Finite element simulation method and system for tower top saddle of suspension bridge

Abstract

This invention discloses a finite element simulation method and system for a suspension bridge tower top saddle. The method includes: collecting multiple types of parameters; iteratively solving for tangential and normal forces based on an initial tangential stiffness matrix; calculating the actual contact friction coefficient based on the coupling relationship between temperature and contact normal pressure; calculating a tangential correction coefficient based on the actual contact friction coefficient, the ratio of tangential to normal forces, and the linkage relationship between the saddle geometric parameters; dynamically adjusting the tangential stiffness matrix based on the correction coefficient, the saddle pre-offset, and the synergistic relationship between cable stress; constructing a finite element model and simulating it; and iteratively optimizing until convergence. The system corresponds to the modules described above. This invention optimizes simulation accuracy through multi-factor coupling and linkage, adapting to complex working conditions and providing reliable support for the design and construction of suspension bridges.

Description

Technical Field

[0001] This invention relates to the field of finite element simulation technology for suspension bridges, specifically to a finite element simulation method and system for the saddle seat at the top of a suspension bridge tower. Background Technology

[0002] As a core component supporting and steering the main cable, the saddle atop the suspension bridge tower directly impacts the reliability of the bridge's overall alignment and stress analysis due to the accuracy of its simulation of the contact relationship with the cable. Existing finite element simulation methods for suspension bridge tower saddles generally treat the basic friction coefficient between the saddle and cable (a fixed value under standard conditions) as a fixed value, neglecting the effects of temperature changes on the surface roughness of the saddle material and the influence of contact normal pressure on the contact state in actual engineering. This leads to significant discrepancies between the calculated and actual contact friction coefficients. Furthermore, existing methods fail to consider the nonlinear effect of the ratio of cable tangential force to normal force on the tangent point location, and do not establish a dynamic linkage between the saddle pre-deflection and cable stress. This results in the simulated tangent point coordinates failing to accurately reflect the actual location under extreme temperature conditions and during construction jacking, making it difficult for the tangent stiffness matrix to dynamically adapt to changes in working conditions. Consequently, the reliability of the overall alignment and stress analysis results for the suspension bridge is insufficient, posing potential risks to bridge design and construction safety.

[0003] Therefore, there is an urgent need for a finite element simulation technology for suspension bridge tower top saddles that can comprehensively integrate the coupled effects of multiple factors and improve simulation accuracy. Summary of the Invention

[0004] The purpose of this invention is to provide a finite element simulation method for the saddle at the top of a suspension bridge tower, comprising the following steps: S1: Collect saddle material parameters, cable parameters, environmental parameters, contact parameters, construction parameters, and standard working condition parameters; S2: Based on the initial tangent stiffness matrix, perform initial finite element iteration to solve for the tangential and normal forces at the contact point between the cable and the saddle; S3: Calculate the actual contact friction coefficient based on the coupling relationship between temperature and contact normal pressure; S4: Calculate the tangent point correction coefficient based on the actual contact friction coefficient, the ratio of tangential force to normal force, and the linkage relationship of saddle geometric parameters; S5: Based on the synergistic relationship between the tangent correction coefficient, saddle pre-offset, and cable stress, dynamically adjust the tangent stiffness matrix; S6: Construct a finite element model using the adjusted dynamic tangent stiffness matrix, perform finite element simulation of the suspension bridge tower top saddle, and output the simulation results; S7: Determine whether the simulation result has converged. If it has not converged, feed back the coordinates of the tangent point in the simulation result to step S2, and repeat steps S3 to S7. If it has converged, output the final simulation result.

[0005] Preferably, the saddle material parameters include the saddle material yield strength and the base friction coefficient; the cable parameters include the cable cross-sectional area, elastic modulus, uniformly distributed load per meter, and stress-free length; the environmental parameters include the actual working temperature; the contact parameters include the contact area and contact length between the cable and the saddle; the construction parameters include the actual pre-deflection of the saddle, the design reference length, and the saddle arc radius; and the standard working condition parameters include the standard reference temperature and the ratio of tangential force to normal force under standard working conditions.

[0006] In a further preferred embodiment, in step S2, the initial iteration of the finite element method adopts the modified influence matrix method. By establishing an initial finite element model, applying the self-weight load of the cable, and solving the tangential force components and normal force components along the X-axis, Y-axis, and Z-axis directions at the contact point between the cable and the saddle, the tower-saddle cable element in the initial finite element model is a three-node structure, including the left cable segment, the right cable segment, and the tower top saddle contact segment.

[0007] In a further preferred embodiment, in step S2, before solving for the tangential force and the normal force, it is necessary to determine the initial values ​​for iteration. The initial values ​​for iteration include the horizontal component force at the tangent point and the angle between the tangent and the horizontal line. The angle between the tangent and the horizontal line is calculated based on the target node coordinates and the geometric relationship of the saddle. The horizontal component force at the tangent point is solved in two cases according to the relationship between the stress-free length of the cable and the chord length. When the stress-free length of the cable is greater than the chord length, the elastic effect is ignored. When the stress-free length of the cable is less than the chord length, the elastic effect is taken into account.

[0008] In a further preferred embodiment, in step S3, the actual contact friction coefficient is solved by the formula for calculating the actual contact friction coefficient. This formula integrates the influence of temperature change on the surface properties of the saddle material and the effect of contact normal pressure on the contact state, thereby quantifying the actual contact friction coefficient.

[0009] Further preferably, in step S4, the tangent correction coefficient is solved by the tangent correction coefficient calculation formula, which integrates the effect of the actual contact friction coefficient, the ratio of tangential force to normal force, and the influence of saddle stress. Further preferably, in step S5, the dynamic tangent stiffness matrix is ​​solved by the dynamic tangent stiffness matrix calculation formula, which combines the correction effect of the tangent correction coefficient, the change of saddle pre-offset, and the influence of cable stress to achieve dynamic adaptation of the stiffness matrix.

[0010] In a further preferred embodiment, when the suspension bridge is a three-dimensional cable system, steps S3 to S5 also include the following operations: decomposing the three-dimensional tower-saddle cable unit into arc segments projected onto the vertical and horizontal planes, establishing the transformation relationship between the unit coordinate system and the global coordinate system, and unifying all parameters to the global coordinate system through the coordinate transformation matrix; taking into account the projected component of the contact area in three-dimensional space when calculating the actual contact friction coefficient; supplementing the constraints of the transverse geometric parameters when calculating the tangent correction coefficient; incorporating the transverse stress component of the cable in three-dimensional space when calculating the dynamic tangent stiffness matrix, and finally constructing a three-node, 12-DOF three-dimensional tower-saddle cable unit finite element model.

