Finite element parametric modeling method and system for small and medium span bridges

Abstract

The application discloses a finite element parameterized modeling method and system for small and medium span bridges, comprising: obtaining bridge design parameters; determining cross-section geometric parameters according to the type of the main beam; determining the in-bridge direction coordinates of the inter-beam connecting unit according to the arrangement rule of the inter-beam connecting unit and removing the repeated coordinates; taking the removed coordinates as control nodes, encrypting the nodes of each main beam according to the span, and generating the in-bridge direction node sequence of the main beam; calculating the cross-bridge direction coordinates of the main beam according to the transverse arrangement parameters of the main beam, and pairing the in-bridge direction coordinates and the cross-bridge direction coordinates to generate the node sequence of the main beam; positioning the constraint nodes in the in-bridge direction node sequence of the main beam by using a minimum distance matching algorithm, and applying boundary conditions at the constraint nodes; generating a data interface file that can be analyzed by finite element analysis software, and generating a finite element reference model after analysis; the application supports batch processing, significantly improves the modeling efficiency and standardization level, and is suitable for the rapid construction of finite element reference models in the health monitoring of a large number of small and medium span bridges.

Description

Technical Field

[0001] This application relates to the field of bridge structure modeling technology, specifically to a finite element parametric modeling method and system for small and medium span bridges. Background Technology

[0002] In bridge structural health monitoring systems, high-precision finite element baseline models are crucial for setting early warning thresholds, identifying abnormal responses, and assessing load-bearing capacity. Currently, my country's small and medium-span bridges are characterized by their large number and wide distribution. Taking Jiangsu Province as an example, hundreds of small and medium-span bridges are newly added or need to be included in the monitoring sequence every year. These bridges are diverse in type (such as prefabricated box girder bridges, T-beam bridges, and hollow slab girder bridges), and most are in a long-term operational monitoring state. There is an urgent need for efficient, consistent, and batch-implementable modeling methods to support the operation of large-scale monitoring networks.

[0003] Currently, among the bridge-specific finite element analysis software widely used in the industry, Midas Civil has become the mainstream tool for domestic design institutes and monitoring units to construct bridge finite element benchmark models due to its mature bridge modeling functions and reliable calculation engine. This software was specifically developed for the analysis and design of civil structures, especially bridge structures, and has been widely used in major projects such as the Sutong Bridge and the Aizhai Bridge. While other general-purpose finite element software (such as ABAQUS and ANSYS) have advantages in nonlinear analysis and local detail simulation (such as block 0, anchorage zone, diaphragm, etc.), they lack specialized modules for the overall structural analysis of bridges, resulting in complex and inefficient modeling processes, and are rarely used for simulating the overall stress performance of the entire bridge.

[0004] In existing Midas modeling practices, to achieve the highest level of precision control over the model, engineers primarily rely on manual operation or manually writing command flows, requiring them to complete node definitions, element division, cross-section assignment, and boundary condition application one by one. This process is not only time-consuming and labor-intensive but also struggles to address the challenges posed by the large number and wide distribution of small and medium-sized bridges. Unlike large-span bridges with diverse structures that require individual construction, small and medium-span bridges largely adopt standardized designs using provincial and ministerial general atlases, resulting in relatively uniform structural forms. This provides the technical prerequisite for parametric modeling but also amplifies the drawbacks of the traditional Midas modeling approach: when faced with hundreds or thousands of small and medium-sized bridges with similar structures but different parameters, repetitive work easily leads to fatigue errors; when correcting bridge geometry or material parameters (such as span, beam height, and lateral arrangement) based on as-built data or inspection data, the traditional modeling process lacks a flexible parameter linkage mechanism, often requiring the redrawing of a large number of primitives, severely impacting the efficiency and accuracy of model updates. Furthermore, due to the lack of unified modeling standards, the models built by different engineers vary significantly in terms of naming rules, element types, and cross-section definition methods, making it difficult to process the models in batches or integrate them into automated monitoring platforms.

[0005] In summary, the large number and wide distribution of small and medium-span bridges create a sharp contradiction with existing manual modeling methods. Therefore, providing a technology that can automatically parse structural parameters from design documents and generate standardized finite element models that conform to the syntax of bridge structure finite element analysis software with a single click has become crucial for supporting the efficient operation of health monitoring for a massive number of small and medium-span bridges. Summary of the Invention

[0006] To address the problems existing in the prior art, this application proposes a finite element parametric modeling method and system for small and medium-span bridges, which can provide technical support for the efficient, standardized, and automated generation of finite element models for a large number of small and medium-span bridges in structural health monitoring.

[0007] Firstly, this application provides a finite element parametric modeling method for small-to-medium span bridges, including the following: Obtain bridge design parameters, including bridge structure type and main beam parameters. The main beam parameters include main beam type, main beam transverse arrangement parameters, number of spans of each main beam, span diameter of each span, and arrangement rules of inter-beam connection units. The cross-sectional geometric parameters are determined according to the type of the main beam, and the cross-sectional geometric parameters include basic geometric parameters and derived geometric parameters. Based on the arrangement rules of the inter-beam connection units, the longitudinal coordinates of the inter-beam connection units are determined, and the longitudinal coordinates of the inter-beam connection units are merged into an initial set of inter-beam connection unit positions. The coordinate elements in the initial set of inter-beam connection unit positions are deduplicated, and a unique set of inter-beam connection unit positions for the entire bridge is output. The coordinate elements in the set of inter-beam connection unit locations are used as control nodes; the nodes of each main beam are densified according to the span to generate a non-repeating main beam longitudinal node sequence; Based on the transverse arrangement parameters of the main beams, calculate the transverse coordinates of each main beam; pair the transverse coordinates of each main beam with the longitudinal coordinates of the corresponding main beam in the longitudinal node sequence of the main beams to generate the node sequence of each main beam. The minimum distance matching algorithm is used to locate the constraint nodes in the longitudinal node sequence of the main beam, and the corresponding boundary conditions are applied at the constraint nodes according to the bridge structure type. The bridge design parameters, cross-sectional geometric parameters, beam connection unit location set, node sequence, constraint nodes, and boundary conditions are converted into a data interface file that can be parsed by finite element analysis software. After parsing, a finite element reference model is generated.

