Integral calculation method, system and calculation device for cross-fixed pulley continuous cable structure

Abstract

The application provides a whole calculation method and system of a cross-fixed pulley continuous cable structure and a calculation device, and relates to the technical field of bridge engineering and structural mechanics. The method comprises the following steps: acquiring system parameters and target state parameters; solving initial unstressed cable length; performing continuous calculation in multiple construction stages, updating the structure state based on the result of the previous stage in each stage, cyclically traversing the pulley, calculating the sliding stiffness and sliding amount, adjusting the unstressed cable length, directly updating the cable force by using a cable force-cable length change relationship, and storing the result after the system balance converges; and outputting the calculation results of all stages, which realizes automatic parameter updating and multi-stage continuous analysis, avoids manual modeling and repeated input between stages, has the advantages of high precision, high efficiency and strong reliability, and is suitable for construction control of a large-span cable system.

Description

Technical Field

[0001] This invention relates to the fields of bridge engineering and structural mechanics, and in particular to a method, system and computing equipment for the overall calculation of continuous cable structures spanning fixed pulleys. Background Technology

[0002] Continuous cable systems, with their significant advantages of being lightweight, high-strength, and having strong spanning capabilities, have been widely used in large-span spatial structures such as tensioned beams and cable-stayed domes, as well as in important engineering fields such as bridge construction using the fastening method, cable hoisting systems, double-cable freight ropeways, and high-voltage transmission lines.

[0003] However, existing calculation methods for continuous cable structures spanning fixed pulleys have many limitations and cannot meet the high precision and efficiency requirements of modern complex engineering construction control. Their main shortcomings are reflected in the following aspects:

[0004] 1. Model Simplification Distortion: Existing methods often use straight-line elements to simulate cable segments to simplify calculations. This method completely ignores the sag effect of the cable, leading to significant deviations between the calculated cable shape and cable force and the actual situation. It is particularly unsuitable for accurate analysis of large-span and large-sag conditions. Another common method, the "virtual temperature load method," indirectly simulates the change in stress-free length by applying a temperature field. However, its physical meaning is unclear, the calculation convergence is difficult to control, and it cannot accurately reflect the true mechanical state of the cable structure.

[0005] 2. Poor Construction Adaptability: In construction process simulation, existing technologies typically calculate cable structures and support structures independently. Engineers must rely on external code to repeatedly call and modify the finite element model through interfaces, requiring a new calculation model to be built for each construction stage. More significantly, existing commercial software usually uses the stress-free length of the cable as a fixed input parameter, which cannot be automatically modified during the calculation process once set. For continuous cables spanning pulleys, the stress-free length of the cable segments on both sides of the pulley will be redistributed due to slippage during construction. Operators must manually calculate each change and re-enter it into each model, while also manually updating the coordinate position of the support structure. The entire process is cumbersome, labor-intensive, and prone to errors, failing to accurately reflect the continuous changes between construction stages, and data processing is extremely difficult.

[0006] 3. Complex slip calculation: For the slip calculation of cable segments at pulleys, existing methods are mostly based on solving slip stiffness using complex partial differential equations. The calculation process is complicated, the solution results are unstable, and the calculation time is often too long and convergence is difficult, making it difficult to apply to rapid engineering calculations with multiple pulleys and multiple stages. Summary of the Invention

[0007] To address the aforementioned problems in the existing technology, the first aspect of this invention proposes a method for the overall calculation of a continuous cable structure spanning a fixed pulley, comprising:

[0008] S1. Based on user input, obtain system parameters and target state parameters. The system parameters include the geometric configuration and connection relationship of the support structure, cable structure and fixed pulley. The support structure is used to fix the fixed pulley. The cable structure is a continuous cable that spans multiple fixed pulleys. The fixed pulleys allow the cable structure to slide on it.

[0009] S2. Based on the system parameters and target state parameters, the stress-free length of each cable segment and the total stress-free length in the initial state are generated by the initial stress-free cable length solution method.

[0010] S3. Based on the stress-free length and total stress-free length generated in step S2, the initial construction stage state is generated through the construction stage initialization method. The initial construction stage state includes the initial stress-free length, cable force, and node coordinates.

[0011] S4. Based on the initial construction stage state generated in step S3, the displacement state of the supporting structure and the boundary conditions of the cable structure under the current stage are generated through a multi-construction stage cyclic processing method, based on the calculation results stored in the previous construction stage and through a structural state update method for each construction stage.

[0012] S5. Based on the displacement state and boundary conditions generated in step S4, the stress-free length of the cable segments on both sides of the fixed pulley is adjusted and the cable force is updated through the fixed pulley slip calculation and cable length adjustment method until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, generating the stress-free length, cable force and node coordinates of each cable segment after convergence.

[0013] S6. Based on the converged stress-free length, cable force, and node coordinates of each cable segment generated in step S5, store the results of the current construction stage, and output the calculation results of all construction stages after all construction stages are completed.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0015] This method first uses steps S1 and S2 to systematically generate the stress-free length and total stress-free length of each cable segment in the initial state based on the system parameters and target state parameters input by the user. This lays a reliable foundation for subsequent accurate calculations and avoids model simplification distortion from the outset. Step S3 then uses a construction stage initialization method to generate the initial construction stage state, which includes the initial stress-free length, cable force, and node coordinates, ensuring the accuracy of the calculation starting point.

[0016] The core improvement lies in the multi-stage cyclic processing mechanism comprised of steps S4 to S6. Step S4, based on the results of the previous stage, automatically generates the displacement state of the supporting structure and the boundary conditions of the cable structure under the current stage through a structural state update method. This achieves automatic transfer and updating of the structural state between stages, eliminating the tedious operations of manually rebuilding the model and repeatedly inputting parameters required in traditional methods. Step S5 automatically adjusts the stress-free length of the cable segments on both sides of the fixed pulley and updates the cable force through fixed pulley slip calculation and cable length adjustment methods until the system reaches equilibrium and convergence. This process inherently handles the cable length redistribution problem caused by pulley slippage without manual intervention, and iterative calculation ensures the accuracy of the calculation. Furthermore, the subsequent cable force update method does not require iterative calculation of the entire structure, improving computational efficiency and adapting to structures with a large number of fixed pulleys. Step S6 is responsible for storing and outputting the results of all stages, providing a complete construction process data chain.

[0017] These steps are closely linked, forming a complete closed loop from parameter input and initial state calculation to multi-stage continuous automatic analysis. Their synergistic effect is as follows: S1 and S2 provide precise initial conditions for the entire process; S3 establishes the initial state; S4 ensures seamless data inheritance between stages and automatic evolution of the structural state; S5 fundamentally solves the automation and precision challenges of slippage and cable length adjustment, and works in conjunction with S4 to achieve automatic parameter updates and continuous mechanical state calculation throughout the construction process; S6 finally integrates and outputs the entire process data. This method significantly improves computational efficiency and accuracy, greatly reduces the risk of human error, and provides an efficient and reliable solution for the construction control of complex cable systems. Attached Figure Description

[0018] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 The diagram shown is a flowchart illustrating the overall calculation method for a continuous cable structure spanning a fixed pulley, according to an embodiment of the present invention.

[0020] Figure 2 The diagram shown is a schematic diagram of the state of a three-span continuous cable-stayed bridge provided in an embodiment of the present invention.