[0011] A finite element simulation system for a suspension bridge tower top saddle, applied to the finite element simulation method for suspension bridge tower top saddles as described in any of the above-mentioned methods, includes a parameter acquisition module, a tangential and normal force calculation module, an actual contact friction coefficient calculation module, a tangent point correction coefficient calculation module, a dynamic stiffness matrix adjustment module, a finite element simulation module, and an iterative optimization module. The parameter acquisition module is used to acquire saddle material parameters, cable parameters, environmental parameters, contact parameters, construction parameters, and standard working condition parameters. The tangential and normal force calculation module is used to perform initial finite element iteration based on the initial tangent stiffness matrix to solve for the tangential and normal forces at the cable-saddle contact point. The actual contact friction coefficient calculation module is used to calculate the tangential and normal forces based on temperature and contact normal pressure. The coupling relationship calculation module calculates the actual contact friction coefficient; the tangent correction coefficient calculation module calculates the tangent correction coefficient based on the actual contact friction coefficient, the ratio of tangential force to normal force, and the saddle geometric parameters; the dynamic stiffness matrix adjustment module dynamically adjusts the tangent stiffness matrix based on the tangent correction coefficient, saddle pre-offset, and cable stress; the finite element simulation module constructs a finite element model using the adjusted dynamic tangent stiffness matrix, performs finite element simulation of the suspension bridge tower top saddle, and outputs the simulation results; the iterative optimization module determines whether the simulation results converge. If not, it feeds back the tangent coordinates in the simulation results to the tangential and normal force solution module, triggering each module to repeat the corresponding operation. If converged, it outputs the final simulation results.

[0012] Further preferred options include a 3D adaptation module, which is used to handle parameter conversion of the 3D spatial cable system, calculation of the 3D actual contact friction coefficient, 3D tangent point correction, and adjustment of the 3D dynamic tangent stiffness matrix, and to construct a 3D tower-saddle cable element finite element model; the tangential force and normal force solution module is also used to determine the initial values ​​of the iteration based on the relationship between the stress-free length of the cable and the chord length.

[0013] Compared with the prior art, the present invention has the following advantages: This invention employs innovative techniques to calculate the actual contact friction coefficient through coupling temperature and contact normal pressure, the ratio of tangential force to normal force, and the tangent point correction coefficient through linkage calculation of geometric parameters. It also addresses the core problem of insufficient simulation accuracy caused by neglecting the coupling of multiple factors in existing technologies. This invention achieves accurate simulation of tangent point coordinates and stiffness matrix under extreme working conditions and during construction, providing reliable finite element analysis support for the design and construction of suspension bridges. Attached Figure Description

[0014] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0015] Figure 1 This is a flowchart of the finite element simulation method for the suspension bridge tower top saddle of the present invention; Figure 2 This is a connection block diagram of the finite element simulation system for the suspension bridge tower top saddle of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] The concepts involved in this application will first be described with reference to the accompanying drawings. It should be noted that the following descriptions of various concepts are only for the purpose of making the content of this application easier to understand and do not constitute a limitation on the scope of protection of this application; furthermore, the embodiments and features in the embodiments of this application can be combined with each other unless otherwise specified. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0018] Existing technologies have technical problems such as failing to consider the influence of temperature-pressure coupling on the actual contact friction coefficient, the effect of force ratio-geometric parameter linkage on the tangent point, and the influence of pre-bias-stress synergy on the stiffness matrix, resulting in insufficient simulation accuracy.

[0019] Based on this, please refer to Figures 1-2 This embodiment provides a finite element simulation method for the saddle at the top of a suspension bridge tower, including the following steps: S1: Collect saddle material parameters, cable parameters, environmental parameters, contact parameters, construction parameters, and standard working condition parameters. The collection process needs to combine engineering design documents, laboratory tests, and on-site measurements. Saddle material parameters are obtained through tensile tests to obtain yield strength and foundation friction coefficient. Cable parameters are determined through material factory test reports to determine cross-sectional area, elastic modulus, etc. Environmental parameters are obtained by real-time collection of actual working temperature through temperature sensors deployed on-site. Contact parameters are obtained through 3D scanning technology to obtain the contact area and contact length between the cable and the saddle. Construction parameters are extracted from the construction organization design documents to extract pre-deviation design reference length, etc. Standard working condition parameters refer to industry specifications to set standard reference temperature and the ratio of tangential force to normal force under standard working conditions. S2: Based on the initial tangential stiffness matrix, the tangential and normal forces at the contact point between the cable and the saddle are solved by the initial finite element iteration. The initial tangential stiffness matrix is ​​constructed by establishing an initial mechanical model of the tower saddle cable element. The modified influence matrix method is adopted. First, the cable self-weight load is applied. The initial model is established by finite element software, the element mesh is divided, the boundary conditions are set, and then iterative calculation is performed to solve the tangential force components and normal force components along the X-axis, Y-axis and Z-axis directions. S3: The actual contact friction coefficient is calculated based on the coupling relationship between temperature and contact normal pressure. Temperature is fed back in real time by a sensor, and contact normal pressure is obtained through initial iteration results. The influence of the two is quantified and integrated through the coupling formula to realize the dynamic calculation of the actual contact friction coefficient. S4: Calculate the tangent point correction coefficient based on the ratio of actual contact friction coefficient to normal force and the linkage relationship of saddle geometric parameters. Substitute the actual contact friction coefficient obtained in S3 into the formula, and combine the force ratio obtained in the initial iteration with the measured saddle geometric parameters to adjust the tangent point position deviation through the correction formula. S5: Based on the synergistic relationship between the tangent correction coefficient, saddle pre-offset, and cable stress, the tangent stiffness matrix is ​​dynamically adjusted. The correction coefficient of S4 is combined with the measured value of the construction pre-offset and the calculated result of the cable stress, and the stiffness matrix is ​​updated through the stiffness adjustment formula. S6: Construct a finite element model using the adjusted dynamic tangent stiffness matrix, and use general finite element software or a custom-developed calculation program to import the adjusted stiffness matrix, define element type constraints and load conditions, perform finite element simulation of the suspension bridge tower top saddle, and output simulation results such as tangent point coordinates, cable line shape, and nodal force. S7: Determine whether the simulation results have converged. The convergence criterion is set as follows: the difference between the coordinates of the tangent point in two adjacent iterations is less than 0.001 meters and the difference in the nodal force is less than 100 N. If convergence has not occurred, the coordinates of the tangent point in the current simulation results are fed back to step S2 as new input parameters, and the force solution coefficients are calculated, stiffness is adjusted and simulated again. If convergence has occurred, the final simulation results are output. The core of this technical solution lies in constructing a three-level progressive coupling logic of actual contact friction coefficient, tangent point correction, and stiffness matrix. Each step addresses the core deficiencies of existing technologies. Step S1 comprehensively collects multi-dimensional parameters to provide a data foundation for subsequent coupling calculations. The collected parameters are all key factors affecting the contact relationship between the saddle and the cable, and none can be omitted. Step S2 solves the initial force state using the modified influence matrix method to ensure the stability of the iteration. Steps S3 to S5 are the core innovation, breaking the single-parameter calculation logic of existing technologies through multi-factor coupling, and achieving accurate transmission from the actual contact friction coefficient to the tangent point position and then to the stiffness matrix. Steps S6 and S7 ensure the convergence of simulation results through iterative optimization, guaranteeing the reliability of the simulation. This solution forms a closed-loop simulation logic through the close connection of each step, effectively solving the problem of insufficient accuracy in existing technologies, and providing a complete solution for the refined simulation of suspension bridge tower top saddles.

[0020] Existing technologies suffer from technical problems such as incomplete or untargeted parameter collection, leading to a lack of accurate data support for subsequent calculations.

