Line-bridge interaction analysis method and system

Abstract

The present invention provides a track-bridge interaction analysis method and system, belonging to the technical field of railway engineering design. Based on finite element theory and the nonlinear interlayer force transmission relationship of the track structure, a track sub-model is established; based on finite element theory and the force characteristics of bridge structural components, a bridge sub-model is established. Using the longitudinal and vertical displacements of the bridge structure as fundamental unknowns, the track sub-model and the bridge sub-model are repeatedly iterated until the displacements converge, resulting in the longitudinal force of the rail, the longitudinal displacement of the rail, the longitudinal and vertical displacements of the bridge, and the longitudinal force of the pier. The present invention establishes a ballasted track model and a bridge finite element model, each of which exists independently, achieving decoupling of the track-bridge coupling model. It clarifies the construction methods of the finite element models of ballasted track, ballastless track, and bridge, and proposes a method for setting the boundary conditions of the track model. The system can fully consider the effects of material nonlinearity and structural nonlinearity, such as the roadbed and fastener resistance.

Description

Technical Field

[0001] The present invention relates to the technical field of railway engineering design, and in particular to a line-bridge interaction analysis method and system. Background Art

[0002] To ensure the safety of high-speed railway operations, track smoothness requirements are becoming increasingly stringent, and the proportion of seamless tracks in railway lines is gradually increasing. When laying seamless tracks on bridges, the complex interaction between the seamless tracks and the bridges causes the seamless tracks on the bridges to bear enormous additional forces, posing a challenge to the coordination of deformation between the bridges and the seamless tracks.

[0003] To ensure the safe service of seamless railway and bridge structures, studying the railway-bridge interaction relationship under the coupling of multiple factors and clarifying the longitudinal force distribution characteristics of the seamless railway on the bridge and the relative displacement characteristics of the beam and rail are key scientific issues that must be addressed to ensure the healthy service of the railway infrastructure and the safe and smooth operation of trains. In recent years, researchers at home and abroad have conducted extensive research on the railway-bridge interaction relationship on medium and small span bridges, established a large number of railway-bridge interaction coupling analysis models, and achieved fruitful results. However, with the rapid increase in the number of bridges and the widespread use of special ultra-long span bridges such as cable-stayed and suspension bridges, the shortcomings of railway-bridge interaction coupling models have gradually become apparent, such as complex modeling, the construction of a specific interaction model for each bridge, and low simulation calculation efficiency. Therefore, it is urgent to propose some new and universal railway-bridge interaction analysis methods to quickly analyze the railway-bridge interaction relationship and improve the efficiency of simulation calculation analysis.

[0004] Calculating the track-bridge interaction relationship is fundamental to analyzing the longitudinal mechanical behavior of seamless railway tracks on bridges. It is a key issue that must be addressed to improve the operational quality of high-speed trains and ensure the safe service of tracks on bridges. Currently, research on track-bridge interaction both domestically and internationally still uses the traditional method of establishing a spatially coupled finite element model of track-bridge interaction, analyzing the ballasted track and bridge as a coupled system. However, when analyzing the beam-rail interaction of seamless railway tracks on long-span bridges, the small spacing between sleepers and fasteners results in a small, dense mesh size and a very large number of elements in the spatially coupled model. For example, when considering only the refined bridge model (with the same mesh size as the track), the total number of elements and nodes is 33,925 and 20,599, respectively. When considering the track structure, the total number of elements in the coupled model reaches 221,697 and the total number of nodes reaches 69,583, increasing the number of elements and nodes by 7 times and 2.5 times, respectively, making the model computation very slow. At the same time, due to the low stiffness of the track structure and the high stiffness of the bridge structure, parameters such as the line longitudinal resistance are extremely nonlinear. As a result, when the line and bridge are coupled with each other, it is very easy to encounter problems such as ill-conditioned stiffness matrix, small principal elements, and rigid displacement of some structural components of the track. This causes the solution of the coupling model to diverge and be difficult to converge. In addition, the structure of long-span bridges is complex, and the beam-track interaction analysis model on the bridge needs to be built for each bridge. Model establishment and debugging require a lot of time and effort. Summary of the Invention

[0005] The object of the present invention is to provide a wire-bridge interaction analysis method and system to solve at least one technical problem existing in the above-mentioned background technology.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention provides a wire-bridge interaction analysis method, comprising:

[0008] Based on the finite element theory and the nonlinear inter-layer force transmission relationship of the track structure, combined with the finite element simulation software, a track finite element model, namely the track sub-model, is established;

[0009] Based on finite element theory and the mechanical characteristics of bridge structural components, combined with finite element simulation software, a bridge finite element model, namely a bridge sub-model, is established;

[0010] Taking the longitudinal and vertical displacements of the bridge structure as the basic unknowns, the track sub-model and the bridge sub-model are repeatedly iterated until the displacement converges, and the longitudinal force of the rail, the longitudinal displacement of the rail, the longitudinal and vertical displacements of the bridge, and the longitudinal force of the pier are obtained.

[0011] As a further limitation of the first aspect of the present invention, the longitudinal and vertical displacements of the bridge structure are taken as basic unknown quantities, and the track sub-model and the bridge sub-model are repeatedly iteratively calculated until the displacement converges to obtain the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and pier longitudinal force, including: assuming the initial displacement of the bridge and taking it as the boundary condition of the track structure, calculating the bridge force, that is, the longitudinal force and vertical force transmitted to the bridge by the roadbed; applying the bridge force to the bridge finite element model, and calculating the longitudinal and vertical deformations of the bridge; applying the calculated bridge longitudinal and vertical deformations as boundary conditions to the line track finite element model in the form of forced displacement to calculate the bridge force; repeatedly iteratively calculating the bridge longitudinal and vertical deformations and bridge force until the difference between the two iterative bridge displacements converges, stopping the iteration, and obtaining the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and pier longitudinal force.