[0008] In one possible implementation of the first aspect, the bridge design parameters are obtained by one or more of the following methods: reading design documents, querying general drawing sets, calling databases, calculating using empirical formulas, and user-defined input.

[0009] In one possible implementation of the first aspect, determining the cross-sectional geometric parameters according to the main beam type includes: When the main beam type is a standard beam type, the basic geometric parameters of the corresponding standard beam type are determined; and based on the basic geometric parameters, the derived geometric parameters are calculated by calling the standard algorithm associated with the standard beam type geometric rule library. When the main beam type is a user-defined cross-section beam, the cross-sectional geometric data provided by the user is obtained, or the derived geometric parameters are calculated by calling the parametric expression based on the basic geometric parameters provided by the user.

[0010] In one possible implementation of the first aspect, the standard beam geometry rule library is constructed based on provincial or ministerial general drawing sets and is used to establish the mapping relationship between the span of bridges with different spans and basic geometric parameters, as well as the mapping relationship between basic geometric parameters and derived geometric parameters.

[0011] In one possible implementation of the first aspect, determining the longitudinal coordinates of the inter-beam connection units according to the arrangement rules of the inter-beam connection units, and merging the longitudinal coordinates of the inter-beam connection units into an initial set of inter-beam connection unit positions, includes: Virtual beams are arranged at equal intervals according to the preset loading spacing to generate a sequence of virtual beam positions; structural diaphragms / hinge joint connectors are arranged according to structural design requirements to generate a sequence of transverse connector positions. The position sequence of the virtual crossbeams in the same span is merged with the position sequence of the transverse connectors to generate an initial set of inter-beam connection unit positions; the position of the coordinate elements in the initial set of inter-beam connection unit positions is represented by the longitudinal coordinates.

[0012] In one possible implementation of the first aspect, the deduplication of coordinate elements in the initial set of inter-beam connection element locations includes: Traverse the coordinate elements in the initial set of inter-beam connection unit positions and calculate any two longitudinal abscissas. and The absolute value of the difference i and j are the index numbers of the coordinate elements; like Then and Considered as the same inter-beam connection element location, only one of them is retained in the initial set of inter-beam connection element locations, and δ is the preset tolerance.

[0013] In one possible implementation of the first aspect, the step of using coordinate elements in the set of inter-beam connection unit locations as control nodes, and segmenting each main beam by span to densify nodes and generate a non-repeating main beam longitudinal node sequence includes: For each span, the longitudinal coordinate of the inter-beam connection unit location set located within the span range is used as the control node for that span; Within each span, node encryption is performed between adjacent control nodes according to the preset target unit length to generate the sequential node sequence of that span. For each main beam, the longitudinal node sequence of each span is spliced ​​together in span order to generate a non-repeating longitudinal node sequence of the main beam.

[0014] In one possible implementation of the first aspect, calculating the transverse coordinates of each main girder based on the transverse arrangement parameters of the main girder includes: Calculate the transverse coordinates of each main girder using the transverse centerline of the bridge as the origin. : ; in, Let be the transverse coordinate of the k-th main girder, n be the number of main girders, k be the main girder number, k = 1, 2, ..., n, and d be the spacing between the main girders.

[0015] In one possible implementation of the first aspect, the step of employing a minimum distance matching algorithm to locate constraint nodes in the longitudinal node sequence of the main girder, and applying corresponding boundary conditions at the constraint nodes according to the bridge structure type, includes: Based on the theoretical support position calculated for each span, for each theoretical support position, traverse the candidate nodes within a preset distance range on both sides of the theoretical support position in the non-repeating main beam longitudinal node sequence. Calculate the difference between the longitudinal coordinate of each candidate node and the longitudinal coordinate of the theoretical support location, and select the candidate node with the smallest absolute value of the difference as the constraint node of the support. When the bridge structure is a simply supported beam, a fixed hinge constraint is applied at the constraint node corresponding to the first end support to constrain the translational degrees of freedom in the longitudinal, transverse, and vertical directions, as well as the rotational degrees of freedom about the longitudinal direction; a movable hinge constraint is applied at the constraint node corresponding to the last end support to constrain the translational degrees of freedom in the transverse and vertical directions, as well as the rotational degrees of freedom about the longitudinal direction. When the bridge structure is a continuous beam, a fixed hinge constraint is applied at the constraint node corresponding to the first end support to constrain the translational degrees of freedom in the longitudinal, transverse, and vertical directions, as well as the rotational degrees of freedom about the longitudinal direction; a movable hinge constraint is applied at the constraint node corresponding to the other supports to constrain the translational degrees of freedom in the transverse and vertical directions, as well as the rotational degrees of freedom about the longitudinal direction.

[0016] Secondly, this application provides a system for implementing the aforementioned finite element parametric modeling method for small-to-medium span bridges, comprising: The design parameter acquisition module is used to acquire bridge design parameters, including bridge structure type and main beam parameters; The section definition module is used to determine the section geometry parameters based on the main beam type. The beam connection unit layout module determines the longitudinal coordinates of the beam connection units according to the beam connection unit layout rules, merges the longitudinal coordinates of the beam connection units into an initial beam connection unit position set, removes duplicate coordinate elements from the initial beam connection unit position set, and outputs a unique beam connection unit position set for the entire bridge. The node sequence generation module includes a transverse bridge positioning unit and a longitudinal bridge division unit. The transverse bridge positioning unit calculates the transverse bridge coordinates of each main beam according to the transverse arrangement parameters of the main beam. The longitudinal bridge division unit uses the coordinate elements in the set of inter-beam connection unit positions as control nodes, and densifies the nodes between adjacent control nodes in each span according to the preset target unit length to generate a longitudinal bridge node sequence of the main beam. The node sequence pairing module is used to pair the transverse coordinates of each main beam with the longitudinal coordinates in the longitudinal node sequence of the main beam to generate the node sequence of each main beam. The boundary condition configuration module uses a minimum distance matching algorithm to locate constraint nodes in the longitudinal node sequence of the main beam and apply corresponding boundary conditions at the constraint nodes according to the bridge structure type. The finite element reference model output module is used to convert the bridge design parameters, cross-sectional geometric parameters, beam connection element location set, node sequence, constraint nodes, and boundary conditions into a data interface file that can be parsed by finite element analysis software, and generate a finite element reference model after parsing.