[0021] Based on this, the saddle material parameters include the saddle material yield strength and basic friction coefficient. The yield strength of the saddle material is determined by a standard tensile test. A standard specimen of the saddle material is selected, and a tensile test is performed on a universal testing machine. The stress value at which the specimen yields is recorded as the yield strength. The basic friction coefficient is determined by a friction test. A contact friction test is performed on specimens of the saddle material and the cable material. The actual contact friction coefficient when the two slide relative to each other is measured at a standard reference temperature and is used as the basic friction coefficient. The cable parameters include the cable cross-sectional area, elastic modulus, and stress-free length per meter of uniformly distributed load. The cable cross-sectional area is calculated by measuring the cable's diameter or cross-sectional dimensions and combining it with the cable's structural form. The elastic modulus is determined by a tensile test of the cable material. The uniformly distributed load per meter is obtained by weighing the cable per unit length. The stress-free length is determined by the cable's factory test data or on-site tension test. Environmental parameters include the actual operating temperature, which is collected in real time by deploying temperature sensors near the saddle during construction and use. During the process, the ambient temperature data and sensor placement should be close to the contact area between the cable and the saddle to ensure the accuracy of the measurement data. Contact parameters include the contact area and contact length between the cable and the saddle. The contact area is obtained by scanning the contact area between the cable and the saddle using 3D laser scanning technology and calculating the area using image processing software. The contact length is determined by measuring the arc length of the contact part between the cable and the saddle. Construction parameters include the actual pre-deflection of the saddle, the design reference length, and the radius of the saddle arc. The actual pre-deflection of the saddle is obtained through measurement data during construction. The deviation between the actual position and the design position of the saddle is monitored using measuring instruments such as a total station. The design reference length is determined according to the design drawings of the saddle. The radius of the saddle arc is obtained by measuring the arc dimension of the saddle groove. Standard operating condition parameters include the standard reference temperature and the ratio of tangential force to normal force under standard operating conditions. The standard reference temperature is set at 20℃ according to relevant industry standards. The ratio of tangential force to normal force under standard operating conditions is determined through simulation calculations or experiments under standard operating conditions. This technical solution clarifies the specific content and acquisition methods of each type of parameter, ensuring the comprehensiveness and relevance of parameter collection. The yield strength and basic friction coefficient in the saddle material parameters are the core foundation for calculating the actual contact friction coefficient, directly affecting the initial benchmark and pressure adaptation characteristics of the actual contact friction coefficient. Cable parameters encompass geometric mechanics and load characteristics, providing data support for stress calculation and stress-free length analysis. The actual operating temperature in the environmental parameters is a key variable in temperature-pressure coupling calculations. Contact parameters directly reflect the contact state between the cable and the saddle, influencing pressure distribution and friction effects. Construction parameters such as the pre-deviation design benchmark length are core data for simulating the jacking process. Standard working condition parameters provide a reference benchmark for calculations, ensuring the comparability of results. By clarifying the parameter composition and acquisition methods, this solution avoids calculation errors caused by missing or redundant parameters, laying a solid data foundation for accurate calculations in subsequent steps.

[0022] Existing technologies suffer from poor adaptability of initial force solution methods and unclear definitions of tower-saddle cable unit structures, leading to insufficient accuracy in initial force calculation.

[0023] Based on this, in step S2, the initial finite element iteration adopts the modified influence matrix method. The specific implementation process of this method is as follows: First, the influence matrix is ​​established. By applying unit force to the key nodes of the tower-saddle cable element, the displacement response of each node is calculated, and then the influence matrix is ​​constructed. Then, combined with the cable self-weight load, a linear equation system of force and displacement is established. The initial force state is obtained by solving the equation system. By establishing the initial finite element model, the model construction process includes defining the element type and selecting the tower-saddle cable element as a three-node structure, including the left cable segment, the right cable segment, and the tower top saddle contact segment. The left cable segment and the right cable segment are simulated using catenary elements, and the tower top saddle contact segment is simulated using rigid elements. When dividing the element mesh, according to the saddle... The complexity of the contact area with the cable is reasonably divided into mesh densities, and the mesh density of the contact area is refined to improve the calculation accuracy. When setting boundary conditions, node 2 of the tower-saddle cable element is fixed to the main tower, restricting its translational and rotational degrees of freedom. Nodes 1 and 3 are free ends, and only unreasonable displacements are restricted. When applying the cable's self-weight load, the uniformly distributed load per meter of the cable is applied evenly to the cable element, with the load direction vertically downward. When solving for the tangential and normal force components along the X, Y, and Z axes at the contact point between the cable and the saddle, the iterative method is used through the solution module of the finite element software. First, the iteration convergence criterion is set. When the force difference between two adjacent iterations is less than the set threshold, the iteration stops, and the final tangential and normal force components are output. The three-node tower-saddle cable unit structure clearly defines the contact range between the cable and the saddle. The left and right cable segments simulate the cable portions on both sides of the saddle, respectively, while the saddle contact segment at the top of the tower simulates the contact area between the cable and the saddle, conforming to the force transmission logic of the actual structure. The forces of the left and right cable segments are transmitted to the main tower through the contact segment, providing a clear structural foundation for subsequent tangent point calculations and stiffness matrix derivation. This scheme effectively improves the accuracy of initial force solutions by combining the modified influence matrix method with the three-node tower-saddle cable unit structure. Compared with traditional methods, the modified influence matrix method improves the convergence speed and accuracy of force solutions through optimized iterative logic, avoiding cascading errors in subsequent calculations due to initial force deviations. Applying the cable's self-weight load conforms to the actual stress scenario, ensuring the authenticity of the force state. Solving for the three-dimensional force components can comprehensively reflect the contact stress state between the cable and the saddle, avoiding the one-sidedness caused by single-direction force calculations, and providing a reliable starting point for the entire simulation process.

[0024] Existing technologies suffer from technical problems such as slow iteration convergence or results deviating from reality due to unreasonable methods for determining initial values ​​during iteration.

