-network sub-model Its instantaneous engineering strain is The real-time axial tension inside The calculation formula is shown below: ； In the formula, This represents the initial cross-sectional area of ​​the network cable unit. , , It is the nonlinear elastic stiffness coefficient.

4. The multi-scale numerical calculation method for the stress of deep-sea cage mesh structure according to claim 3, characterized in that, S3 includes: S31, in macroscopic time step At the end, the spatial positions, displacement vectors, and axial tensions of the macroscopic rope nodes in the target mesh region of the microscopic sub-model of the package are extracted in real time. S32. For any microscopic boundary node Determine the macroscopic unit to which it belongs and define its dimensionless local coordinates. As shown in the following formula: ； In the formula, This represents the global spatial coordinate vector under the initial stress-free state. and These are the two endpoints of a macroscopic wire rope unit; S33, Using a one-dimensional shape function matrix Calculate the mapped displacement vector inherited by the microscopic boundary nodes. As shown in the following formula: ； In the formula, Represents the dynamic displacement field. Indicates the macroscopic time step. The next macroscopic time step maps the displacement vector. Indicates in Micro-nodes calculated through spatial interpolation at every moment The known displacement, Indicates in Micro-nodes calculated through spatial interpolation at every moment The known displacement, This indicates the time step for solving the microscopic model; The mapped displacement vector is loaded as a Dirichlet boundary condition into the micro-fine mesh finite element sub-model.

5. The multi-scale numerical calculation method for the stress of deep-sea cage mesh structure according to claim 4, characterized in that, S4 includes: S41. Assemble the multi-degree-of-freedom nonlinear dynamic control equations of the micro-net-soil model, as shown in the following equation: ； In the formula, This represents the global quality matrix of the microscopic sub-model. Represents the global damping matrix of the microscopic sub-model. This represents the nonlinear internal force vector of a microscopic system, which is obtained by transforming the axial tension of each microscopic nonlinear cable element to the global coordinate system and assembling nodal forces. This represents the true local fluid load vector directly acting on the microstructure lines, calculated in S24. , , These are the global displacement, velocity, and acceleration vectors for all nodes at the microscopic level, respectively. S42. Rearrange the system's displacement vector as follows: The index of the internal free node is The known node indices of the boundary are The dimensionality-reduced dynamic equations containing only the responses of unknown free nodes are extracted, as shown in the following equation: ； In the formula, This represents the displacement vector of the internal free nodes. This represents the displacement vector of the boundary node. This represents the mass matrix of the internal unknown free nodes themselves. Indicates the internal unknown free node in The acceleration vector at time t. This represents the damping matrix of the internal unknown free nodes themselves. Indicates the internal unknown free node in The unknown velocity vector at time t, This represents the nonlinear elastic internal force vector of a free node. This represents the displacement of an unknown free node within the node. This represents the displacement of the known internal boundary nodes. Indicates direct external load; This represents the coupling quality matrix between free nodes and boundary nodes. This represents the acceleration vector of a known boundary node. This represents the coupling damping matrix between free nodes and boundary nodes. Represents the velocity vector of a known boundary node; S43, at each time step The Newton-Raphson iterative algorithm is introduced to calculate the elastic stiffness matrix. and geometric stiffness matrix Nonlinear tangent stiffness matrix formed by superposition As shown in the following formula: ； In the formula, This represents the nonlinear internal force vector of the internal free nodes. This indicates the axial tension of a single network cable unit; Solve for the displacement increment and update the nodal displacements until the residual force converges; S44. Perform relaxation detection. If a network cable unit shows a relaxation test... Then set its internal force to zero, and assemble the tangent stiffness matrix in the next time step. When this happens, the stiffness contribution of that element is removed.

6. The multi-scale numerical calculation method for the stress of a deep-sea cage mesh structure according to claim 5, characterized in that, S5 includes: S51. Set a unified output time series to perform spatiotemporal synchronization and full dataset aggregation of the time history data of macroscopic ropes and microscopic nets. S52. Under the set full-condition environmental load matrix, extract the tension extreme values ​​of macroscopic wire rope elements and microscopic wire mesh elements, and calculate the minimum safety factor for the full-condition load. S53. Based on scalar field color mapping algorithm and multi-detail level rendering technology, generate and output multi-scale force response cloud map and video containing macroscopic overall force of the rope and microscopic local force of a single wire. Specifically, the scalar field color mapping algorithm involves setting a lower limit value for tension. With upper limit Calculate the normalized stress index It is then mapped to three channels of the RGB color space using a multi-segment linear color interpolation function.

7. The multi-scale numerical calculation method for the stress of a deep-sea cage mesh structure according to claim 6, characterized in that, S52 includes: Finding physical units under the full set of operating conditions Tension extremes in time-history response As shown in the following formula: ； In the formula, Indicates operating conditions. This represents the full-condition environmental load parameter matrix. Representing the unit Specific working conditions Below, at a specific time The instantaneous axial tension it bears; Calculate the minimum safety factor using tension extreme values. As shown in the following formula: ； In the formula, This represents the allowable breaking tensile strength threshold for the mesh material.

8. A system applied to the multi-scale numerical calculation method for the stress of a deep-sea cage mesh structure as described in claim 7, characterized in that, include: Macroscopic dynamics solution module: used to extract the main load-bearing skeleton of deep-sea cages, establish a macroscopic coupled dynamic response analysis model of deep-sea cages containing only the rope system through the hydrodynamic equivalent compensation algorithm, and solve and output the time history displacement and tension data of macroscopic rope nodes; Microscopic Sub-model Construction Module: Used to establish a microscopic fine mesh finite element sub-model of a deep-sea cage in a local high-risk area, with macroscopic ropes as the spatial boundary and containing real microscopic mesh geometry and nonlinear material characteristics; Data mapping nesting module: used for spatial registration and time synchronization between macro and micro models, and to map the displacement of macro framework nodes to the forced boundary conditions of micro sub-models in real time through shape function interpolation; Sub-model finite element solution module: Receives the mapped boundary conditions, performs matrix partitioning dimensionality reduction and nonlinear iterative solution on the micro-fine mesh finite element sub-model, and calculates the nodal displacement and axial tension of a single micro-mesh wire; Multi-scale cloud map output module: Aggregates macroscopic and microscopic force response data, performs extreme value envelope analysis and color mapping under all working conditions, renders and outputs multi-scale axial force cloud maps and nodal displacement cloud maps.

Images