Sealing cable anti-bending stiffness analysis method based on digital twinning

Abstract

The application discloses a sealed cable anti-bending stiffness analysis method based on digital twinning, relates to the technical field of structural mechanics numerical simulation, acquires geometric structure parameters and material properties of a sealed cable to be measured, and constructs a three-dimensional finite element analysis model; boundary conditions of two ends of the three-dimensional finite element analysis model are set, and preset transverse external loads are applied to the three-dimensional finite element analysis model; the three-dimensional finite element analysis model to which the transverse external loads are applied is calculated through a display dynamics calculation method, and deformation deflections of each section after the loads are applied are extracted; the sealed cable is equivalent to an equal-section homogeneous beam, equivalent anti-bending stiffness under current external loads is obtained through back calculation based on beam bending theory and by using the extracted deformation deflections, and resource cost input is reduced, and safety hazards caused by single constant stiffness are avoided.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology in structural mechanics, and in particular to a method for analyzing the bending stiffness of a sealed cable based on digital twins. Background Technology

[0002] As a key load-bearing component in the engineering field, cables are widely used in aerospace, machinery, coal mining, construction, bridges and many other fields, and are an indispensable core load-bearing component in modern infrastructure construction.

[0003] Traditional cable systems face numerous limitations in engineering applications. Their loose structure leads to poor sealing, allowing external moisture and dust to easily penetrate the cable body, causing steel wire corrosion and accelerating failure. Against this backdrop, a new type of sealed cable has emerged. Its outer layer consists of tightly interlocked shaped steel wires forming a fully enclosed structure. It boasts advantages such as high load-bearing capacity, wear resistance, corrosion resistance, ease of inspection and maintenance, and resistance to compression, and has already been applied in projects such as aerial cableways and highway suspension bridges.

[0004] Bending stiffness is a key parameter determining the bending deformation and stress distribution of wire ropes when wound around pulleys, turning, and bearing lateral loads. Especially in wind-resistant and seismic design, bending stiffness (EI), as a core mechanical parameter, directly determines the lateral bending deformation amplitude, dynamic response characteristics, and resonance risk of the suspender under wind loads and seismic actions. Existing engineering applications have shown that sealed cables have superior wind, rain, and vibration resistance compared to traditional cables, and the appropriate value of their bending stiffness is crucial to ensuring the structural stability against wind and earthquakes.

[0005] Currently, there are many methods for calculating the bending stiffness of different types of wire ropes. For parallel cables, the calculation of their bending stiffness is mostly based on the superposition of the bending stiffness of individual wires. This method calculates the bending stiffness of the wire rope by simply superimposing the stiffness of individual wires, ignoring friction and slippage between wires. Although this method is simple, it has limitations and is only applicable to loosely arranged parallel wire ropes with a single stress form. In addition, some scholars have simplified parallel wire ropes into equal-width friction-type stacked beams for research. For ordinary stranded wire ropes, although there are corresponding theoretical models and empirical formulas for their bending stiffness, their core is also based on a series of simplification assumptions. For example, traditional empirical formulas are often based on the assumption of no friction or simple friction, or the bending stiffness of the wire rope is obtained through a combination of experiments and theory, but this significantly increases the input of resources and costs.

[0006] Compared to relatively simple parallel wire ropes and ordinary wire ropes, the novel sealing cable exhibits extremely complex mechanical behavior due to its intricate geometry and the presence of irregularly shaped wires, making the calculation of its bending stiffness particularly difficult. Existing research largely considers slings composed of circular cross-section wires; theoretical and experimental results for calculating the bending stiffness of slings composed of irregularly shaped wires are severely lacking. Therefore, the bending stiffness calculation methods used for parallel and ordinary wire ropes cannot be simply applied to the novel sealing cable.

[0007] It is evident that there is an urgent need to develop a method for calculating the bending stiffness of novel sealing cables. This paper analyzes the bending deformation characteristics of sealing steel wire ropes and, based on finite element analysis and theoretical analysis, proposes a conceptually clear and easily applied method for calculating bending stiffness through reasonable mechanical simplification. This method aims to provide an efficient and reliable tool for related engineering design and safety assessment, and has theoretical significance and practical value for improving the application technology of sealing cables and promoting their application in wind-resistant and earthquake-resistant engineering. Summary of the Invention

[0008] The technical problem solved by this invention is that existing technologies are difficult to calculate the bending stiffness of novel sealing cables; they only consider slings made of circular cross-section steel wires and lack precise calculations for sealing cables made of irregularly shaped steel wires; and they ignore the influence of load changes in actual engineering such as wind resistance and earthquake resistance on bending stiffness.

[0009] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A method for analyzing the bending stiffness of a sealed cable based on digital twins includes the following steps: Step S1: Obtain the geometric structural parameters and material properties of the sealing cable to be tested, and construct a three-dimensional finite element analysis model; Step S2: Set the boundary conditions at both ends of the three-dimensional finite element analysis model, and apply the preset lateral external load to the three-dimensional finite element analysis model; Step S3: The three-dimensional finite element analysis model under lateral external load is calculated using the explicit dynamic calculation method to extract the deformation deflection of each section after the load is applied. Step S4: The sealing cable is equivalent to a homogeneous beam with a uniform cross-section. Based on the beam bending theory, the extracted deformation deflection is used for back calculation to obtain the equivalent bending stiffness under the current external load.

[0010] Preferably, step S1 includes the following sub-steps: Step S11: Obtain the geometric structure parameters of the sealing cable to be tested. The geometric structure parameters include the total number of layers of the wire rope, the cross-sectional type of each layer of wire, the diameter of each layer of wire, the converted diameter, the distribution radius, the number of wires, the direction of twist, and the twist pitch. Step S12: Obtain the material properties of each layer of steel wire, including the density, elastic modulus, Poisson's ratio, yield strength and coefficient of friction of the high-strength galvanized aluminum rare earth alloy steel wire material. Step S13: Based on the geometric structural parameters, a three-dimensional solid model of the suspension cable with a length of l is created in the three-dimensional modeling software. The processing logic of the three-dimensional solid model of the suspension cable is as follows: Based on the cross-sectional type and diameter of each layer of steel wires, a two-dimensional cross-sectional profile of a single steel wire is drawn on a preset distribution radius of each layer. The two-dimensional cross-sectional profile includes a circular cross-sectional profile in the inner layer and a Z-shaped cross-sectional profile in the outer layer. Through a sweeping process, the two-dimensional cross-sectional profile is swept along the corresponding three-dimensional spiral trajectory line to obtain a three-dimensional spiral solid model of a single steel wire. Based on the preset number of steel wires in each layer, the three-dimensional spiral solid model of the single steel wire is processed into a ring array to obtain a set of steel wire solids in each layer. The inner and outer steel wire solid sets are then nested and combined to obtain a three-dimensional solid model of the sling. Step S14: Perform finite element analysis on the three-dimensional solid model of the sling and obtain a three-dimensional finite element analysis model through reliability verification.