[0012] As a further limitation of the first aspect of the present invention, an iterative acceleration factor is used to reduce the number of iterations. That is, when performing displacement calculations, except for the first step, the displacement of each subsequent step is calculated by calculating the difference between the actual bridge displacement caused by the bridge force and the bridge displacement applied to the track sub-model in the previous step, multiplying this displacement difference by the iterative acceleration factor, and then adding it to the bridge displacement applied to the track sub-model in the previous step.

[0013] As a further limitation of the first aspect of the present invention, when performing displacement calculation, except for the first step, the displacement calculation expression of each subsequent step is as follows:

[0014] X n =X n-1 +α(X' n -X n-1 )

[0015] Y n =Y n-1 +α(Y n '-Y n-1 )

[0016] Among them, X n 、Y n represent the longitudinal displacement and vertical displacement of the bridge applied to the track sub-model in the nth step; X n-1 、Y n-1 represent the longitudinal displacement and vertical displacement of the bridge applied to the track sub-model in the n-1th step; X n ′ and Y n ′ represents the true longitudinal displacement and vertical displacement of the bridge caused by the bridge force in step n-1, α is the iteration acceleration factor, 0<α<1.

[0017] As a further limitation of the first aspect of the present invention, in the iterative calculation, the initial value of the longitudinal displacement is set to 0.0001m, and the initial value of the vertical displacement is set to 0.001m.

[0018] As a further limitation of the first aspect of the present invention, the longitudinal and vertical deformations and bridge forces of the bridge are calculated repeatedly until the difference between the bridge displacements obtained from two iterations is less than 10 -5 m.

[0019] In a second aspect, the present invention provides a wire-bridge interaction analysis system, comprising:

[0020] The first building block is used to establish a track finite element model, i.e., a track sub-model, based on finite element theory and the nonlinear inter-layer force transmission relationship of the track structure, combined with finite element simulation software;

[0021] The second building module is used to establish a bridge finite element model, i.e., a bridge sub-model, based on finite element theory and the stress characteristics of bridge structural components in combination with finite element simulation software;

[0022] The calculation module is used to perform iterative calculations on the track sub-model and the bridge sub-model using the longitudinal and vertical displacements of the bridge structure as basic unknowns until the displacements converge, thereby obtaining the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and pier longitudinal force.

[0023] In a third aspect, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the line-bridge interaction analysis method as described in the first aspect is implemented.

[0024] In a fourth aspect, the present invention provides a computer device comprising a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the wire-bridge interaction analysis method as described in the first aspect.

[0025] In a fifth aspect, the present invention provides an electronic device comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes instructions for implementing the wire-bridge interaction analysis method as described in the first aspect.

[0026] The beneficial effects of the present invention are as follows: a ballasted track model and a bridge finite element model are established separately, and the two models exist independently, thereby realizing the decoupling of the track-bridge coupling model; the construction method of the finite element models of the ballasted track, ballastless track and bridge is clarified, and a method for setting the boundary conditions of the track model is proposed; the influence of material nonlinearity and structural nonlinearity such as the roadbed and fastener resistance can be fully considered.

[0027] Additional advantages of the present invention will be more clearly given in the following description or learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0029] Figure 1 This is a flow chart of the decoupled iterative calculation method for line-bridge interaction analysis according to an embodiment of the present invention.

[0030] Figure 2 Schematic diagram of a commonly used coupled finite element model for wire-bridge interaction analysis according to an embodiment of the present invention.

[0031] Figure 3 This is a schematic diagram of the decoupled track sub-model and bridge sub-model according to an embodiment of the present invention.

[0032] Figure 4 This is a schematic diagram of the equivalent axial force of a node according to an embodiment of the present invention.

[0033] Figure 5 This is a schematic diagram of the equivalent vertical force of a node according to an embodiment of the present invention.

[0034] Figure 6 Schematic diagram of the longitudinal force on the rails of a 32m simply supported beam bridge under telescopic working conditions as described in an embodiment of the present invention.

[0035] Figure 7 Schematic diagram of the line-bridge relative displacement of a 32m simply supported beam bridge under telescopic working conditions described in an embodiment of the present invention.

[0036] Figure 8 Schematic diagram of the longitudinal force on a 32m simply supported beam bridge pier under telescopic working conditions described in an embodiment of the present invention.

[0037] Figure 9 Schematic diagram of the longitudinal force on the rails of a 32m simply supported beam bridge under braking conditions according to an embodiment of the present invention.

[0038] Figure 10Schematic diagram of the line-bridge relative displacement of a 32m simply supported beam bridge under braking conditions described in an embodiment of the present invention.

[0039] Figure 11 Schematic diagram of the longitudinal force on a 32m simply supported beam bridge pier under braking conditions according to an embodiment of the present invention.

[0040] Figure 12 Schematic diagram of the longitudinal force of rails on a (72+128+72)m continuous beam bridge under the telescopic working condition described in an embodiment of the present invention.

[0041] Figure 13 This is a schematic diagram of the relative displacement of the beam and rail of a (72+128+72)m continuous beam under the telescopic working condition described in an embodiment of the present invention.

[0042] Figure 14 Schematic diagram of the longitudinal force on a (72+128+72)m continuous beam bridge pier under the telescopic working condition described in an embodiment of the present invention.

[0043] Figure 15 Schematic diagram of the longitudinal force of the rails on a (72+128+72)m continuous beam bridge under the braking condition described in an embodiment of the present invention.

[0044] Figure 16 This is a schematic diagram of the relative displacement of the beam and rail of a (72+128+72)m continuous beam under the braking condition described in an embodiment of the present invention.

[0045] Figure 17 Schematic diagram of the longitudinal force on a (72+128+72)m continuous beam bridge pier under the braking condition described in an embodiment of the present invention.