[0017] Compared with existing methods, this application has the following advantages: 1. This application uses automatic parsing of design documents and full-process algorithm-driven processing, eliminating the need for manual definition of nodes, elements, sections, and boundary conditions. As verified by examples, the modeling time for a single small-to-medium span bridge is reduced from several hours to several minutes using traditional manual methods, significantly improving efficiency. It supports daily batch processing of hundreds of bridges, meeting the timeliness requirements of large-scale health monitoring projects. 2. This application separates the transverse bridge positioning and longitudinal bridge densification processes, and then combines them to form complete node coordinates, realizing modularization and precise control of node division; on this basis, a proportional subdivision strategy within the span is adopted, so that the length of each span element can be adaptively adjusted according to the span, ensuring that the mesh density is coordinated with the structural scale; 3. This application merges the positions of the virtual beam and the transverse connector and performs deduplication, which effectively avoids the problem of repeated model definition caused by the position conflict between the two types of beam connection units. At the same time, the set of positions of the deduplicated beam connection units is used as control nodes for node densification, so that the densified node sequence can simultaneously meet the construction requirements of the transverse connector and the load analysis accuracy requirements of the virtual beam, thus achieving a balance between the dual requirements of structural stress and moving load analysis. 4. The non-repeating sequential bridge node sequence constructed in this application provides a complete set of candidate nodes for constraint node localization; and the minimum distance matching algorithm is used to automatically find constraint nodes in this node sequence, eliminating the need for manual selection of node numbers one by one, avoiding the error-prone problem of manual operation, and ensuring the accuracy of constraint application position; the integrity of the node sequence and the accuracy of the matching algorithm support each other, jointly ensuring the reliability of boundary condition configuration. 5. This application can batch execute the modeling process based on multiple bridge design files and automatically generate multiple corresponding structured command flow files; when the design parameters change, only the design parameters need to be updated to automatically rebuild the model, avoiding coordinate misalignment or attribute omission caused by manual adjustment; this mechanism realizes rapid and standardized modeling of small and medium span bridge groups, and provides technical support for the construction of regional bridge health monitoring systems. Attached Figure Description

[0018] Figure 1 A flowchart illustrating a finite element parametric modeling method for small-to-medium span bridges, provided for the implementation of this application; Figure 2 A flowchart for generating a set of locations for beam-to-beam connection elements is provided for embodiments of this application; Figure 3 A flowchart for generating a sequence of main beam nodes along the bridge direction is provided for the implementation of this application; Figure 4 A flowchart for applying boundary conditions at constraint nodes is provided for embodiments of this application; Figure 5 This application provides a finite element reference model of a three-span continuous small box girder bridge generated by importing an MCT file into Midas Civil software. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the application will now be described in further detail with reference to the accompanying drawings.

[0020] It should be understood that the described embodiments are merely some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0021] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. The singular forms “a,” “the,” and “the” used in the embodiments of this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0022] like Figure 1 As shown, this application provides a finite element parametric modeling method for small-to-medium span bridges, including the following steps: S100: Obtain bridge design parameters, including bridge structure type and main beam parameters. The main beam parameters include main beam type, main beam transverse arrangement parameters, number of spans of each main beam, span diameter of each span, and arrangement rules of inter-beam connection units. The transverse arrangement parameters of the main beams are used to describe the arrangement rules of the main beams in the transverse direction of the bridge (i.e., the direction of bridge width), including the number of main beams and the spacing between them. The arrangement rule of the inter-beam connection unit indicates the setting rule of the inter-beam connection unit in the longitudinal direction (i.e., the length direction of the bridge) of each span; the inter-beam connection unit includes virtual crossbeams and transverse connectors, wherein the virtual crossbeams are used for vehicle load distribution in moving load analysis, and the transverse connectors are used for structural stress, including structural diaphragms (applicable to box girders and T-beams) or hinged joint connectors (applicable to hollow slab beams). In this application, the beam connection unit includes virtual crossbeams and transverse connectors; the arrangement rules of the two types of beam connection units are independent; the virtual crossbeams are set at preset intervals to realize vehicle load distribution when performing moving load analysis in finite element analysis software; at the same time, the transverse connectors that exist in the bridge structure itself are used to improve the torsional stiffness and transverse stability of the beam, and the type and configuration position of the transverse connectors need to be determined according to the structural design requirements of different types of bridges.

[0023] S200: Determine the cross-sectional geometric parameters according to the type of main beam. The cross-sectional geometric parameters include basic geometric parameters and derived geometric parameters.

[0024] S300: Based on the arrangement rules of the inter-beam connection units, determine the longitudinal coordinates of the inter-beam connection units, merge the longitudinal coordinates of the inter-beam connection units into an initial set of inter-beam connection unit positions; perform deduplication on the coordinate elements in this set, and output a unique set of inter-beam connection unit positions for the entire bridge. As mentioned above, the arrangement rules of the virtual beam and the transverse connector are independent. If they are directly superimposed, two beam connection units may be generated at the same position, resulting in duplicate definition of the model and thus affecting the accuracy of the analysis results. Merging the position coordinates of the two types of beam connection units and then performing deduplication can avoid positional conflicts between the two, ensuring both the stress requirements of the transverse connector and the analysis accuracy requirements of the virtual beam.

[0025] S400: The coordinate elements in the set of inter-beam connection unit positions are used as control nodes, and the control nodes are non-uniformly distributed within their respective spans; the nodes of each main beam are densified according to the span, generating a non-repeating main beam longitudinal node sequence.