[0011] Preferably, the processing logic of the three-dimensional finite element analysis model, obtained through reliability verification, is as follows: One end of the three-dimensional finite element analysis model is subjected to full-degree-of-freedom constraints, and axial tensile displacement is applied to the other end. Axial tensile simulation is performed using quasi-static simulation to obtain the simulated breaking force of the sealing cable during the simulated tensile process. The relative deviation is calculated by comparing the nominal breaking force and the simulated breaking force of the sealing cable. The expression for the relative deviation is as follows: ; in, This is a relative deviation. Nominal breaking force, To simulate breaking force; A preset safety error threshold is used to compare the relative deviation with the preset safety error threshold. When the relative deviation is less than the preset safety error threshold, the three-dimensional finite element analysis model is determined to have passed the accuracy verification, and the three-dimensional finite element analysis model that has passed the accuracy verification is used as the input data for step S2.

[0012] Preferably, step S2 includes the following sub-steps: Step S21: Set boundary conditions at both ends of the three-dimensional finite element analysis model. The logic for setting the boundary conditions at both ends is as follows: The left and right end faces of the three-dimensional finite element analysis model along the axial direction are selected. All nodes on the left and right end faces are subjected to full degree of freedom constraints. The translational degrees of freedom of all nodes on the left and right end faces along the X, Y, and Z axes are restricted, as are the rotational degrees of freedom of all nodes on the left and right end faces about the X, Y, and Z axes. Step S22: Set the loading type and load size of the lateral external load. The loading type includes uniformly distributed load case and concentrated load case. Step S23: Apply a preset lateral external load to the three-dimensional finite element analysis model. The processing logic for applying the load is as follows: The load application direction is defined as a transverse direction perpendicular to the axis of the three-dimensional finite element analysis model; When the loading type is uniformly distributed load, the preset uniformly distributed load is extracted as the lateral external load, and the uniformly distributed load is uniformly distributed and applied within the length l of the axial direction of the three-dimensional finite element analysis model. When the loading type is concentrated load condition, the preset concentrated load is extracted as the lateral external load and applied to the mid-span position of the three-dimensional finite element analysis model in the axial direction. The mid-span position is the position where the distance from the left end face section and the right end face section is half the length l.

[0013] Preferably, step S3 includes the following sub-steps: Step S31: Obtain the minimum sample feature length and the elastic wave velocity of the material properties in the three-dimensional finite element analysis model. Use the minimum sample feature length and the elastic wave velocity to calculate the stable time step through explicit dynamics. The expression for calculating the stable time step is: ; in, To stabilize the time step, The minimum unit feature length, The elastic wave velocity of the material; Step S32: Perform mass scaling convergence analysis on the three-dimensional finite element analysis model under the applied transverse external load to obtain the target mass scaling factor. Step S33: The three-dimensional finite element analysis model is subjected to equivalent density magnification using the target mass scaling factor to obtain the enlarged three-dimensional finite element analysis model. Step S34: The central difference method is used to perform numerical solution and iterative calculation on the enlarged three-dimensional finite element analysis model, and the target cross-sections at several coordinate positions are intercepted along the axial direction to extract the deformation deflection of the target cross-sections at several coordinate positions under the action of transverse external load.

[0014] Preferably, the logic of the quality scaling convergence analysis process is as follows: Multiple sets of test mass scaling factors are input into the three-dimensional finite element analysis model for pre-calculation processing, and the maximum deformation deflection corresponding to each set of test mass scaling factors is extracted. Set the maximum deformation deflection corresponding to the test mass scaling factor of 1 as the reference maximum deflection, and calculate the relative deflection deviation between the maximum deformation deflection corresponding to the other test mass scaling factors and the reference maximum deflection. The relative deviation of deflection is compared with a preset accuracy threshold, and the test quality scaling factor with a relative deviation of deflection less than the preset accuracy threshold is selected as the target quality scaling factor.

[0015] Preferably, the central difference method is used to perform numerical solution iterative calculation on the enlarged three-dimensional finite element analysis model. The processing logic is as follows: Obtain the preset total physical analysis time, and use the increased stable time step as the time increment step of the iteration process; For the enlarged three-dimensional finite element analysis model, the sets of external nodal forces and internal nodal forces acting on all nodes are extracted. The sets of external nodal forces are subtracted from the sets of internal nodal forces to obtain the sets of remaining nodal forces for all nodes. Extract the set of all nodal masses corresponding to the magnified equivalent material density, calculate the ratio of the remaining nodal force set to the set of all nodal masses, and obtain the set of nodal accelerations of all nodes in the current time increment step; Based on the set of node accelerations and the increased stable time step, the set of node velocities corresponding to all nodes in half a time increment step is updated, and time integration is performed to obtain the set of node displacements corresponding to all nodes in the next time increment step. The update operations of the nodal acceleration set, nodal velocity set, and nodal displacement set are repeatedly repeated until the total time of all time increment steps reaches the total physical analysis time, thus completing the numerical solution iterative calculation; Several target sections at coordinate positions are intercepted along the axial direction of the three-dimensional finite element analysis model. The final displacement values ​​of the nodes on the target sections along the direction of the applied transverse external load are extracted, and the final displacement values ​​are used as the deformation deflection under the action of the transverse external load.

[0016] Preferably, step S4 specifically includes: Step S41: The sealing cable is equivalent to a homogeneous beam with uniform cross-section fixed at both ends. The centroid of the left end section is taken as the coordinate far point. The direction along the axial direction of the homogeneous beam with uniform cross-section and from the left end section to the right end section is set as the positive direction of the y-axis. The direction of the transverse external load is set as the z-axis. In the left end section, the direction perpendicular to the y-axis and z-axis is set as the x-axis. A three-dimensional rectangular coordinate system is established. The coordinate values ​​of the target section along the y-axis in the three-dimensional rectangular coordinate system are extracted as the target coordinate variables. The average displacement of all wire nodes in the target section along the z-axis is extracted as the deformation deflection. Step S42: When the loading type is uniformly distributed load, based on the bending differential equation of the beam with fixed ends, the deformation deflection along the z-axis of the target section at several coordinate positions is used for back calculation to obtain several equivalent bending stiffnesses corresponding to the target sections at several coordinate positions. The calculation expressions for the several equivalent bending stiffnesses are as follows: ; in, Let be the equivalent bending stiffness corresponding to the i-th target section, q be the magnitude of the uniformly distributed load under the uniformly distributed load condition, and l be the length. Let i be the coordinate variable corresponding to the i-th target section. , Let be the absolute value of the deformation deflection corresponding to the extracted i-th target section.