[0046] Figure 18 Schematic diagram of the longitudinal force of rails on a cable-stayed bridge under telescopic working conditions according to an embodiment of the present invention.

[0047] Figure 19 Schematic diagram of the relative displacement of beams and rails on a cable-stayed bridge under telescopic working conditions according to an embodiment of the present invention.

[0048] Figure 20 Schematic diagram of the vertical displacement of the main beam of a cable-stayed bridge under the telescopic working condition described in an embodiment of the present invention.

[0049] Figure 21 Schematic diagram of the longitudinal force of rails on a cable-stayed bridge under braking conditions according to an embodiment of the present invention.

[0050] Figure 22 Schematic diagram of the relative displacement of beams and rails on a cable-stayed bridge under braking conditions according to an embodiment of the present invention.

[0051] Figure 23 Schematic diagram of the vertical displacement of the main beam of a cable-stayed bridge under braking conditions according to an embodiment of the present invention.

[0052] Figure 24 This is a partially enlarged view of the vertical displacement of the main beam of the cable-stayed bridge within the range of 785m-825m described in an embodiment of the present invention.

[0053] Figure 25 This is a schematic diagram of the longitudinal force on the rails on a cable-stayed bridge under telescopic working conditions after the regulator is installed according to an embodiment of the present invention.

[0054] Figure 26 This is a schematic diagram of the relative displacement of the beam and rail on a cable-stayed bridge under the telescopic working condition after the adjuster is set according to an embodiment of the present invention.

[0055] Figure 27 This is a schematic diagram of the vertical displacement of the main beam of a cable-stayed bridge under the telescopic working condition after the regulator is set according to an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The embodiments of the present invention are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention and are not to be construed as limiting the present invention.

[0057] Those skilled in the art will understand that unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art to which this invention belongs.

[0058] It should also be understood that terms, such as those defined in commonly used dictionaries, should be understood to have a meaning consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless as defined herein.

[0059] Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a," "an," "said," and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the stated features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0060] In the description of this specification, reference to the terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Those skilled in the art may combine and integrate different embodiments or examples described in this specification, as well as features of different embodiments or examples, unless otherwise contradictory.

[0061] To facilitate understanding of the present invention, the present invention is further explained below with reference to specific embodiments in conjunction with the accompanying drawings. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0062] Those skilled in the art should understand that the drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily necessary for implementing the present invention.

[0063] The present invention proposes a decoupling iterative algorithm for line-bridge interaction analysis, which changes the traditional idea of ​​integrated coupled modeling analysis of line-bridge interaction. Specifically, the algorithm includes: dividing the line-bridge interaction model into a line sub-model and a bridge sub-model, and establishing the two models separately; combining the generation mechanism of line-bridge interaction, taking the longitudinal and vertical displacements of the bridge structure as the basic unknown quantities, and calculating the force deformation of the track structure and the force applied by the track to the bridge (hereinafter referred to as "bridge force") based on the line structure sub-model; applying the bridge force to the bridge sub-model, and calculating the longitudinal displacement and vertical displacement of the bridge structure; updating the longitudinal and vertical displacements of the bridge structure based on the iteration factor, and applying the updated displacement as the boundary condition to the line finite element model to calculate the bridge force; iterating repeatedly until the bridge displacement converges to a certain value, and finally verifying the correctness of the iterative algorithm through implementation cases. The iterative algorithm can take into account key parameters such as the longitudinal and vertical stiffness of the track bed, and the longitudinal and vertical stiffness of the fasteners. It can calculate the line-bridge interaction relationship under complex effects such as temperature, train deflection, and braking, and realize rapid analysis of the line-bridge interaction relationship on the bridge, avoiding the establishment of a complex line-bridge coupling space model, and greatly improving the calculation efficiency of the line-bridge interaction relationship.

[0064] Example 1

[0065] In this embodiment 1, a line-bridge interaction analysis system is first provided, including: a first construction module, which is used to establish a line track finite element model, i.e., a track sub-model, based on finite element theory and the nonlinear inter-layer force transmission relationship of the track structure, combined with finite element simulation software; a second construction module, which is used to establish a bridge finite element model, i.e., a bridge sub-model, based on finite element theory and the force characteristics of bridge structure components, combined with finite element simulation software; a calculation module, which is used to repeatedly iteratively calculate the track sub-model and the bridge sub-model with the longitudinal and vertical displacements of the bridge structure as basic unknown quantities until the displacement converges, thereby obtaining the longitudinal force of the rail, the longitudinal displacement of the rail, the longitudinal and vertical displacements of the bridge, and the longitudinal force of the pier.

[0066] In this embodiment, the above-mentioned system is used to implement a line-bridge interaction analysis method. A line structure sub-model and a bridge sub-model are established separately. Based on these two sub-models, an iterative method is used to solve the interaction relationship between the line and the bridge. The process steps include the following:

[0067] Based on finite element theory and the nonlinear interlayer force transmission relationship of the track structure, combined with finite element simulation software such as ANSYS and SPA2000, a track finite element model is established.

[0068] Based on the finite element principle and the stress characteristics of bridge structural components, a finite element model of the bridge is established by combining finite element simulation software such as ANSYS and SPA2000.

[0069] Taking the longitudinal and vertical displacements of the bridge structure as the basic unknowns, the iterative method is used to solve the line-bridge interaction. The specific solution process is as follows: (1) Assuming the initial displacement of the bridge, use it as the boundary condition of the track structure to calculate the longitudinal force and vertical force (hereinafter referred to as "bridge force") transmitted to the bridge by the roadbed under complex conditions such as complex temperature, deflection, and braking. (2) Apply the bridge force to the finite element model of the bridge and calculate the longitudinal and vertical deformations of the bridge. (3) Apply the calculated longitudinal and vertical deformations of the bridge as boundary conditions to the track finite element model in the form of forced displacement to calculate the bridge force. (4) Repeat (2) and (3) until the difference between the bridge displacements obtained in the two iterations is less than 10 -5 m, stop the iteration, and extract the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacement, and pier longitudinal force.