[0026] S500: Calculate the transverse coordinates of each main beam based on the transverse arrangement parameters of the main beam; pair the transverse coordinates of each main beam with the longitudinal coordinates of the corresponding main beam in the longitudinal node sequence of the main beam to generate the node sequence of each main beam; the node sequence defines the spatial position of all nodes in the model; on this basis, connect adjacent nodes according to the preset topology rules to form finite element meshes such as beam elements and plate elements; It should be understood that this application is applicable to both frame model and full bridge model models. When building a frame model, it is only necessary to pair the transverse bridge coordinates with the longitudinal bridge coordinates to generate a two-dimensional node sequence, and the vertical coordinates of all nodes are uniformly set to preset constants. When building a full bridge model, it is also necessary to set the vertical coordinates of each node according to the structural design requirements to generate a three-dimensional node sequence.

[0027] S600: The minimum distance matching algorithm is used to locate the constraint nodes in the longitudinal node sequence of the main beam, and the corresponding boundary conditions are applied at the constraint nodes according to the bridge structure type.

[0028] S700: Convert the bridge design parameters, cross-sectional geometric parameters, beam connection unit location set, node sequence, constraint nodes, and boundary conditions into a data interface file that can be parsed by finite element analysis software, and generate a finite element reference model after parsing.

[0029] In one possible implementation, step S100 obtains the bridge design parameters by reading design documents, querying general drawing sets, calling databases, calculating using empirical formulas, or user-defined input; the design documents include, but are not limited to, drawings, structural calculation sheets, and written reports.

[0030] In one possible implementation, step S200 includes the following: The main beam type is either a standard beam or a user-defined cross-section beam, wherein the standard beam type includes, but is not limited to, box beams, T-beams, and hollow slab beams; The cross-sectional geometric parameters belong to the main beam parameters, which can be divided into basic geometric parameters and derived geometric parameters. The basic geometric parameters include, but are not limited to, beam height / slab height and beam width / slab width, which can be determined according to the span of each span. The derived geometric parameters include, but are not limited to, top slab thickness, bottom slab thickness, web slope, and cantilever length, which can be calculated based on the basic geometric parameters. When the main beam type is a standard beam type, the basic geometric parameters of the corresponding standard beam type are determined; and based on the basic geometric parameters, the derived geometric parameters are calculated by calling the standard algorithm associated with the standard beam type geometric rule library, thereby determining all cross-sectional geometric data; When the main beam type is a user-defined cross-section beam type, obtain the cross-section geometric data provided by the user, or calculate the derived geometric parameters by calling the parametric expression based on the basic geometric parameters provided by the user. For user-defined cross-section beams, the cross-section geometric parameters and cross-section geometric properties can be associated and stored to build a reusable custom cross-section library; Preferredly, the cross-sectional geometric parameters are read directly from the design documents. When the design documents are missing or the parameters are incomplete, the basic geometric parameters such as beam height / slab height and beam width / slab width can be determined by looking up tables in provincial or ministerial general atlases or design specifications based on the span of each span. Then, derived geometric parameters can be obtained through databases, empirical formulas, or direct user input. The above methods can be flexibly combined according to the actual situation, and this application does not limit them. For example, for a standard beam type, based on the known span of each span, the corresponding beam height / slab height and beam width / slab width can be queried from the standard beam type geometric rule library according to the maximum span value as basic geometric parameters; then, the standard algorithm stored in the standard beam type geometric rule library is used to calculate the derived geometric parameters based on the beam height / slab height and beam width / slab width.

[0031] Furthermore, in a preferred embodiment, the standard beam geometry rule library is constructed based on provincial or ministerial general drawing sets, and is used to establish the mapping relationship between the span and basic geometric parameters of bridges with different spans, that is, to determine basic geometric parameters such as beam height / slab height and beam width / slab width based on the span; and the mapping relationship between basic geometric parameters and derived geometric parameters, that is, to derive derived geometric parameters such as top slab thickness, bottom slab thickness, web slope, and cantilever length from basic geometric parameters such as beam height / slab height and beam width / slab width through parametric expressions.

[0032] like Figure 2 As shown, in one possible implementation, step S300 divides each main girder into multiple spans along the bridge direction. For each span, the positions of the inter-beam connection units are determined and non-uniform node division is performed as follows: S310: Arrange virtual crossbeams for vehicle load distribution at preset loading intervals (e.g., 5m) to generate a virtual crossbeam position sequence; the virtual crossbeams serve as the loading carriers for vehicle loads when performing moving load analysis in finite element analysis software, distributing the load to the main beams on both sides. S320: Arrange transverse connectors to improve structural stiffness and stability according to structural design requirements, and generate a sequence of transverse connector positions; For example, for continuous box girders, the transverse connectors are structural diaphragms, specifically including end support diaphragms, middle support diaphragms, and mid-span diaphragms; wherein, the end support diaphragms are set at a preset offset (e.g., 0.65m) from the beam end in the inward direction; the middle support diaphragms are set at the middle support position; and the mid-span diaphragms are set at the mid-span position when the span is greater than or equal to a preset threshold (e.g., 25m); for hollow slab beam bridges, the transverse connectors are hinged joints and do not involve structural diaphragms.

[0033] S330: Merge the virtual beam position sequence and the transverse connector position sequence of the same span to generate the initial beam connection unit position set for that span. The position of the coordinate elements in the set is represented by the longitudinal coordinate.

[0034] In one possible implementation, step S300 further sets a preset tolerance δ, and performs tolerance-based numerical deduplication on the initial set of inter-beam connection unit positions, as follows: S340: Traverse the coordinate elements in the initial set of inter-beam connection unit positions, and calculate the longitudinal abscissa of any two inter-beam connection units. and The absolute value of the difference i and j are the index numbers of the coordinate elements; S350: If Then and Treating them as the same inter-beam connection element location, only one of their coordinates is retained in the initial set of inter-beam connection element locations; S360: After performing the above comparison and merging process on all coordinate elements, output a unique set of inter-beam connection unit positions for the entire bridge, which is used for subsequent node densification. Considering engineering accuracy and computational efficiency, the value of δ is preferably in the range of 0.001m to 0.05m, and more preferably 0.01m.