[0021] Figure 3 The figure shown is a schematic diagram of the overall calculation system for a continuous cable structure spanning a fixed pulley provided in an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0023] The specific embodiments of the present invention will be described below.

[0024] Example 1

[0025] like Figure 1 and Figure 2 As shown, this invention proposes a method for the overall calculation of a continuous cable structure spanning a fixed pulley, including:

[0026] S1. Based on user input, obtain system parameters and target state parameters. The system parameters include the geometric configuration and connection relationship of the support structure, cable structure and fixed pulley. The support structure is used to fix the fixed pulley. The cable structure is a continuous cable that spans multiple fixed pulleys. The fixed pulleys allow the cable structure to slide on it.

[0027] S2. Based on the system parameters and target state parameters, the stress-free length of each cable segment and the total stress-free length in the initial state are generated by the initial stress-free cable length solution method.

[0028] S3. Based on the stress-free length and total stress-free length generated in step S2, the initial construction stage state is generated through the construction stage initialization method. The initial construction stage state includes the initial stress-free length, cable force, and node coordinates.

[0029] S4. Based on the initial construction stage state generated in step S3, the displacement state of the supporting structure and the boundary conditions of the cable structure under the current stage are generated through a multi-construction stage cyclic processing method, based on the calculation results stored in the previous construction stage and through a structural state update method for each construction stage.

[0030] S5. Based on the displacement state and boundary conditions generated in step S4, the stress-free length of the cable segments on both sides of the fixed pulley is adjusted and the cable force is updated through the fixed pulley slip calculation and cable length adjustment method until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, generating the stress-free length, cable force and node coordinates of each cable segment after convergence.

[0031] S6. Based on the converged stress-free length, cable force, and node coordinates of each cable segment generated in step S5, store the results of the current construction stage, and output the calculation results of all construction stages after all construction stages are completed.

[0032] A comprehensive calculation method for continuous cable structures spanning fixed pulleys establishes a complete computational framework, achieving accurate simulation of the construction process through an ordered sequence of steps. The first step is to acquire system parameters and target state parameters based on user input. System parameters include the geometric configuration and connection relationships of the support structure, cable structure, and fixed pulleys. The support structure provides fixed support for the fixed pulleys, the cable structure is a load-bearing system spanning multiple fixed pulleys in a continuous manner, and the fixed pulleys are mechanical components that allow the cable structure to slide freely on them. This step requires the complete collection of information such as the structure's geometric dimensions, material properties, boundary constraints, and the target construction state, establishing a complete data foundation for subsequent calculations. Based on the system parameters and target state parameters, the initial stress-free cable length solution method generates the stress-free length of each cable segment and the total stress-free length in the initial state. This process uses precise mechanical models such as catenary theory, considering factors such as the cable's self-weight and elastic deformation, to derive the baseline length parameters of the cable in the stress-free state. Based on the generated stress-free length and total stress-free length, the initial construction stage state is generated through a construction stage initialization method. This state includes key parameters such as the initial stress-free length, cable force, and node coordinates, forming the starting point for construction analysis.

[0033] After establishing the initial state, the method enters a multi-stage construction cycle processing phase. Based on the calculation results stored in the previous construction stage, the displacement state of the supporting structure and the boundary conditions of the cable structure under the current stage are generated through a structural state update method. This step automatically inherits the convergence results of the previous stage and updates the structural configuration according to new load conditions or geometric changes, achieving seamless connection between stages. Based on the generated displacement state and boundary conditions, the stress-free lengths of the cable segments on both sides of the fixed pulley are adjusted and the cable forces are updated through fixed pulley slip calculation and cable length adjustment methods. This process iterates through each pulley, calculates the cable length redistribution caused by slippage, and iteratively calculates to bring the cable forces on both sides of all fixed pulleys to a balanced state, while ensuring structural displacement convergence. Based on the converged stress-free lengths, cable forces, and node coordinates of each cable segment, the results of the current construction stage are stored, and all calculation results are output after all construction stages are completed, forming a complete construction process record.

[0034] This method constructs an automated process from parameter input to result output through the organic coordination of steps. Each step forms a complete computational chain: initial parameter acquisition ensures the integrity of the computational foundation; stress-free cable length calculation provides an accurate baseline state; construction stage initialization establishes the analysis starting point; multi-stage iterative processing enables continuous simulation of the construction process; structural state updates ensure the coherence of data between stages; slip calculation and cable length adjustment accurately simulate the mechanical behavior at the pulley; and result storage and output provide a complete analysis record. This systematic approach effectively solves the model simplification and distortion problems existing in traditional methods, ensuring the authenticity of the calculation results through an accurate mechanical model; it also overcomes the shortcomings of poor construction adaptability by avoiding the tedious manual modeling operations between stages through automation; and it improves the complexity of slip calculation by ensuring stable convergence through a systematic iterative method. The entire method, through its precise modeling, automated processing, and continuous analysis, provides reliable technical support for the construction control of complex cable systems.

[0035] In some implementations, step S2 includes:

[0036] S21. Based on the system parameters and target state parameters, the initial value of the iterative cable force is obtained through the iterative cable force initial value calculation method.

[0037] S22. Based on the initial value of the iterative cable force obtained in step S21, the stress-free length of the single-span cable on one side of the first fixed pulley is solved by the algorithm for solving the stress-free length of the single-span cable.

[0038] S23. Based on the stress-free length obtained in step S22 and the force balance constraint at the fixed pulley, the stress-free length of the single-span cable on the other side of the first fixed pulley is obtained by using the stress-free length solution algorithm for the single-span cable on the other side.

[0039] S24. Based on the stress-free length obtained in step S23, the stress-free length of adjacent cable segments is repeatedly obtained through the process of crossing with a fixed pulley and continuous solution, until the stress-free length of all cable segments is obtained, and the stress-free length of each cable segment and the total stress-free length are generated in the initial state.

[0040] Step S2 provides a detailed process for solving the initial stress-free cable length, ensuring accuracy through layered calculations. Based on system parameters and target state parameters, iterative initial cable force values ​​are obtained using an iterative cable force initial value calculation method. This process selects an appropriate theoretical model based on the cable's sag-to-span ratio characteristics. For large sag-to-span ratios, parabolic theory is used to provide initial estimates, while for small sag-to-span ratios, the unknown load factor method is used to ensure that the initial values ​​conform to mechanical principles and are computationally feasible. Based on the obtained iterative initial cable force values, the stress-free length of the single-span cable on one side of the first fixed pulley is solved using a single-span cable stress-free length solution algorithm. This algorithm discretizes the single-span cable into several micro-segments and applies Newton's iteration method combined with the catenary equation to calculate the cable shape and internal forces segment by segment. Through repeated adjustments, the calculated cable shape is made to match the target state. Based on the stress-free length obtained and the force balance constraint at the fixed pulley, the stress-free length of the single-span cable on the other side of the first fixed pulley is solved using an algorithm for solving the stress-free length of the single-span cable on the other side. This process uses the force balance condition at the pulley to determine the starting point of the calculation and uses a similar iterative method to solve the cable shape parameters to ensure the coordination and consistency of the mechanical states on both sides of the pulley.