[0070] In this embodiment, a ballasted track model and a bridge finite element model need to be established separately. The two models exist independently, realizing the decoupling of the line-bridge coupling model. The line and the bridge are connected through force and displacement compatibility conditions. The longitudinal and vertical deformations of the bridge serve as boundary conditions of the track sub-model, and the vertical force and longitudinal force of the track base serve as one of the load conditions of the bridge structure.

[0071] In this embodiment, a track sub-model needs to be independently established, and reasonable constraints need to be imposed on the contact portion between the bottom of the track model and the bridge. Taking the finite element model of ballasted track as an example, the rails are simulated as continuous point-supported beam elements; the longitudinal resistance and vertical support of the fasteners are simulated as nonlinear spring actions; the sleepers are simulated as beam elements based on their force characteristics; the longitudinal resistance and vertical support stiffness of the roadbed are simulated as spring elements; when the roadbed is located on a bridge, one end node of the roadbed spring element is connected to the sleepers, and the other end node applies the longitudinal and vertical forced displacements of the bridge in the longitudinal and vertical directions. When the ballasted roadbed is located in the roadbed section, one end of the spring element is connected to the sleepers, and the other end is fully constrained; taking the CRTSIII slab track as an example, the rails in the model are simulated using beam elements, and the track plate and self-compacting concrete are considered as a composite plate structure, and the two are combined and simulated as shell elements; the base plate is simulated using shell elements. Since the base plate is connected to the bridge through a sleeve, the sleeve is simulated as a spring element with high stiffness. One end of the sleeve spring is connected to the bottom of the base plate, and the other end applies the forced longitudinal and vertical displacements of the bridge.

[0072] In this example, a separate finite element model of a bridge is required, and a method for building a finite element model of a typical bridge is proposed. Bridge types primarily include special bridges such as simply supported beam bridges, continuous beam bridges, rigid frame bridges, arch bridges, cable-stayed bridges, and suspension bridges. This article uses continuous beam bridges and cable-stayed bridges as examples to describe the construction of finite element models for long-span bridges.

[0073] A continuous beam bridge consists of a main beam, supports, and piers. Modeling assumes that the supports are consolidated with the pier tops and that the fixed supports can fully transmit force. The continuous main beam is simulated using end-to-end variable-section beam elements, and the piers are simulated using spring elements. During modeling, the beam element size is kept consistent with the track sub-model size as much as possible to reduce deformation interpolation and load equivalence of applied nodal forces during iteration, thereby improving calculation accuracy.

[0074] Long-span cable-stayed bridges primarily consist of a steel box girder, stay cables, main towers, and auxiliary side piers. The steel box girder is modeled using beam elements; the main towers are modeled using spatial beam elements; and the longitudinal dampers between the towers and main girder are modeled using spring elements, which are only used when calculating rail braking forces. The towers and main girder are coupled in the transverse and vertical directions. The stay cables are slender, flexible structures modeled using tension-only rod elements. Their sides are connected to rigid arm nodes extending from the steel box girder and to the main tower nodes, respectively. The bases of the main towers and auxiliary side piers are fully constrained. During modeling, the girder dimensions of the cable-stayed bridge are aligned as closely as possible with the track submodel dimensions to minimize deformation interpolation and load equivalence of applied nodal forces during iterations, thereby improving computational accuracy.

[0075] In this embodiment, the longitudinal displacement and vertical displacement of the bridge are taken as unknown quantities, and the track sub-model and the bridge sub-model are repeatedly iterated until the displacement converges. This includes:

[0076] (1) Assume that the initial longitudinal displacement and vertical displacement of the bridge node are respectively expressed as:

[0077]

[0078] (2) Substitute the initial displacement into the track structure submodel to calculate the force exerted by the track on the bridge:

[0079]

[0080] (3) Substitute the bridge force into the bridge sub-model, superimpose the temperature change and other working conditions, and calculate the bridge displacement, which is expressed as:

[0081]

[0082] (4) The calculated bridge displacement is used as the boundary condition of the track structure and input into the track sub-model in the form of forced displacement to calculate the bridge force, which is recorded as

[0083] (5) Repeat steps (3) and (4) to iterate between the two sub-models, with the displacement difference ε < 10 -5 m is used as the iterative convergence condition: ε=max[abs(X n -X n-1 ),abs(Y n -Y n-1 )]<10 -5 ;

[0084] (6) When the iteration meets the convergence conditions, the calculation results of rail longitudinal force, rail longitudinal displacement, bridge longitudinal displacement, pier longitudinal force, etc. are extracted.

[0085] In this embodiment, the track model grid size and the bridge model grid size are not required to be the same during modeling. When the track model grid size and the bridge model grid size are inconsistent, in order to ensure that the bridge force and bridge forced displacement can accurately act on the two sub-models, the bridge force and bridge forced displacement need to be processed separately through node force equivalence and spline interpolation. When the bridge grid size is larger than the track grid size, the bridge force needs to be converted to the adjacent nodes of the bridge based on the load equivalence principle; after the bridge deformation curve is obtained, the bridge forced displacement curve at the bottom of each fastener node needs to be obtained based on cubic spline curve interpolation.