[0035] like Figure 3 As shown, in one possible implementation, step S400 specifically includes the following: S410: For each span, the longitudinal coordinate of the beam connection unit location set located within the span range is used as the control node of the span; specifically, the basic node location is determined according to the preset virtual beam spacing (e.g., 5m) for each span, and the transverse connector location is superimposed to form a non-uniformly distributed control node set. S420: For each span of each main beam, the nodes between adjacent control nodes are densified according to the preset target unit length to generate the longitudinal node sequence of that span; the node densification adopts an equal subdivision strategy within the span, and the length of each span unit after division can be adaptively adjusted according to the span diameter to ensure that the mesh density is coordinated with the structural scale; so that the node sequence of each span simultaneously meets the loading analysis requirements of the virtual beam and the construction requirements of the transverse connector. S430: For each main beam, splice the longitudinal node sequence of each span in the span order to generate a non-repeating longitudinal node sequence of the main beam.

[0036] In one possible implementation, step S500 calculates the transverse coordinates of each main girder based on the number of main girders and the spacing between them, as follows: Establish a global three-dimensional Cartesian coordinate system: define the longitudinal direction, transverse direction, and vertical direction as the X-axis, Y-axis, and Z-axis, respectively; Let the number of main girders be n, and the spacing between main girders (the distance between the centerlines of adjacent main girders) be d; with the transverse centerline of the bridge as the origin of the Y-axis, calculate the transverse coordinates of each main girder using the following formula. : ; in, Let k be the transverse coordinate of the k-th main girder, where k is the girder number, k=1, 2,...,n; A sequence of transverse coordinates of the main beams is generated based on the transverse coordinates of each main beam. Each coordinate value in the sequence of transverse nodes of the main beams uniquely corresponds to a main beam. It should be noted that the above formula is only applicable to the case where the main beams are arranged at equal intervals and the cross section of the bridge is symmetrical about the centerline. The number of main beams and the spacing between them can be obtained from the design documents. When the design documents are missing or the parameters are incomplete, the spacing between the main beams can be estimated by measuring the total width of the bridge on site and counting the number of main beam segments. When the main beams are not arranged at equal intervals or have special structures, the user can directly specify the transverse coordinates of each main beam through custom input.

[0037] like Figure 4 As shown, in one possible implementation, step S600 specifically includes the following: S610: Calculate the theoretical support position based on the span of each span. For each theoretical support position, traverse the non-repeating main beam longitudinal node sequence and select candidate nodes within a preset distance range on both sides of the theoretical support position. The preset distance can be set according to the modeling accuracy requirements, and it is recommended to take a value of 0.5m to 1.0m. S620: Calculate the difference between the longitudinal coordinate of each candidate node and the longitudinal coordinate of the theoretical support position, and select the candidate node with the smallest absolute value of the difference as the constraint node of the support. S630: Based on the bridge structure type, apply corresponding boundary conditions at the constraint nodes, as follows: Define the translational degree of freedom along the bridge direction (X-axis) as UX, the translational degree of freedom along the bridge direction (Y-axis) as UY, the translational degree of freedom along the vertical direction (Z-axis) as UZ, and the rotational degree of freedom about the X-axis as RX; When the bridge structure is a simply supported beam, a fixed hinge constraint is applied at the constraint node corresponding to the first end support, constraining the degrees of freedom UX, UY, UZ, and RX; a movable hinge constraint is applied at the constraint node corresponding to the last end support, constraining the degrees of freedom UY, UZ, and RX. When the bridge structure is a continuous beam, a fixed hinge constraint is applied at the constraint node corresponding to the first end support, constraining the degrees of freedom UX, UY, UZ, and RX; and a movable hinge constraint is applied at the constraint node corresponding to the other supports, constraining the degrees of freedom UY, UZ, and RX.

[0038] In one possible implementation, step S700 first converts the bridge design parameters, cross-sectional geometric parameters, set of inter-beam connection unit locations, node sequence, constraint nodes, and boundary conditions into a structured command stream that conforms to the syntax of finite element software, and then outputs the structured command stream as a data interface file that can be parsed by finite element software through compilation and other operations. For example, the cross-sectional geometric parameters are converted into cross-sectional definition statements using a preset parameter-syntax mapping table. The parameter-syntax mapping table is a pre-established set of conversion rules for converting cross-sectional geometric parameters into cross-sectional definition statements that conform to the syntax specifications of the target finite element analysis software. When the user directly provides a custom cross-sectional definition statement that can be parsed by the finite element analysis software, it is directly embedded and used.

[0039] Furthermore, to improve the reliability of the model, the finite element parametric modeling method for small-to-medium span bridges also includes a geometric consistency verification step, including: Before generating the structured command flow, verify whether the longitudinal length of the main beam matches the sum of the spans of each span, and whether the positions of the inter-beam connection units exceed the span range. If a conflict is found during verification, an error message will be output and the generation of the structured command stream file will be terminated.

[0040] Based on the same inventive concept, this application also provides a system for performing the aforementioned finite element parametric modeling method, comprising: The design parameter acquisition module is used to acquire bridge design parameters, including bridge structure type and main beam parameters; The section definition module is used to determine the section geometry parameters based on the main beam type. The beam connection unit layout module determines the longitudinal coordinates of the beam connection units according to the beam connection unit layout rules, merges the longitudinal coordinates of the beam connection units into an initial beam connection unit position set, removes duplicate coordinate elements from the initial beam connection unit position set, and outputs a unique beam connection unit position set for the entire bridge. The node sequence generation module includes a transverse positioning unit and a longitudinal division unit. The transverse positioning unit calculates the transverse coordinates of each main beam based on the transverse arrangement parameters of the main beam. The longitudinal division unit uses the coordinate elements in the set of inter-beam connection unit positions (including transverse connectors and virtual beams) as control nodes, and densifies the nodes between adjacent control nodes in each span according to the preset target unit length to generate a longitudinal node sequence of the main beam. The node sequence pairing module is used to pair the transverse coordinates of each main beam with the longitudinal coordinates in the longitudinal node sequence of the main beam to generate the node sequence of each main beam. The boundary condition configuration module uses a minimum distance matching algorithm to locate constraint nodes in the longitudinal node sequence of the main beam and apply corresponding boundary conditions at the constraint nodes according to the bridge structure type. The finite element reference model output module is used to convert the bridge design parameters, cross-sectional geometric parameters, beam connection element location set, node sequence, constraint nodes, and boundary conditions into a data interface file that can be parsed by finite element analysis software, and generate a finite element reference model after parsing.