[0041] Based on the solved stress-free length, the stress-free lengths of adjacent cable segments are repeatedly solved through a fixed pulley crossing and continuous solution process. This process uses the results of the solved cable segments as input conditions for adjacent cable segments, proceeding sequentially until the calculation of all cable segments is completed, ultimately generating the initial stress-free lengths of each cable segment and the total stress-free length. The entire step S2 forms a systematic calculation process, from initial value estimation to single-span solution, and then to continuous expansion, gradually constructing a complete stress-free state model. The iterative cable force initial value calculation method provides a reasonable starting point for subsequent accurate calculations, avoiding iterative divergence; the single-span cable stress-free length solution algorithm ensures single-span accuracy through refined local calculations; the other single-span cable stress-free length solution algorithm maintains mechanical coordination at the pulley; and the fixed pulley crossing and continuous solution process ensure the overall consistency of the multi-span system. The synergistic effect of these technical features ensures both local accuracy and overall coordination in the initial stress-free cable length solution, laying a solid foundation for subsequent construction stage analysis and effectively improving the reliability and engineering applicability of the overall calculation method.

[0042] In some implementations, step S21 includes:

[0043] S211. Based on the target state parameters, the initial cable force value is generated for a cable with a specific sag-span ratio by applying parabolic theory.

[0044] S212. Based on the initial cable force value generated in step S211, the horizontal and vertical components of the cable force are generated through a component calculation process.

[0045] S213. Based on the horizontal and vertical components generated in step S212, determine the cable end inclination angle and integrate them to generate the initial value of the iterative cable force.

[0046] Step S21 focuses on the reasonable determination of the initial values ​​of the iterative cable forces, ensuring their reliability through theoretical analysis and parameter transformation. Based on the target state parameters, initial cable force values ​​are generated for a specific sag-to-span ratio using parabolic theory. Parabolic theory is applicable here to cases with large sag-to-span ratios, utilizing its approximate effectiveness under large sag conditions to quickly estimate the horizontal component of the cable force, providing a preliminary reference for subsequent accurate calculations. Based on the generated initial cable force values, horizontal and vertical components of the cable force are generated through a component calculation process. This process decomposes the overall cable force into horizontal and vertical components based on the cable end geometry and equilibrium conditions, facilitating subsequent mechanical analysis and geometric calculations. Based on the generated horizontal and vertical components, the cable end inclination angle is determined and integrated to generate the initial values ​​of the iterative cable forces. The cable end inclination angle is calculated through the geometric relationships of the force components. The final iterative cable force initial values ​​contain information on the magnitude and direction of the forces, providing complete initial conditions for the catenary iteration.

[0047] The technical foundation of this series of operations lies in the rational utilization of the applicability of different theories. Parabolic theory can provide sufficiently accurate initial estimates under large sag-to-span ratios, component calculations decompose complex spatial force systems into manageable scalar parameters, the determination of cable end inclination angles establishes a relationship between force and geometry, and the final integrated iterative cable force initial values ​​possess both mechanical rationality and computational feasibility. Obtaining initial estimates through the application of parabolic theory avoids the uncertainty of relying entirely on trial and error, the component calculation process simplifies the handling of complex force states, the determination of cable end inclination angles bridges mechanics and geometry, and the integration of iterative cable force initial values ​​provides a complete computational starting point. These technical effects enable subsequent accurate iterative calculations to converge quickly, reduce computational resource consumption, and ensure the numerical stability of the calculation process, providing an important guarantee for the reliable implementation of the overall method.

[0048] In some implementations, step S22 includes:

[0049] S221. Based on the iterative initial value of cable force, the single-span cable is divided into several micro-segments through a micro-segmentation process;

[0050] S222. Based on the micro-segments divided in step S221, the force and shape of each micro-segment are derived segment by segment using Newton's iteration method and the catenary equation.

[0051] S223. Based on the shape derived in step S222, the calculated cable end point elevation difference is compared with the target elevation difference through the elevation difference comparison process.

[0052] S224. Based on the comparison results of step S223, if the elevation difference error exceeds the allowable value, the initial value of the iteration is adjusted and recalculated using the iterative initial value adjustment method until the elevation difference error is within the allowable range, and the stress-free length of the single-span cable on the first fixed pulley side is generated.

[0053] Step S22 ensures the accuracy of the stress-free length calculation for a single-span cable through meticulous discretization and iterative correction. Based on the initial values ​​of the iterative cable force, the single-span cable is divided into several micro-segments through a micro-segmentation process. This division determines the segment density based on the cable's curvature variation and load distribution, reasonably controlling the calculation scale while ensuring calculation accuracy. Each micro-segment is considered a cable element with constant internal force and curvature. Based on the divided micro-segments, the force and shape of each micro-segment are derived segment by segment using Newton's iteration method and the catenary equation. Starting from the cable segment's starting point, the relationship between the micro-segment's geometry and internal force is established using the catenary equation. The nonlinear equation is solved using Newton's iteration method, and the end force and spatial coordinates of each micro-segment are calculated sequentially to form a complete cable shape description. Based on the derived shape, the calculated cable shape endpoint elevation difference is compared with the target elevation difference through an elevation difference comparison process. The difference between the actual solved cable shape endpoint elevation and the design target is calculated to evaluate the accuracy of the current calculation results.

[0054] If the elevation difference error exceeds the allowable value, the initial values ​​are adjusted using an iterative initial value adjustment method, and the calculation is recalculated. The initial force values ​​are modified according to a predetermined strategy based on the magnitude and direction of the error. The process of micro-segment division and cable shape derivation is repeated until the elevation difference error is within the allowable range, thus generating the stress-free length of the single-span cable on the first fixed pulley side. The micro-segment division process transforms the continuous problem into a discrete problem through discretization, reducing the solution difficulty. The application of Newton's iteration method and the catenary equation ensures the theoretical accuracy of each micro-segment calculation. Elevation difference comparison provides an objective accuracy evaluation standard. Iterative initial value adjustment achieves self-optimization of the calculation process. The combination of these technical features allows the calculation of the stress-free length of the single-span cable to gradually approach the true solution, ensuring both computational efficiency and numerical stability. Strict error control ensures the reliability of the results, providing an accurate local model for subsequent continuous solutions and effectively supporting the implementation of the overall calculation method.

[0055] In some implementations, step S23 includes:

[0056] S231. Based on the constraint of force balance at the fixed pulley, determine the starting force for the calculation of the right cable segment;

[0057] S232. Based on the starting force determined in step S231, solve the cable shape of each segment according to the catenary equation through the catenary iterative solution process.

[0058] S233. Based on the cable shape obtained in step S232, the calculated cable shape endpoint elevation difference is compared with the target elevation difference through the elevation difference comparison process.

[0059] S234. Based on the comparison results of step S233, if the elevation difference error exceeds the allowable value, the initial value of the vertical force is adjusted and recalculated using the initial value adjustment method of the vertical force until the elevation difference error is within the allowable range, and the stress-free length of the single span cable on the other side of the first fixed pulley is generated.

[0060] The key to step S23 is to use the mechanical equilibrium conditions at the pulley to solve for the stress-free length of the cable segment on the other side. Based on the constraint of force equilibrium at the fixed pulley, the starting force for calculating the right cable segment is determined. The core of this process lies in utilizing the principle of equal tangential forces at the pulley, that is, the tension of the cable segment on the left side of the pulley at the point of tangency is balanced with the tension of the cable segment on the right side at the point of tangency in the tangential direction of the pulley, thus providing clear boundary conditions for the calculation of the right cable segment. Based on the determined starting force, the cable shape of each segment is solved according to the catenary equation through the iterative solution process. This process starts from the pulley, dividing the right cable segment into an appropriate number of micro-segments. The basic equation of the catenary is applied to each micro-segment, considering parameters such as the cable's self-weight, elastic modulus, and cross-sectional area. The geometric shape and internal force distribution of each micro-segment are solved step by step through numerical methods to form a complete cable shape description. Based on the solved cable shape, the calculated cable shape endpoint elevation difference is compared with the target elevation difference through the elevation difference comparison process. This step establishes a quantitative accuracy evaluation index by calculating the difference between the cable shape endpoint elevation and the design target elevation, ensuring that the calculation results meet the engineering requirements.

