A prefabrication method for the elastic suspension cable and electrical connection of the high-speed railway catenary based on BIM

Abstract

The present application discloses a prefabrication processing method for an elastic suspension cable and electrical connection of a high-speed railway catenary based on BIM, which relates to the field of elastic suspension cable processing and includes: establishing a knowledge base, and establishing an initial elastic suspension cable BIM model of the target project through parametric modeling; establishing an initial finite element analysis model of the target project through mesh division and material property mapping; using the incremental iteration method to calculate the internal force and deformation of the elastic suspension cable under static load; performing dynamic time history analysis using the direct integration method to obtain the time history curve of the elastic suspension cable under different seismic waves; according to the static and dynamic analysis results, extracting the stress-strain response of the elastic suspension cable, and using the topology optimization method, with the minimum strain of the elastic suspension cable as the goal and the stress constraint of the elastic suspension cable as the condition, optimizing the initial elastic suspension cable BIM model; using the optimized elastic suspension cable BIM model to update the finite element analysis model. The present application improves the degree of parametric design of the elastic suspension cable.

Description

Technical Field

[0001] The present application relates to the field of elastic sling processing, and particularly to a prefabrication processing method for an elastic sling and electrical connection of a high-speed rail catenary based on BIM. Background Art

[0002] The rapid development of high-speed railways has put forward higher requirements for the reliability and stability of the catenary. As a key component of the high-speed rail power supply system, the performance of the catenary directly affects the safe operation and operation efficiency of trains. To adapt to complex working conditions such as high speed, heavy load, and high density, the catenary needs to continuously improve the scientific and refined levels of design, construction, and operation and maintenance. However, the traditional catenary design and production methods have problems such as experience dependence, information silos, and insufficient analysis, and it is difficult to meet the technical requirements of the new era. It is urgent to introduce advanced informatization and intelligent technologies to promote the transformation and upgrading of the catenary design and production mode.

[0003] As a representative technology of construction industry informatization, BIM (Building Information Modeling) has been widely used in the field of engineering construction in recent years. BIM uses a digital model as a carrier to integrate information such as geometry, attributes, and status in the whole life cycle of the project, and significantly improves the efficiency and quality of project implementation through means such as visualization, collaboration, and optimization. Introducing BIM into the catenary design and production is expected to break through the current technical bottlenecks, realize the integration of design, construction, and operation and maintenance, and improve the catenary construction level. This is not only an inevitable choice to conform to the trend of informatization development, but also an important measure to promote the technological progress and industrial upgrading of high-speed railways.

[0004] The elastic sling is one of the key components of the catenary and is crucial for ensuring the geometric shape and dynamic performance of the catenary. The traditional elastic sling design mainly relies on experience, lacks theoretical guidance and informatization support, and it is difficult to meet the increasingly high technical requirements. The design lacks a unified information expression standard, and the attribute data such as geometry, materials, and processes are scattered and incomplete, making it difficult to establish associations between specialties, and the parameterization and intelligent levels need to be improved urgently. The elastic sling needs to bear various loads such as wind load, ice load, and earthquake, and the existing design lacks systematic static and dynamic performance analysis, making it difficult to comprehensively evaluate the stress characteristics and safety margin. The elastic sling layout scheme has a significant impact on the catenary performance, but currently, the empirical method or parameter method is mainly used for optimization, lacking advanced topology optimization and intelligent optimization means, and the scientific nature and efficiency of optimization need to be strengthened. Summary of the Invention

[0005] Aiming at the problem of low parametric design level of elastic slings in the existing technology, the present application provides a prefabrication method for elastic slings and electrical connections of high-speed railway catenaries based on BIM, evaluates the response of elastic slings under complex loads through static and dynamic analysis, and introduces a topology optimization algorithm to optimize the layout scheme of elastic slings, thereby improving the parametric design level on the premise of ensuring the safety of elastic slings.

[0006] The purpose of the present application is achieved through the following technical solutions.

[0007] The present application provides a prefabrication method for elastic slings and electrical connections of high-speed railway catenaries based on BIM, including: collecting the design parameters and processing data of different types of elastic slings of high-speed railway catenaries, and establishing a knowledge base including geometric parameters, material properties and processing technologies; according to the knowledge base, through parametric modeling, establishing an initial elastic sling BIM model of the target project; the initial elastic sling BIM model includes the spatial position, size and material property parameters of the elastic sling; according to the initial elastic sling BIM model, through mesh generation and material property mapping, establishing an initial finite element analysis model of the target project; in the initial finite element analysis model, applying static load conditions, and using the incremental iteration method to calculate the internal force and deformation of the elastic sling under static loads; the static loads include dead loads and live loads; in the initial finite element analysis model, inputting simulated seismic waves, and performing dynamic time history analysis using the direct integration method to obtain the displacement, velocity, acceleration and internal force time history curves of the elastic sling under different seismic waves; according to the static and dynamic analysis results, extracting the stress-strain response of the elastic sling, and using the topology optimization method, with the minimum strain of the elastic sling as the goal and the stress constraint of the elastic sling as the condition, optimizing the initial elastic sling BIM model; using the optimized elastic sling BIM model to update the finite element analysis model until the performance of the elastic sling meets the design requirements to obtain the final elastic sling BIM model; according to the final elastic sling BIM model, deriving the processing parameters of the elastic sling.

[0008] Further, in the initial finite element analysis model, a static load condition is applied, and the incremental iteration method is used to calculate the internal force and deformation of the elastic sling under the action of static load, including: mapping the dead load information and live load information in the initial elastic sling BIM model into dead load data and live load data respectively; linearly superposing the dead load data and live load data as the static load data applied to the initial finite element model; discretizing the static load data into multiple incremental step data according to the arc length method; obtaining the nonlinear state index of the elastic sling response, and adjusting the step size of the incremental step when the nonlinear state index exceeds the threshold; when the nonlinear state index exceeds the preset extreme value, using the secant method to interpolate the incremental step data; where the nonlinear state index includes deflection; for each incremental step data, adopting the Newton-Raphson iteration format, extracting the displacement increment data in the first iteration and substituting it into the tangent stiffness matrix to form the tangent stiffness equation; extracting the displacement increment data in the subsequent iterations and substituting it into the secant stiffness matrix to form the secant stiffness equation; at the same time, using the energy criterion to correct the direction of the displacement increment data to generate the optimized displacement increment data; after all incremental steps are calculated, extracting the characteristic point data reflecting the deformation failure mode of the elastic sling from the displacement field, stress field and strain field data, and the characteristic points include the maximum deflection point; statistically analyzing the characteristic point data to obtain the weak parts of the elastic sling and forming the elastic sling response data under the action of static load.

[0009] Further, a secant stiffness equation is formed, including: extracting the element stress data and element strain data of the initial finite element analysis model, inputting the element stress data and element strain data into the tangent stiffness matrix to obtain the tangent stiffness matrix data of the elastic sling at the current increment step; in the first iteration, extracting the displacement increment component data from the arc length increment data of the current increment step, substituting the displacement increment component data and the tangent stiffness matrix data into the tangent stiffness equation to solve the node displacement data of the first iteration; updating the element stress data and element strain data by using the node displacement data of the first iteration; inputting the updated element stress data and element strain data into the secant stiffness matrix to obtain the secant stiffness matrix data of the second iteration; extracting the displacement increment component data from the arc length increment data of the current increment step, substituting the displacement increment component data and the secant stiffness matrix data into the secant stiffness matrix to solve the node displacement data of the second iteration; calculating the displacement difference data between the two iterations based on the node displacement data of the first iteration and the node displacement data of the second iteration; if the displacement difference data is less than the convergence threshold, taking the node displacement data of the second iteration as the convergence displacement data of the current increment step and stopping the iterative calculation, otherwise entering the next iterative calculation; updating the element stress data and element strain data by using the node displacement data of the second iteration, and inputting the updated element stress data and element strain data into the secant stiffness matrix to obtain the secant stiffness matrix of the next iteration.

[0010] Further, optimized displacement increment data is generated, including: taking the arc length increment data of the current increment step and the node displacement data of the previous iteration as inputs, and solving the displacement increment direction correction coefficient of the current iteration by minimizing the potential energy; multiplying the displacement increment direction correction coefficient by the displacement increment component data of the current increment step to obtain the corrected displacement increment component data; substituting the corrected displacement increment component into the secant stiffness matrix to solve the node displacement data of the current iteration, and returning to the displacement convergence judgment step until the node displacement data of the current increment step converges.

[0011] Further, obtain the displacement, velocity, acceleration, and internal force time history curves of the elastic sling under different seismic waves, including: select a set of representative seismic waves from the seismic wave database as the input seismic wave data according to the intensity and site category of the area where the project is located; use the modal decomposition response spectrum method to perform baseline correction and amplitude adjustment on the input seismic wave data to obtain simulated seismic wave data; convert the simulated seismic wave data into node load time history data and apply it to the base node degrees of freedom of the initial finite element analysis model to establish the dynamic equilibrium equation considering seismic action, and use the Newmark-β method to directly integrate and solve the dynamic equilibrium equation to obtain the node displacement, node velocity, and node acceleration data at each time step; according to the node displacement data at each time step, calculate the element strain data using the strain-displacement relationship and update the element stress data using the constitutive relationship; multiply the element stress data by the element volume and integrate to obtain the equivalent nodal force data of the element; assemble the equivalent nodal force data of the element into the overall nodal load data and substitute it into the dynamic equilibrium equation for the next integration calculation; after completing the full-time history dynamic integration calculation, extract the node displacement, node velocity, node acceleration, and element stress data at each time step to form the displacement, velocity, acceleration, and internal force time history curve data of the elastic sling under seismic action.