[0017] Preferably, step S4 further includes: Extract the equivalent bending stiffness corresponding to the target section at several coordinate positions, and apply this to all equivalent bending stiffnesses. The mean value is calculated to obtain the mean value of the equivalent bending stiffness, and the mean value of the equivalent bending stiffness is used as the equivalent bending stiffness under the current external load. When the loading type is concentrated load condition, based on the bending differential equation of the beam fixed at both ends under concentrated load at mid-span, the equivalent bending stiffness under the current external load is obtained by back-calculation using the deformation deflection at the mid-span location. The calculation expression for the equivalent bending stiffness under the current external load is as follows: ; in, This is the equivalent bending stiffness under the current external load. The value of l represents the magnitude of the concentrated load under the concentrated load condition, and l represents the length. This represents the absolute value of the deformation deflection at the mid-span location. Establish a one-to-one correspondence between the equivalent bending stiffness under the current external load and the magnitude of the currently applied lateral external load, wherein the magnitude of the lateral external load includes the magnitude of the uniformly distributed load and the magnitude of the concentrated load.

[0018] Preferably, the process of treating the sealing cable as an equivalent homogeneous beam with uniform cross-section fixed at both ends includes: The macroscopic deformation state of the sealing cable under the action of transverse external load is extracted. The discontinuous contact state characteristics and frictional slip characteristics between the multiple layers of steel wires inside the sealing cable are ignored. The macroscopic bending stiffness of the sealing cable along the axial direction is set to a constant stiffness value under the current transverse external load. The sealing cable is mapped to a geometric section that is consistent along the axial direction to obtain a homogeneous beam with uniform cross-section. The beneficial effects of this invention are as follows: By rationally matching the twisting directions of the steel wires in each layer of the sealing cable, the twisting stress is kept in a balanced state. By equating the complex sealing cable with a homogeneous beam of uniform cross-section, and based on beam bending theory and finite element simulation, the equivalent bending stiffness is obtained by deflection back calculation. For the first time, a bending stiffness calculation system applicable to a new type of sealing cable composed of irregular steel wires has been established, filling the technical gap in this field. The equivalent homogeneous beam and deflection back calculation method proposed in this invention simplify the complex multi-layer steel wire rope mechanics problem into a classic beam bending problem. Based on finite element numerical simulation, through explicit dynamic calculation and mass scaling convergence analysis, the computational efficiency is significantly improved while ensuring computational accuracy. Compared with traditional solid test methods, it greatly reduces resource cost input and shortens the design cycle. Through comparative calculations of multiple loads of different magnitudes, it was found that the equivalent bending stiffness of the new sealing cable is not a single constant value, but has a clear correlation with the applied load. The larger the load, the greater the equivalent bending stiffness. This provides an important theoretical basis for the structural design under dynamic loads such as wind and earthquake resistance, and avoids the safety hazards caused by using a single constant stiffness. Furthermore, the method proposed in this invention is not only applicable to uniformly distributed load and concentrated load conditions, but can also be extended to the calculation of bending stiffness under concentrated load at any location. At the same time, this method can be used to study the influence of structural parameters such as twist pitch, number of layers, and twist direction on bending stiffness, providing an important technical path for subsequent research. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the steps of a method for analyzing the bending stiffness of a sealing cable based on digital twins, as provided in one embodiment of the present invention; Figure 2 This is a schematic diagram of the cross-section of the new sealing cable; Figure 3 A schematic diagram of the cross-section of a Z-shaped steel wire; Figure 4 A finite element analysis model for a novel sealing cable; Figure 5 Boundary conditions and load cases; Figure 6 This is a schematic diagram of a beam with fixed supports at both ends; Figure 7 This is a deformable cloud map (UL-1); Figure 8 A comparison diagram of deflection-position curves and uniformly distributed load; Figure 9 A comparison diagram of equivalent flexural stiffness under different types of loads; Figure 10 The diagram shows a comparison of deflection-position curves and concentrated loads. Detailed Implementation

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0021] Example, refer to Figures 1-10 This paper presents a method for analyzing the bending stiffness of a sealed cable based on digital twins, comprising the following steps: Step S1: Obtain the geometric structural parameters and material properties of the sealing cable to be tested, and construct a three-dimensional finite element analysis model; Step S2: Set the boundary conditions at both ends of the three-dimensional finite element analysis model, and apply the preset lateral external load to the three-dimensional finite element analysis model; Step S3: The three-dimensional finite element analysis model under lateral external load is calculated using the explicit dynamic calculation method to extract the deformation deflection of each section after the load is applied. Step S4: The sealing cable is equivalent to a homogeneous beam with a uniform cross-section. Based on the beam bending theory, the extracted deformation deflection is used for back calculation to obtain the equivalent bending stiffness under the current external load.

[0022] This embodiment is based on a bridge reconstruction project. First, the geometric structural parameters and material properties of the sealing cable to be tested are obtained. Then, based on the geometric structural parameters and material properties, a three-dimensional finite element analysis model is constructed in finite element software, such as... Figure 4 As shown, then, boundary conditions with fixed supports at both ends are set for the constructed three-dimensional finite element analysis model, and preset lateral external loads, such as uniformly distributed loads or concentrated loads, are applied to the model. Figure 5As shown; next, the model after the load is applied is simulated using explicit dynamic calculation methods, and the deformation deflection values ​​of the sling at different cross-sections are extracted from the calculation results; the complex sealing cable is equivalent to a homogeneous beam with a uniform cross-section, and based on the classical beam bending theory, the equivalent bending stiffness of the sling under the current external load is calculated using the extracted deformation deflection values. Through the reasonable matching of the twist directions of the steel wires in each layer of the sealing cable, the twisting stress is in a balanced state and has extremely strong anti-rotation properties. Secondly, the surface of the designed sealing cable is tightly twisted, eliminating the need for a PE sheath, thus avoiding the aging problem of the PE sheath. At the same time, there is no need to consider fire prevention issues. In the casting part of the sealing cable head, the irregular steel wire surface... The sealing cable has a higher surface area than the parallel wire bundle, which improves the resistance to pull-out at the connection point. The elastic modulus of the sealing cable is between that of ordinary round strand slings and parallel wire bundle slings. It can prevent bridge deformation damage caused by the relatively large elastic elongation of ordinary round strand slings, and can also reduce the hard damage caused by the excessive elastic modulus and insufficient elastic elongation of parallel wire bundle slings. The sealing cable has natural spiral grooves on its surface, which improves wind resistance, reduces cable vibration, and enhances the service life of the sealing cable. In addition, the sealing cable of this invention does not require a PE sheath and has a smaller diameter than the parallel wire bundle, which has strong wind and corrosion resistance. The process design of adding drainage grooves to the sealing cable anchor solves the corrosion problem caused by rainwater accumulation inside the anchor.