[0061] If the elevation difference error exceeds the allowable value, the initial vertical force value is adjusted using a vertical force initial value adjustment method and recalculated. This adjustment process corrects the initial vertical force value according to the magnitude and direction of the elevation difference error and a predetermined correction strategy. Then, the catenary iterative solution process is re-executed until the elevation difference error is within the allowable range, thereby generating the stress-free length of the single-span cable on the other side of the first fixed pulley. This complete calculation process embodies a systematic method from establishing mechanical conditions to iterative solution and then to accuracy control. The constraint of force balance at the fixed pulley ensures the physical rationality of the calculation starting point, the catenary iterative solution guarantees the theoretical accuracy of the calculation process, the elevation difference comparison provides an objective accuracy verification standard, and the adjustment of the initial vertical force value realizes the self-optimization of calculation parameters. Through this progressive calculation method, this approach effectively solves the problem of local calculation deviation caused by ignoring the special mechanical conditions at the pulley in traditional algorithms, while also avoiding the numerical instability of solving complex coupled equation systems. Its technical effects are manifested on multiple levels: determining the starting force based on force balance ensures the mechanical correctness of the calculation basis; iterative solution of the catenary ensures the theoretical accuracy of the cable shape calculation; the elevation difference comparison process establishes an effective error monitoring mechanism; and the adjustment of the initial value of the vertical force realizes the self-improvement of the calculation process. These effects work synergistically to ensure that the solution of the stress-free length of this side cable segment maintains both local calculation accuracy and consistency with the overall mechanical state of the system, providing a reliable guarantee for the subsequent continuous solution process and significantly enhancing the practicality and engineering applicability of the overall calculation method.

[0062] In some implementations, step S24 includes:

[0063] S241. Based on the calculation results of the previous cable segment, the next fixed pulley is regarded as a new starting point through the fixed pulley crossing process;

[0064] S242. Based on the new starting point of step S241, obtain the cable force parameters on one side of the fixed pulley through the cable force parameter acquisition method;

[0065] S243. Based on the cable force parameters obtained in step S242, the stress-free length of adjacent cable segments is solved using the single-span cable stress-free length solution algorithm.

[0066] S244. Repeat steps S241 to S243 until the stress-free length of all cable segments is solved, generating the stress-free length of each cable segment and the total stress-free length in the initial state.

[0067] Step S24, through systematic extended calculations, fully determines the stress-free length of a multi-span continuous cable system. Based on the calculation results of the previous cable segment, the next fixed pulley is considered a new starting point through the fixed pulley crossing process. This operation logically achieves an orderly transfer of the calculation focus while maintaining the continuity of mechanical parameters, providing a feasible calculation path for analyzing complex cable systems containing multiple pulleys. Based on the new starting point, the cable force parameters on one side of the fixed pulley are obtained through a cable force parameter acquisition method. This method extracts key mechanical state information such as the tension value and direction angle at the pulley tangent point from the convergence results of the previous cable segment, ensuring the accuracy and consistency of parameter transfer and avoiding uncertainties introduced by re-assumptions. Based on the obtained cable force parameters, the stress-free length of adjacent cable segments is solved using a single-span cable stress-free length solution algorithm. This algorithm applies the same catenary theory and iterative method as the initial cable segment, ensuring the uniformity of the calculation method and the comparability of the results for the entire system, and maintaining the constancy of the calculation standard.

[0068] Repeat the above process until the stress-free lengths of all cable segments are solved, thus generating the stress-free lengths of each cable segment and the total stress-free length in the initial state. This iterative expansion mechanism, through the iterative application of proven and reliable algorithms, gradually constructs a complete stress-free state description of the entire multi-span cable system, forming a systematic calculation model. The key to the implementation of step S24 lies in its systematicity and scalability. It decomposes the complex multi-span continuous cable problem into a series of manageable single-span cable problems, while maintaining the overall consistency of the solution through precise parameter transfer. This method effectively avoids the computational complexity and convergence difficulties caused by the need to solve all unknowns simultaneously in traditional methods, providing a clear and feasible computational path. Its technical effects are reflected in multiple aspects: the fixed pulley crossing process realizes the logical expansion and orderly advancement of the calculation range; the acquisition of cable force parameters ensures the accurate transfer and continuity of the mechanical state between stages; the repeated application of proven algorithms ensures the consistency and reliability of the calculation accuracy of the entire system; and the final generation of a complete stress-free state provides accurate benchmark parameters for subsequent construction stage analysis. These effects work together to enable the method to efficiently handle complex cable systems with multiple pulleys, while maintaining the stability of the calculation process and the reliability of the results. Through a systematic decomposition and recombination strategy, complex problems are transformed into a series of simple problems, providing a practical and efficient analysis tool for engineering applications and significantly improving the feasibility and accuracy of calculations for multi-span cable systems.

[0069] In some implementations, step S4 includes:

[0070] S41. Based on the calculation results stored in the previous construction stage, obtain the displacement state of the support structure and the boundary conditions of the cable structure.

[0071] S42. Based on the displacement state and boundary conditions obtained in step S41, the displacement state of the support structure and the boundary conditions of the cable structure at the current stage are generated through the structural state update method.

[0072] Step S4 focuses on the coherent updating and data inheritance of the structural state between construction stages. Based on the calculation results stored in the previous construction stage, the displacement state of the supporting structure and the boundary conditions of the cable structure are obtained. This process reads the deformation parameters such as nodal displacements and rotations of the supporting structure, as well as the boundary information such as anchorage conditions and constraints of the cable structure, from the stored convergence results to form the initial dataset for the current stage calculation. Based on the obtained displacement state and boundary conditions, the displacement state of the supporting structure and the boundary conditions of the cable structure under the current stage are generated through a structural state update method. This update process comprehensively considers various changing factors that occur during the construction process, including new loads, geometric configuration adjustments, and changes in constraint conditions. Through a systematic state transition algorithm, the final state of the previous stage is transformed into the initial conditions of the current stage, forming an analytical basis adapted to the new stage.

[0073] Step S4 embodies the principles of state continuity and data inheritance in construction process simulation. By establishing an information transfer mechanism between stages, it effectively transforms the convergence results of the previous stage into the starting conditions of the current stage. This method fundamentally changes the traditional approach where each construction stage requires an independent computational model, eliminating the need for manual data transfer and model reconstruction between stages. Its technical effects are multifaceted: obtaining the initial state based on stored results ensures accurate inheritance of historical data and computational continuity; the structural state update method can flexibly adapt to various changes in construction conditions, maintaining the timeliness of the analysis; and the entire process achieves automated transitions between stage analyses, significantly improving computational efficiency. These combined effects effectively solve the problem of poor construction adaptability in the background technology. Automated state transfer avoids errors that may be introduced by manual intervention, ensuring the consistency and reliability of multi-stage analysis. This provides a solid technical foundation for continuous simulation of complex construction processes, making construction process simulation more closely resemble actual engineering conditions.