[0041] It should be understood that the above division of the modules / units in the system of this application is based on their logical functions. In practical applications, these modules / units can be fully or partially integrated into a single physical entity, or they can be physically separated. Furthermore, the processing modules / units in the system can be implemented by a processor calling software; for example, the system includes a processor connected to memory, which stores instructions. The processor calls the instructions stored in memory to implement any of the above methods or to implement the functions of each processing unit in the system. The processor is a general-purpose processor, such as a central processing unit or a microprocessor, and the memory is either internal or external to the system.

[0042] Thirdly, this application also provides a computer-readable storage medium having computer program instructions stored thereon, which, when executed by a processor, implement the methods described in the above embodiments.

[0043] For example, the above can be achieved Figure 1 The steps of the finite element parametric modeling method for small and medium span bridges are shown below.

[0044] A computer-readable storage medium can be a tangible device capable of holding and storing instructions used by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof.

[0045] The computer program instructions used to perform the operations of this application may be source code or object code written in any combination of one or more programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server.

[0046] The feasibility and effectiveness of this application will be explained in detail below with an application example.

[0047] Twenty-five in-service small-span bridges built between 2005 and 2010 were selected as the subjects of this study. These bridges included 17 precast prestressed concrete small box girder bridges and 8 prestressed concrete hollow slab girder bridges using the pre-tensioned method, all of which were standard beam types. The 17 precast prestressed concrete small box girder bridges primarily had span combinations of 20m+20m, 25m+25m, and 30m+30m+30m, with 4–6 main girders and a spacing of 2.4–2.8m between them. The 8 prestressed concrete hollow slab girder bridges were single-span or double-span bridges with spans of 10–16m and a single slab width of 1.2m, connected laterally by hinged joints to form an integrated load-bearing system.

[0048] According to the latest periodic inspection report, the overall structural condition of these bridges is good, and no major defects affecting their load-bearing capacity have been found. However, there is a general lack of finite element benchmark models that can be used for condition assessment. If the traditional manual modeling method is used, engineers need to manually define the geometry, elements, sections and boundary conditions of each bridge in Midas Civil, which takes an average of about 5 hours per bridge and a total of more than 125 hours. At the same time, due to the lack of unified modeling standards, the generated models have significant differences in naming rules, element types and section definitions (such as chaotic file names), which seriously restricts the efficiency of batch calculation, data comparison and automated assessment.

[0049] 1. Source of design documents: Collect as-built drawings (PDF documents) and structural calculation reports (Word documents) of 25 bridges, extract bridge design parameters, and form a JSON-formatted bridge structured input file.

[0050] In this embodiment, the bridge structured input file includes the bridge number, bridge structure type, main beam type, rule base reference standard, number of main beams, main beam spacing, number of spans of each main beam, span diameter of each span, and arrangement rules for beam connection units.

[0051] 2. Obtaining cross-sectional parameters: For 17 small box girder bridges, based on the maximum span L1=30m, the beam height h1=1.6m and beam width b1=2.8m were determined in the built-in box girder geometric rule library; based on the beam height h1=1.6m and beam width b1=2.8m, 28 cross-sectional geometric parameters of the box girder, such as the top plate thickness, bottom plate thickness, web slope, and cantilever length, were determined by calling the box girder geometric rule library. For the eight hollow slab girder bridges, based on the maximum span L2=16m, the slab height h2=0.8m and single slab width b2=1.2m were determined in the built-in hollow slab girder geometric rule library. Based on the slab height h2=0.8m and single slab width b2=1.2m, 12 cross-sectional geometric parameters, such as circular aperture, tongue and groove size, and hinge width, were determined by calling the hollow slab girder geometric rule library.

[0052] 3. Parameter integrity verification: Check the bridge structured input file for anomalies such as missing required fields, non-positive spans, and fewer than 2 beams.

[0053] 4. Beam connection unit settings: This will be illustrated using a 30m span three-span continuous small box girder bridge as an example; Establish a global three-dimensional Cartesian coordinate system: the X-axis is along the bridge direction, the Y-axis is across the bridge direction, and the Z-axis is vertical; Based on the arrangement rules of its inter-beam connection units, virtual beams, end support diaphragms, middle support diaphragms, and mid-span diaphragms are set up: (1) Virtual crossbeams: A virtual crossbeam is set at a spacing of about 3m in each span; for a span of 30m, the longitudinal X-axis coordinates of the virtual crossbeams are as follows: 1st span 3m, 6m, 9m, 12m, 15m, 18m, 21m, 24m and 27m, 2nd span 33m, 36m, 39m, 42m, 45m, 48m, 51m, 54m and 57m, 3rd span 63m, 66m, 69m, 72m, 75m, 78m, 81m, 84m and 87m; (2) End support transverse diaphragm: A transverse diaphragm is installed at both ends of each beam body 0.65m from the beam end in the direction of the span; for a 3×30m span bridge, the longitudinal X-axis coordinates of the end support transverse diaphragm are 0.65m and 89.35m respectively. (3) Mid-support transverse diaphragm: For a 3×30m span bridge, the longitudinal X-axis coordinates of the mid-support transverse diaphragm are 30m, 60m and 90m respectively; (4) Mid-span diaphragm: A mid-span diaphragm is set at the mid-span of each span; for a 3×30m span bridge, the mid-span diaphragm is located at the midpoint of each span, that is, the X-axis coordinates along the bridge direction are: 15m for the first span, 45m for the second span, and 75m for the third span; The above-mentioned longitudinal X-axis coordinates are merged into an initial set {0.65,3,6,9,12,15,15,18,21,24,27,30,33,36,39,42,45,45,48,51,54,57, 60,63,66,69,72,75,75,78,81,84,87,89.35,90}. A numerical deduplication algorithm based on a tolerance δ=0.01m is then performed on this set. The virtual crossbeam and the mid-span diaphragm coincide at positions of 15m, 45m, and 75m. After merging, the diaphragm position set is output as {0.65,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57}. 60,63,66,69,72,75,78,81,84,87,89.35,90}.