[0023] Step S1 includes the following sub-steps: Step S11: Obtain the geometric structure parameters of the sealing cable to be tested. The geometric structure parameters include the total number of layers of the wire rope, the cross-sectional type of each layer of wire, the diameter of each layer of wire, the converted diameter, the distribution radius, the number of wires, the direction of twist, and the twist pitch. Step S12: Obtain the material properties of each layer of steel wire, including the density, elastic modulus, Poisson's ratio, yield strength and coefficient of friction of the high-strength galvanized aluminum rare earth alloy steel wire material. Step S13: Based on the geometric structural parameters, create a 3D solid model of the suspension cable with a length of l in the 3D modeling software. The processing logic for the 3D solid model of the suspension cable is as follows: Based on the cross-sectional type and diameter of each layer of steel wire, a two-dimensional cross-sectional profile of a single steel wire is drawn on the preset distribution radius of each layer. The two-dimensional cross-sectional profile includes a circular cross-sectional profile in the inner layer and a Z-shaped cross-sectional profile in the outer layer, as referenced. Figure 2 and Figure 3 By using a sweeping process, the two-dimensional cross-sectional contour is swept along the corresponding three-dimensional spatial spiral trajectory line to obtain a three-dimensional spiral solid model of a single steel wire. Based on the preset number of steel wires in each layer, the three-dimensional spiral solid model of the single steel wire is processed into a ring array to obtain a set of steel wire solids in each layer. The inner and outer steel wire solid sets are then nested and combined to obtain a three-dimensional solid model of the sling. Step S14: Perform finite element analysis on the three-dimensional solid model of the sling and obtain a three-dimensional finite element analysis model through reliability verification.

[0024] To obtain the geometric structural parameters of the sealing cable under test, in this embodiment, the new sealing cable is designed with a seven-layer sealing structure. Its cross-sectional structure includes four inner layers of circular steel wires and three outer layers of Z-shaped steel wires, covering eight different diameter steel wires (named Y1, Y2, Y3, Y3_1, Y4, Z1, Z2, and Z3 from the inside out). Taking the new sealing cable used in the reconstruction project of Baiguotuo Bridge as an example, the main design parameters of the steel wire rope are shown in Table 1: Table 1 Main design parameters: ; Obtain material properties: the steel wire is a high-strength galvanized aluminum rare earth alloy; parameters such as density, elastic modulus, Poisson's ratio, yield strength, and coefficient of friction are provided by the material supplier. Establish a three-dimensional solid model of the sling, such as... Figure 2 and Figure 3 As shown, based on the parameters in Table 1, two-dimensional cross-sectional outlines of circular and Z-shaped steel wires are drawn on a preset distribution radius. In the 3D modeling software, these two-dimensional cross-sectional outlines are swept along a preset spiral trajectory line to generate a 3D spiral solid model of a single steel wire. Then, based on the number of steel wires in each layer, the single steel wire models are arranged in a circular array to obtain the steel wire solid sets for each layer. Finally, the inner layer of circular steel wire sets and the outer layer of Z-shaped steel wire sets are nested and combined to complete the establishment of a 1m long 3D solid model of the suspension cable. Figure 4 As shown, the established three-dimensional solid model is meshed using finite element methods, and through subsequent reliability verification, a three-dimensional finite element analysis model that can be used for simulation analysis is obtained. The Z-shaped steel wires of the sealing cable are circumferentially interlocked, and the Z-shaped steel wires of adjacent layers and the same layer are in a "surface contact" state, forming a closed circle. The contact stress between the steel wires is small, the compressive strength is strong, and it can also prevent rainwater and other debris from entering the cable body and causing corrosion.

[0025] Through reliability verification, the processing logic of the three-dimensional finite element analysis model is obtained as follows: One end of the three-dimensional finite element analysis model is subjected to full-degree-of-freedom constraints, and axial tensile displacement is applied to the other end. Axial tensile simulation is performed using quasi-static simulation to obtain the simulated breaking force of the sealing cable during the simulated tensile process. The relative deviation is calculated by comparing the nominal breaking force and the simulated breaking force of the sealing cable. The expression for the relative deviation is as follows: ; in, This is a relative deviation. Nominal breaking force, To simulate breaking force; A preset safety error threshold is used to compare the relative deviation with the preset safety error threshold. When the relative deviation is less than the preset safety error threshold, the three-dimensional finite element analysis model is determined to have passed the accuracy verification, and the three-dimensional finite element analysis model that has passed the accuracy verification is used as the input data for step S2.

[0026] This embodiment provides a detailed explanation of the reliability verification in step S14. First, one end of the constructed three-dimensional finite element analysis model of the sling is constrained with full degrees of freedom (fixed support). Then, axial tensile displacement is applied to the other end of the model, and quasi-static tensile simulation is performed to calculate the simulated breaking force of the model. The nominal breaking strength is 3861 kN. Obtain the nominal breaking strength of this type of wire rope from the manufacturer. The value is 3935 kN. According to the relative deviation calculation expression, the relative deviation is calculated to be 1.88%, as shown in Table 2. Table 2 Comparison of Breaking Force: ; The preset safety error threshold is 5%. Since the calculated relative deviation of 1.88% is less than 5%, the three-dimensional finite element analysis model is determined to have passed the accuracy verification and can be used for subsequent lateral load simulation analysis.

