Line-bridge interaction analysis method and system

Abstract

The invention provides a line-bridge interaction analysis method and system, and belongs to the technical field of railway engineering design, and the method comprises the steps: building a track sub-model based on a finite element theory and a non-linear interlayer force transfer relation of a track structure; building a bridge sub-model based on a finite element theory and stress characteristics of bridge structural components; and taking the longitudinal and vertical displacements of the bridge structure as basic unknown quantities, carrying out repeated iterative calculation on the track sub-model and the bridge sub-model until the displacements converge, and obtaining the longitudinal force of the steel rail, the longitudinal displacement of the steel rail, the longitudinal and vertical displacements of the bridge and the longitudinal force of the bridge pier. According to the method, the ballast track model and the bridge finite element model are established respectively, the two models exist independently, and decoupling of the line-bridge coupling model is achieved; a construction method of a ballast track, a ballastless track and a bridge finite element model is defined, and a setting mode of track model boundary conditions is provided; and the influence of material nonlinearity and structure nonlinearity such as ballast bed and fastener resistance can be fully considered.

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] In order to ensure the safety of high-speed railway operation, the requirements for track smoothness are becoming higher and higher, 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 huge additional forces, and the bridges and seamless tracks face the problem of deformation coordination.

[0003] In order to ensure the safe service of seamless lines and bridge structures, it is necessary to study the line-bridge interaction relationship under the coupling of multiple factors, clarify the longitudinal force distribution characteristics of the seamless line on the bridge and the relative displacement characteristics of the beam and rail, which are key scientific issues that must be solved to ensure the healthy service of the line infrastructure and the safe and stable operation of trains. In recent years, domestic and foreign researchers have conducted a lot of research on the line-bridge interaction relationship on medium and small span bridges, established a large number of line-bridge interaction coupling analysis models, and achieved rich results. However, with the rapid increase in the number of bridges and the widespread application of special super-long span bridges such as cable-stayed and suspension bridges, the defects of the line-bridge interaction coupling model are gradually highlighted, such as complex modeling, one-bridge-one-interaction model, and low simulation calculation efficiency. Therefore, it is urgent to propose some new and universal line-bridge interaction analysis methods to quickly analyze the line-bridge interaction relationship and improve the efficiency of simulation calculation analysis.

[0004] The calculation of the line-bridge interaction relationship is the basis for analyzing the longitudinal mechanical behavior of the seamless line on the bridge, and is a key issue that must be solved to improve the running quality of high-speed trains and ensure the safe service of the line on the bridge. At present, the traditional method is still used in the research on line-bridge interaction at home and abroad, that is, to establish a spatial coupling finite element model of line-bridge interaction, and to analyze the ballasted line and bridge as a coupling system; however, when analyzing the beam-rail interaction of the seamless line on a large-span bridge, due to the small spacing between the sleepers and fasteners, the grid size of the spatial coupling model is small, the grid is dense, and the number of units is extremely large. Taking a kilometer-level bridge as an example, when only the bridge refined model is considered (the bridge grid size is the same as the track grid size), the total number of units is 33,925 and the total number of nodes is 20,599. After considering the line structure, the total number of coupling model units reaches 221,697 and the total number of nodes reaches 69,583. The number of coupling model units has increased by 7 times, the number of nodes has increased by 2.5 times, and the model calculation speed is 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 longitudinal resistance of the line are extremely nonlinear, which leads to the occurrence of ill-conditioned stiffness matrix, small principal elements, and rigid displacement of some structural components of the track when the line and bridge are coupled with each other, resulting in divergence in the solution of the coupling model and difficulty in convergence. 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, and model establishment and debugging requires 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 line-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 stress 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 unknown quantities, 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 iterated and calculated until the displacement converges to obtain the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and bridge pier longitudinal force, including: assuming an initial displacement of the bridge, taking it as a boundary condition of the track structure, and 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 bridge longitudinal and vertical deformations; applying the calculated bridge longitudinal and vertical deformations as boundary conditions to the line track finite element model in the form of forced displacement, and calculating 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 bridge pier longitudinal force.