[0054] 5. Three-dimensional finite element mesh construction: Given n=5 and d=2.8m, with the transverse centerline of the bridge as the origin, calculate the transverse coordinates of each main girder: Beam No. 1 (Left Beam): ; Beam No. 2: ; Beam No. 3 (Middle Beam): ; Beam No. 4: ; Beam No. 5 (Right Beam): ; The Y-coordinate sequence of the main girder in the transverse direction is obtained as: [-5.6, -2.8, 0, 2.8, 5.6].

[0055] Using the coordinate elements in the above-output set of diaphragm positions as the control nodes of the span, the nodes are densified between each adjacent control node according to a preset subdivision spacing. For a small box girder with a span of 3×30m, the node subdivision spacing is set to 1.0m. After densification of the first and second spans, a total of 31 nodes (including both ends) are generated per span. After densification of the third span, a total of 32 nodes (including both ends) are generated per span. Pair the Y-axis coordinates and X-axis coordinates of each main beam to generate a node sequence, and connect adjacent nodes to form a beam element.

[0056] 6. Boundary condition configuration: The small box girder is a continuous beam. A fixed hinge constraint is applied at the left end (constraining the degrees of freedom of UX, UY, UZ, and RX), and a movable hinge constraint is applied at the other three supports (constraining the degrees of freedom of UY, UZ, and RX). The hollow slab beam is a simply supported beam. A fixed hinge constraint is applied at the first end (constraining the degrees of freedom of UX, UY, UZ, and RX), and a movable hinge constraint is applied at the last end (constraining the degrees of freedom of UY, UZ, and RX). Constraint node positioning: Traverse the end nodes and select the one with the smallest deviation between the X-axis coordinate and the theoretical position of the support (0, 30, 60, 90 m). Record the matching error as <0.005m.

[0057] 7. MCT file generation: The model data generated in the above steps is converted into a structured MCT (Midas Civil Text) command stream conforming to the Midas Civil syntax specification, containing approximately 1850 lines of commands, including a material definition block (C50, E=3.45×10). 4 (MPa), section definition block, node definition block, element definition block, boundary condition block, etc.; in the material definition block, C50 represents the concrete strength grade, E=3.45×10 4 MPa represents the elastic modulus of a material; Among them, the cross-sectional geometric parameters of small box girders and hollow slab girders are mapped to PSC statements and DBUSER statements respectively through the parameter-Midas syntax mapping table; The final output is a .mct file that can be parsed by Midas Civil, enabling one-click import of the model, such as... Figure 5 The image shown is a rendering of the generated finite element baseline model of a three-span continuous small box girder bridge.

[0058] 8. Performance Verification: Five bridges were randomly selected and imported into Midas Civil 2022; the model loading success rate was 100%. To verify the calculation accuracy of the model in this application, the mid-span deflection calculated by the model in this application is compared with the theoretical design value obtained by the traditional modeling method. The results are shown in Table 1: Table 1 Comparison of mid-span deflection values ​​between this application and traditional modeling methods

[0059] As shown in Table 1, the mid-span deflection values ​​calculated based on the model of this application are basically consistent with the theoretical design values, with errors ranging from 1.38% to 5.39%, all less than 6%. It is evident that the finite element benchmark model generated in this application can accurately reflect the vertical deformation characteristics of the bridge under Highway-I lane loads.

[0060] Table 2 Efficiency Comparison between this application and traditional modeling methods

[0061] According to Table 2, the modeling time for a single small-to-medium span bridge has been reduced from 4.8 hours to 4.2 minutes using the traditional manual method, improving efficiency by approximately 68 times. This supports daily batch processing of hundreds of bridges and can meet the timeliness requirements of large-scale health monitoring projects.

[0062] The above embodiments are only for illustrating the technical concept and features of this application, and are intended to enable those skilled in the art to understand the content of this application and implement it accordingly. They should not be used to limit the scope of protection of this application. For those skilled in the art, several improvements and modifications can be made without departing from the principles of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A finite element parametric modeling method for small-to-medium span bridges, characterized in that, Includes the following: Obtain bridge design parameters, including bridge structure type and main beam parameters. The main beam parameters include main beam type, main beam transverse arrangement parameters, number of spans of each main beam, span diameter of each span, and arrangement rules of inter-beam connection units. The cross-sectional geometric parameters are determined according to the type of the main beam, and the cross-sectional geometric parameters include basic geometric parameters and derived geometric parameters. Based on the arrangement rules of the inter-beam connection units, the longitudinal coordinates of the inter-beam connection units are determined, and these coordinates are merged into an initial set of inter-beam connection unit positions. The coordinate elements in this initial set are then deduplicated to output a unique set of inter-beam connection unit positions for the entire bridge. Specifically: Virtual beams are arranged at equal intervals according to a preset loading spacing to generate a sequence of virtual beam positions. Structural diaphragms / hinge connectors are arranged according to structural design requirements to generate a sequence of transverse connector positions. The sequence of virtual beam positions and the sequence of transverse connector positions in the same span are merged to generate an initial set of inter-beam connection unit positions. The positions of coordinate elements in the initial set of inter-beam connection unit positions are represented by longitudinal bridge coordinates. The coordinate elements in the initial set of inter-beam connection unit positions are traversed, and any two longitudinal bridge transverse coordinates are calculated. and The absolute value of the difference Where i and j are the index numbers of the coordinate elements; if Then and Considered as the same inter-beam connection element location, only one of them is retained in the initial set of inter-beam connection element locations, and δ is the preset tolerance; The coordinate elements in the set of inter-beam connection unit locations are used as control nodes; the nodes of each main beam are densified according to the span to generate a non-repeating main beam longitudinal node sequence; Based on the transverse arrangement parameters of the main beams, calculate the transverse coordinates of each main beam; pair the transverse coordinates of each main beam with the longitudinal coordinates of the corresponding main beam in the longitudinal node sequence of the main beams to generate the node sequence of each main beam. The minimum distance matching algorithm is used to locate the constraint nodes in the longitudinal node sequence of the main beam, and the corresponding boundary conditions are applied at the constraint nodes according to the bridge structure type. The bridge design parameters, cross-sectional geometric parameters, beam connection unit location set, node sequence, constraint nodes, and boundary conditions are converted into a data interface file that can be parsed by finite element analysis software. After parsing, a finite element reference model is generated.