[0027] Step S2 includes the following sub-steps: Step S21: Set boundary conditions at both ends of the three-dimensional finite element analysis model. The logic for setting the boundary conditions at both ends is as follows: The left and right end faces of the three-dimensional finite element analysis model along the axial direction are selected. All nodes on the left and right end faces are subjected to full degree of freedom constraints. The translational degrees of freedom of all nodes on the left and right end faces along the X, Y, and Z axes are restricted, and the rotational degrees of freedom of all nodes on the left and right end faces about the X, Y, and Z axes are also restricted. Step S22: Set the loading type and load size of the lateral external load. The loading type includes uniformly distributed load case and concentrated load case. Step S23: Apply a preset lateral external load to the three-dimensional finite element analysis model. The processing logic for applying the load is as follows: The load application direction is defined as the transverse direction perpendicular to the axis of the three-dimensional finite element analysis model; When the loading type is uniformly distributed load, the preset uniformly distributed load is extracted as the lateral external load, and the uniformly distributed load is applied uniformly within the length l of the axial direction of the three-dimensional finite element analysis model. When the loading type is concentrated load condition, the preset concentrated load is extracted as the lateral external load and applied to the mid-span position of the three-dimensional finite element analysis model in the axial direction. The mid-span position is the position where the distance from the left end face section and the right end face section is half the length l.

[0028] This embodiment specifies step S2 in detail. First, boundary conditions are set. The left and right end faces of the 1m long suspension cable finite element model are selected, and all nodes on these two end faces are subject to full degree of freedom constraints, that is, their translation and rotation in the X, Y, and Z directions are restricted, simulating the fixed boundary conditions in engineering, such as... Figure 5 As shown, next, the load type and magnitude are set. In this embodiment, two load types are set: uniformly distributed load parameters and concentrated load parameters, as shown in Tables 3 and 4: Table 3. Uniformly distributed load parameters: ; Table 4. Concentrated load parameters: ; Finally, define the load direction as perpendicular to the cable axis (lateral). For uniformly distributed load conditions, apply a preset uniformly distributed load (e.g., 100 kN / m) evenly across the entire length (1m) of the cable model; for concentrated load conditions, apply a preset concentrated load (e.g., 50 kN) at the mid-span of the cable model, i.e., at a distance of 0.5m from both the left and right end faces. Figure 5 As shown.

[0029] Step S3 includes the following sub-steps: Step S31: Obtain the minimum sample feature length and the elastic wave velocity of the material properties in the three-dimensional finite element analysis model. Use the minimum sample feature length and the elastic wave velocity to calculate the stable time step through explicit dynamics. The expression for calculating the stable time step is: ; in, To stabilize the time step, The minimum unit feature length, The elastic wave velocity of the material; Step S32: Perform mass scaling convergence analysis on the three-dimensional finite element analysis model with applied transverse external load to obtain the target mass scaling factor. Step S33: The three-dimensional finite element analysis model is subjected to equivalent density magnification using the target mass scaling factor to obtain the enlarged three-dimensional finite element analysis model. Step S34: The central difference method is used to perform numerical solution and iterative calculation on the enlarged three-dimensional finite element analysis model, and the target cross-sections at several coordinate positions are intercepted along the axial direction to extract the deformation deflection of the target cross-sections at several coordinate positions under the action of transverse external load.

[0030] The minimum element characteristic length and material elastic wave velocity were extracted from the finite element model. Based on the steady-state time step formula, the steady-state time step for explicit dynamic analysis was calculated. Then, a mass scaling convergence analysis was performed. To balance computational efficiency and accuracy, calculation results were tested under a large uniformly distributed load of 1000 kN / m with mass scaling factors of 10000, 100, 80, 40, 10, and 1, as shown in Table 5. Table 5. Convergence Analysis of Quality Scaling Factor: ; Comparative analysis revealed that as the mass scaling factor decreased, the computation time of the model gradually increased, but the computational accuracy significantly improved. When the mass scaling factor was less than or equal to 100, the maximum deflection of the sling gradually stabilized, and further reducing the mass scaling factor no longer significantly improved the computational accuracy. Therefore, considering both computational efficiency and computation time, a mass scaling factor of 100 was ultimately selected as the benchmark parameter for subsequent analysis. When the mass scaling factor was less than or equal to 100, the maximum deflection tended to stabilize. After comprehensive consideration, a mass scaling factor of 100 was selected as the target mass scaling factor to ensure a balance between accuracy and efficiency.

[0031] The logic for quality scaling convergence analysis is as follows: Multiple sets of test mass scaling factors are input into the three-dimensional finite element analysis model for pre-calculation processing, and the maximum deformation deflection corresponding to each set of test mass scaling factors is extracted. Set the maximum deformation deflection corresponding to the test mass scaling factor of 1 as the reference maximum deflection, and calculate the relative deflection deviation between the maximum deformation deflection corresponding to the other test mass scaling factors and the reference maximum deflection. The relative deviation of deflection is compared with a preset accuracy threshold, and the test quality scaling factor with a relative deviation of deflection less than the preset accuracy threshold is selected as the target quality scaling factor.

[0032] This embodiment provides a detailed explanation of the mass scaling convergence analysis in step S32. To ensure simulation accuracy, convergence analysis is performed under a uniformly distributed load of 1000 kN / m. Multiple sets of test mass scaling factors (e.g., 1, 10, 40, 80, 100, 10000) are input into the finite element model for pre-calculation, and the maximum deflection value corresponding to each set is extracted. Then, the maximum deflection of 53.76 mm calculated when the mass scaling factor is 1 (no mass scaling) is set as the benchmark maximum deflection. The relative deviation between the maximum deflection corresponding to other mass scaling factors and this benchmark value is calculated. The deviation is 0.54% when the mass scaling factor is 10, and the deviation is [missing value] when it is 40. The deviation was 3.31% when the value was 80, 5.38% when the value was 100, and 4.61% when the value was 100. Finally, the calculated relative deviation of the deflection was compared with the preset accuracy threshold (e.g., 5%). When the mass scaling factor was 10, 40, and 100, the relative deviation was less than 5%. Considering the calculation efficiency (calculation time), the calculation time (8 hours) when the mass scaling factor was 100 was much shorter than that when the mass scaling factor was 10 (27 hours), and the accuracy met the requirements. Therefore, the mass scaling factor of 100 was selected as the target mass scaling factor.