[0074] In some implementations, step S5 includes:

[0075] S51. For each fixed pulley, calculate the slip stiffness based on the stress-free length of the cable segments on both sides of the fixed pulley;

[0076] S52. Based on the ratio of the difference in cable force on both sides of the current fixed pulley to the slip stiffness calculated in step S51, the slip amount of the cable segment is calculated using a preset slip amount calculation formula.

[0077] S53. Based on the slippage calculated in step S52, adjust the stress-free length of the cable segments on both sides of the fixed pulley through the stress-free cable length adjustment process.

[0078] S54. Based on the stress-free length adjusted in step S53, update the cable force through the preset cable force-cable length variation formula, and iterate until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, generating the stress-free length, cable force and node coordinates of each cable segment after convergence.

[0079] Step S5, through refined slip processing and systematic iterative balancing, achieves coordinated control of cable length and force at the pulley. For each fixed pulley, the slip stiffness is calculated based on the stress-free length of the cable segments on both sides of the fixed pulley. This parameter characterizes the change in cable force caused by a unit change in the stress-free length of the cable segment, reflecting the sensitivity of the cable segment to length changes and providing key mechanical characteristic parameters for subsequent slip analysis. Based on the ratio of the current cable force difference on both sides of the fixed pulley to the calculated slip stiffness, the slip amount of the cable segment is calculated using a preset slip amount calculation formula. This formula establishes a quantitative relationship between the degree of cable force imbalance and the required cable length adjustment, derived from the mechanical balance principle at the pulley, providing a theoretical basis for determining the slip amount. Based on the calculated slip amount, the stress-free length of the cable segments on both sides of the fixed pulley is adjusted through a stress-free cable length adjustment process. This adjustment, while keeping the total stress-free length of the cable segments on both sides of the pulley constant, redistributes the individual stress-free lengths of the cable segments on both sides according to the slip amount, accurately simulating the actual cable segment slip phenomenon during construction.

[0080] Based on the adjusted stress-free length, the cable force is updated through a preset cable force-cable length variation formula. This formula, derived from catenary theory, describes the quantitative relationship between cable length variation and cable force response, allowing direct calculation of cable force change from cable length variation, avoiding the tedious process of iterative solution. The iteration continues until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, generating the converged stress-free length, cable force, and node coordinates for each cable segment. This iterative process continuously updates the mechanical state of the system, gradually eliminating unbalanced forces at each pulley, while considering the displacement coordination of the supporting structure, ultimately achieving a stable equilibrium state for the system. Step S5 constructs a complete cable length-cable force coordination system. The slip stiffness calculation provides a description of the system's mechanical response characteristics, the slip amount calculation determines a reasonable adjustment range, the stress-free cable length adjustment executes specific parameter modifications, the cable force-cable length variation formula enables direct updating of the mechanical state, and the iterative equilibrium ensures the reliability of the final result.

[0081] This method, through its systematic processing, effectively solves the problems of complex slip calculation and convergence difficulties in the background technology. Its technical effects are reflected in the following aspects: the slip stiffness calculation accurately characterizes the mechanical properties of the system, laying the foundation for slip analysis; the slip amount calculation formula provides a clear adjustment basis, ensuring the physical rationality of the solution; the stress-free cable length adjustment realizes automatic parameter updates, avoiding manual intervention; the cable force-length relationship avoids repeated iterative solutions, improving computational efficiency; and the iterative balancing mechanism ensures the accuracy and reliability of the final result. These effects work synergistically, enabling efficient and accurate handling of slip phenomena at the pulley, gradually approximating the true solution through systematic iterative optimization, significantly improving the practicality and engineering applicability of the overall calculation method, and providing an effective technical means for the construction control of complex cable systems.

[0082] In some embodiments, the relationship between cable force and cable length variation is as follows:

[0083] ;

[0084] in: ;

[0085] The left side of the above equation is the force vector, H i V i These represent the horizontal force and vertical force at end i, respectively, and H. j V j These represent the horizontal and vertical forces at end j, respectively. The right side shows the stiffness matrix and the cable length variation vector. k ij For the sake of i , j The parameter matrix of the force-displacement stiffness at both ends, its elements k 11 , k 12 , k 21 , k 22 u is obtained from the nonlinear equation of cable end force-stress-free cable length. i v i These are the horizontal and vertical displacements at end i, calculated from the change in cable length, respectively, and u. j v j These are the horizontal and vertical displacements at end j, calculated from the change in cable length, respectively. After a change in cable length, this equation allows for the direct calculation of the change in cable force from the change in cable length, thus avoiding the need to iterate and solve for the new cable force again using the catenary equation.

[0086] In actual calculations, after obtaining the cable length slippage from pulley balancing, the left and right span cables are respectively calculated according to the slippage, and the above-mentioned change equation is called to solve for the new cable force, so as to realize the direct update of the structural mechanical state from the change of cable length.

[0087] In some embodiments, the formula for calculating the cable segment slip is: ;

[0088] Where: K j Let x be the total slip stiffness of the j-th pulley. j Let be the slippage at the j-th pulley.

[0089] In some implementations, step S51 includes:

[0090] S511. For each fixed pulley, based on the stress-free length of the cable segments on both sides of the fixed pulley, the stress-free length of the cable segments on both sides of the fixed pulley is increased by one unit by the unit length increase method.

[0091] S512. Based on the stress-free length after increasing the unit quantity in step S511, calculate the change in cable force.

[0092] S513. Based on the ratio of the change in cable force to the increment per unit length calculated in step S512, the slip stiffness is generated using a preset slip stiffness calculation formula.

[0093] The specific implementation of step S51 provides a practical method for solving slip stiffness using the unit increment method. For each fixed pulley, based on the stress-free length of the cable segments on both sides of the fixed pulley, the stress-free length of the cable segments on both sides of the fixed pulley is increased by one unit using the unit length increase method. This operation involves only a small perturbation to the stress-free length of the adjacent cable segments on both sides of the target pulley while keeping other system parameters constant. The perturbation amount should be small enough to ensure the accuracy of the calculation, but not too small to avoid numerical calculation errors. Based on the stress-free length after the unit increase, the change in cable force is calculated. This process requires recalculating the equilibrium state of the system under the new stress-free length distribution to obtain the change in cable force on both sides of the pulley. The chain effect of cable length change on the overall mechanical state of the system needs to be considered during the calculation. Based on the ratio of the calculated change in cable force to the unit length increment, the slip stiffness is generated through a preset slip stiffness calculation formula. This formula essentially defines the sensitivity of cable force change to cable length change, reflecting the stiffness characteristics of the system under a specific state.

[0094] The technical foundation of this series of operations lies in utilizing the principle of micro-perturbation to probe the mechanical response characteristics of a system. The unit length increase method introduces controllable small perturbations to probe the local behavior of the system, avoiding the computational burden of directly solving complex differential equations. The process of calculating the change in cable force accurately captures the degree of influence of the cable length change on the cable force by comparing the system state before and after the perturbation. The preset slip stiffness calculation formula ultimately quantifies the probe results into specific stiffness parameters, providing key inputs for subsequent slip calculations. Introducing controllable perturbations through the unit length increase method effectively probes the local mechanical characteristics of the system; the process of calculating the change in cable force accurately captures the system's response sensitivity; and the preset slip stiffness calculation formula quantifies the probe results into practical parameters. These technical effects ensure both computational efficiency and numerical stability in the solution of slip stiffness. By replacing complex differential solutions with simple arithmetic operations, computational complexity is significantly reduced, providing a reliable parameter basis for pulley slip analysis and effectively supporting the engineering practicality of the overall calculation method.