[0086] The track sub-model and the bridge sub-model are decoupled for iterative calculation. To ensure that the iteration can proceed smoothly, when selecting the initial value of the displacement, the initial value of the longitudinal displacement is set to 0.0001m, and the initial value of the vertical displacement is set to 0.001m. At the same time, in this embodiment, in order to accelerate convergence, it is proposed to use an iteration acceleration factor to reduce the number of iterations. That is, when performing displacement calculations, except for the first step, the displacement of each subsequent step is: calculate the difference between the actual displacement of the bridge caused by the bridge force and the displacement of the bridge applied to the track sub-model in the previous step, multiply the displacement difference by the iteration acceleration factor, and then add it to the bridge displacement applied to the track sub-model in the previous step. Specifically, the displacement expression of each subsequent step can be expressed as follows:

[0087] X n =X n-1 +α(X' n -X n-1 )

[0088] Y n =Y n-1 +α(Y n '-Y n-1 )

[0089] Where X n 、Y n represents the longitudinal displacement and vertical displacement of the bridge applied to the track sub-model in step n; X n-1 、Y n-1 represents the longitudinal and vertical displacements of the bridge applied to the track sub-model in step n-1; X n ′ and Y n ′ represents the true longitudinal displacement and vertical displacement of the bridge caused by the bridge force in step n-1, α is the iteration acceleration factor, 0<α<1.

[0090] In this embodiment, the line-bridge interaction analysis can be carried out by establishing a track sub-model and a bridge sub-model separately, without the need to establish a large-span bridge-track line coupling finite element model. In addition, since the track structure laid on the bridge is relatively simple, the track structure sub-model has good versatility. When performing subsequent line-bridge interaction analysis on other bridges, only the bridge finite element model needs to be established, which improves modeling efficiency.

[0091] Example 2

[0092] In view of the increasingly prominent defects of the line-bridge interaction coupling analysis model, such as the complex modeling, one-bridge-one-analysis model, and low simulation calculation efficiency, this embodiment 2 proposes a decoupled iterative calculation method for line-bridge interaction analysis. This method breaks the traditional line-bridge interaction analysis method, establishes a line structure sub-model and a bridge sub-model respectively, and adopts an iterative method based on the two sub-models to solve the interaction relationship between the line and the bridge, which has the advantages of being fast, efficient, and accurate.

[0093] In this embodiment, the specific analysis steps include: (1) establishing a track structure sub-model and a bridge finite element model based on the finite element principle; (2) assuming the initial displacement of the bridge, taking it as the boundary condition of the track structure, substituting it into the track sub-model, and calculating the longitudinal force and vertical force transmitted to the bridge by the roadbed under complex loads such as complex temperature, deflection, and braking; (3) applying the bridge force to the bridge finite element model and calculating the longitudinal and vertical deformations of the bridge; (4) applying the calculated longitudinal and vertical deformations of the bridge as boundary conditions to the track finite element model in the form of forced displacement, and calculating the bridge force; (5) repeating steps (3) and (4) until the displacement of the bridge structure converges to a constant value, and stopping the iteration; (6) extracting the longitudinal force of the rail, the longitudinal displacement of the rail, the longitudinal and vertical displacements of the bridge, and the longitudinal force of the pier.

[0094] This embodiment proposes a decoupled iterative calculation method for line-bridge interaction analysis. This analysis method breaks the traditional analysis ideas and decouples the line-bridge interaction coupling model. This analysis method requires the establishment of a ballasted track model and a bridge finite element model respectively. The two models exist independently, realizing the decoupling of the line-bridge coupling model. The track model and the bridge model are connected through force and displacement compatibility conditions. The longitudinal and vertical deformations of the bridge serve as boundary conditions of the track sub-model, and the vertical force and longitudinal force of the track base serve as one of the load conditions of the bridge structure. This embodiment proposes a decoupled iterative calculation method for line-bridge interaction analysis. This method clarifies the construction method of the finite element models of ballasted track, ballastless track and bridge, and proposes a way to set the boundary conditions of the track model. It can fully consider the influence of material nonlinearity and structural nonlinearity such as the roadbed and fastener resistance.

[0095] Taking the finite element model of ballasted track as an example, the rails are simulated as continuous point-supported beam elements; the longitudinal resistance and vertical support of the fasteners are simulated as nonlinear spring actions; the sleepers are simulated as beam elements based on their force characteristics; the longitudinal resistance and vertical support stiffness of the roadbed are simulated as spring elements; the roadbed spring element of the bridge section has one end node connected to the sleeper and the other end node is laterally constrained, and the longitudinal and vertical forced displacements of the bridge are applied longitudinally and vertically; the roadbed spring element of the roadbed section has one end node connected to the sleeper and the other end node is fully constrained; taking the CRTSIII slab track as an example, the rails in the model are simulated using beam elements, the track plate and self-compacting concrete are regarded as a composite plate structure, and the two are combined and simulated using shell elements; the base plate is simulated using shell elements, and since the base plate is connected to the bridge through a sleeve, the sleeve is simulated as a spring element with very high stiffness, one end of the sleeve spring is connected to the bottom of the base plate, and the other end applies the forced longitudinal and vertical displacements of the bridge. When calculating the deformation of a bridge structure, the bridge force applied by the track to the bridge acts together with loads such as bridge temperature and settlement.

[0096] This embodiment proposes a decoupled iterative calculation method for line-bridge interaction analysis. This method uses bridge displacement as the basic unknown quantity and solves the line-bridge interaction relationship through an iterative method. The calculation process and convergence conditions of the proposed iterative method specifically include:

[0097] (1) Assume that the initial longitudinal displacement and vertical displacement of the bridge node are expressed as:

[0098]

[0099] (2) Substitute the assumed displacement into the track structure submodel and calculate the force exerted by the track on the bridge, which is expressed as:

[0100] (3) Substitute the bridge force into the bridge sub-model, superimpose the temperature change and other working conditions, calculate the bridge displacement, and use the accelerated iteration factor to process the bridge displacement. The processed displacement is recorded as:

[0101]

[0102] (4) Taking the bridge displacement as the boundary condition of the track structure, the track sub-model is input in the form of forced displacement to calculate the bridge force, which is recorded as

[0103] (5) Repeat steps (3) and (4) to iterate between the two sub-models, with the displacement difference ε < 10 -5 m is used as the iterative convergence condition:

[0104] ε=max[abs(X n -Xn-1 ),abs(Y n -Y n-1 )]<10 -5

[0105] (6) When the iteration meets the convergence conditions, the calculation results of rail longitudinal force, rail longitudinal displacement, bridge longitudinal displacement, pier longitudinal force, etc. are extracted.