[0025] Based on this, in step S2, before solving for the tangential and normal forces, it is necessary to determine the initial values ​​for iteration. The initial values ​​include the horizontal component force at the tangent point and the angle between the tangent and the horizontal line. The angle between the tangent and the horizontal line is calculated based on the coordinates of the target node and the geometric relationship between the saddle and the target node. The specific calculation process is as follows: first, obtain the design coordinates of the target node (i.e., the cable endpoint) and the geometric parameters of the saddle, including the radius of the saddle arc and the coordinates of the center. Calculate the angle between the line connecting the target node and the center of the saddle and the horizontal line through geometric calculations. Combined with the geometric condition that the cable is tangent to the saddle, derive the initial value of the angle between the tangent and the horizontal line. The horizontal component force at the tangent point is solved in two cases based on the relationship between the stress-free length of the cable and the chord length. First, calculate the stress-free length of the cable and the chord length... The length of the cable without stress is obtained from the cable's factory inspection data. The chord length is the straight-line distance between the tangent point and the target node. When the cable's without stress length is greater than the chord length, the elastic deformation of the cable is small and the elastic effect can be ignored. In this case, the approximate formula of the catenary theory is used to calculate the horizontal component force. Assuming that the cable's shape is close to a parabola, the calculation formula for the horizontal component force is derived through the parabola equation, and the chord length, load, and other parameters are substituted to calculate the force. When the cable's without stress length is less than the chord length, the elastic deformation of the cable cannot be ignored, and the elastic effect is taken into account. In this case, the elastic catenary theory is used to calculate the horizontal component force. The elastic modulus and cross-sectional area of ​​the cable are considered, and the relationship equation between force and deformation is established. The initial value of the horizontal component force is obtained by solving the equation. The horizontal component of the force at the tangent point and the angle between the tangent and the horizontal line in the initial values ​​of the iteration are the core inputs for the subsequent calculation of the actual contact friction coefficient and the tangent correction coefficient. Their accuracy directly affects the entire simulation result. The angle between the tangent and the horizontal line is calculated based on the target node coordinates and the geometric relationship of the saddle. The structural geometric constraints are fully utilized to ensure that the initial angle conforms to the actual spatial position relationship. The horizontal component of the force at the tangent point is handled according to the relationship between the stress-free length of the cable and the chord length. Considering the significant effect of the presence or absence of elasticity on the force state, when the stress-free length is greater than the chord length, the elastic deformation of the cable can be ignored to simplify the calculation while ensuring accuracy. When the stress-free length is less than the chord length, the elastic deformation cannot be ignored and the elasticity effect is included to ensure the accuracy of the force calculation. This scheme improves the iteration convergence speed and the reliability of the results through a scientific initial value determination method, avoids simulation failure or insufficient accuracy caused by unreasonable initial values, and enables the subsequent coupled calculations to converge quickly to accurate results.

[0026] Existing technologies have the technical problem that the calculation of the actual contact friction coefficient does not take into account the coupling of multiple factors, resulting in a large deviation from the actual contact state.

[0027] Based on this, in step S3, the actual contact friction coefficient is calculated using the formula for the actual contact friction coefficient, which is: ; The actual contact friction coefficient is a dimensionless parameter that reflects the frictional resistance characteristics when the cable contacts the saddle. It is the core output of this formula and is directly used to calculate the subsequent tangent correction coefficient. Standard reference temperature The basic coefficient of friction, dimensionless, is determined under standard test conditions (constant temperature). The friction test under standard pressure conditions is the benchmark value for calculating the actual contact friction coefficient, ensuring consistency in calculations under different working conditions. Temperature influence coefficient, dimensions are Through multiple temperature gradient tests (such as...) to Data fitting determines and quantifies the linear effect of unit temperature change on the actual contact friction coefficient, and the effects on different saddle materials (such as cast steel and wear-resistant alloys) are determined. The values ​​differ. Actual operating temperature, dimensionless Temperature data is collected in real time by temperature sensors deployed on-site, with the collection points close to the contact area between the cable and the saddle, to ensure that the data reflects the actual temperature state of the contact environment. Standard reference temperature, dimensionless Referencing bridge design specifications (usually...) This serves as a benchmark for calculating the effects of temperature, making the actual contact friction coefficients comparable under different ambient temperatures. The normal force of contact between the cable and the saddle, with dimensions of The pressure of the cable on the saddle is obtained through the initial finite element iteration in step S2, and it directly reflects the tightness of the contact. The contact area between the cable and the saddle, with dimensions of After scanning the contact area using 3D laser scanning technology, the physical range of actual contact between the two is accurately described by image processing software. : Yield strength of saddle material, dimensionless ( The normal pressure is determined by the standard tensile test of the saddle material and is a key parameter characterizing the load-bearing capacity of the saddle material, affecting the effect of the normal pressure on the contact state. Pressure sensitivity coefficient, dimensionless, is determined by fitting friction test data under all working conditions from low pressure to high pressure. It is specifically used to correct the calculation deviation of the actual contact friction coefficient in the low pressure range (such as when the cable tension is small in the early stage of construction) to ensure the calculation accuracy across the entire pressure range.

[0028] The theoretical basis of this formula comes from the contact mechanics theory in tribology. Temperature changes will change the surface roughness and molecular activity of the saddle material. When the temperature rises, the molecular activity of the material surface increases and the surface roughness decreases. The actual contact friction coefficient shows a linear trend. The contact normal pressure will change the tightness of the contact between the cable and the saddle and the actual contact area. When the pressure increases, the contact area increases. The actual contact friction coefficient shows a non-linear growth, but the growth rate gradually slows down, which is consistent with the non-linear relationship between pressure and actual contact friction coefficient in contact mechanics.

[0029] Using the baseline friction coefficient μ0 at a standard reference temperature T0 as the benchmark, μ0 is a benchmark value determined through friction tests under standard test conditions to ensure initial accuracy of the calculation. A temperature influence term α·(T-T0) is introduced, where α is the temperature influence coefficient, determined by the rate of change of the actual contact friction coefficient at different temperatures through experimental calibration. This linear term directly reflects the linear influence trend of temperature change on the actual contact friction coefficient, addressing the deficiency of existing technologies that ignore temperature influence. The term reflects the nonlinear regulation of the effect of normal pressure on temperature. Where σ is the relative pressure intensity, A is the contact area, and σ is the relative pressure intensity. s The ratio represents the yield strength of the saddle material, reflecting the strength of the normal pressure relative to the saddle's ultimate bearing capacity. The logarithmic function ensures that the moderating effect of temperature gradually stabilizes as pressure increases, preventing excessive pressure from causing uncontrolled temperature fluctuations. Finally, through... The addition of a correction term for the actual contact friction coefficient in the low-pressure range, where β is the pressure sensitivity coefficient, is determined by fitting experimental data under low-pressure conditions. The cube root term ensures the accuracy of the calculation of the actual contact friction coefficient in the low-pressure range, solving the problem of large errors in existing technologies under low-pressure conditions.

[0030] The formula is implemented as follows: First, calibration parameters such as μ0T0αβ are obtained. Through friction tests under multiple temperature and pressure combinations, the specific values ​​of these parameters are determined using a data fitting method. Then, F is obtained through step S2. n TAσ is obtained through step S1. s Substitute these parameters into the formula, calculate the temperature effect term, pressure regulation term, and low pressure correction term in sequence, and finally sum them to obtain the basic friction coefficient μ.

[0031] Existing technologies generally treat the actual contact friction coefficient as a fixed value or only consider the influence of a single factor. This formula, through the coupled design of a linear temperature term and a nonlinear pressure term, simultaneously covers the effects of temperature and pressure, solving the problem of calculation error of the actual contact friction coefficient under extreme temperature and variable pressure conditions. The temperature influence term is related to pressure through a logarithmic function, realizing the dynamic coupling of temperature and pressure rather than simple superposition, which conforms to the interaction law of temperature and pressure in actual contact process. The introduction of a low-pressure correction term fills the accuracy gap under low-pressure conditions, enabling the formula to cover the entire working condition range from low pressure to high pressure, significantly improving the calculation accuracy of the actual contact friction coefficient under different working conditions, and providing accurate basic parameters for subsequent tangent point correction and stiffness adjustment.

[0032] Existing technologies have a technical problem: the correction accuracy is insufficient because the correction of the tangent position does not take into account the interaction of multiple factors.