[0012] Further, the node displacement, node velocity, and node acceleration data at each time step are obtained, including: multiplying the simulated seismic wave data by the elastic sling mass matrix to convert it into node load time history data and applying it to the base nodes of the initial finite element analysis model; introducing a Rayleigh damping matrix into the initial finite element analysis model to establish a dynamic equilibrium equation containing the stiffness, mass, and damping terms of the elastic sling, and obtaining a differential equation describing the response of the elastic sling under earthquake action; discretizing the node displacement, node velocity, and node acceleration in the dynamic equilibrium equation using the central difference scheme, selecting the integration step size according to the earthquake duration and the elastic sling period, and discretizing the time interval into multiple time steps; integrating the dynamic equilibrium equation through the Newmark parameters β and γ to establish an iterative format between the node displacement, velocity, and acceleration at the current time step; setting the node displacement, node velocity, and node acceleration of the elastic sling at the initial moment to zero, and at the first time step, using the node load data as the input and explicitly solving the node displacement, node velocity, and node acceleration at the first time step using the Newmark iterative format; at the second time step, according to the node displacement data obtained in the previous time step, calculating the element strain increment at the current time step using the strain-displacement relationship, updating the element stress using the constitutive relationship, and multiplying and integrating the element stress by the element volume to obtain the node equivalent force increment at the current time step; substituting the node velocity obtained in the previous step into the damping force expression to calculate the damping force increment at the current time step; introducing the node load increment, damping force increment, and node equivalent force increment at the current time step into the dynamic equilibrium equation to establish an algebraic equation system reflecting the node force equilibrium state at the current moment; solving the algebraic equation system to obtain the node displacement increment at the second time step, and using the Newmark iterative relationship to update the node velocity increment and node acceleration increment at the second time step; adding the node displacement increment, node velocity increment, and node acceleration increment to the calculation results of the previous time step respectively to obtain the node displacement, node velocity, and node acceleration at the current time step; repeating the time step iteration update until the full-time dynamic response calculation is completed, extracting the node displacement, node velocity, and node acceleration data at each time step, and forming a dynamic response time history curve of the elastic sling under earthquake action.

[0013] Furthermore, the initial elastic sling BIM model is optimized, including: according to the elastic sling response data under static load conditions and the elastic sling response data under seismic action, by combining the displacement field, stress field and strain field data under different conditions, the envelope surface data reflecting the response characteristics of the elastic sling under the combined action of loads is calculated; the stress-strain properties of the elastic sling elements in the initial elastic sling BIM model are updated using the envelope surface data; taking the strain energy density distribution of the elastic sling as the optimization objective, the strain energy density attribute parameters of the elastic sling elements are input into the SIMP interpolation model, and a non-linear mapping relationship between the strain energy of the elastic sling and the layout density of the elastic sling is established through an interpolation equation in the form of a power function; taking the Mises stress distribution of the elastic sling as the constraint condition; the Mises stress attribute parameters of the elastic sling elements are input into the KS aggregation function, and the local stress constraint is transformed into a global stress constraint equation through an aggregation equation in the form of a P-norm; the sensitivity analysis of the layout density of the elastic sling is carried out using the MMA optimization criterion, and a linearized optimization sub-problem is established based on the first-order derivatives of the objective function and the constraint conditions; the dual method is used to solve the optimization sub-problem to obtain the optimal elastic sling layout scheme at the current iteration step; the strain energy density data and Mises stress attribute parameters of the elastic sling elements are updated using the optimal elastic sling layout scheme, and the updated attribute parameters are substituted into the optimization criterion function to calculate the objective function value and the constraint function value at the current iteration step; it is judged whether the difference between the objective function value at the current iteration step and the objective function value at the previous step is less than the convergence threshold. If so, the iteration is stopped and the final elastic sling layout scheme is output; the final elastic sling layout scheme is discretized into the geometric information of the elastic sling, and the initial elastic sling BIM model is parameter-corrected using the set geometric information to generate an optimized elastic sling layout BIM model.

[0014] Furthermore, taking the strain energy density distribution of the elastic sling as the optimization objective, it includes: inputting the strain energy density attribute parameters of the updated elastic sling elements into the SIMP interpolation model, establishing a non-linear relationship between the strain energy of the elastic sling and the layout density of the elastic sling through interpolation mapping formed by power function of the strain energy density attribute parameters, obtaining the expression of the strain energy of the elastic sling as the optimization objective function; inputting the Mises stress attribute parameters of the updated elastic sling elements into the KS aggregation function, transforming the stress constraint reflecting the local stress level of the elastic sling into a global stress constraint equation reflecting the overall stress level of the elastic sling through aggregation operation in the form of P-norm of the Mises stress attribute parameters, obtaining the violation function as the optimization constraint function; according to the optimization objective function and the optimization constraint function, taking the layout density of the elastic sling as the design variable, establishing a mathematical model with the minimum strain energy of the elastic sling as the optimization objective and the overall stress of the elastic sling meeting the strength requirements as the optimization constraint; using the heuristic optimization algorithm to iteratively solve the established mathematical model to obtain the layout scheme of the elastic sling at the current iteration step.

[0015] Furthermore, the expression of the optimization objective function is as follows: , where is the total strain energy expression of the elastic sling, i is the number of elements in the finite element model of the elastic sling, is the volume of the i-th element, is the relative density of the i-th element, i.e., the layout density of the elastic sling, and its value range is from 0 to 1, is the initial strain energy density of the i-th element; is the penalty factor of the SIMP interpolation model, which is used to suppress the intermediate value of the layout density of the elastic sling and promote the optimization of the layout scheme of the elastic sling towards the discretization direction, and usually takes the value of 3, is the corrected strain energy density of the element; , in the formula, is the initial strain energy density of the element.

[0016] Furthermore, the expression of the optimization constraint function is as follows: , where, is the optimization constraint function, i.e., the violation function. When , it means that the optimization design meets the stress constraint conditions; is the Mises equivalent stress of the i-th element, which is a function of the relative density of the element and can be obtained through finite element analysis calculation; is the allowable stress limit of the Mises equivalent stress, and usually takes the yield strength of the material; is the aggregation factor of the KS aggregation function, which is used to adjust the contribution degree of the local stress constraint to the global violation function, The larger the value is, the more sensitive the violation function is to the maximum stress value. When the value is infinite, it is equivalent to the mini stress constraint; 〈 〉 is the Macaulay bracket. When ... ... otherwise ... that is, only the contribution of the stress values exceeding the allowable stress limit to the violation function is considered.

[0017] Compared with the prior art, the advantages of this application are as follows:

[0018] By collecting the design and processing data of different types of elastic slings, establishing a knowledge base containing geometric parameters, material properties and process attributes, and performing parametric modeling based on the knowledge base, an initial elastic sling BIM model with associative relevance can be quickly generated. This model contains rich semantic information, which facilitates subsequent performance analysis and topology optimization, and realizes the parametric expression of elastic slings from design to processing.

[0019] The incremental iteration method and the secant method are introduced in the static analysis, which can overcome the convergence difficulties caused by material and geometric nonlinearities; the direction of the displacement increment is corrected through the energy criterion, improving the calculation efficiency and stability. In the dynamic analysis, the Newmark integration format and the Rayleigh damping model are adopted, which can accurately simulate the dynamic response of elastic slings under seismic loads. The displacement field, stress and strain fields obtained through static and dynamic analysis provide a reliable basis for the topology optimization of elastic slings.

[0020] Taking the minimum strain energy of the elastic sling as the optimization objective and the Mises stress meeting the strength requirements as the optimization constraint, a topology optimization mathematical model with the layout density of the elastic sling as the design variable is constructed. The continuous expression of the objective function and the constraint function is realized through SIMP interpolation and KS aggregation function respectively, and the sensitivity analysis of the design variable is carried out using the MMA optimization criterion to obtain the optimal elastic sling layout scheme. Topology optimization makes the material distribution of the elastic sling match the stress characteristics, and minimizes the material usage under the premise of ensuring safety performance.