2. The finite element parametric modeling method for small-to-medium span bridges according to claim 1, characterized in that, The bridge design parameters are obtained through one or more of the following methods: reading design documents, querying general drawing sets, calling databases, calculating using empirical formulas, and user-defined input.

3. The finite element parametric modeling method for small-to-medium span bridges according to claim 1, characterized in that, The determination of cross-sectional geometric parameters based on the main beam type includes: When the main beam type is a standard beam type, the basic geometric parameters of the corresponding standard beam type are determined; and based on the basic geometric parameters, the derived geometric parameters are calculated by calling the standard algorithm associated with the standard beam type geometric rule library. When the main beam type is a user-defined cross-section beam, the cross-sectional geometric data provided by the user is obtained, or the derived geometric parameters are calculated by calling the parametric expression based on the basic geometric parameters provided by the user.

4. The finite element parametric modeling method for small-to-medium span bridges according to claim 3, characterized in that, The standard beam geometry rule library is constructed based on provincial or ministerial general drawing sets and is used to establish the mapping relationship between the span and basic geometric parameters of bridges with different spans, as well as the mapping relationship between basic geometric parameters and derived geometric parameters.

5. The finite element parametric modeling method for small-to-medium span bridges according to claim 1, characterized in that, The method of using coordinate elements in the set of inter-beam connection unit locations as control nodes, and densifying the nodes of each main beam by span segmentation to generate a non-repeating main beam longitudinal node sequence includes: For each span, the longitudinal coordinate of the inter-beam connection unit location set located within the span range is used as the control node for that span; Within each span, node encryption is performed between adjacent control nodes according to the preset target unit length to generate the sequential node sequence of that span. For each main beam, the longitudinal node sequence of each span is spliced ​​together in span order to generate a non-repeating longitudinal node sequence of the main beam.

6. The finite element parametric modeling method for small-to-medium span bridges according to claim 1, characterized in that, The calculation of the transverse coordinates of each main girder based on the transverse arrangement parameters of the main girder includes: Calculate the transverse coordinates of each main girder using the transverse centerline of the bridge as the origin. : ； in, Let be the transverse coordinate of the k-th main girder, n be the number of main girders, k be the main girder number, k = 1, 2, ..., n, and d be the spacing between the main girders.

7. The finite element parametric modeling method for small-to-medium span bridges according to claim 1, characterized in that, The minimum distance matching algorithm is used to locate constraint nodes in the longitudinal node sequence of the main girder, and to apply corresponding boundary conditions at the constraint nodes according to the bridge structure type, including: Based on the theoretical support position calculated for each span, for each theoretical support position, traverse the candidate nodes within a preset distance range on both sides of the theoretical support position in the non-repeating main beam longitudinal node sequence. Calculate the difference between the longitudinal coordinate of each candidate node and the longitudinal coordinate of the theoretical support location, and select the candidate node with the smallest absolute value of the difference as the constraint node of the support. When the bridge structure is a simply supported beam, a fixed hinge constraint is applied at the constraint node corresponding to the first end support to constrain the translational degrees of freedom in the longitudinal, transverse, and vertical directions, as well as the rotational degrees of freedom about the longitudinal direction; a movable hinge constraint is applied at the constraint node corresponding to the last end support to constrain the translational degrees of freedom in the transverse and vertical directions, as well as the rotational degrees of freedom about the longitudinal direction. When the bridge structure is a continuous beam, a fixed hinge constraint is applied at the constraint node corresponding to the first end support to constrain the translational degrees of freedom in the longitudinal, transverse, and vertical directions, as well as the rotational degrees of freedom about the longitudinal direction; a movable hinge constraint is applied at the constraint node corresponding to the other supports to constrain the translational degrees of freedom in the transverse and vertical directions, as well as the rotational degrees of freedom about the longitudinal direction.

8. A system for performing the finite element parametric modeling method for small-to-medium span bridges as described in any one of claims 1-7, characterized in that, include: The design parameter acquisition module is used to acquire bridge design parameters, including bridge structure type and main beam parameters; The section definition module is used to determine the section geometry parameters based on the main beam type. The beam connection unit layout module determines the longitudinal coordinates of the beam connection units according to the beam connection unit layout rules, merges the longitudinal coordinates of the beam connection units into an initial beam connection unit position set, removes duplicate coordinate elements from the initial beam connection unit position set, and outputs a unique beam connection unit position set for the entire bridge. The node sequence generation module includes a transverse bridge positioning unit and a longitudinal bridge division unit. The transverse bridge positioning unit calculates the transverse bridge coordinates of each main beam according to the transverse arrangement parameters of the main beam. The longitudinal bridge division unit uses the coordinate elements in the set of inter-beam connection unit positions as control nodes, and densifies the nodes between adjacent control nodes in each span according to the preset target unit length to generate a longitudinal bridge node sequence of the main beam. The node sequence pairing module is used to pair the transverse coordinates of each main beam with the longitudinal coordinates in the longitudinal node sequence of the main beam to generate the node sequence of each main beam. The boundary condition configuration module uses a minimum distance matching algorithm to locate constraint nodes in the longitudinal node sequence of the main beam and apply corresponding boundary conditions at the constraint nodes according to the bridge structure type. The finite element reference model output module is used to convert the bridge design parameters, cross-sectional geometric parameters, beam connection element location set, node sequence, constraint nodes, and boundary conditions into a data interface file that can be parsed by finite element analysis software, and generate a finite element reference model after parsing.

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