[0033] Based on this, in step S4, the tangent correction coefficient is calculated using the formula for the tangent correction coefficient: ; The tangent point correction coefficient is dimensionless and is used to correct the deviation of the initial tangent point coordinates. It is a key intermediate parameter connecting the actual contact friction coefficient, force state, and geometric parameters, and directly determines the accuracy of the tangent point coordinates. The actual contact friction coefficient is dimensionless and is calculated in step S3. It reflects the frictional characteristics between the cable and the saddle. Its value directly affects the sliding tendency of the cable relative to the saddle, and thus affects the tangent point offset. The tangential force of the cable contacting the saddle, with dimensions of The component of the horizontal tension along the saddle surface of the cable is obtained through the initial finite element iteration solution in step S2, and it characterizes the cable's sliding driving capability. The normal force of contact between the cable and the saddle, with dimensions of With claim 5 Using the same parameter ensures parameter consistency and reflects the constraint effect of the degree of contact tightness on the tangent state. : Radius of the saddle arc, dimensionless The parameters, obtained from saddle design drawings or through on-site measurements, are the core parameters of the saddle geometry and determine the constraint strength of the saddle on the offset of the tangent point. The contact length between the cable and the saddle, with dimensions of The longitudinal range of the cable-saddle contact is measured using three-dimensional laser scanning technology. The longer the contact length, the more significant the constraint on the tangent point offset. The correction attenuation factor is dimensionless and determined by fitting multiple sets of force ratio deviation test data. It controls the correction attenuation rate when the force ratio deviates from the standard working condition, avoids overcorrection caused by sudden changes in force state, and ensures a smooth correction process. The ratio of tangential force to normal force under standard working conditions is dimensionless and is calculated with reference to the standard load conditions of bridge design. It serves as a benchmark for judging whether the force state deviates from the normal range, so that the correction coefficient can be used to adjust the force state deviation in a targeted manner.

[0034] The formula is based on the contact position equilibrium theory in structural mechanics. The position of the tangent point is determined by the actual contact friction coefficient, force state, and geometric constraints. The actual contact friction coefficient affects the relative sliding tendency of the cable and the saddle, the force ratio reflects the force direction characteristics of the cable, and the geometric parameters constrain the spatial position range of the tangent point. The dynamic balance of the three determines the actual position of the tangent point. Existing technology ignores the linkage relationship among the three, resulting in a large deviation in the simulation of the tangent point position.

[0035] This formula uses 1 as the baseline value to ensure the rationality of the initial baseline for the correction coefficient; through The term reflects the synergistic effect of the actual contact friction coefficient-force ratio and geometric parameters. μ is the actual contact friction coefficient calculated in step S3, which directly reflects the driving effect of friction on tangential sliding. The larger μ is, the stronger the tendency to drive tangential sliding. The ratio of tangential force to normal force reflects the directional characteristics of the force on the cable; the larger the ratio, the stronger the tangential driving effect. The ratio of the saddle arc radius to the contact length reflects the strength of the geometric constraint. A larger radius and longer contact length indicate a stronger constraint. The product of these three factors precisely describes this dynamic equilibrium relationship and quantifies the offset trend of the tangent point. The effect of the deviation of the corrected force ratio from the standard working condition. γ is the force ratio under standard working conditions, and γ is the correction attenuation factor. It is determined by experimentally measuring the correction effect under different force ratio deviations. The exponential term ensures that when the force ratio deviates from the standard value, the correction coefficient is attenuated and adjusted to avoid overcorrection caused by sudden changes in force state, making the correction process more stable.

[0036] The formula is implemented as follows: First, obtain μ through step S3, and then obtain F through step S2. t F n RL_c is obtained through step S1. The value of γ is calibrated through experiments; these parameters are then substituted into the formula to calculate the force ratio. Then, calculate the synergistic effect term and the attenuation correction term, and multiply the two to obtain the tangent correction coefficient κ. Apply κ to correct the initial tangent coordinates. The initial tangent coordinates are initially determined through geometric relationships. The corrected tangent coordinates = initial tangent coordinates × κ, thereby achieving precise adjustment of the tangent position.

[0037] Existing technologies only consider the influence of geometric parameters or force states on the tangent point. This formula realizes a three-factor linkage correction of the actual contact friction coefficient, force state, and geometric parameters, comprehensively covering the key factors affecting the tangent point position. By quantifying the dynamic balance relationship through product terms, the contribution of each factor to the tangent point offset is clarified, solving the problem of ambiguous correction logic in existing technologies. An exponential decay term is introduced to handle the deviation of the force ratio from the working condition, avoiding over-correction and improving the correction stability under extreme force states. The correction coefficient κ is a dimensionless parameter, ensuring compatibility with other parameters and achieving seamless connection with subsequent stiffness matrix adjustments, significantly improving the simulation accuracy of the tangent point position and laying the foundation for improving the overall simulation accuracy.

[0038] Existing technologies suffer from the technical problem that the tangent stiffness matrix cannot dynamically adapt to changes in working conditions, resulting in large deviations between stiffness simulation and reality.

[0039] Based on this, in step S5, the dynamic tangent stiffness matrix is ​​solved using the dynamic tangent stiffness matrix calculation formula, which is: ; The dynamically adjusted tangent stiffness matrix, with dimensions of , is the core output of this formula, which is directly used to construct the finite element model and reflects the stiffness characteristics of the tower-saddle cable element under different working conditions. Initial tangent stiffness matrix, with dimensions of Based on the initial geometric parameters (such as cable cross-sectional area and saddle geometry) and material parameters (such as elastic modulus) of the tower-saddle cable unit, it serves as the reference value for dynamic adjustment of the stiffness matrix. : Tangent correction coefficient, dimensionless, calculated in step S4, integrates the correction effect of tangent position into the stiffness matrix to achieve linkage between tangent state and stiffness characteristics. The pre-deflection-cable stress coupling coefficient is dimensionless and determined by fitting experimental data of the pre-deflection and cable stress. It quantifies the intensity of their synergistic influence on the stiffness matrix. Different bridge construction techniques correspond to different coefficients. value. Actual pre-offset of the saddle, dimensionless. The initial offset of the saddle, obtained through total station measurements during construction, directly reflects the actual state of the construction conditions. The design reference length of the saddle, with dimensions of The design drawings of the saddle are taken from the reference for measuring the relative size of the pre-offset, so that the influence of the pre-offset has a unified quantitative standard. The tangential force of the cable contacting the saddle, with dimensions of With claim 6 Using the same parameter ensures consistency and reflects the influence of the cable's stress state on its stiffness. : Elastic modulus of cable, dimensionless ( The stress-stress ratio (TSR) is a key parameter for characterizing the elastic deformation characteristics of cable materials, determined through standard tensile tests, and directly affects the relationship between cable stress and stiffness. : Cable cross-sectional area, dimensionless It is calculated by measuring the diameter of the cable and combining it with the cable structure (such as parallel steel wire bundles or steel strands), which accurately reflects the load-bearing cross-section size of the cable.

[0040] The formula is based on the dynamic adjustment theory of stiffness matrix in structural mechanics. The tangent stiffness matrix needs to change dynamically with the construction pre-deflection at the tangent point and the stress state of the cable in order to accurately reflect the actual stress characteristics of the structure. Existing technologies use fixed stiffness matrices or single parameter adjustments, which cannot adapt to changes in working conditions.