[0095] In some embodiments, the formula for calculating slip stiffness is: ;

[0096] Where K jL K jR These represent the left and right sliding stiffness of pulley j, respectively, and T. jL T jR These are the initial left and right cable forces of pulley j, respectively, T' jL 、T' jR s represents the left and right cable forces after a unit length increase in cable length without stress, and s represents the unit increase in cable length.

[0097] In some implementations, step S52 includes:

[0098] S521. Based on the current cable forces on both sides of the fixed pulley, obtain the current difference in cable forces on both sides of the fixed pulley;

[0099] S522. Based on the ratio of the cable force difference obtained in step S521 to the slip stiffness calculated in step S51, the slip amount of the cable segment is generated using a preset slip amount calculation formula.

[0100] The key point of step S52 is to determine a reasonable cable length adjustment based on the degree of mechanical imbalance. Based on the cable forces on both sides of the current fixed pulley, the difference in cable forces between the two sides is obtained. This process quantifies the degree of imbalance of the current system at that pulley by directly comparing the numerical difference between the cable forces on the left and right sides of the pulley, providing clear input parameters for calculating the slip. Based on the ratio of the obtained cable force difference to the slip stiffness calculated in step S51, the slip of the cable segment is generated using a preset slip calculation formula. This formula is derived based on the principle of mechanical equilibrium and establishes a linear relationship between cable force imbalance and the required cable length adjustment, reflecting the regulating effect of cable length changes on cable force balance.

[0101] The technical principle behind this calculation process lies in using stiffness parameters to transform force imbalance into geometric adjustment. Obtaining the force difference between the two sides of the fixed pulley directly reflects the mechanical imbalance state of the system at that point, providing a clear target for adjustment. The preset slip calculation formula maps the force domain imbalance to the geometric domain adjustment amount through stiffness parameters, realizing the conversion from mechanical state to geometric parameters. By accurately quantifying the degree of system imbalance through the force difference between the two sides of the fixed pulley, and establishing the force-geometry conversion relationship using slip stiffness, the preset slip calculation formula achieves a precise mapping from mechanical imbalance to geometric adjustment. These technical effects give the determination of slip a clear physical meaning and computational reliability. A reasonable adjustment amount can be obtained through simple ratio calculations, avoiding the complex trial-and-error process in traditional methods, significantly improving computational efficiency, and ensuring the rationality of the adjustment amount. This provides precise guiding parameters for stress-free cable length adjustment, effectively supporting the accurate implementation of pulley slip analysis.

[0102] In some implementations, step S53 includes:

[0103] S531. Based on the slippage, determine the stress-free length adjustment amount of the cable segments on both sides of the fixed pulley;

[0104] S532. Based on the stress-free length adjustment amount determined in step S531, adjust the stress-free length of the cable segments on both sides of the fixed pulley through the stress-free length modification process.

[0105] S533. Based on the stress-free length adjusted in step S532, the total stress-free length of the cable segments on both sides of the fixed pulley remains unchanged through the total length verification process, and the adjusted stress-free length is output.

[0106] Step S53 systematically completes the actual adjustment process of the stress-free cable length. Based on the slippage, the stress-free length adjustment amount of the cable segments on both sides of the fixed pulley is determined. This process determines the stress-free length modification value of each cable segment on both sides according to the direction and magnitude of the slippage and the principle of conservation of the total stress-free length at the pulley. Generally, the stress-free length of the cable segment on the side with smaller cable force decreases, while the stress-free length of the cable segment on the side with larger cable force increases accordingly. Based on the determined stress-free length adjustment amount, the stress-free length of the cable segments on both sides of the fixed pulley is adjusted through the stress-free length modification process. In actual calculations, this is reflected in updating the stress-free length parameter value of the corresponding cable segment and recording this modification in the system database to ensure that subsequent calculations are based on the updated parameters. Based on the adjusted stress-free length, the total length verification process verifies that the total stress-free length of the cable segments on both sides of the fixed pulley remains unchanged, and outputs the adjusted stress-free length. This verification is done by calculating the sum of the stress-free lengths of the cable segments on both sides after adjustment and comparing it with the total length before adjustment, confirming that it remains constant within the numerical accuracy range, thus ensuring that the adjustment process conforms to the physical conservation law.

[0107] The process of determining the stress-free length adjustment of the cable segments on both sides of the fixed pulley ensured the physical rationality of the adjustment scheme. The stress-free length modification process realized the actual update of parameters, and the total length verification process provided a mechanism to verify the correctness of the adjustment. By determining the specific adjustment value of the stress-free length of the cable segments on both sides of the fixed pulley, the stress-free length modification process realized the actual update of parameters, and the total length verification process ensured the physical correctness of the adjustment process. These technical effects together ensured the accurate implementation of the stress-free cable length adjustment. Through a systematic adjustment and verification process, both the reasonable redistribution of cable length and the conservation characteristics of the total stress-free length of the system were achieved, providing a correct geometric basis for subsequent cable force updates and effectively supporting the accurate simulation of pulley slippage.

[0108] In some implementations, step S54 includes:

[0109] S541. Based on the adjusted stress-free length, update the cable force through the preset cable force-cable length variation formula;

[0110] S542. Based on the updated cable force in step S541, verify the cable force balance on both sides of the fixed pulley through the cable force balance verification process.

[0111] S543. Based on the verification results of step S542, if the structure is not balanced, repeat steps S51 to S54 until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, and generate the stress-free length, cable force and node coordinates of each cable segment after convergence.

[0112] Step S54 ensures the system reaches equilibrium through iterative updates and verification mechanisms. Based on the adjusted stress-free length, the cable force is updated using a pre-defined force-length relationship. This process utilizes the established mathematical relationship between cable length and force, directly calculating the new force distribution from the updated stress-free length, avoiding complex catenary iterations and significantly improving computational efficiency. Based on the updated force, a force balance verification process verifies the balance of the cable forces on both sides of the fixed pulleys. This verification compares the numerical differences in the cable forces on both sides of each pulley to determine if the preset balance tolerance requirements are met, providing a criterion for iterative convergence. Based on the verification results, if unbalanced, steps S51 to S54 are repeated until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges. The converged stress-free length, force, and node coordinates of each cable segment are generated. This iterative cycle reflects the system's gradual approach to equilibrium, with each iteration improving upon the previous result until all convergence conditions are met.

[0113] Rapid updates to the mechanical state are achieved by updating cable forces using a pre-defined cable force-length variation formula. The cable force balance verification process provides a monitoring mechanism for the iterative progress, and repeated iterations until convergence ensure the reliability of the final result. The efficient updating of cable forces is achieved using a pre-defined cable force-length variation formula, and the accuracy of the results is ensured by monitoring the iterative progress through the cable force balance verification process and repeating iterations until convergence. These technical effects enable the balance solution process to maintain both computational efficiency and result accuracy. Through a systematic iterative update mechanism, unbalanced forces within the system are gradually eliminated, while considering the displacement coordination of the supporting structure, ultimately obtaining a convergent solution that satisfies all equilibrium conditions. This provides a reliable description of the termination state for construction stage analysis, effectively supporting the practicality and reliability of the overall calculation method.