[0021] The elastic sling layout scheme obtained by topology optimization is fed back into the BIM model, and the geometric information of the elastic sling is updated through parameter drive to obtain a performance-optimized elastic sling BIM model. Based on this model, the numerical control code required for the processing of the elastic sling can be directly exported, realizing the seamless connection of design, optimization and processing, and improving the manufacturing efficiency of the elastic sling. Description of the Drawings

[0022] Figure 1It is an exemplary flowchart of a prefabrication processing method for an elastic suspension cable and electrical connection of a high-speed railway catenary based on BIM according to the present application;

[0023] Figure 2 It is an exemplary flowchart of obtaining response data of the elastic suspension cable under static load according to the present application;

[0024] Figure 3 It is an exemplary flowchart of obtaining the time history curve under seismic action according to the present application;

[0025] Figure 4 It is an exemplary flowchart of obtaining an optimized BIM model for the layout of the elastic suspension cable according to the present application. Detailed implementation manners

[0026] The methods and systems provided in the embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0027] Figure 1 It is an exemplary flowchart of a prefabrication processing method for an elastic suspension cable and electrical connection of a high-speed railway catenary based on BIM according to the present application, including: collecting reinforcement data of different types of elastic suspension cables to establish a reinforcement knowledge base; the reinforcement knowledge base includes geometric parameters, load conditions, material properties, and reinforcement rules of the elastic suspension cable; according to the reinforcement knowledge base, through parametric modeling, an initial BIM model of the elastic suspension cable of the target project is established; the initial BIM model of the elastic suspension cable includes the spatial position, size, and material property parameters of the elastic suspension cable; according to the initial BIM model of the elastic suspension cable, through mesh division and material property mapping, an initial finite element analysis model of the target project is established; in the initial finite element analysis model, static load conditions are applied, and the incremental iteration method is used to calculate the internal force and deformation of the elastic suspension cable under static load; the static load includes dead load and live load; in the initial finite element analysis model, a simulated seismic wave is input, and direct integration method is used for dynamic time history analysis to obtain the displacement, velocity, acceleration, and internal force time history curves of the elastic suspension cable under different seismic waves; according to the static and dynamic analysis results, the stress-strain response of the elastic suspension cable is extracted, and the topology optimization method is used to optimize the initial BIM model of the elastic suspension cable with the minimum strain of the elastic suspension cable as the goal and the stress constraint of the elastic suspension cable as the condition; using the optimized BIM model of the elastic suspension cable to update the finite element analysis model, and repeating until the performance of the elastic suspension cable meets the design requirements to obtain the final BIM model of the elastic suspension cable; according to the final BIM model of the elastic suspension cable, the processing parameters of the elastic suspension cable are exported.

[0028] Collect the design parameters and processing data of different types of pantograph catenary elastic slings, establish a knowledge base containing geometric parameters, material properties and processing technologies, collect document materials such as design drawings, product samples, and technical standards of pantograph catenary elastic slings and electrical connections, and extract key design parameters, such as geometric parameters like length, cross-sectional dimension, taper, weight, etc., and material parameters like material grade, mechanical property index, conductivity, corrosion resistance, etc. Collect the production and processing records, process documents, operating procedures, quality inspection reports, etc. of elastic sling and electrical connection products, and extract key processing parameters, such as forging process parameters, heat treatment process parameters, surface treatment process parameters, assembly process parameters, geometric tolerances and surface roughness, etc. Classify and standardize the collected data. Use technologies such as text mining and pattern recognition to convert unstructured design and production data into structured parametric data; perform preprocessing operations such as screening, denoising, and normalization on the original data.

[0029] Adopt the ontology construction method to define the core concepts, attributes, relationships, etc. in the field of design and manufacturing of pantograph catenary elastic slings and electrical connections, and form a domain ontology model. For example, define "elastic sling" and "electrical connection" as core concepts, "geometric parameters", "material properties", and "processing technologies" as attribute concepts, and "adopted material" and "processing method" as relationships. Map the processed structured parametric data into the ontology model to establish parametric associations at the semantic level. At the same time, consider the coupling relationship and constraint conditions between parameters to construct a parametric association matrix. For example, establish a mapping relationship between material selection and heat treatment process through the association between material mechanical property parameters and processing technology parameters. Formalize the ontologized design and manufacturing knowledge as a knowledge base. Knowledge representation methods such as frame representation, production representation, and semantic network can be used to realize the logical organization and storage of the knowledge base. Establish index links between the collected original document materials and the knowledge base entries to form a document knowledge base.

[0030] According to the established knowledge base of elastic suspension ropes and electrical connections, through parametric modeling technology, the rapid generation of the initial BIM model of the elastic suspension rope for the target project can be achieved. A parametric main model of the elastic suspension rope is constructed using parametric 3D modeling software (such as Catia, UG, Solidworks, etc.). Taking the geometric parameters of the elastic suspension rope in the knowledge base (such as length, cross-sectional dimensions, taper, etc.) as the driving parameters of the main model, through the constraint relationships between parameters, the rapid generation of the 3D model of the elastic suspension rope is realized. Based on the main model, through parametric assembly technology, the mating model of the elastic suspension rope and electrical connection is constructed. According to the assembly relationship parameters of the two (such as flange dimensions, number and distribution of bolt holes, etc.), assembly constraints are automatically generated to realize the rapid definition of the mating model. Using parametric feature library technology, a series of detailed feature models of the elastic suspension rope are predefined, such as end tapered holes, vibration damper mounting holes, vibration damper mounting plates, etc. Through parameter transfer, the detailed feature models are implanted into the main model to improve the modeling efficiency.

[0031] BIM model property definition. Import the 3D parametric model of the elastic suspension rope into BIM software (such as Revit, Tekla, etc.). Using the parametric property definition function of BIM software, assign the material grade, mechanical property parameters, appearance color number, etc. in the knowledge base to the material property parameters of the model. Using the spatial positioning function of BIM software, through measurement and lofting, accurately define the spatial installation position and elevation of the elastic suspension rope model in the catenary. Considering the avoidance relationship with surrounding components, reasonably adjust the spatial position parameters. Based on the assembly relationship of the elastic suspension rope, define its logical association relationship with adjacent components such as electrical connections and anchoring devices in the BIM model. Through the transfer of associated parameters, when parameters such as the position and angle of the elastic suspension rope change, the coordinated change of adjacent components is automatically triggered.

[0032] Based on the established initial BIM model of the elastic sling, the finite element analysis method can be used to achieve the digital simulation analysis of the mechanical properties of the elastic sling. The initial BIM model of the elastic sling is exported through a neutral format (such as STEP, IGES, etc.) and opened in a finite element pre-processing software (such as Hypermesh, ANSA, etc.) for model conversion. The BIM model is appropriately simplified, and the detailed features that have little influence on the structural stress, such as chamfers, small round holes, etc., are removed. The key features such as the end tapered holes and the vibration damping hammer mounting holes are retained. The simplified model is subjected to topological inspection to repair geometric defects such as small gaps and intersections between surfaces to ensure the integrity and continuity of the model. The material properties of the elastic sling are defined in the finite element software. The mechanical parameters such as the elastic modulus, Poisson's ratio, and density of the material are extracted from the knowledge base and assigned to the finite element material grade. The material properties are mapped to different regions of the geometric model. Using the topological structure and naming rules of the model, different parts such as the sling body, tapered head, and vibration damping hammer mounting plate are automatically identified and corresponding material properties are assigned. Considering the anisotropic mechanical properties of the material, the material parameters in different directions are defined, such as the difference in elastic modulus between the transverse and longitudinal directions, etc.

[0033] According to the purpose and accuracy requirements of the simulation analysis, select appropriate finite element element types, such as solid elements, beam elements, shell elements, etc. The simplified geometric model is meshed. An automatic meshing algorithm (such as the Delaunay algorithm, the Advancing Front algorithm, etc.) is used to generate structured triangular or quadrilateral mesh elements on the surface model. The key parts (such as the tapered head transition area, around the vibration damping hammer mounting hole, etc.) are meshed densely to improve the accuracy of stress and strain calculation. The mesh quality is evaluated, and the quality indicators such as element size and distortion are checked, and the distorted elements are adjusted or remeshed. The attributes of the mesh elements are defined, such as element thickness, cross-sectional area, moment of inertia, etc. The corresponding cross-sectional parameters are extracted from the knowledge base and automatically assigned to the mesh elements.

[0034] According to the stress state of the elastic sling in the catenary, the boundary conditions are defined. Displacement constraints or hinge constraints are applied to the end nodes of the sling to simulate its connection relationship with the anchoring device. According to the design specifications, the forces on the elastic sling under working conditions such as icing and wind vibration are calculated. The loads are applied to the corresponding nodes or element faces of the finite element model to simulate the actual stress state. Considering the influence of temperature loads, the thermal expansion coefficient of the model is defined and the temperature field is applied. The divided finite element mesh model is visually inspected to confirm the correctness of the mesh quality and material property mapping. The finite element model file in neutral format (such as Nastran, Abaqus format) is output for subsequent finite element solution analysis.

[0035] Figure 2It is an exemplary flowchart for obtaining the response data of a static load elastic sling according to the present application. The load information in the initial elastic sling BIM model is mapped into the static load data of the finite element model, and the arc-length method and secant method are used for incremental step control. The dead load information of the elastic sling is extracted in the BIM model, mainly including the self-weight of the sling and its accessories. Using the material property parameters (density) and geometric parameters (volume) in the BIM model, the self-weight of each component is calculated, and the self-weight value is assigned to the corresponding nodes of the component to form node loads. The live load information applied to the elastic sling is extracted in the BIM model, such as wind load, ice coating load, etc. The wind load can be calculated according to the wind pressure and wind direction data at the location where the sling is located, and the wind load acting on the projection surface of the sling is calculated; the ice coating load can be calculated according to the meteorological parameters, and the ice thickness and ice density on the surface of the sling are calculated and converted into additional mass. The load combination coefficient is used to linearly combine the dead load data and the live load data. The combination coefficients under different working conditions can refer to the design specifications. The combined load data is applied to the corresponding nodes or element surfaces of the finite element model to form static load data.