[0033] The central difference method is used to perform numerical solution iterative calculations on the enlarged three-dimensional finite element analysis model. The processing logic is as follows: Obtain the preset total physical analysis time, and use the increased stable time step as the time increment step of the iteration process; For the enlarged three-dimensional finite element analysis model, the sets of external nodal forces and internal nodal forces acting on all nodes are extracted. The sets of external nodal forces are subtracted from the sets of internal nodal forces to obtain the sets of remaining nodal forces for all nodes. Extract the set of all nodal masses corresponding to the magnified equivalent material density, calculate the ratio of the remaining nodal force set to the set of all nodal masses, and obtain the set of nodal accelerations of all nodes in the current time increment step; Based on the set of node accelerations and the increased stable time step, the set of node velocities corresponding to all nodes in half a time increment step is updated, and time integration is performed to obtain the set of node displacements corresponding to all nodes in the next time increment step. The update operations of the nodal acceleration set, nodal velocity set, and nodal displacement set are repeatedly repeated until the total time of all time increment steps reaches the total physical analysis time, thus completing the numerical solution iterative calculation; Several target sections at coordinate positions are intercepted along the axial direction of the three-dimensional finite element analysis model. The final displacement values ​​of the nodes on the target sections along the direction of the applied transverse external load are extracted, and the final displacement values ​​are used as the deformation deflection under the action of the transverse external load.

[0034] This embodiment provides a detailed explanation of the explicit dynamics iterative calculation process. After determining the target mass scaling factor (e.g., 100) and increasing the model density, the explicit dynamics solution begins: the total physical analysis time T is set, and the increased stabilization time step after mass scaling is used. As the time increment step of the iteration, the calculation process in each increment step is as follows: Extract the set of external node forces and the set of internal node forces acting on all nodes of the model, calculate the remaining node forces, extract the set of mass M of all nodes after amplification, and calculate the set of node accelerations at the current time increment step. Based on the speed of the current node Using the calculated acceleration 'a', the nodal velocities are updated after half a time increment step using the central difference method. : ; Based on the updated node velocity, calculate the node displacement for the next time increment step. : ; Repeat the above steps until the total time of all time increment steps reaches the preset total physical analysis time T, and complete the entire iterative calculation. Extract the final lateral displacement of the nodes at different cross-sections along the axial direction of the cable from the calculation results, which is the deformation deflection of the cross-section under load.

[0035] Step S4 specifically includes: Step S41: The sealing cable is equivalent to a homogeneous beam with uniform cross-section and fixed at both ends. The centroid of the left end section is taken as the coordinate far point. The direction along the axial direction of the homogeneous beam with uniform cross-section and from the left end section to the right end section is set as the positive direction of the y-axis. The direction of the transverse external load is set as the z-axis. In the left end section, the direction perpendicular to the y-axis and z-axis is set as the x-axis. A three-dimensional rectangular coordinate system is established. The coordinate values ​​of the target section along the y-axis in the three-dimensional rectangular coordinate system are extracted as the target coordinate variables. The average displacement of all wire nodes in the target section along the z-axis is extracted as the deformation deflection. The positions y=0 and y=l correspond to the two fixed end sections of the three-dimensional finite element analysis model, respectively. Step S42: When the loading type is uniformly distributed load, based on the bending differential equation of the beam with fixed ends, the deformation deflection along the z-axis of the target section at several coordinate positions is used for back calculation to obtain several equivalent bending stiffnesses corresponding to the target sections at several coordinate positions. The calculation expressions for the several equivalent bending stiffnesses are as follows: ; in, Let be the equivalent bending stiffness corresponding to the i-th target section, q be the magnitude of the uniformly distributed load under the uniformly distributed load condition, and l be the length. Let i be the coordinate variable corresponding to the i-th target section. , Let be the absolute value of the deformation deflection corresponding to the extracted i-th target section.

[0036] This embodiment refers to Figure 6 The uniformly distributed load case is explained in detail. The complex cable is equivalent to a homogeneous beam with uniform cross-section and fixed at both ends. A three-dimensional rectangular coordinate system is established with the centroid of the left end face as the origin, the positive y-axis along the axial direction to the right as the positive z-axis, and the transverse load direction as the z-axis. A Cartesian coordinate system is established, with y=0 and y=l (l=1m) corresponding to the fixed ends of the model. The coordinates of each target cross-section (such as y=300mm, 400mm, etc.) are extracted as... The average displacement of all nodes along the z-axis on these sections is extracted as the deformation deflection. ; When the load is a uniformly distributed load, based on the bending differential equation of the beam fixed at both ends, the equivalent bending stiffness of each section is calculated by using the deflection values ​​of multiple sections extracted in step S41 and the equivalent bending stiffness calculation expression. Taking the UL-1 load case (q=100 kN / m) as an example, the bending stiffness of each section is calculated according to the formula, and the results are shown in Table 6: Table 6 UL-1 Cable Section Location, Deflection and EI Equivalent Calculation Results: ; Step S4 also includes: Extract the equivalent bending stiffness corresponding to the target section at several coordinate positions, and apply this to all equivalent bending stiffnesses. The mean value is calculated to obtain the mean value of the equivalent bending stiffness, and the mean value of the equivalent bending stiffness is used as the equivalent bending stiffness under the current external load. When the loading type is concentrated load case, based on the bending differential equation of the beam fixed at both ends under concentrated load at mid-span, the equivalent bending stiffness under the current external load is obtained by back-calculation using the deformation deflection at mid-span. The expression for calculating the equivalent bending stiffness under the current external load is as follows: ; in, This is the equivalent bending stiffness under the current external load. The value of l represents the magnitude of the concentrated load under the concentrated load condition, and l represents the length. This represents the absolute value of the deformation deflection at the mid-span location. Establish a one-to-one correspondence between the equivalent bending stiffness under the current external load and the magnitude of the currently applied lateral external load, which includes the magnitude of the uniformly distributed load and the magnitude of the concentrated load.

[0037] This embodiment provides supplementary explanations regarding the process of calculating the final equivalent bending stiffness. For the uniformly distributed load case, the average value of the bending stiffness of each section calculated in Table 6 is taken, resulting in an average equivalent bending stiffness of 11925 N·m² for this load case (UL-1). The equivalent bending stiffness for other uniformly distributed load cases (UL-2, UL-3) is calculated using the same method, and the results are shown in Table 7. Table 7 Equivalent values ​​of bending stiffness of wire rope - uniformly distributed load: ; For concentrated load conditions, based on the bending differential equation of a beam fixed at both ends under concentrated load, the general expression for deflection calculation is as follows: ; Where a is the distance from the point of application of the concentrated load P to the left end of the wire rope at y=0, and b is the distance from the point of application of the concentrated load P to the right end of the wire rope at y=l. Based on the general deflection calculation formula, the deflection through any cross section can be derived. Inverse calculation of equivalent bending stiffness General expression: ; When a concentrated load acts at the mid-span, i.e. Utilizing mid-span deflection Simplified form of the formula for back-calculating the equivalent bending stiffness of the suspension cable: ; The equivalent bending stiffness was calculated and compared with that of UL-1 (q=100kN / m). Figure 9 As shown in Table 8: Table 8 Equivalent values ​​of bending stiffness of wire rope - concentrated load: ; Finally, a one-to-one correspondence between the equivalent bending stiffness and the corresponding external load was established; for example, a uniformly distributed load of 10 kN / m corresponds to an equivalent bending stiffness of 2091 N·m², and a concentrated load of 5 kN corresponds to 2079 N·m². This clearly shows that the equivalent bending stiffness increases with increasing load.