[0114] It should be noted that the automatic cable length slippage and adjustment must be considered in conjunction with the subsequent cable force update, as these two processes constitute the main iterative flow of slippage in a single construction segment. The main differences from the traditional manual calculation process are twofold: First, the original manual calculations are based on various principles and generally rely on other numerical calculation tools. In terms of calculation principles, this invention uses a simpler incremental method, primarily relying on the one-to-one correspondence between cable length and cable force under certain boundary conditions, resulting in faster calculations. Currently, commonly used calculation methods derive nonlinear partial differential equations of cable force and length from the basic cable equations, which are more complex to solve. Second, after completing the cable length slippage adjustment, the previous manual calculations relied on external numerical tools to calculate the cable length. Adjusting the amount of cable force and manually changing the model values, then recalculating the entire model, requires resolving all the catenaries to obtain the adjusted cable force results. This calculation is time-consuming. If there are many pulleys and the cable forces on both sides of the pulleys are difficult to adjust in one go, the entire structure needs to be calculated repeatedly, significantly increasing the calculation time and easily leading to non-convergence. The cable force update method adopted in this invention starts from the basic equation of the cable structure, and uses the small amount of cable length increase as equivalent to the cable end displacement. It obtains the stiffness matrix related to the cable force at both ends of each cable and the change in cable length. Then, it directly obtains the new cable force based on the slippage of each pulley. It quickly compares the cable force results on both sides of all pulleys after the cable length adjustment to determine whether convergence has been achieved. The calculation speed is fast and it has strong adaptability to structures with a large number of pulleys.

[0115] Although the overall process of automatic and manual calculation is the same, the internal calculation methods are different. In particular, the cable force update part proposed in this invention has a significant improvement over the manual calculation method.

[0116] Example 2

[0117] like Figure 3 As shown, in a second aspect, the present invention proposes an overall calculation system for a continuous cable structure spanning a fixed pulley. The system employs the overall calculation method for a continuous cable structure spanning a fixed pulley provided in any of the above embodiments. The system includes:

[0118] The parameter acquisition module is used to acquire system parameters and target state parameters based on user input. The system parameters include the geometric configuration and connection relationship of the support structure, cable structure and fixed pulleys. The support structure is used to fix the fixed pulleys. The cable structure is a continuous cable that spans multiple fixed pulleys. The fixed pulleys allow the cable structure to slide on them.

[0119] The initial stress-free cable length calculation module is used to generate the stress-free length of each cable segment and the total stress-free length in the initial state based on the system parameters and target state parameters, using the initial stress-free cable length calculation method.

[0120] The construction phase initialization module is used to generate the initial construction phase state based on the stress-free length and total stress-free length using the construction phase initialization method. The initial construction phase state includes the initial stress-free length, cable force, and node coordinates.

[0121] The multi-construction stage processing module is used to generate the displacement state of the supporting structure and the boundary conditions of the cable structure under the current stage based on the initial construction stage state and through a multi-construction stage cyclic processing method. For each construction stage, based on the calculation results stored in the previous construction stage, the module uses a structural state update method.

[0122] The pulley slip and cable length adjustment module is used to adjust the stress-free length of the cable segments on both sides of the fixed pulley and update the cable force based on the displacement state and boundary conditions, through fixed pulley slip calculation and cable length adjustment method, until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, and generates the stress-free length, cable force and node coordinates of each cable segment after convergence;

[0123] The data storage and output module is used to store the results of the current construction stage based on the stress-free length, cable force and node coordinates of each cable segment after convergence, and to output the calculation results of all construction stages after all construction stages are completed.

[0124] The present invention also provides a computing device, comprising:

[0125] processor;

[0126] Memory used to store processor-executable instructions;

[0127] The processor is used to execute the method provided in any of the above embodiments.

[0128] The present invention also provides a computer-readable storage medium storing a computer program for performing the method provided in any of the above embodiments.

[0129] Computer-readable storage media may take the form of any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may, for example, include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for integral calculation of a continuous cable structure across a fixed pulley, characterized by, include: S1. Based on user input, obtain system parameters and target state parameters. The system parameters include the geometric configuration and connection relationship of the support structure, cable structure and fixed pulley. The support structure is used to fix the fixed pulley. The cable structure is a continuous cable that spans multiple fixed pulleys. The fixed pulleys allow the cable structure to slide on it. S2. Based on the system parameters and target state parameters, the stress-free length of each cable segment and the total stress-free length in the initial state are generated using the initial stress-free cable length calculation method; wherein, step S2 includes: S21. Based on system parameters and target state parameters, the initial value of the cable force is obtained through the iterative cable force initial value calculation method; the theoretical model is selected according to the cable sag-to-span ratio characteristics. For the case of large sag-to-span ratio, the parabolic theory is used to provide the initial estimate, and for the case of small sag-to-span ratio, the unknown load factor method is used. S22. Based on the initial value of the iterative cable force obtained in step S21, the stress-free length of the single-span cable on one side of the first fixed pulley is solved by the algorithm for solving the stress-free length of the single-span cable. The single-span cable is discretized into several micro-segments, and the cable shape and internal force are calculated segment by segment by Newton's iteration method combined with the catenary equation. The calculated cable shape is made to match the target state by repeated adjustments. S23. Based on the stress-free length and force balance constraint at the fixed pulley obtained in step S22, the stress-free length of the single-span cable on the other side of the first fixed pulley is solved using the stress-free length solution algorithm for the single-span cable on the other side. The calculation starting point is determined by using the force balance condition at the pulley, and the cable shape parameters are solved by Newton's iteration method to ensure the coordination and consistency of the mechanical state on both sides of the pulley. S24. Based on the stress-free length obtained in step S23, the stress-free length of adjacent cable segments is repeatedly obtained through the fixed pulley crossing and continuous solution process until the stress-free length of all cable segments is obtained, generating the stress-free length of each cable segment and the total stress-free length in the initial state; the results of the solved cable segments are used as the input conditions for adjacent cable segments, and the process is continued until the calculation of all cable segments is completed, finally generating the stress-free length of each cable segment and the total stress-free length in the initial state; Step S24 includes: S241. Based on the calculation results of the previous cable segment, the next fixed pulley is regarded as a new starting point through the fixed pulley crossing process; S242. Based on the new starting point of step S241, obtain the cable force parameters on one side of the fixed pulley through the cable force parameter acquisition method; S243. Based on the cable force parameters obtained in step S242, the stress-free length of adjacent cable segments is solved using the single-span cable stress-free length solution algorithm. S244. Repeat steps S241 to S243 until the stress-free length of all cable segments is solved, generating the stress-free length of each cable segment and the total stress-free length in the initial state. S3. Based on the stress-free length and total stress-free length generated in step S2, the initial construction stage state is generated through the construction stage initialization method. The initial construction stage state includes the initial stress-free length, cable force, and node coordinates. S4. Based on the initial construction stage state generated in step S3, using a multi-construction stage iterative processing method, for each construction stage, based on the calculation results stored in the previous construction stage, a structural state update method is used to generate the displacement state of the supporting structure and the boundary conditions of the cable structure under the current stage; wherein, step S4 includes: S41. Based on the calculation results stored in the previous construction stage, obtain the displacement state of the support structure and the boundary conditions of the cable structure. S42. Based on the displacement state and boundary conditions obtained in step S41, the displacement state of the support structure and the boundary conditions of the cable structure under the current stage are generated through the structural state update method. S5. Based on the displacement state and boundary conditions generated in step S4, the stress-free length of the cable segments on both sides of the fixed pulley is adjusted and the cable force is updated through the fixed pulley slip calculation and cable length adjustment method until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, generating the stress-free length, cable force and node coordinates of each cable segment after convergence. S6. Based on the converged stress-free length, cable force, and node coordinates of each cable segment generated in step S5, store the results of the current construction stage, and output the calculation results of all construction stages after all construction stages are completed.