[0036] According to the nonlinear characteristics of the elastic sling, the arc-length method is used to discretize the static load data in incremental steps. The arc-length method can adaptively adjust the load increment and displacement increment by restricting the length of the load-displacement curve (i.e., the arc length) of each incremental step, and can capture complex nonlinear paths. Before solving each incremental step, an index value reflecting the nonlinear state of the elastic sling is obtained, such as the maximum deflection of the sling. The deflection value of the current incremental step is compared with a preset threshold (such as the ratio of deflection to span). When the deflection exceeds the threshold, the arc length of the current incremental step is reduced, the load increment is decreased, and the calculation accuracy is improved. At the same time, monitor whether the nonlinear state index of the sling exceeds the preset extreme value (such as the maximum allowable deflection). When the index exceeds the extreme value, the secant method is used to interpolate the current incremental step, and intermediate points are added on the load-displacement curve to avoid non-convergence of the calculation. The secant method forms a secant line by connecting two points on the curve, and uses the secant slope to replace the tangent stiffness, which can cross the local stiffness degradation area.

[0037] Deflection is an important index for evaluating the nonlinear state of the elastic sling. By extracting the displacement field data of the sling at the current incremental step, the maximum deflection value of the sling is calculated. Usually, the vertical displacement at the mid-span of the sling is concerned. The crack width can also be used as a nonlinear state index. By the stress field data, the principal tensile stress on the surface of the sling is calculated and compared with the tensile strength of the material to judge whether it cracks. According to the strain field data, the cracking displacement in the crack area is calculated to estimate the crack width. Other nonlinear state indexes also include the stress level, plastic strain, etc. of the sling. By extracting the stress-strain data of the sling, the equivalent stress, equivalent plastic strain, etc. are calculated to evaluate the nonlinear degree of the sling.

[0038] In each increment step, the Newton-Raphson iteration format is adopted to solve the nonlinear equation of the elastic sling, and the element stress data is extracted from the initial finite element analysis model. and the element strain data . It is assumed that the elastic sling is discretized by four-node quadrilateral plane stress elements, with the element number being e and the node numbers being i, j = 1, 2, 3, 4. For element e, its stress data is , , , and the strain data is , , . According to the constitutive relationship of the material, such as the elastic modulus E and Poisson's ratio ν, the coefficients of the tangent stiffness matrix of the element are calculated . For example, for an isotropic elastic material, the expression of is: ; ; The others . Using 2x2 Gaussian quadrature, the tangent stiffness matrix of element e is calculated . Let the element node coordinates be , the shape function be , the Gaussian quadrature point coordinates be , and the weight coefficient be . Then the expression of is: where is the strain-displacement matrix at Gaussian point k, is the tangent stiffness coefficient matrix at Gaussian point k, and the expression of is: ; Using the element assembly operation, the tangent stiffness matrices of all elements are assembled into the tangent stiffness matrix K_T of the overall structure. Let the degree-of-freedom numbers of the overall structure be I, J, then the assembly process of is: where is the total number of elements; i = 1, 2, 3, 4; ID is the global degree-of-freedom number of the i-th node of element e; j = 1, 2, 3, 4; ; the diagonal element of is modified: , α is the penalty factor, taking a very large positive number, such as ; thus obtaining the tangent stiffness matrix data of the elastic sling at the current increment step .

[0039] First iteration solution: Let the arc length increment at the current increment step be , which includes the load increment and the displacement increment two components. Through the arc length equation constraint, determine the relationship between and : ; where, is the reference length, usually taking the initial arc length. Given and , solve the above nonlinear equation by the Newton iteration method to obtain the displacement increment component . Substitute the displacement increment component and the tangent stiffness matrix into the tangent stiffness equation to form a linear equation system about the nodal displacement increment : ; where, P is the reference load vector. Solve the above equation system by the LU decomposition method to obtain the nodal displacement increment of the first iteration. Utilize the nodal displacement increment , through the displacement-strain relationship, update the strain increment of the element: ; where, is the element strain-displacement matrix. Through the elastoplastic constitutive equation, such as the Mises yield criterion and the associated flow rule, update the stress increment of the element: ; where, is the elastoplastic tangent stiffness matrix. The element stress and strain are updated to: ; .

[0040] Subsequent iteration solution: Substitute the updated element stress and strain into the expression of the secant stiffness matrix K_S^e to calculate the element secant stiffness matrix: ; where, D_s is the secant stiffness coefficient matrix. Adopt the element assembly operation to assemble it into the secant stiffness matrix of the overall structure: ; Introduce the boundary conditions and perform singular treatment on the secant stiffness matrix to obtain the secant stiffness matrix of the second iteration. Extract the displacement increment component from the arc length increment data of the current increment step, combine it with the secant stiffness matrix Substitute it into the secant stiffness equation to form a new system of equations for the incremental nodal displacements: ; Solve the above system of equations to obtain the incremental nodal displacements for the second iteration . Based on the incremental nodal displacements from the first iteration and the incremental nodal displacements from the second iteration, calculate the displacement difference for the two iterations: ; Adopt the Euclidean norm , and compare it with the preset convergence threshold ε. If , it is considered that the calculation has converged, let , and stop the iteration. Otherwise, proceed to the next iteration. Utilize the incremental nodal displacements from the second iteration to update the incremental element stress and strain, and recalculate the secant stiffness matrix to prepare for the next iteration. Repeat the iteration process until the displacement difference converges.

[0041] On the basis of the Newton - Raphson iteration format, introduce an energy criterion to correct the direction of the displacement increment in order to accelerate the iteration convergence speed. The correction process is nested within the iteration loop for each increment step until the displacement of the current increment step converges. Take the arc - length increment data of the current increment step and the nodal displacement data from the previous iteration as inputs and substitute them into the potential energy function Π of the elastic sling: , where, [K] is the secant stiffness matrix of the elastic sling, is the current load, is the load increment corresponding to the unit arc - length increment. Minimize the potential energy function Π to obtain the displacement increment direction correction coefficient α: , where, is the initial displacement increment for the current iteration. Solve the above equation to obtain the correction coefficient α: , multiply the displacement increment direction correction coefficient α by the displacement increment component data of the current increment step to obtain the corrected displacement increment component data : , substitute the corrected displacement increment component into the secant stiffness matrix [K] and solve for the nodal displacement data of the current iteration: , judge the nodal displacement The convergence. If it converges, the current incremental step calculation is completed; otherwise, return for the next iteration until the nodal displacement data of the current incremental step converges. By modifying the direction of the displacement increment through the energy criterion, the displacement direction with the minimum potential energy can be searched for in each iteration, thereby accelerating the convergence rate of the Newton-Raphson iteration and reducing the number of iterations. At the same time, since only the direction of the displacement increment needs to be modified without changing the magnitude of the displacement increment, the control effect of the arc length increment is not affected.

[0042] After all incremental steps are calculated, extract the characteristic points of the deformation failure mode of the elastic sling and form the response data. Let the total number of nodes of the elastic sling be , and the total number of elements be . After all incremental steps are calculated, the following data fields are obtained: Displacement field data: , , j = 1, 2, 3, representing the displacement component of the i-th node in the j-th direction. Stress field data: , , , , representing the stress component of the e-th element. Strain field data: , , , , representing the strain component of the e-th element. From the above data fields, extract the characteristic point data reflecting the deformation failure mode of the elastic sling: Maximum deflection point: In the displacement field data, search for the maximum displacement component in the j = 2 direction (i.e., the y direction), and determine its corresponding node number . The coordinates of the maximum deflection point are , where . is the initial coordinate of the -th node. Stress-strain extreme point: In the stress field and strain field data, search for , , , , , for the maximum and minimum values, and determine their corresponding element numbers and . The coordinates of the stress-strain extreme point are the central coordinates and of elements and . Buckling instability point: For compression bar elements, if their axial compressive stress exceeds the critical buckling stress , then determine that this element is a buckling instability point. can be calculated according to the Euler buckling formula: , where E is the elastic modulus of the material, I is the moment of inertia of the unit cross-section, A is the cross-sectional area of the unit, and l is the unit length. The coordinates of the buckling instability point are the central coordinates of element e . Strength failure point: For each element, calculate the equivalent stress according to its stress state , such as the Mises equivalent stress: , and compare with the allowable stress of the material . If , then determine that this element is a strength failure point. The coordinates of the strength failure point are the central coordinates of element e .