[0012] As a further limitation of the first aspect of the present invention, an iteration acceleration factor is used to reduce the number of iterations, that is, when performing displacement calculation, except for the first step, the displacement of each subsequent step is: calculating 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, multiplying the displacement difference by the iteration 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 the n-1th step, 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 of the bridge and the bridge forces 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 module 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 in combination 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 take the longitudinal and vertical displacements of the bridge structure as the basic unknown quantities, and repeatedly iterate the track sub-model and the bridge sub-model until the displacement converges, so as to obtain 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.

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

[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 executable 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, 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 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 respectively, and the two models exist independently, thereby realizing the decoupling of the track-bridge coupling model; the construction method of the ballasted track, ballastless track and bridge finite element models is clarified, and a setting method of the track model boundary conditions is proposed; the influence of material nonlinearity and structural nonlinearity such as the ballast bed 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 the 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 accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

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

[0030] Figure 2 It is a schematic diagram of a commonly used coupled finite element model for line-bridge interaction analysis described in 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 of the rails of a 32m simply supported beam bridge under the telescopic working condition described in an embodiment of the present invention.

[0035] Figure 7 It is a schematic diagram of the relative displacement between the line and the bridge of a 32m simply supported beam bridge under the telescopic working condition described in an embodiment of the present invention.

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

[0037] Fig. 9 Schematic diagram of the longitudinal force of the rails of a 32m simply supported beam bridge under braking conditions described in an embodiment of the present invention.

[0038] Fig.10It is a schematic 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] Fig.11 It is a schematic diagram of the longitudinal force of a 32m simply supported beam bridge pier under braking conditions described in an embodiment of the present invention.

[0040] Fig.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] Fig.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] Fig.14 It is a schematic diagram of the longitudinal force on the (72+128+72)m continuous beam bridge pier under the telescopic working condition described in an embodiment of the present invention.

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

[0044] Fig.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] Fig.17 It is a schematic diagram of the longitudinal force on the (72+128+72)m continuous beam bridge pier under the braking condition described in an embodiment of the present invention.

[0046] Fig.18 Schematic diagram of the longitudinal force of rails on a cable-stayed bridge under telescopic conditions described in an embodiment of the present invention.

[0047] Fig.19 Schematic diagram of the relative displacement of the beam rails on a cable-stayed bridge under the telescopic working condition described in an embodiment of the present invention.

[0048] Fig. 20 It is a 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] Fig.21 Schematic diagram of the longitudinal force of rails on a cable-stayed bridge under braking conditions described in an embodiment of the present invention.

[0050] Fig. 22 Schematic diagram of the relative displacement of the beam and rail on a cable-stayed bridge under braking conditions described in an embodiment of the present invention.

[0051] Fig.23 It is a schematic diagram of the vertical displacement of the main beam of a cable-stayed bridge under braking conditions described in an embodiment of the present invention.

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

[0053] Fig.25 It is a schematic diagram of the longitudinal force of the rails on the cable-stayed bridge under the telescopic working condition after the adjuster is set according to the embodiment of the present invention.

[0054] Fig.26 It is a schematic diagram of the relative displacement of the beam rails on the cable-stayed bridge under the telescopic working condition after the adjuster is set according to the embodiment of the present invention.

[0055] Fig. 27 It 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, and 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 with the same or similar functions. The embodiments described below by the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0057] It should be understood by those skilled in the art 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 that 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 features, integers, steps, operations, elements and / or components, but does not exclude 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, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", 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 one or more embodiments or examples in a suitable manner. Different embodiments or examples described in this specification and features of different embodiments or examples may be combined and combined by those skilled in the art without contradiction.