[0106] In the decoupled iterative calculation, to ensure that the bridge forces and displacements can accurately act on the bridge model and track model during the iteration process, when the mesh size of the bridge structure is inconsistent with the mesh size of the track structure, the bridge forces and displacements need to be processed accordingly.

[0107] When modeling a bridge, it is not mandatory that the mesh size of the bridge model and the mesh size of the track model be the same. When the mesh size of the track model is inconsistent with the mesh size of the bridge model, in order to ensure that the bridge forces and bridge forced displacements can accurately act on the two sub-models, it is necessary to process the bridge forces and bridge forced displacements separately through methods such as nodal force equivalence and spline interpolation. When the bridge mesh size is larger than the track mesh size, the bridge forces need to be converted to the adjacent bridge nodes based on the load equivalence principle; after the bridge deformation curve is obtained, the bridge forced displacement curve at the bottom of each fastener node needs to be interpolated based on the cubic spline curve. It should be noted that: although this method does not require the unit size of the track model to be the same as the unit size of the bridge model, it is still recommended that the bridge be divided into meshes according to the size of the track structure as much as possible to facilitate the extraction and application of nodal forces and nodal displacements, and avoid the work of nodal force equivalence and displacement spline interpolation.

[0108] In order to ensure that the iterative calculation can proceed smoothly, when selecting the initial value of displacement, the initial value of longitudinal displacement is set to 0.0001m, and the initial value of vertical displacement is set to 0.001m.

[0109] To accelerate iterative convergence, avoid iterative oscillation, and reduce the number of iterations, an iterative acceleration factor is proposed. That is, when performing displacement calculations, except for the first step, the displacement applied to the track bridge in each subsequent step is associated with the bridge displacement in the previous step and the bridge displacement calculated by the finite element in the current step. The specific calculation method is as follows:

[0110] X n =X n-1 +α(X' n -X n-1 )

[0111] Y n =Y n-1 +α(Y n '-Y n-1 )

[0112] Where: X n 、Y n represents the longitudinal displacement and vertical displacement of the bridge applied to the track sub-model in step n; X n-1 、Y n-1 represents the longitudinal and vertical displacements of the bridge applied to the track sub-model in step n-1; X n ′ and Y n ′ represents the true longitudinal displacement and vertical displacement of the bridge caused by the bridge force in the n-1th step. α is the iteration acceleration factor, 0<α<1. Its value has a certain relationship with the span of the bridge. After many trials, when α is 0.25-0.3, the iterative algorithm has better convergence and the number of iterations is appropriate. It is recommended that α be 0.25 in general.

[0113] Example 3

[0114] like Figures 1 to 3 As shown, in this embodiment 3, a decoupled iterative calculation method for line-bridge interaction analysis is provided, and the specific implementation path is: (1) Assuming the initial displacement of the bridge, it is used as the boundary condition of the track structure to calculate the longitudinal force and vertical force transmitted to the bridge by the roadbed under complex conditions such as complex temperature, deflection, and braking. (2) The bridge force is applied to the bridge finite element model, the longitudinal and vertical deformations of the bridge are calculated, and the deformation is processed using an accelerated iteration factor. (3) The processed longitudinal and vertical deformations of the bridge are applied to the track finite element model in the form of forced displacement as boundary conditions to calculate the bridge force. (4) Repeat (2) and (3) until the difference between the bridge displacements obtained from the two iterations is less than the convergence condition, stop the iteration, and extract the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacement, and pier longitudinal force. This embodiment breaks the traditional line-bridge interaction spatial coupling model analysis method. Its core idea is to decouple the line-bridge interaction coupling analysis model into a track structure sub-model and a bridge structure sub-model, take the bridge deformation as the basic unknown quantity, and use an iterative method based on the track sub-model and the bridge sub-model to solve the line-bridge interaction relationship.

[0115] Figure 3 The decoupled track and bridge submodels are shown in Figure 2. The decoupled track submodel requires reasonable constraints on the nodes of the roadbed springs. For example, in the finite element model of ballasted track, one end of the roadbed spring unit is connected to the sleeper, while the other end node applies the longitudinal and vertical displacements of the bridge. When the ballasted roadbed is located in the subgrade section, one end of the spring unit is connected to the sleeper, while the other end node is fully constrained. The decoupled bridge submodel requires the bridge force transmitted from the roadbed to the bridge, which is applied in both longitudinal and vertical directions.

[0116] Figure 4This is a schematic diagram of the equivalent axial force of the node provided in this embodiment. When the bridge model grid size is larger than the track grid size, multiple bridge axial forces will act on a single bridge unit. For example, taking two bridge axial forces acting on a single beam unit as an example, the bridge unit is subjected to the following forces: Figure 4 shown. Figure 4 The bridge unit has two nodes A and B, the unit size is L, and the axial forces acting on the bridge are F1 and F2 respectively, where F1 is a1 away from point A and b1 away from point B, and F2 is a2 away from point A and b2 away from point B. The spacing between the fasteners is the difference between a2 and a1. Then the equivalent nodal axial forces F at A and B are A and F B As shown in the following formula:

[0117] Figure 5 This is a schematic diagram of the equivalent vertical force of the node provided in this embodiment. Taking two vertical forces acting on a single beam element as an example, the bridge element is subjected to the force Figure 4 shown. Figure 4 The bridge unit has two nodes A and B, the unit size is L, and the vertical forces acting on the bridge are F1 and F2 respectively, where the distance between F1 and point A is a1 and the distance between F1 and point B is b1, and the distance between F2 and point A is a2 and the distance between F2 and point B is b2, where the spacing between the fasteners is the difference between a2 and a1. Then the equivalent vertical force F at A and B is A 、F B , equivalent node bending moment M A 、M B As shown in the following formula:

[0118]

[0119] To verify the correctness of the decoupled iterative calculation method, a 5-span 32m simply supported beam bridge with a ballasted track seamless line is considered. The roadbed on both sides is 150m long, the longitudinal stiffness of the abutments is 3000kN / cm, the longitudinal stiffness of the piers is 500kN / cm, and the iteration factor is 0.25. Two methods are used to calculate the line-bridge interaction under expansion and contraction conditions and braking conditions, respectively. Figure 6-Figure 8 are the rail longitudinal force, beam-rail relative displacement and pier longitudinal force under the telescopic working condition calculated in this example; Figures 9-11 These are the rail longitudinal force, rail-beam relative displacement, and pier longitudinal force calculated for the braking condition in this example. The solid line represents the results of the decoupling iteration method, while the dashed line represents the results of the spatial coupling model. As can be seen from the figure, the results calculated by the two methods are nearly identical. Table 1 shows the peak values ​​and their errors calculated by the two methods. As can be seen from the table, the peak values ​​calculated by the two methods differ slightly, with the corresponding errors within 2%, demonstrating the correctness of the decoupling iteration algorithm.

[0120] Table 13 Peak values ​​and errors of the calculation results of the two methods corresponding to the 2m simply supported beam bridge working condition

[0121]

[0122] To verify the versatility of the decoupled iterative calculation method, a 3×24m simply supported beam bridge + a (72+128+72)m continuous beam bridge + a 3×24m simply supported beam bridge with a ballasted track seamless line is considered. The roadbed on both sides is 150m long, the longitudinal stiffness of the abutments on both sides is 3000kN / cm, the longitudinal stiffness of the piers is 550kN / cm, and the iteration factor is 0.25. Two methods are used to calculate the line-bridge interaction under expansion and contraction conditions and braking conditions, respectively. Figure 12-14 are the rail longitudinal force, beam-rail relative displacement and pier longitudinal force under the telescopic working condition calculated in this example; Figure 15-17 These are the rail longitudinal force, rail-beam relative displacement, and pier longitudinal force under braking conditions calculated in this example. The solid line represents the results calculated using the decoupling iterative method, while the dashed line represents the results calculated using the spatial coupling model. As can be seen from the figure, the results calculated using the two methods are nearly identical. Table 2 shows the peak values ​​and their corresponding errors calculated using the two methods. As can be seen from the table, the peak values ​​calculated using the two methods differ only slightly, with the corresponding errors both within 1%, demonstrating the adaptability of the decoupling iterative algorithm to continuous beam bridges.

[0123] Table 2 Peak values ​​and errors of the calculation results of the two methods under the (72+128+72)m continuous beam bridge condition

[0124]

[0125] To verify the adaptability of the decoupled iterative calculation method to super-long-span bridges, a continuous track is laid on a (2×50+224+672+174+3×50)m twin-tower cable-stayed bridge with a roadbed length of 150m on both sides. The iteration factor is 0.25, and two methods are used to calculate the cable-bridge interaction under expansion and contraction conditions and braking conditions, respectively. Figures 18-20 are the rail longitudinal force, beam-rail relative displacement, and bridge vertical displacement under the telescopic working condition calculated in this example; Figure 21-24 These are the rail longitudinal force, rail-beam relative displacement, and pier longitudinal force calculated for the braking condition in this example. The solid line represents the results calculated using the decoupling iterative method, while the dashed line represents the results calculated using the spatial coupling model. As can be seen from the figure, the results calculated using the two methods are nearly identical. Table 3 shows the peak values ​​and their corresponding errors calculated using the two methods. As can be seen from the table, the peak values ​​calculated using the two methods differ only slightly, with the corresponding errors both within 1%, demonstrating the excellent adaptability of the decoupling iterative algorithm to cable-stayed bridges.

[0126] Table 3 Peak values ​​and errors of the calculation results of the two methods under the working condition of cable-stayed bridge

[0127]

[0128] In order to verify the adaptability of the decoupled iterative calculation method to the regulator working conditions, rail expansion regulators are laid at the beam ends on both sides of the cable-stayed bridge. The iteration factor is set as 0.25, and two methods are used to calculate the rail-bridge interaction under expansion and braking conditions, respectively. Figure 25-27 The figures represent the longitudinal rail force, relative displacement of the rail and beam, and vertical displacement of the bridge under the telescopic condition calculated in this example. The solid line represents the result calculated using the decoupling iterative method, while the dashed line represents the result calculated using the spatial coupling model. As can be seen from the figure, the results calculated by the two methods are almost identical. Table 4 shows the peak values ​​and their errors calculated by the two methods. As can be seen from the table, the peak values ​​calculated by the two methods differ slightly, and the corresponding errors are both within 1%, demonstrating the adaptability of the decoupling iterative algorithm to the regulator.

[0129] Table 4 Peak values ​​and errors of calculation results corresponding to the two methods under regulator working conditions

[0130]

[0131] From the above working conditions, it can be seen that as the bridge span increases, the calculation errors of the decoupling iterative model and the spatial coupling model become smaller and smaller, and an iteration factor of 0.25 is reasonable for long-span bridges.

[0132] To verify the correctness of the iterative acceleration factor mentioned in the decoupled iterative calculation method, the condition of laying a seamless line on a 5-span simply supported beam bridge is taken as an example. Considering α as 0.1, 0.2, 0.25, 0.3, and 0.5, and the bridge temperature dropping by 15°C, the corresponding number of iterations under different iterative factors are shown in Table 5 below.