[0043] Statistical analysis of the above characteristic point data: Calculate the number of various characteristic points , , , , and obtain the distribution of the weak parts of the elastic sling. Calculate the mean value of the coordinates of various characteristic points and the standard deviation , and obtain the spatial distribution characteristics of the weak parts. Correlate the characteristic point data with the geometric parameters (span , sag f), material parameters (elastic modulus E, allowable stress [σ]), load parameters (vertical uniform load q), etc. of the elastic sling, and establish the response function of the elastic sling under static load, such as: ; ; where is the cross-sectional area of the sling, is the maximum stress of the sling

[0044] Figure 3 is an exemplary flowchart for obtaining the time history curve under seismic action according to the present application. Select the input seismic wave according to the site conditions, convert it into the time history data of the nodal load, establish the dynamic equilibrium equation, and select a set of representative seismic waves from the seismic wave database (such as PEER) according to the fortification intensity I and site category S of the project area. The fortification intensity values are 6, 7, 8, and 9 degrees, and the site category values are I, II, III, and IV categories. Each set of seismic waves includes two horizontal (x-direction and y-direction) and one vertical (z-direction) acceleration time history curves, and the sample size is not less than 10 groups. The peak ground acceleration PGA, duration , non-zero time history points , and other parameters should meet the requirements of the fortification intensity. For example, select the following set of seismic wave data:

[0045]

[0046] Using the mode superposition response spectrum method, baseline correction and amplitude adjustment are performed on the above seismic wave data. Let the original acceleration time history curve of the i-th group of seismic waves be , where i = 1, 2,..., 10, j = x, y, z, . The following processing is carried out: Calculate the mode superposition response spectrum of the seismic wave , where is the natural vibration period and ξ is the damping ratio, taking 5%. According to the design response spectrum of the project engineering site, calculate the target adjustment coefficient : ; Perform baseline correction on the original seismic wave to obtain the corrected acceleration time history : ; where . Multiply the corrected seismic wave by the adjustment coefficient to obtain the simulated seismic wave : ; Convert the simulated seismic wave into node load time history data. Let the number of nodes of the initial finite element model of the elastic sling be , the seismic action direction is the j-direction (j = x, y, z), and the displacement time history of node i in the j-direction is . From the dynamic equilibrium equation: ; where M, C, and K are the mass, damping, and stiffness matrices of the structure respectively, I is the unit column vector, is the acceleration time history of the simulated seismic wave in the j-direction. The node load time history is: ; where is the mass of node i. Apply to the j-direction degree of freedom of node i to establish the dynamic equilibrium equation considering seismic action: ; where is the node load time history array.

[0047] Introduce the Rayleigh damping matrix into the initial finite element analysis model to establish the dynamic equilibrium equation including the stiffness, mass, and damping terms of the elastic sling, and obtain the differential equation describing the response of the elastic sling under seismic action. Introduce the damping of the elastic sling into the dynamic equilibrium equation, and the Rayleigh damping model can be adopted, that is, the damping matrix [C] is a linear combination of the mass matrix [M] and the stiffness matrix [K]: , where α and β are the Rayleigh damping coefficients, which can be obtained according to the first two natural vibration frequencies and of the elastic sling and the corresponding damping ratios and : , the damping ratio ξ is generally taken as 3% - 5% to consider the energy dissipation of the elastic sling under seismic action. Substituting the mass matrix [M], the stiffness matrix [K], and the Rayleigh damping matrix [C] into the dynamic equilibrium equation, a second-order ordinary differential equation describing the response of the elastic sling under seismic action is obtained: .

[0048] The central difference scheme is used to discretize the nodal displacements, nodal velocities, and nodal accelerations in the dynamic equilibrium equation. The integration time step is selected according to the seismic duration and the period of the elastic sling, and the time interval is discretized into multiple time steps. Taking the nodal displacement as the unknown, perform Taylor expansion on both sides of the dynamic equilibrium equation at time , and take the second-order term to obtain: , where , , are the nodal acceleration, velocity, and displacement at time respectively, and , , are the increments of the nodal acceleration, velocity, and displacement within the time step . Using the central difference scheme, we have: , , , where , , , are the nodal displacement, velocity, and acceleration at the next time step . Substitute the difference relationship into the dynamic equilibrium equation and organize to get: , and the selection of the time step should meet the integral stability and convergence conditions, and is generally taken as 1 / 10 - 1 / 20 of the period of the elastic sling, that is: . The period can be estimated from the first natural frequency of the elastic sling: , and can be obtained by solving the eigenvalues of the initial finite element analysis model through the Rayleigh quotient iteration method. For high-rise buildings, generally is in the order of 1s - 5s, and take as 0.02s - 0.1s. Divide the total seismic duration by , and the number of integration steps N can be determined: , and the time interval is discretized into N time steps, and the time sequence is: , , ,......, 。

[0049] Integrate the dynamic equilibrium equation through the Newmark parameters β and γ to establish an iterative format between the nodal displacements, velocities, and accelerations at the current time step. The Newmark-β method is an implicit direct integration algorithm that uses two parameters β and γ to control the integration format. β reflects the contribution of the time-averaged acceleration to the displacement, and γ reflects the contribution of the time-averaged acceleration to the velocity. Let: , 。When β = 1 / 4 and γ = 1 / 2, it is the constant acceleration method, which has second-order accuracy and unconditional stability; when β = 1 / 6 and γ = 1 / 2, it is the linear acceleration method, which has third-order accuracy and conditional stability. Substitute the Newmark iterative relation into the dynamic equilibrium equation and organize it to get: ,where, , ,and [A] is called the Newmark effective stiffness matrix, is the Newmark effective load vector.

[0050] Set the nodal displacements, nodal velocities, and nodal accelerations of the elastic sling at the initial moment to zero. At the first time step, using the nodal load data as the input, explicitly solve for the nodal displacements, nodal velocities, and nodal accelerations at the first time step using the Newmark iterative format. The initial conditions are: , , ;At the first time step ,the seismic load is ,substitute it into the Newmark effective load vector : ;Substitute it into the Newmark effective stiffness equation and solve for the nodal acceleration at time : ;Then, from the Newmark iterative relation, update the nodal velocity and the nodal displacement at time : , 。At the second time step, according to the nodal displacement data obtained in the previous time step, use the strain-displacement relation to calculate the element strain increment at the current time step, update the element stress using the constitutive relation, and multiply the element stress by the element volume and integrate to obtain the nodal equivalent force increment at the current time step. For each element e, interpolate the element displacement field from the nodal displacement ,and then convert it to the element strain using the strain-displacement relation matrix : ; According to the material constitutive relationship, such as elastic, elastoplastic or damage constitutive, update the element stress from the element strain Update the element stress . Taking elasticity as an example, assume the elastic matrix is , then: ; Decompose the element stress into the equivalent nodal forces , and we have: ; is the spatial domain of element e. Assemble the equivalent nodal forces of all elements to obtain the nodal equivalent force increment of the overall elastic sling at time: . Substitute the nodal velocity obtained in the previous step into the damping force expression to calculate the damping force increment at the current time step. The damping force of the elastic sling at time is: . Subtract from the damping force at time to obtain the damping force increment : . Introduce the nodal load increment, damping force increment and nodal equivalent force increment at the current time step into the dynamic equilibrium equation to establish an algebraic equation system reflecting the nodal force equilibrium state at the current time. Substitute the seismic load increment at , damping force increment and nodal equivalent force increment into the dynamic equilibrium equation to get: .

[0051] Further substitute into the Newmark effective stiffness equation and effective load vector to obtain: , where , , , and [A] is the same as in the first time step. Solve the algebraic equation system to obtain the nodal acceleration increment at the second time step, and use the Newmark iteration relationship to update the nodal velocity increment and nodal displacement increment at the second time step. Solve the Newmark effective stiffness equation to obtain the nodal acceleration at time. It can be solved by direct method or iterative method, such as LU decomposition, Pardiso solver, etc. Then, update the nodal velocity and nodal displacement at time according to the Newmark iteration relationship: ; Accumulate the nodal acceleration, nodal velocity, and nodal displacement into the calculation results of the previous time step respectively to obtain the nodal acceleration, nodal velocity, and nodal displacement at the current time step. , , . Repeat the time step iteration update until the dynamic response calculation for the entire time history is completed. Extract the nodal displacement, nodal velocity, and nodal acceleration data at each time step to form the time history curve of the dynamic response of the elastic sling under seismic action. According to the time step , calculate in sequence the nodal acceleration, velocity, and displacement responses at the moment. Extract the nodal response data at each time step , and plot the time history curves of acceleration, velocity, and displacement for the nodes of interest, then the dynamic response characteristics of the elastic sling during the entire seismic process can be comprehensively analyzed to evaluate the seismic performance of the elastic sling.

[0052] According to the nodal displacement data at each time step, calculate the element strain data using the strain-displacement relationship, and update the element stress data using the constitutive relationship; multiply the element stress data by the element volume and integrate to obtain the equivalent nodal force data of the element; assemble the equivalent nodal force data of the element into the global nodal load data and substitute it into the dynamic equilibrium equation for the next integration calculation. Calculate the element strain data based on the nodal displacement data. Assume that the nodal displacement vector of the elastic sling at the moment is . For each element e, the element displacement field is interpolated from the nodal displacements as follows: , where [N^e] is the element shape function matrix, is the element nodal displacement vector, which is extracted from the global nodal displacement vector by selecting the element nodal degrees of freedom. The element strain is obtained from through the strain-displacement relationship matrix as follows: , which depends on the element type and the degree of the shape function, and has standard expressions for common elements such as beam elements and shell elements.

[0053] According to the material constitutive relationship, update the element stress from the element strain . It is divided into two cases: elastic and inelastic. For elastic materials, the stress-strain relationship is linear: , where is the elastic matrix, which is related to the elastic modulus and Poisson's ratio of the material. For inelastic materials, such as elastoplastic and damaged plasticity, the incremental theory and implicit iteration algorithm are required to update the element stress. Taking ideal elastoplasticity as an example, according to the element stress at the previous time step ​ and the element strain increment , updated by the elastoplastic return mapping algorithm : (Elastic prediction), (Yield function). If f > 0, then: (Plastic correction), , where f is the Mises yield function, is the second invariant of the stress deviator, is the yield strength, is the normal of the yield surface, is the plastic multiplier. For non-linear hardening and damaged materials, the evolution law of the strength parameter needs to be considered in the stress update. Calculate the equivalent nodal force data of the element, and decompose the element stress into equivalent nodal , there is: , is the spatial domain of element e, and can be calculated by numerical integration such as Gauss integration. This step is called the stress equilibrium solution.