[0041] Specifically, using the initial tangent stiffness matrix K0 as a benchmark, K0 is constructed through an initial finite element model and determined based on stiffness calculation theory in mechanics of materials, ensuring the rationality of the initial stiffness. By multiplying by the tangent correction coefficient κ, the correction effect of the tangent position is incorporated into the stiffness matrix. κ reflects the influence of tangent offset on stiffness characteristics; the larger the tangent offset, the greater the stiffness adjustment, thus achieving a dynamic correlation between the stiffness matrix and the tangent position. This item reflects the synergistic effect of pre-deflection and cable stress. This is the ratio of the actual pre-deflection of the saddle to the design reference length, reflecting changes in construction conditions. Changes in the pre-deflection directly affect the stress state of the cable. The ratio of the cable's tangential force to the product of its elastic modulus and cross-sectional area reflects the cable's stress state. The greater the stress, the greater the contribution to the cable's stiffness. The square root term ensures the rationality of the stress influence. δ is the pre-deflection-cable stress coupling coefficient, determined by experimental calibration of the stiffness change rate under different pre-deflection and stress combinations. The product of the two describes this synergistic effect, ensuring that the influence of pre-deflection and stress is accurately quantified.

[0042] The formula is implemented as follows: First, calculate K0 using the initial finite element model; then obtain κ in step S4; finally obtain ΔLL0EA_c in step S1; and finally obtain F in step S2. t The value of δ is calibrated through experiments; these parameters are then substituted into the formula to calculate... and Then, calculate the synergistic effect term and multiply it by κ and K0 in sequence to obtain the dynamic tangent stiffness matrix K; apply K to the stiffness update of the finite element model, replace the initial stiffness matrix, and ensure that the model stiffness can adapt to the current working conditions.

[0043] Existing technologies only adjust a single parameter of the stiffness matrix. This formula achieves coordinated adjustment of three factors: pre-biasing at the tangent point location, cable stress, and other factors, comprehensively covering key influencing factors of changing working conditions. The tangent point correction coefficient is directly integrated into the stiffness matrix calculation, realizing the linkage between the tangent point location and the stiffness matrix, solving the problem of disconnect between the two in existing technologies. The synergistic term of pre-biasing and stress is in the form of a product, accurately reflecting the interaction between the two and avoiding errors caused by simple superposition. The dynamic stiffness matrix can adapt to complex working conditions such as extreme temperature construction and jacking in real time, solving the deficiency of insufficient adaptability of the stiffness matrix in existing technologies and significantly improving the simulation accuracy under different working conditions.

[0044] Existing technologies have limitations in their ability to adapt to the simulation range of three-dimensional cable systems.

[0045] Based on this, when the suspension bridge is a three-dimensional cable system, steps S3 to S5 also include the following operations: Decomposing the three-dimensional tower-saddle cable unit into circular arc segments projected onto the vertical and horizontal planes. The vertical plane projection corresponds to the vertical curvature of the cable, and the horizontal plane projection corresponds to the lateral curvature of the cable. The decomposition process is based on the principle of spatial geometric projection, projecting the spatial coordinates of the three-dimensional unit onto the vertical and horizontal planes respectively to obtain the parameters of the circular arc segments in the two planes. The radius and center coordinates of the circular arc segments are calculated through the projected coordinates. Establishing the transformation relationship between the unit coordinate system and the global coordinate system, the unit coordinate system has node 2 as the origin, the X-axis along the height direction of the main tower, the Y-axis along the transverse direction of the bridge, and the Z-axis along the longitudinal direction of the bridge. The global coordinate system adopts the geodetic coordinate system commonly used in bridge engineering. The transformation relationship is based on the spatial coordinate transformation theory and is achieved through rotation and translation matrices. The rotation matrix is ​​determined according to the angle between the unit coordinate system and the global coordinate system, and the translation matrix is ​​determined according to the coordinates of node 2 in the global coordinate system. Unifying all parameters to the global coordinate system through the coordinate transformation matrix, the transformation matrix is: ; Where α is the rotation angle of the unit coordinate system about the Z-axis of the global coordinate system, and β is the rotation angle of the unit coordinate system about the Y-axis of the global coordinate system, the force parameters and coordinate parameters of the cable are transformed to the global coordinate system through this matrix; the projection component of the contact area in three-dimensional space is taken into account when calculating the actual contact friction coefficient. The three-dimensional contact area is obtained through spatial scanning, and its projection components in the vertical and horizontal planes are calculated separately. When substituting them into the actual contact friction coefficient formula, the weighted average of the projection components is used, and the weight is determined according to the force ratio of the two planes; when calculating the tangent correction coefficient, the constraints of the transverse bridge geometric parameters are added. The transverse bridge geometric parameters include the transverse bridge arc radius and the transverse bridge contact length, which are obtained through three-dimensional scanning and substituted together with the longitudinal bridge geometric parameters into the tangent correction coefficient. The positive coefficient formula supplements the influence of the transverse constraint term. The calculation of the dynamic tangential stiffness matrix incorporates the transverse stress component of the cable in three-dimensional space. The transverse stress component is obtained through three-dimensional finite element iteration. It is superimposed with the longitudinal stress component and substituted into the dynamic tangential stiffness matrix formula to realize the synergistic influence of three-dimensional stress on stiffness. Finally, a three-node, 12-DOF three-dimensional tower-saddle cable element finite element model is constructed. Each node contains three translational degrees of freedom and three rotational degrees of freedom. The translational degrees of freedom of nodes 1 and 3 correspond to the three directions in three-dimensional space, and the rotational degrees of freedom reflect the torsional characteristics of the cable. The translational and rotational degrees of freedom of node 2 reflect the connection characteristics between the main tower and the saddle, ensuring that the deformation and stress characteristics of the element in three-dimensional space can be fully described. This scheme overcomes the limitations of existing technologies for two-dimensional systems through a series of three-dimensional adaptation optimizations. It decomposes the three-dimensional unit into arc segments of two projection planes, simplifying the complexity of three-dimensional calculations while ensuring that the spatial characteristics of the structure are not lost. It establishes coordinate system transformation relationships to ensure that all parameters are calculated under a unified coordinate system, avoiding errors caused by coordinate confusion. The calculation of the actual contact friction coefficient incorporates the three-dimensional projection component of the contact area, taking into account the actual distribution characteristics of the contact area in three-dimensional space. The calculation of the tangency correction coefficient supplements the transverse geometric parameter constraints, conforming to the multi-directional constraint characteristics of the tangency point in three-dimensional space. The stiffness matrix calculation incorporates the transverse stress component to comprehensively reflect the stress state of the three-dimensional cable, achieving accurate simulation of the three-dimensional cable system.

[0046] Existing technologies suffer from technical problems such as mismatched simulation system module functions, which prevent efficient implementation of multi-factor coupled simulation processes.