[0133] Table 5 Convergence times corresponding to different acceleration iteration factors

[0134]

[0135] Table 5 shows that the number of convergence iterations decreases as the iteration factor increases. It should be noted that when the iteration factor is 0.25, the iterations gradually approach the true value from the given initial value. When it is 0.3, the iterations approach the true value after oscillating around it. When the iteration factor is 0.5, the convergence of this method is poor for a 32m simply supported beam bridge. However, when calculating the line-bridge interaction of a cable-stayed bridge, an iteration factor of 0.5 corresponds to nearly half the number of iterations compared to 0.25.

[0136] Example 4

[0137] This embodiment 4 provides a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the wire-bridge interaction analysis method described above is implemented.

[0138] Example 5

[0139] This embodiment 5 provides a computer device, including a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the wire-bridge interaction analysis method described above.

[0140] Example 6

[0141] This embodiment 6 provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to execute instructions for implementing the wire-bridge interaction analysis method as described above.

[0142] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solutions disclosed in the present invention without the need for creative work should be included in the scope of protection of the present invention.

Claims

1. A line-bridge interaction analysis method, characterized in that: include: Based on the finite element theory and the nonlinear inter-layer force transmission relationship of the track structure, combined with the finite element simulation software, a track finite element model, namely the track sub-model, is established; Based on finite element theory and the mechanical characteristics of bridge structural components, combined with finite element simulation software, a bridge finite element model, namely a bridge sub-model, is established; Taking the longitudinal and vertical displacements of the bridge structure as basic unknowns, the track sub-model and the bridge sub-model are repeatedly iterated until the displacement converges, and the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and pier longitudinal force are obtained; including: assuming the initial displacement of the bridge and taking it as the boundary condition of the track structure, calculating the bridge force, that is, the longitudinal force and vertical force transmitted to the bridge by the roadbed; applying the bridge force to the finite element model of the bridge and calculating the longitudinal and vertical deformation of the bridge; applying the calculated longitudinal and vertical deformation of the bridge as boundary conditions to the track finite element model in the form of forced displacement, and calculating Calculate the bridge force; repeatedly iterate and calculate the longitudinal and vertical deformations of the bridge and the bridge force until the difference between the bridge displacements obtained from two iterations converges, then stop the iteration to obtain the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and pier longitudinal force; an iteration acceleration factor is used to reduce the number of iterations, that is, when performing displacement calculations, except for the first step, the displacement of each subsequent step is: calculate the difference between the actual bridge displacement caused by the bridge force and the bridge displacement applied to the track sub-model in the previous step, multiply the displacement difference by the iteration acceleration factor, and then add it to the bridge displacement applied to the track sub-model in the previous step.

2. The line-bridge interaction analysis method according to claim 1, characterized in that: When performing displacement calculation, except for the first step, the displacement calculation expression for each subsequent step is as follows: X n =X n-1 +α(X' n -X n-1 ) AND n =And n-1 +α(Y n '-AND n-1 ) Among them, X n 、Y n represent the longitudinal displacement and vertical displacement of the bridge applied to the track sub-model in the nth step; X n-1 、Y n-1 represent the longitudinal displacement and vertical displacement of the bridge applied to the track sub-model in the n-1th step; X n ′ and Y n ′ represents the true longitudinal displacement and vertical displacement of the bridge caused by the bridge force in step n-1, α is the iteration acceleration factor, 0<α<1.

3. The line-bridge interaction analysis method according to claim 2, characterized in that: In the iterative calculation, the initial values ​​of the longitudinal displacement are set to 0.0001m, and the initial values ​​of the vertical displacement are set to 0.001m.

4. The line-bridge interaction analysis method according to claim 1, characterized in that: Repeat the iterative calculation of the longitudinal and vertical deformations and bridge forces of the bridge until the difference between the bridge displacements obtained from two iterations is less than 10 -5 m.

5. A wire-bridge interaction analysis system, characterized in that: include: The first building block is used to establish a track finite element model, i.e., a track sub-model, based on finite element theory and the nonlinear inter-layer force transmission relationship of the track structure, combined with finite element simulation software; The second building module is used to establish a bridge finite element model, i.e., a bridge sub-model, based on finite element theory and the stress characteristics of bridge structural components in combination with finite element simulation software; The calculation module is used to perform iterative calculations on the track sub-model and the bridge sub-model with the longitudinal and vertical displacements of the bridge structure as the basic unknown quantities until the displacement converges, thereby obtaining the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and pier longitudinal force. The module includes: assuming the initial displacement of the bridge as the boundary condition of the track structure, calculating the bridge force, that is, the longitudinal force and vertical force transmitted to the bridge by the roadbed; applying the bridge force to the bridge finite element model to calculate the longitudinal and vertical deformations of the bridge; applying the calculated longitudinal and vertical deformations of the bridge as boundary conditions to the track finite element model in the form of forced displacement. model, calculate the bridge force; repeatedly iteratively calculate the longitudinal and vertical deformations of the bridge and the bridge force until the difference between the bridge displacements obtained from two iterations converges, then stop the iteration to obtain the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and pier longitudinal force; wherein, an iteration acceleration factor is used to reduce the number of iterations, that is, when performing displacement calculations, except for the first step, the displacement of each subsequent step is: calculate the difference between the actual bridge displacement caused by the bridge force and the bridge displacement applied to the track sub-model in the previous step, multiply the displacement difference by the iteration acceleration factor, and then add it to the bridge displacement applied to the track sub-model in the previous step.

6. A non-transitory computer-readable storage medium, characterized in that The non-transitory computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the wire-bridge interaction analysis method according to any one of claims 1 to 4 is implemented.

7. A computer device, characterized in that: The method comprises a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the line-bridge interaction analysis method according to any one of claims 1 to 4.

8. An electronic device, characterized in that: include: A processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to execute instructions for implementing the wire-bridge interaction analysis method according to any one of claims 1 to 4.

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