[0054] Assemble the global nodal load data, assemble the equivalent nodal forces of all elements, and obtain the equivalent nodal force of the global elastic sling at time: , the assembly process is similar to the total stiffness assembly in the static analysis of finite elements. Substitute into the dynamic equilibrium equation for the next integration calculation, and use as the internal force term at the next time step , together with the external load, damping force, and inertial force to form the load term of the dynamic equilibrium equation: , where, 、 are respectively the seismic load increment and damping force increment at time. [K] is the tangent stiffness matrix, considering the stiffness degradation caused by material non-linearity. Repeatedly solve the integration of the dynamic equilibrium equation by the Newmark-β method, and the nodal acceleration, velocity, and displacement responses at time can be obtained, realizing the two-way coupling analysis of material non-linearity and the dynamics of the elastic sling. After completing the dynamic integral calculation of the full time history, extract the nodal displacement, nodal velocity, nodal acceleration, and element stress data at each time step to form the time history curve data of the displacement, velocity, acceleration, and internal force of the elastic sling under seismic action. For the time step (n = 0, 1, 2,......, N), read the nodal acceleration vector , the nodal velocity vector , and the nodal displacement vector respectively, and organize them into a matrix form according to the nodal numbers: , , , the number of rows of the matrix is the total number of nodes, and the number of columns is the total number of time steps. These matrices are called node response time history matrices. Similarly, the stress time history (n = 0, 1,......, N) of each element e is organized into a matrix by columns: , where is the stress component vector of each integration point of element e at time . It is called the element stress time history matrix. Extract the acceleration, velocity, and displacement components of the nodes of interest from the node response time history matrices , , and plot the response time history curves. The ordinate is the response quantity, and the abscissa is time. For example, for the displacement time history of node i in the x direction: , , . Similarly, extract the Mises equivalent stress time history of key elements such as supports, node regions, and the edges of openings from the element stress time history matrix , . Through the response time history curves at key positions, the dynamic characteristics of the elastic sling during an earthquake can be visually evaluated, such as the peak values of displacement, velocity, and acceleration and their occurrence times, the residual displacement, and the displacement and stress recovery after unloading. Output the node response time history matrices , , and the element stress time history matrix to an external file in a certain format for post-processing analysis. Commonly used data formats include.txt (text file),.mat (Matlab data file),.xls (Excel spreadsheet file), etc.

[0055] Figure 4It is an exemplary flowchart for obtaining an optimized BIM model of the elastic sling layout according to the present application. According to the static and dynamic analysis results, the stress-strain response of the elastic sling is extracted, and the topology optimization method is used to optimize the initial BIM model of the elastic sling with the minimum strain of the elastic sling as the goal and the stress constraint of the elastic sling as the condition, including: S61, according to the response data of the elastic sling under the static load condition and the response data of the elastic sling under the earthquake action, by combining the displacement field, stress field and strain field data under different conditions, the envelope surface data reflecting the response characteristics of the elastic sling under the combined action of loads is calculated; the stress-strain attributes of the elastic sling elements in the initial BIM model of the elastic sling are updated using the envelope surface data. For static conditions such as permanent load (D), variable load (L), wind load (W), etc., linear elastic finite element analysis is performed respectively to obtain the nodal displacements of the elastic sling under each condition , element stresses and element strains . Taking the permanent load as an example, let the nodal displacement under its action be , the element stress be , and the element strain be . For the variable load and wind load, they are represented by the subscripts L and W. Using nonlinear dynamic time history analysis, the dynamic responses of the elastic sling under different earthquake levels (frequent, fortification, rare) are simulated to obtain the nodal displacement time history , element stress time history and element strain time history . Taking the frequent earthquake (E1) as an example, let the nodal displacement time history under its action be , the element stress time history be , and the element strain time history be . For the fortification earthquake (E2) and rare earthquake (E3), they are represented by the subscripts E2 and E3.

[0056] According to the rules of load combination, the displacement, stress and strain responses of the static condition and the earthquake condition are combined to obtain the envelope surface data reflecting the response characteristics of the elastic sling under the combined action of loads. For the nodal displacement envelope surface , there is: , where represents taking the modulus of the vector, and max represents taking the maximum value of the displacement modulus for all nodes. represents the nodal displacement under the permanent load, represents the nodal displacement under the variable load; represents the nodal displacement under the wind load; represent the nodal displacement time histories under the frequent, fortification and rare earthquakes respectively.

[0057] For the element stress envelope surface , there is: Unit strain envelope surface The calculation of is similar. Just change the equivalent stress to equivalent strain. The envelope surface data , , reflect the upper limits of the displacement, stress, and strain responses of the elastic sling under the combined action of loads, and can be used to evaluate the overall performance and stress state of the elastic sling. represents the unit stress under the permanent load, represents the unit stress under the variable load; represents the unit stress under the wind load; respectively represent the unit stress time histories under frequent, fortification, and rare earthquakes.

[0058] Update the properties of the elastic sling in the BIM model using the envelope surface data. In the initial elastic sling BIM model, each elastic sling unit has its material properties and geometric properties. The material properties include the initial elastic modulus, Poisson's ratio, yield strength, etc., and the geometric properties include the cross-sectional dimensions, elastic sling diameter, and spacing, etc. These properties determine the stress-strain relationship of the elastic sling unit. Using the envelope surface data , , the yield strength of the elastic sling unit can be updated : (take the maximum value of the unit stress envelope surface). For the elastic sling, take its tensile yield strength, and for concrete, take the standard value of its compressive strength. At the same time, the unit stress-strain time histories [σ], [ε] obtained from the nonlinear dynamic analysis can be used to fit the hysteresis curve of the elastic sling unit, and the degraded secant stiffness can be determined: (take the slope of the line connecting the peak points of the stress-strain time history). The update of the above yield strength and secant stiffness makes the stress-strain relationship of the elastic sling unit in the BIM model able to reflect the strength degradation and stiffness degradation of the material under the combined action of loads, improving the accuracy of the BIM model.

[0059] Establish a mathematical model with the minimum strain energy of the elastic sling as the objective and the stress of the elastic sling meeting the strength requirements as the constraint. Extract the initial strain energy density and volume of each unit in the finite element model of the elastic sling. The initial strain energy density is calculated through the unit stress and strain : , where and It can be obtained from the envelope surface data of S61 , The unit volume can be directly extracted from the element property table of the finite element model. ρᵢ reflects the volume ratio of the elastic sling arrangement in the i-th element and is a continuous variable with a domain of [0, 1]. When , it means that there is no elastic sling arranged in element i; when , it means that a solid elastic sling is arranged in element i. Using the SIMP (Solid Isotropic Material with Penalization) interpolation model, a non-linear mapping relationship between the element strain energy density and the elastic sling arrangement density is established: , where is the corrected element strain energy density, is the initial element strain energy density, is the relative density of the elastic sling arrangement in the element, is the penalty factor, taking 3. For this power function form of interpolation, when takes 0 or 1, the correction coefficient is also 0 or 1, corresponding to the two extreme cases of no elastic sling or solid elastic sling. And when takes an intermediate value such as 0.5, the correction coefficient will be much smaller than , making the element strain energy density smaller, thus suppressing the tendency of the elastic sling arrangement density to take intermediate values and promoting the optimization of the elastic sling arrangement towards the solidification direction.

[0060] An optimization objective function for minimizing the total strain energy of the elastic sling is established: , where is the total strain energy of the elastic sling, which is obtained by accumulating the product of the corrected strain energy of each element and the unit volume . is the relative density of the elastic sling arrangement in the i-th element, and there are n as design variables, and n is the total number of elements in the elastic sling finite element model. Based on the KS function, an optimization constraint function is established, and the Mises stress function of each element in the elastic sling finite element model is extracted. The element Mises stress is also a function of the elastic sling arrangement density . Substitute the envelope surface data {σ}_env into the three-dimensional Mises stress formula: , where , , are the principal stresses of the element and can be obtained from Principal stress extraction. The KS (Kreisselmeier-Steinhauser) aggregation function is introduced to aggregate the element stress function into the violation function : , where σ is the allowable stress, taking the smaller value of the tensile strength of the elastic sling and the compressive strength of the concrete. is the Macaulay bracket. When is positive, otherwise it is 0. p is the aggregation parameter. The larger p is, is closer to . The introduction of the Macaulay bracket makes the violation function only consider the over-stress area without having to pay attention to the low-stress area. When the stress level of the full elastic sling is lower than the allowable value, ; conversely, . Therefore, selecting as the optimization constraint condition can ensure that the elastic sling meets the strength requirements under the action of the load.

[0061] Establish the optimization constraint function for the overall stress constraint of the elastic sling: . Establish the mathematical model for the topology optimization of the elastic sling of the elastic sling concrete. Taking the minimum total strain energy of the elastic sling as the optimization goal, taking the overall stress of the elastic sling meeting the strength requirements as the optimization constraint, and taking the relative density of the element elastic sling layout as the design variable, establish the following mathematical model: , constraint conditions: , , where is the lower limit of the layout density of the elastic sling, generally taking 0.001 to avoid singularity of the element stiffness matrix. On the premise that the elastic sling meets the overall strength requirements, find the layout scheme of the elastic sling with the minimum total strain energy. The minimum total strain energy means the optimal internal force of the elastic sling, giving full play to the mechanical properties of the material. By solving the mathematical model, the optimal topological configuration of the elastic sling of the elastic sling concrete can be obtained, that is, the optimal layout scheme of the elastic sling . Under this configuration, the force of the elastic sling is more reasonable, the utilization rate of the elastic sling is higher, and the mechanical properties are improved. Substitute into the envelope surface data , , , and the displacement field, stress field, and strain field under the optimized configuration can be obtained.