[0038] The process of treating the sealing cable as an equivalent homogeneous beam with uniform cross-section, fixed at both ends, includes: The macroscopic deformation state of the sealing cable under the action of transverse external load is extracted. The discontinuous contact state characteristics and frictional slip characteristics between the multiple layers of steel wires inside the sealing cable are ignored. The macroscopic bending stiffness of the sealing cable along the axial direction is set to a constant stiffness value under the current transverse external load. The sealing cable is mapped to a geometric section that is consistent along the axial direction to obtain a homogeneous beam with uniform cross-section.

[0039] This embodiment provides a principled explanation of the key equivalent process. In this method, the complex sealing cable is equivalent to a homogeneous beam with a uniform cross-section, based on the observation of the macroscopic bending deformation law of the sling. Figure 7 and Figure 8 As shown, under uniformly distributed load and concentrated load, the deflection-position curve of the suspender is in high agreement with the calculation curve of classical beam theory, indicating that its macroscopic deformation behavior is consistent with that of a homogeneous beam. Therefore, in the equivalent process, the complex discontinuous contact, friction and slippage between the multiple layers of steel wires inside are ignored. Instead, its macroscopic bending stiffness under a specific external load is regarded as a constant value, i.e., the equivalent bending stiffness. At the same time, along its axial direction, its ability to resist bending deformation is simplified to uniform distribution, thus mapping it to an ideal beam model with the same geometric length, constant cross-section and homogeneous material.

[0040] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0041] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. 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 be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the protection scope of the present invention.

Claims

1. A method for analyzing the bending stiffness of a sealing cable based on digital twins, characterized in that, Includes the following steps: Step S1: Obtain the geometric structural parameters and material properties of the sealing cable to be tested, and construct a three-dimensional finite element analysis model; Step S2: Set the boundary conditions at both ends of the three-dimensional finite element analysis model, and apply the preset lateral external load to the three-dimensional finite element analysis model; Step S3: The three-dimensional finite element analysis model under lateral external load is calculated using the explicit dynamic calculation method to extract the deformation deflection of each section after the load is applied. Step S4: The sealing cable is equivalent to a homogeneous beam with a uniform cross-section. Based on the beam bending theory, the extracted deformation deflection is used for back calculation to obtain the equivalent bending stiffness under the current external load.

2. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 1, characterized in that, Step S1 includes the following sub-steps: Step S11: Obtain the geometric structure parameters of the sealing cable to be tested. The geometric structure parameters include the total number of layers of the wire rope, the cross-sectional type of each layer of wire, the diameter of each layer of wire, the converted diameter, the distribution radius, the number of wires, the direction of twist, and the twist pitch. Step S12: Obtain the material properties of each layer of steel wire, including the density, elastic modulus, Poisson's ratio, yield strength and coefficient of friction of the high-strength galvanized aluminum rare earth alloy steel wire material. Step S13: Based on the geometric structural parameters, a three-dimensional solid model of the suspension cable with a length of l is created in the three-dimensional modeling software. The processing logic of the three-dimensional solid model of the suspension cable is as follows: Based on the cross-sectional type and diameter of each layer of steel wires, a two-dimensional cross-sectional profile of a single steel wire is drawn on a preset distribution radius of each layer. The two-dimensional cross-sectional profile includes a circular cross-sectional profile in the inner layer and a Z-shaped cross-sectional profile in the outer layer. Through a sweeping process, the two-dimensional cross-sectional profile is swept along the corresponding three-dimensional spiral trajectory line to obtain a three-dimensional spiral solid model of a single steel wire. Based on the preset number of steel wires in each layer, the three-dimensional spiral solid model of the single steel wire is processed into a ring array to obtain a set of steel wire solids in each layer. The inner and outer steel wire solid sets are then nested and combined to obtain a three-dimensional solid model of the sling. Step S14: Perform finite element analysis on the three-dimensional solid model of the sling and obtain a three-dimensional finite element analysis model through reliability verification.

3. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 2, characterized in that, Through reliability verification, the processing logic of the three-dimensional finite element analysis model is obtained as follows: One end of the three-dimensional finite element analysis model is subjected to full-degree-of-freedom constraints, and axial tensile displacement is applied to the other end. Axial tensile simulation is performed using quasi-static simulation to obtain the simulated breaking force of the sealing cable during the simulated tensile process. The relative deviation is calculated by comparing the nominal breaking force and the simulated breaking force of the sealing cable. The expression for the relative deviation is as follows: ； in, This is a relative deviation. Nominal breaking force, To simulate breaking force; A preset safety error threshold is used to compare the relative deviation with the preset safety error threshold. When the relative deviation is less than the preset safety error threshold, the three-dimensional finite element analysis model is determined to have passed the accuracy verification, and the three-dimensional finite element analysis model that has passed the accuracy verification is used as the input data for step S2.

4. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 1, characterized in that, Step S2 includes the following sub-steps: Step S21: Set boundary conditions at both ends of the three-dimensional finite element analysis model. The logic for setting the boundary conditions at both ends is as follows: The left and right end faces of the three-dimensional finite element analysis model along the axial direction are selected. All nodes on the left and right end faces are subjected to full degree of freedom constraints. The translational degrees of freedom of all nodes on the left and right end faces along the X, Y, and Z axes are restricted, as are the rotational degrees of freedom of all nodes on the left and right end faces about the X, Y, and Z axes. Step S22: Set the loading type and load size of the lateral external load. The loading type includes uniformly distributed load case and concentrated load case. Step S23: Apply a preset lateral external load to the three-dimensional finite element analysis model. The processing logic for applying the load is as follows: The load application direction is defined as a transverse direction perpendicular to the axis of the three-dimensional finite element analysis model; When the loading type is uniformly distributed load, the preset uniformly distributed load is extracted as the lateral external load, and the uniformly distributed load is uniformly distributed and applied within the length l of the axial direction of the three-dimensional finite element analysis model. When the loading type is concentrated load condition, the preset concentrated load is extracted as the lateral external load and applied to the mid-span position of the three-dimensional finite element analysis model in the axial direction. The mid-span position is the position where the distance from the left end face section and the right end face section is half the length l.

5. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 1, characterized in that, Step S3 includes the following sub-steps: Step S31: Obtain the minimum sample feature length and the elastic wave velocity of the material properties in the three-dimensional finite element analysis model. Use the minimum sample feature length and the elastic wave velocity to calculate the stable time step through explicit dynamics. The expression for calculating the stable time step is: ； in, To stabilize the time step, The minimum unit feature length, The elastic wave velocity of the material; Step S32: Perform mass scaling convergence analysis on the three-dimensional finite element analysis model under the applied transverse external load to obtain the target mass scaling factor. Step S33: The three-dimensional finite element analysis model is subjected to equivalent density magnification using the target mass scaling factor to obtain the enlarged three-dimensional finite element analysis model. Step S34: The central difference method is used to perform numerical solution and iterative calculation on the enlarged three-dimensional finite element analysis model, and the target cross-sections at several coordinate positions are intercepted along the axial direction to extract the deformation deflection of the target cross-sections at several coordinate positions under the action of transverse external load.

6. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 5, characterized in that, The logic for the quality scaling convergence analysis is as follows: Multiple sets of test mass scaling factors are input into the three-dimensional finite element analysis model for pre-calculation processing, and the maximum deformation deflection corresponding to each set of test mass scaling factors is extracted. Set the maximum deformation deflection corresponding to the test mass scaling factor of 1 as the reference maximum deflection, and calculate the relative deflection deviation between the maximum deformation deflection corresponding to the other test mass scaling factors and the reference maximum deflection. The relative deviation of deflection is compared with a preset accuracy threshold, and the test quality scaling factor with a relative deviation of deflection less than the preset accuracy threshold is selected as the target quality scaling factor.

7. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 5, characterized in that, The central difference method is used to perform numerical solution iterative calculations on the enlarged three-dimensional finite element analysis model. The processing logic is as follows: Obtain the preset total physical analysis time, and use the increased stable time step as the time increment step of the iteration process; For the enlarged three-dimensional finite element analysis model, the sets of external nodal forces and internal nodal forces acting on all nodes are extracted. The sets of external nodal forces are subtracted from the sets of internal nodal forces to obtain the sets of remaining nodal forces for all nodes. Extract the set of all nodal masses corresponding to the magnified equivalent material density, calculate the ratio of the remaining nodal force set to the set of all nodal masses, and obtain the set of nodal accelerations of all nodes in the current time increment step; Based on the set of nodal accelerations and the increased stable time step, the set of nodal velocities corresponding to all nodes in half a time increment step is updated, and time integration is performed to obtain the set of nodal displacements corresponding to all nodes in the next time increment step. The update operations of the nodal acceleration set, nodal velocity set, and nodal displacement set are repeatedly repeated until the total time of all time increment steps reaches the total physical analysis time, thus completing the numerical solution iterative calculation; Several target sections at coordinate positions are intercepted along the axial direction of the three-dimensional finite element analysis model. The final displacement values ​​of the nodes on the target sections along the direction of the applied transverse external load are extracted, and the final displacement values ​​are used as the deformation deflection under the action of the transverse external load.

8. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 1, characterized in that, Step S4 specifically includes: Step S41: The sealing cable is equivalent to a homogeneous beam with uniform cross-section fixed at both ends. The centroid of the left end section is taken as the coordinate far point. The direction along the axial direction of the homogeneous beam with uniform cross-section and from the left end section to the right end section is set as the positive direction of the y-axis. The direction of the transverse external load is set as the z-axis. In the left end section, the direction perpendicular to the y-axis and z-axis is set as the x-axis. A three-dimensional rectangular coordinate system is established. The coordinate values ​​of the target section along the y-axis in the three-dimensional rectangular coordinate system are extracted as the target coordinate variables. The average displacement of all wire nodes in the target section along the z-axis is extracted as the deformation deflection. Step S42: When the loading type is uniformly distributed load, based on the bending differential equation of the beam with fixed ends, the deformation deflection along the z-axis of the target section at several coordinate positions is used for back calculation to obtain several equivalent bending stiffnesses corresponding to the target sections at several coordinate positions. The calculation expressions for the several equivalent bending stiffnesses are as follows: ； in, Let be the equivalent bending stiffness corresponding to the i-th target section, q be the magnitude of the uniformly distributed load under the uniformly distributed load condition, and l be the length. Let i be the coordinate variable corresponding to the i-th target section. , Let be the absolute value of the deformation deflection corresponding to the extracted i-th target section.

9. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 8, characterized in that, Step S4 also includes: Extract the equivalent bending stiffness corresponding to the target section at several coordinate positions, and apply this to all equivalent bending stiffnesses. The mean value is calculated to obtain the mean value of the equivalent bending stiffness, and the mean value of the equivalent bending stiffness is used as the equivalent bending stiffness under the current external load. When the loading type is concentrated load condition, based on the bending differential equation of the beam fixed at both ends under concentrated load at mid-span, the equivalent bending stiffness under the current external load is obtained by back-calculation using the deformation deflection at the mid-span location. The calculation expression for the equivalent bending stiffness under the current external load is as follows: ； in, This is the equivalent bending stiffness under the current external load. The value of l represents the magnitude of the concentrated load under the concentrated load condition, and l represents the length. This represents the absolute value of the deformation deflection at the mid-span location. Establish a one-to-one correspondence between the equivalent bending stiffness under the current external load and the magnitude of the currently applied lateral external load, wherein the magnitude of the lateral external load includes the magnitude of the uniformly distributed load and the magnitude of the concentrated load.

10. The method for analyzing the bending stiffness of a sealing cable based on digital twins as described in claim 9, characterized in that, The process of treating the sealing cable as an equivalent homogeneous beam with uniform cross-section, fixed at both ends, includes: The macroscopic deformation state of the sealing cable under the action of transverse external load is extracted. The discontinuous contact state characteristics and frictional slip characteristics between the multiple layers of steel wires inside the sealing cable are ignored. The macroscopic bending stiffness of the sealing cable along the axial direction is set to a constant stiffness value under the current transverse external load. The sealing cable is mapped to a geometric section that is consistent along the axial direction to obtain a homogeneous beam with uniform cross-section.

Images