2. The overall calculation method for a continuous cable structure spanning a fixed pulley according to claim 1, characterized in that, Step S21 includes: S211. Based on the target state parameters, the initial cable force value is generated for a cable with a specific sag-span ratio by applying parabolic theory. S212. Based on the initial cable force value generated in step S211, the horizontal and vertical components of the cable force are generated through a component calculation process. S213. Based on the horizontal and vertical components generated in step S212, determine the cable end inclination angle and integrate them to generate the initial value of the iterative cable force.

3. The overall calculation method for a continuous cable structure spanning a fixed pulley according to claim 1, characterized in that, Step S22 includes: S221. Based on the iterative initial value of cable force, the single-span cable is divided into several micro-segments through a micro-segmentation process; S222. Based on the micro-segments divided in step S221, the force and shape of each micro-segment are derived segment by segment using Newton's iteration method and the catenary equation. S223. Based on the shape derived in step S222, the calculated cable end point elevation difference is compared with the target elevation difference through the elevation difference comparison process. S224. Based on the comparison results of step S223, if the elevation difference error exceeds the allowable value, the initial value of the iteration is adjusted and recalculated using the iterative initial value adjustment method until the elevation difference error is within the allowable range, and the stress-free length of the single-span cable on the first fixed pulley side is generated.

4. The overall calculation method for a continuous cable structure spanning a fixed pulley according to claim 1, characterized in that, Step S23 includes: S231. Based on the constraint of force balance at the fixed pulley, determine the starting force for the calculation of the right cable segment; S232. Based on the starting force determined in step S231, solve the cable shape of each segment according to the catenary equation through the catenary iterative solution process. S233. Based on the cable shape obtained in step S232, the calculated cable shape endpoint elevation difference is compared with the target elevation difference through the elevation difference comparison process. S234. Based on the comparison results of step S233, if the elevation difference error exceeds the allowable value, the initial value of the vertical force is adjusted and recalculated using the initial value adjustment method of the vertical force until the elevation difference error is within the allowable range, and the stress-free length of the single span cable on the other side of the first fixed pulley is generated.

5. The overall calculation method for a continuous cable structure spanning a fixed pulley according to claim 1, characterized in that, Step S5 includes: S51. For each fixed pulley, calculate the slip stiffness based on the stress-free length of the cable segments on both sides of the fixed pulley; S52. Based on the ratio of the difference in cable force on both sides of the current fixed pulley to the slip stiffness calculated in step S51, the slip amount of the cable segment is calculated using a preset slip amount calculation formula. S53. Based on the slippage calculated in step S52, adjust the stress-free length of the cable segments on both sides of the fixed pulley through the stress-free cable length adjustment process. S54. Based on the stress-free length adjusted in step S53, update the cable force through the preset cable force-cable length variation formula, and iterate until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, generating the stress-free length, cable force and node coordinates of each cable segment after convergence.

6. The overall calculation method for a continuous cable structure spanning a fixed pulley according to claim 5, characterized in that, Step S51 includes: S511. For each fixed pulley, based on the stress-free length of the cable segments on both sides of the fixed pulley, the stress-free length of the cable segments on both sides of the fixed pulley is increased by one unit by the unit length increase method. S512. Based on the stress-free length after increasing the unit quantity in step S511, calculate the change in cable force. S513. Based on the ratio of the change in cable force to the increment per unit length calculated in step S512, the slip stiffness is generated using a preset slip stiffness calculation formula.

7. The overall calculation method for a continuous cable structure spanning a fixed pulley according to claim 5, characterized in that, Step S52 includes: S521. Based on the current cable forces on both sides of the fixed pulley, obtain the current difference in cable forces on both sides of the fixed pulley; S522. Based on the ratio of the cable force difference obtained in step S521 to the slip stiffness calculated in step S51, the slip amount of the cable segment is generated using a preset slip amount calculation formula.

8. The overall calculation method for a continuous cable structure spanning a fixed pulley according to claim 5, characterized in that, Step S53 includes: S531. Based on the slippage, determine the stress-free length adjustment amount of the cable segments on both sides of the fixed pulley; S532. Based on the stress-free length adjustment amount determined in step S531, adjust the stress-free length of the cable segments on both sides of the fixed pulley through the stress-free length modification process. S533. Based on the stress-free length adjusted in step S532, the total stress-free length of the cable segments on both sides of the fixed pulley remains unchanged through the total length verification process, and the adjusted stress-free length is output.

9. The overall calculation method for a continuous cable structure spanning a fixed pulley according to claim 5, characterized in that, Step S54 includes: S541. Based on the adjusted stress-free length, update the cable force through the preset cable force-cable length variation formula; S542. Based on the updated cable force in step S541, verify the cable force balance on both sides of the fixed pulley through the cable force balance verification process. S543. Based on the verification results of step S542, if the structure is not balanced, repeat steps S51 to S54 until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, and generate the stress-free length, cable force and node coordinates of each cable segment after convergence.

10. A comprehensive calculation system for a continuous cable structure spanning a fixed pulley, characterized in that, The system employs the overall calculation method for continuous cable structures spanning fixed pulleys as described in any one of claims 1 to 9, and the system comprises: The parameter acquisition module is used to acquire system parameters and target state parameters based on user input. The system parameters include the geometric configuration and connection relationship of the support structure, cable structure and fixed pulleys. The support structure is used to fix the fixed pulleys. The cable structure is a continuous cable that spans multiple fixed pulleys. The fixed pulleys allow the cable structure to slide on them. The initial stress-free cable length calculation module is used to generate the stress-free length of each cable segment and the total stress-free length in the initial state based on the system parameters and target state parameters, using the initial stress-free cable length calculation method. The construction phase initialization module is used to generate the initial construction phase state based on the stress-free length and total stress-free length using the construction phase initialization method. The initial construction phase state includes the initial stress-free length, cable force, and node coordinates. The multi-construction stage processing module is used to generate the displacement state of the supporting structure and the boundary conditions of the cable structure under the current stage based on the initial construction stage state and through a multi-construction stage cyclic processing method. For each construction stage, based on the calculation results stored in the previous construction stage, the module uses a structural state update method. The pulley slip and cable length adjustment module is used to adjust the stress-free length of the cable segments on both sides of the fixed pulley and update the cable force based on the displacement state and boundary conditions, through fixed pulley slip calculation and cable length adjustment method, until the cable forces on both sides of all fixed pulleys are balanced and the structural displacement converges, and generates the stress-free length, cable force and node coordinates of each cable segment after convergence; The data storage and output module is used to store the results of the current construction stage based on the stress-free length, cable force and node coordinates of each cable segment after convergence, and to output the calculation results of all construction stages after all construction stages are completed.

11. A computing device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is used to execute the overall calculation method for the continuous cable structure across a fixed pulley as described in any one of claims 1 to 9.

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