[0062] Based on the MMA optimization criterion, establish a linearized optimization sub-problem. Using the mathematical model established by S62, respectively, take the first-order derivatives of the objective function and the constraint function with respect to the design variable . The objective function The partial derivative of with respect to is: , where p is the penalty factor of the SIMP interpolation model, taking 3; is the relative density of the elastic sling arrangement of the i-th element; is the initial strain energy density of the i-th element; The partial derivative of the constraint function with respect to is: , where p is the aggregation parameter of the KS aggregation function; is the Mises stress function of the i-th element;

[0063] The Mises stress function The partial derivative of with respect to can be obtained by the implicit function differentiation rule: , where is the principal stress of the i-th element; can be determined by the non-linear relationship between the principal stress and , and numerical differentiation using the material constitutive equation is required. Introduce the design variable improvement , at the current design point perform a first-order Taylor expansion on the objective function and the constraint function to obtain the linearized optimization sub-problem: , constraint conditions: , ; where and are the partial derivatives of the objective function and the constraint function with respect to the i-th design variable, respectively; is the improvement of the i-th design variable; is the lower limit of the elastic sling arrangement density, taking 0.001. The linearized optimization sub-problem constructs a linear approximation of the original problem near the current design point, and its solution indicates the steepest descent direction, which is used to guide the optimization of the design variables.

[0064] The dual method is used to solve the linearized optimization sub-problem. Introduce the Lagrange multiplier λ and the KKT conditions to transform the linearized optimization sub-problem into an unconstrained optimization problem of the following Lagrangian function: , constraint conditions: , . Let The partial derivatives of and λ with respect to

[0065] be equal to 0, and we get: 。

[0066] Combining the above optimality conditions and complementary slackness conditions, a linear complementarity problem (LCP) for λ is obtained: , , , where, is the second-order partial derivative of the Lagrangian function with respect to λ, and corresponds to the linearized constraint function. Solve the above LCP using the Lemke complementary pivot method to obtain the optimal multiplier . Substitute λ into to solve for the improvement amount of the optimal design variable : . It should be noted that since the linearized optimization sub-problem is a local approximation of the original problem at the current design point, its solution can only be used as a reference for design improvement. To ensure global convergence, strategies such as trust regions and movement limits must be combined during the iteration process to be corrected to obtain the actually feasible improvement amount of the design variable .

[0067] Update the design variables, calculate the objective function value and the constraint function value, and use to update the current design variable : . Substitute the updated into the SIMP interpolation model to calculate the element strain energy density : . Substitute the updated into the Mises stress function to calculate the element Mises stress : . Substitute and into the objective function and the constraint function respectively to obtain the objective function value and the constraint function value at the current iteration step: , . Thus, one optimization iteration is completed. and The change trends of

[0068] will determine the direction of the next optimization iteration until the algorithm converges. Calculate the change amount of the objective function value, judge whether the convergence condition is satisfied, and define the convergence control parameters, including the objective function threshold and the maximum number of iteration steps N. Control the change range of the objective function value, generally take ; N controls the upper limit of the number of optimization iterations, which is generally 200. After completing the optimization of the current iteration, extract the objective function value of the previous step And the objective function value of this step , calculate the change of the two: ,like , or the number of iterations has reached N, the optimization process is considered to have converged, and the current elastic sling arrangement scheme is output. As the final optimization result; otherwise, the optimization process is considered to have not converged, and the current The optimal density distribution is used as the basis to continue the next optimization iteration. Transformed into discrete elastic sling arrangement parameters, assuming that the initial parameters of an elastic sling in the BIM model are as follows: concrete section size b×h, longitudinal elastic sling diameter d, number of elastic sling layers n, number of elastic slings per layer m, tensile elastic sling area , elastic sling yield strength f, concrete compressive strength Optimal elastic sling layout Each cell in is divided into two groups according to its density value. Multiply by the unit volume , the volume of the elastic sling actually arranged in the unit after optimization is obtained: ,Will Divide by the unit length , and the unit elastic sling area is obtained : ,in, is the cross-sectional area of ​​the unit. Assume By diameter The elastic sling is configured as follows: ,in The number of elastic slings actually arranged for the unit. , and we get: ,visible, Follow is monotonically increasing. Therefore, The larger the actual required elastic sling diameter The thicker, the worse. Similarly, in the total cross-sectional area Under certain circumstances, the number of unit elastic sling layers can be determined And the number of elastic slings per layer : ,Will , , , Substitute into the specification and calculate the spacing of elastic slings , protective layer thickness , elastic sling reinforcement ratio Whether they meet the construction requirements.

[0069] Using the optimized BIM model of the elastic sling, static and dynamic analyses of the elastic sling are carried out to obtain its displacement field, stress field and strain field responses, evaluate its bearing capacity, stiffness, stability and seismic performance, and compare with the design requirements, namely: displacement response: maximum deflection , where [d] is the deflection limit; stress response: maximum equivalent stress , where [σ] is the strength limit; stability: critical buckling load , where is the design load, and K is the stability safety factor; seismic performance: maximum displacement response , maximum stress response , where and are the displacement and stress limits under seismic conditions respectively. According to the final BIM model of the elastic sling , the processing parameters of the elastic sling are derived, including: sling length , i = 1, 2,..., , where is the total number of slings; sling cross-section type (circular, square or flat), cross-section size (diameter or width , height ); sling material type (steel wire rope, threaded steel bar or high-strength hinge), material grade; sling end construction type (fork head, anchor or thimble), end geometric dimensions; sling installation elevation and horizontal offset ; prestress or initial strain magnitude ; The above parameters can be exported as processing construction drawings to guide the cutting, processing, transportation and installation of elastic slings.

Claims

1. A BIM-based high-speed railway contact network elastic sling and electrical connection prefabrication processing method, characterized in that: include: Collect design parameters and processing data of different types of high-speed rail contact network elastic slings, and establish a knowledge base including geometric parameters, material properties and processing technology; According to the knowledge base, an initial elastic sling BIM model of the target project is established through parametric modeling; the initial elastic sling BIM model includes the spatial position, size and material property parameters of the elastic sling; According to the initial elastic sling BIM model, the initial finite element analysis model of the target project is established through meshing and material property mapping; In the initial finite element analysis model, static load conditions are applied, and the internal forces and deformations of the elastic slings under static loads are calculated using the incremental iteration method. Static loads include dead loads and live loads, including: The dead load information and live load information in the initial elastic sling BIM model are mapped into dead load data and live load data respectively; the dead load data and live load data are linearly superimposed as static load data applied to the initial finite element model; The static load data is discretized into multiple incremental step data according to the arc length method; the nonlinear state index of the elastic sling response is obtained, and when the nonlinear state index exceeds the threshold, the step size of the incremental step is adjusted; when the nonlinear state index exceeds the preset extreme value, the incremental step data is interpolated by the secant method; wherein the nonlinear state index includes deflection; For each incremental step data, the Newton-Raphson iteration format is used. In the first iteration, the displacement increment data is extracted and substituted into the tangent stiffness matrix to form the tangent stiffness equation; in the subsequent iterations, the displacement increment data is extracted and substituted into the secant stiffness matrix to form the secant stiffness equation; at the same time, the energy criterion is used to correct the direction of the displacement increment data to generate optimized displacement increment data; After all incremental calculations are completed, characteristic point data reflecting the deformation and failure mode of the elastic sling are extracted from the displacement field, stress field and strain field data. The characteristic points include the maximum deflection points. Statistical analysis is performed on the characteristic point data to obtain the weak parts of the elastic sling and form the response data of the elastic sling under static load. In the initial finite element analysis model, simulated seismic waves were input, and the direct integration method was used to perform dynamic time history analysis to obtain the displacement, velocity, acceleration and internal force time history curves of the elastic sling under different seismic waves; According to the results of static and dynamic analysis, the stress-strain response of the elastic sling is extracted, and the topology optimization method is used to optimize the initial elastic sling BIM model with the goal of minimizing the strain of the elastic sling and the stress constraint of the elastic sling as the condition; Using the optimized elastic sling BIM model, the finite element analysis model is updated until the performance of the elastic sling meets the design requirements, and the final elastic sling BIM model is obtained; According to the final elastic sling BIM model, the elastic sling processing parameters are derived.