[0047] Based on this, this embodiment provides a finite element simulation system for a suspension bridge tower top saddle, including a parameter acquisition module, a tangential and normal force solution module, an actual contact friction coefficient calculation module, a tangent correction coefficient calculation module, a dynamic stiffness matrix adjustment module, a finite element simulation module, and an iterative optimization module. The parameter acquisition module is used to collect saddle material parameters, cable parameters, environmental parameters, contact parameters, construction parameters, and standard working condition parameters. The inputs to this module are engineering design documents, laboratory test data, and field measured data. The output is a structured parameter dataset, which is connected to other modules through a data interface to transmit parameters to subsequent calculation modules in real time. The tangential and normal force solution module is used to calculate the tangential stiffness matrix based on the initial tangential stiffness matrix. The module performs initial finite element iterations to solve for the tangential and normal forces at the cable-saddle contact point. The inputs to this module are parameters and an initial tangential stiffness matrix provided by the parameter acquisition module. The output is three-dimensional component data of the tangential and normal forces. Force solutions are achieved through an internal modified influence matrix method calculation unit, with parameter data called in real-time during the calculation. The actual contact friction coefficient calculation module calculates the actual contact friction coefficient based on the coupling relationship between temperature and contact normal pressure. The inputs to this module are parameters such as temperature, contact area, and saddle material yield strength provided by the parameter acquisition module, and normal force data provided by the tangential and normal force solution module. The output is the actual contact friction coefficient. This is achieved through a built-in actual contact... The friction coefficient calculation formula enables coupled calculation; the tangent correction coefficient calculation module is used to calculate the tangent correction coefficient based on the ratio of tangential force to normal force of the actual contact friction coefficient and the saddle geometric parameters. The input of this module is the actual contact friction coefficient data provided by the actual contact friction coefficient calculation module, the tangential and normal force data provided by the tangential and normal force solution module, and the saddle geometric parameters provided by the parameter acquisition module. The output is the tangent correction coefficient. Multi-factor linkage calculation is realized through the built-in tangent correction coefficient calculation formula; the dynamic stiffness matrix adjustment module is used to dynamically adjust the tangential stiffness matrix based on the saddle pre-offset and cable stress of the tangent correction coefficient. The input of this module is the tangent correction coefficient calculation formula. The module provides correction coefficient data, parameters such as pre-biased cable elastic modulus and cross-sectional area from the parameter acquisition module, and tangential force data from the tangential force and normal force solution module. The output is a dynamic tangential stiffness matrix, which is adjusted collaboratively through the built-in dynamic tangential stiffness matrix calculation formula. The finite element simulation module is used to construct a finite element model using the adjusted dynamic tangential stiffness matrix to perform finite element simulation of the suspension bridge tower top saddle and output simulation results. The input of this module is the dynamic stiffness matrix provided by the dynamic stiffness matrix adjustment module and the structural parameters provided by the parameter acquisition module. The output is simulation result data such as tangential point coordinates, cable line shape, and nodal force. The simulation process is realized through finite element modeling units and solution units.The iterative optimization module is used to determine whether the simulation results have converged. If they have not converged, the coordinates of the tangent point in the simulation results are fed back to the tangential force and normal force solution module to trigger each module to repeat the corresponding operation. If they have converged, the final simulation result is output. The input of this module is the simulation result data provided by the finite element simulation module, and the output is the convergence judgment signal and the final simulation result. The result is verified by the convergence judgment unit. The convergence judgment criterion is that the difference between the coordinates of the tangent point in two adjacent simulations is less than 0.001 meters and the difference between the nodal forces is less than 100 Newtons. The technical solution features a modular setup and methodological steps that correspond one-to-one, forming a highly efficient and collaborative system architecture. The parameter acquisition module provides data input to the entire system, ensuring accurate data support for each calculation module. The tangential and normal force solution module outputs the initial force state, providing input for subsequent coefficient calculation modules. The actual contact friction coefficient calculation module, tangent point correction coefficient calculation module, and dynamic stiffness matrix adjustment module progressively implement the core logic of multi-factor coupled calculation. The finite element simulation module transforms the stiffness matrix into a simulation model and outputs simulation results. The iterative optimization module implements closed-loop control of the simulation process, ensuring result convergence. Each module has a clearly defined function and is tightly integrated, avoiding redundancy or functional deficiencies. This allows for efficient automated execution of the methodological process, improving simulation efficiency and reliability, and providing efficient system support for the finite element simulation of suspension bridge tower top saddles.

[0048] Existing technologies suffer from technical problems such as a lack of 3D adaptation capabilities and inconsistent parameter and initial value transfer.

[0049] Based on this, the system also includes a 3D adaptation module. This module handles parameter conversion of the 3D cable system, calculation of the actual 3D contact friction coefficient, correction of the 3D tangent point, and adjustment of the 3D dynamic tangent stiffness matrix, constructing a 3D tower-saddle cable element finite element model. The inputs to this module are the 3D structural parameters provided by the parameter acquisition module and the 2D calculation results provided by each calculation module. The outputs are the 3D adapted parameters and model data. This functionality is achieved through a coordinate transformation unit, a 3D coefficient calculation unit, and a 3D model construction unit. The coordinate transformation unit, based on spatial coordinate transformation theory, realizes parameter conversion between the element coordinate system and the global coordinate system. The 3D coefficient calculation unit supplements the 3D component influence on the 2D calculation formula. The 3D model construction unit constructs a three-node, 12-DOF finite element model. The Vita-saddle cable element model; the parameters acquired by the parameter acquisition module are consistent with those described in claim 2, ensuring the uniformity of parameter definition and acquisition methods, and avoiding calculation errors caused by parameter inconsistencies. The parameter acquisition module transmits parameters to each calculation module and the 3D adaptation module through a standardized data interface, ensuring the accuracy and consistency of parameter transmission; the tangential force and normal force solving module is also used to determine the initial value of the iteration based on the relationship between the stress-free length of the cable and the chord length. The initial value of the iteration is consistent with the initial value of the iteration described in claim 4. This module calculates the initial value of the iteration through a built-in initial value calculation unit. The initial value calculation unit solves the problem according to the relationship between the stress-free length of the cable and the chord length, and transmits the calculated initial value of the iteration to the force solving unit, providing accurate initial value input for the initial iteration. This technical solution improves the system's 3D simulation capabilities by adding a 3D adaptation module, enabling the system to adapt to both 2D and 3D cable systems and expanding its applicability. The 3D adaptation module covers key aspects of 3D simulation, from parameter conversion to 3D calculation of various coefficients and 3D unit model construction, forming a complete 3D adaptation process. The parameter acquisition module maintains consistency with the parameters in claim 2, ensuring the uniformity and accuracy of system data input. The tangential and normal force solution module maintains consistency with the iterative initial values ​​in claim 4, ensuring the scientific and rational nature of the initial value determination method and closely echoing the method flow. This solution further improves the system architecture, enhances the system's adaptability and reliability, and ensures that the system can accurately reproduce the core logic of the method through module function supplementation and parameter initial value unification.

[0050] The embodiments and / or implementation methods described above are merely preferred embodiments and / or implementation methods for implementing the technology of the present invention, and are not intended to limit the implementation methods of the technology of the present invention in any way. Any person skilled in the art can make some modifications or alterations to other equivalent embodiments without departing from the scope of the technical means disclosed in the content of the present invention, but they should still be regarded as the technology or embodiments that are substantially the same as the present invention.