2. The method for prefabrication of elastic slings and electrical connections for high-speed railway overhead contact network based on BIM according to claim 1 is characterized in that: The secant stiffness equation is formed, including: Extract the unit stress data and unit strain data of the initial finite element analysis model, input the unit stress data and unit strain data into the tangent stiffness matrix, and obtain the tangent stiffness matrix data of the elastic sling in the current incremental step; in the first iteration, extract the displacement increment component data from the arc length increment data of the current incremental step, substitute the displacement increment component data and the tangent stiffness matrix data into the tangent stiffness equation, and solve the node displacement data of the first iteration; Use the node displacement data of the first iteration to update the unit stress data and unit strain data; input the updated unit stress data and unit strain data into the secant stiffness matrix to obtain the secant stiffness matrix data of the second iteration; extract the displacement increment component data from the arc length increment data of the current increment step, substitute the displacement increment component data and the secant stiffness matrix data into the secant stiffness matrix, and solve the node displacement data of the second iteration; Based on the node displacement data of the first iteration and the node displacement data of the second iteration, the displacement difference data of the two iterations are calculated; if the displacement difference data is less than the convergence threshold, the node displacement data of the second iteration is used as the converged displacement data of the current incremental step and the iterative calculation is stopped, otherwise the next iterative calculation is entered; The node displacement data of the second iteration is used to update the unit stress data and the unit strain data, and the updated unit stress data and the unit strain data are input into the secant stiffness matrix to obtain the secant stiffness matrix of the next iteration.

3. The method for prefabrication of elastic slings and electrical connections for high-speed railway contact network based on BIM according to claim 2 is characterized in that: Generate optimized displacement increment data, including: The arc length increment data of the current incremental step and the node displacement data of the previous iteration are used as input, and the displacement increment direction correction coefficient of the current iteration is solved through the minimum potential energy; Multiply the displacement increment direction correction coefficient by the displacement increment component data of the current increment step to obtain the corrected displacement increment component data; Substitute the corrected displacement increment component into the secant stiffness matrix, solve the node displacement data of the current iteration, and return to the displacement convergence judgment step until the node displacement data of the current increment step converges.

4. The method for prefabrication of elastic slings and electrical connections for high-speed railway contact network based on BIM according to claim 1, characterized in that: Obtain the displacement, velocity, acceleration and internal force time history curves of the elastic cable under different seismic waves, including: According to the intensity and site category of the project area, a group of representative seismic waves are selected from the seismic wave database as input seismic wave data; the input seismic wave data are baseline corrected and amplitude adjusted using the vibration mode decomposition response spectrum method to obtain simulated seismic wave data; The simulated seismic wave data is converted into node load time history data, applied to the basic node degrees of freedom of the initial finite element analysis model, and the dynamic equilibrium equation considering the seismic effect is established; The Newmark-β method is used to directly integrate and solve the dynamic equilibrium equation to obtain the node displacement, node velocity and node acceleration data at each time step; According to the node displacement data of each time step, the unit strain data is calculated using the strain-displacement relationship, and the unit stress data is updated using the constitutive relationship; the unit stress data is multiplied and integrated with the unit volume to obtain the unit node equivalent force data; the unit node equivalent force data is assembled into the overall node load data and substituted into the dynamic balance equation for the next step of integral calculation; After completing the dynamic integral calculation of the entire time course, the node displacement, node velocity, node acceleration and unit stress data of each time step are extracted to form the displacement, velocity, acceleration and internal force time history curve data of the elastic cable under earthquake action.

5. The method for prefabrication of elastic slings and electrical connections for high-speed railway overhead contact network based on BIM according to claim 4 is characterized in that: Get the node displacement, node velocity and node acceleration data for each time step, including: The simulated seismic wave data is multiplied by the elastic sling mass matrix to be converted into node load time history data, and then applied to the foundation nodes of the initial finite element analysis model; The Rayleigh damping matrix is ​​introduced into the initial finite element analysis model, and the dynamic equilibrium equation including the elastic cable stiffness, mass and damping terms is established, and the differential equation describing the elastic cable response under earthquake action is obtained; The central difference format is used to discretize the node displacement, node velocity and node acceleration in the dynamic equilibrium equation. The integration step is selected according to the earthquake duration and the elastic cable period, and the time interval is discretized into multiple time steps. The dynamic equilibrium equation is integrated through Newmark parameters β and γ to establish the iterative format between the node displacement, velocity and acceleration of the current time step; The node displacement, node velocity and node acceleration of the elastic sling are set to zero at the initial moment. In the first time step, the node load data is used as input, and the node displacement, node velocity and node acceleration of the first time step are explicitly solved using the Newmark iteration format; In the second time step, according to the node displacement data obtained in the previous time step, the unit strain increment of the current time step is calculated using the strain-displacement relationship, the unit stress is updated using the constitutive relationship, and the unit stress is multiplied by the unit volume and integrated to obtain the node equivalent force increment of the current time step; Substitute the node velocity obtained in the previous step into the damping force expression to calculate the damping force increment of the current time step; introduce the node load increment, damping force increment and node equivalent force increment of the current time step into the dynamic equilibrium equation to establish an algebraic equation group reflecting the node force equilibrium state at the current moment; Solve the algebraic equations to obtain the node displacement increment of the second time step, and use the Newmark iteration relationship to update the node velocity increment and node acceleration increment of the second time step; add the node displacement increment, node velocity increment and node acceleration increment to the calculation results of the previous time step, respectively, to obtain the node displacement, node velocity and node acceleration of the current time step; Repeat the iterative update of the time step until the dynamic response calculation of the entire time history is completed, extract the node displacement, node velocity and node acceleration data of each time step, and form the dynamic response time history curve of the elastic cable under earthquake action.

6. The method for prefabrication of elastic slings and electrical connections for high-speed railway overhead contact network based on BIM according to claim 5, characterized in that: Optimize the initial elastic sling BIM model, including: Based on the response data of the elastic sling under static load conditions and the response data of the elastic sling under earthquake action, the envelope surface data reflecting the response characteristics of the elastic sling under the combined action of loads are calculated by combining the displacement field, stress field and strain field data under different working conditions; the envelope surface data is used to update the stress and strain properties of the elastic sling unit in the initial elastic sling BIM model; Taking the strain energy density distribution of the elastic sling as the optimization target, the strain energy density attribute parameters of the elastic sling unit are input into the SIMP interpolation model, and the nonlinear mapping relationship between the strain energy of the elastic sling and the elastic sling arrangement density is established through the interpolation equation in the form of a power function; the Mises stress distribution of the elastic sling is taken as the constraint condition; the Mises stress attribute parameters of the elastic sling unit are input into the KS aggregation function, and the local stress constraint is converted into a global stress constraint equation through the aggregation equation in the form of a P norm; The MMA optimization criterion is used to conduct sensitivity analysis on the elastic sling arrangement density of the elastic sling. Based on the first-order derivatives of the objective function and the constraints, a linearized optimization sub-problem is established. The dual method is used to solve the optimization sub-problem and the optimal elastic sling arrangement scheme of the current iteration step is obtained. The strain energy density data and Mises stress attribute parameters of the elastic sling unit are updated using the optimal elastic sling arrangement scheme, and the updated attribute parameters are substituted into the optimization criterion function to calculate the objective function value and constraint function value of the current iteration step; Determine whether the difference between the objective function value of the current iteration step and the objective function value of the previous step is less than the convergence threshold. If so, stop the iteration and output the final elastic sling arrangement plan; The final elastic sling arrangement scheme is discretized into the geometric information of the elastic sling, and the geometric information is used to modify the parameters of the initial elastic sling BIM model to generate the optimized elastic sling arrangement BIM model.

7. The method for prefabrication of elastic slings and electrical connections for high-speed railway overhead contact network based on BIM according to claim 6, characterized in that: Taking the strain energy density distribution of the elastic sling as the optimization target, the strain energy density attribute parameters of the elastic sling unit are input into the SIMP interpolation model, and the nonlinear mapping relationship between the strain energy of the elastic sling and the elastic sling arrangement density is established through the interpolation equation in the form of a power function, including: The updated strain energy density attribute parameters of the elastic sling unit are input into the SIMP interpolation model, and the nonlinear relationship between the strain energy of the elastic sling and the density of the elastic sling arrangement is established by performing interpolation mapping formed by a power function on the strain energy density attribute parameters, and the strain energy expression of the elastic sling is obtained as the optimization objective function; The updated Mises stress attribute parameters of the elastic sling unit are input into the KS aggregation function. By performing a P-norm aggregation operation on the Mises stress attribute parameters, the stress constraint reflecting the local stress level of the elastic sling is transformed into a global stress constraint equation reflecting the overall stress level of the elastic sling, and a violation function is obtained as an optimization constraint function. According to the optimization objective function and optimization constraint function, the elastic sling arrangement density is taken as the design variable, and a mathematical model is established with the elastic sling strain energy being minimized as the optimization objective and the elastic sling overall stress meeting the strength requirement as the optimization constraint. The heuristic optimization algorithm is used to iteratively solve the established mathematical model and obtain the elastic sling arrangement scheme for the current iteration step.

8. The method for prefabrication of elastic slings and electrical connections for high-speed railway contact network based on BIM according to claim 7, characterized in that: The optimization objective function expression is as follows: in, is the total strain energy expression of the elastic sling, i is the unit number in the finite element model of the elastic sling, is the volume of the ith unit, is the relative density of the i-th unit, i.e., the elastic sling arrangement density, ranging from 0 to 1. is the initial strain energy density of the i-th unit; is the penalty factor of the SIMP interpolation model.

9. The method for prefabrication of elastic slings and electrical connections for high-speed railway overhead contact network based on BIM according to claim 8, characterized in that: The optimization constraint function expression is as follows: in, represents the constraint function; represents the stress of the ith element as a function of relative density; is a given stress threshold.

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