[0051] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. The above descriptions are only preferred embodiments of this application. It should be noted that due to the limitations of written expression, while there are objectively infinite specific structures, those skilled in the art can make several improvements, modifications, or changes without departing from the principles of this application, and can also combine the above technical features in an appropriate manner. These improvements, modifications, changes, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of this application.

Claims

1. A finite element simulation method for a saddle-shaped support at the top of a suspension bridge tower, characterized in that, Includes the following steps: S1: Collect saddle material parameters, cable parameters, environmental parameters, contact parameters, construction parameters, and standard working condition parameters; S2: Based on the initial tangent stiffness matrix, perform initial finite element iteration to solve for the tangential and normal forces at the contact point between the cable and the saddle; S3: Calculate the actual contact friction coefficient based on the coupling relationship between temperature and contact normal pressure; S4: Calculate the tangent point correction coefficient based on the actual contact friction coefficient, the ratio of tangential force to normal force, and the linkage relationship of saddle geometric parameters; S5: Based on the synergistic relationship between the tangent correction coefficient, saddle pre-offset, and cable stress, dynamically adjust the tangent stiffness matrix; S6: Construct a finite element model using the adjusted dynamic tangent stiffness matrix, perform finite element simulation of the suspension bridge tower top saddle, and output the simulation results; S7: Determine whether the simulation result has converged. If it has not converged, feed back the coordinates of the tangent point in the simulation result to step S2, and repeat steps S3 to S7. If it has converged, output the final simulation result.

2. The finite element simulation method for the saddle seat at the top of a suspension bridge tower according to claim 1, characterized in that, The saddle material parameters include the saddle material yield strength and the base friction coefficient; the cable parameters include the cable cross-sectional area, elastic modulus, uniformly distributed load per meter, and stress-free length; the environmental parameters include the actual working temperature; the contact parameters include the contact area and contact length between the cable and the saddle; the construction parameters include the actual pre-deflection of the saddle, the design reference length, and the saddle arc radius; and the standard working condition parameters include the standard reference temperature and the ratio of tangential force to normal force under standard working conditions.

3. The finite element simulation method for the saddle seat at the top of a suspension bridge tower according to claim 1, characterized in that, In step S2, the initial iteration of the finite element method adopts the modified influence matrix method. By establishing the initial finite element model, the self-weight load of the cable is applied, and the tangential force components and normal force components along the X-axis, Y-axis and Z-axis directions at the contact point between the cable and the saddle are solved. The tower-saddle cable element in the initial finite element model is a three-node structure, which includes the left cable segment, the right cable segment and the tower top saddle contact segment.

4. The finite element simulation method for the saddle seat at the top of a suspension bridge tower according to claim 1, characterized in that, In step S2, before solving for the tangential and normal forces, it is necessary to determine the initial values ​​for iteration. The initial values ​​for iteration include the horizontal component force at the tangent point and the angle between the tangent and the horizontal line. The angle between the tangent and the horizontal line is calculated based on the target node coordinates and the geometric relationship of the saddle. The horizontal component force at the tangent point is solved in two cases according to the relationship between the stress-free length of the cable and the chord length. When the stress-free length of the cable is greater than the chord length, the elastic effect is ignored. When the stress-free length of the cable is less than the chord length, the elastic effect is taken into account.

5. The finite element simulation method for the saddle seat at the top of a suspension bridge tower according to claim 1, characterized in that, In step S3, the actual contact friction coefficient is solved by the formula for calculating the actual contact friction coefficient. This formula combines the influence of temperature change on the surface properties of the saddle material and the effect of contact normal pressure on the contact state, thereby quantifying the actual contact friction coefficient.

6. The finite element simulation method for the saddle seat at the top of a suspension bridge tower according to claim 1, characterized in that, In step S4, the tangent correction coefficient is solved by the tangent correction coefficient calculation formula. This formula integrates the effect of the actual contact friction coefficient, the ratio of tangential force to normal force, and the constraint effect of saddle geometric parameters to achieve the correction of the tangent position deviation.

7. The finite element simulation method for the saddle seat at the top of a suspension bridge tower according to claim 1, characterized in that, In step S5, the dynamic tangent stiffness matrix is ​​solved by the dynamic tangent stiffness matrix calculation formula. This formula combines the correction effect of the tangent point correction coefficient, the change of saddle pre-offset, and the influence of cable stress to achieve the adaptation of the dynamic tangent stiffness matrix.

8. The finite element simulation method for the saddle seat at the top of a suspension bridge tower according to claim 1, characterized in that, When the suspension bridge is a three-dimensional cable system, steps S3 to S5 also include the following operations: decomposing the three-dimensional tower-saddle cable unit into circular arc segments projected onto the vertical and horizontal planes, establishing the transformation relationship between the unit coordinate system and the global coordinate system, and unifying all parameters to the global coordinate system through the coordinate transformation matrix; taking into account the projected component of the contact area in three-dimensional space when calculating the actual contact friction coefficient; supplementing the constraints of the transverse geometric parameters when calculating the tangent correction coefficient; incorporating the transverse stress component of the cable in three-dimensional space when calculating the dynamic tangent stiffness matrix, and finally constructing a three-node, 12-DOF three-dimensional tower-saddle cable unit finite element model.

9. A finite element simulation system for a suspension bridge tower top saddle, applied to the finite element simulation method for a suspension bridge tower top saddle as described in any one of claims 1-8, characterized in that, It includes a parameter acquisition module, a tangential and normal force solution module, an actual contact friction coefficient calculation module, a tangent point correction coefficient calculation module, a dynamic stiffness matrix adjustment module, a finite element simulation module, and an iterative optimization module; The parameter acquisition module is used to collect saddle material parameters, cable parameters, environmental parameters, contact parameters, construction parameters, and standard working condition parameters; the tangential and normal force solving module is used to perform initial finite element iteration based on the initial tangential stiffness matrix to solve for the tangential and normal forces at the contact point between the cable and the saddle. The actual contact friction coefficient calculation module is used to calculate the actual contact friction coefficient based on the coupling relationship between temperature and contact normal pressure. The tangent correction coefficient calculation module is used to calculate the tangent correction coefficient based on the actual contact friction coefficient, the ratio of tangential force to normal force, and the saddle geometric parameters. The dynamic stiffness matrix adjustment module is used to dynamically adjust the tangent stiffness matrix based on the tangent correction coefficient, saddle pre-offset, and cable stress; the finite element simulation module is used to construct a finite element model using the adjusted dynamic tangent stiffness matrix, perform finite element simulation of the suspension bridge tower top saddle, and output the simulation results. The iterative optimization module is used to determine whether the simulation results have converged. If they have not converged, the coordinates of the tangent point in the simulation results are fed back to the tangential force and normal force solution module, triggering each module to repeat the corresponding operation. If they have converged, the final simulation results are output.

10. The finite element simulation system for the saddle seat at the top of a suspension bridge tower according to claim 9, characterized in that, It also includes a 3D adaptation module, which is used to handle parameter conversion of the 3D cable system, calculation of the 3D actual contact friction coefficient, 3D tangent point correction and 3D dynamic tangent stiffness matrix adjustment, and to construct a 3D tower-saddle cable element finite element model; the tangential force and normal force solution module is also used to determine the initial values ​​of the iteration based on the relationship between the stress-free length of the cable and the chord length.

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