[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, and 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 decoupled iterative algorithm for line-bridge interaction analysis, which changes the traditional idea of ​​integrated coupled modeling and analysis of line-bridge interaction, specifically including: 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 basic unknown quantities, and calculating the force deformation of the track structure and the force applied to the bridge by the track (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, applying the updated displacement as the boundary condition to the line finite element model, and calculating 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, the longitudinal and vertical stiffness of the fasteners, and can calculate the line-bridge interaction relationship under complex effects such as temperature, train deflection, and braking, thereby realizing rapid analysis of the line-bridge interaction relationship on the bridge, avoiding the establishment of a complex line-bridge coupling spatial 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 nonlinear interlayer force transmission relationship of 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 force characteristics of bridge structure components, combined with finite element simulation software; a calculation module, which is used to repeatedly iterate and 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, so as to obtain 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 system is used to implement the line-bridge interaction analysis method, and the line structure sub-model and the bridge sub-model are established respectively. The interaction relationship between the line and the bridge is solved by an iterative method based on the two sub-models. The following process steps are included:

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

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

[0069] The longitudinal and vertical displacements of the bridge structure are taken as the basic unknowns, and 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 iteration, extract rail longitudinal force, rail longitudinal displacement, bridge longitudinal, vertical displacement, and pier longitudinal force.

[0070] In this embodiment, it is necessary to establish 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 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 base vertical force and longitudinal force of the track 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 bottom of the track model in contact with the bridge. Taking the finite element model of ballasted track as an example, the rails are simulated as continuous point-supported beam units; the longitudinal resistance and vertical support of the fasteners are simulated as nonlinear spring actions; the sleepers are simulated as beam units based on their force characteristics; the longitudinal resistance and vertical support stiffness of the ballast bed are simulated as spring units; when the ballast bed is located on the bridge, the node at one end of the ballast bed spring unit is connected to the sleepers, and the node at the other end applies the longitudinal and vertical forced displacements of the bridge longitudinally and vertically; when the ballasted ballast bed is located in the roadbed section, one end of the spring unit 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 by beam units, the track plate and self-compacting concrete are used as composite plate structures, and the two are combined and simulated as shell units; the base plate is simulated by shell units, and since the base plate is connected to the bridge through a sleeve, the sleeve is simulated as a spring unit 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 embodiment, a bridge finite element model needs to be established separately, and a method for establishing a typical bridge finite element model is proposed. Bridge types mainly include special bridges such as simply supported beam bridges, continuous beam bridges, rigid frame bridges, arch bridges, cable-stayed bridges, and suspension bridges. The method for constructing a finite element model of a large-span bridge is introduced by taking a continuous beam bridge and a cable-stayed bridge as examples.

[0073] The continuous beam bridge consists of a main beam, supports and piers. When modeling, it is assumed that the supports are consolidated with the pier tops and the fixed supports can fully transmit force. The continuous main beam is simulated using variable-section beam units connected end to end, and the piers are simulated using spring units. When modeling, the size of the beam unit is kept consistent with the size of the track sub-model as much as possible to reduce the deformation interpolation and load equivalence of the applied node force during iteration, thereby improving the calculation accuracy.

[0074] The long-span cable-stayed bridge mainly includes steel box main beam, cable, main tower, auxiliary side pier and other structures. The steel box main beam is simulated by beam unit; the main tower is simulated by spatial beam unit; the longitudinal damper between the main tower and the main beam is simulated by spring unit, which only plays a role in calculating the braking force of the rail. The bridge tower and the main beam are coupled in the horizontal and vertical directions. The cable is a slender and flexible structure, which is simulated by a rod unit that can only bear tension. The two sides of the cable are connected to the rigid arm node and the main tower node extending from the steel box beam. The bottom of the main tower and the bottom of the auxiliary side pier are fully constrained. When modeling, the size of the main beam of the cable-stayed bridge should be consistent with the size division of the track sub-model as much as possible to reduce the deformation interpolation and load equivalence of the applied node force during iteration, and improve the calculation 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 and calculated until the displacement converges. Including:

[0076] (1) Assume that the initial longitudinal displacement and vertical displacement of the bridge node are 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 temperature changes and other working conditions, and calculate the displacement of the bridge, 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 until 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, it is not mandatory to have the same grid size for the track model and the same grid size for the bridge model during modeling. When the grid size of the track model and the grid size of the bridge model are inconsistent, in order to ensure that the bridge force and the forced displacement of the bridge can accurately act on the two sub-models, it is necessary to process the bridge force and the forced displacement of the bridge respectively by means of 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, it is also necessary to interpolate the bridge forced displacement curve at the bottom of each fastener node based on the cubic spline curve.

[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 calculation, 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 the nth step; X n-1 , Y n-1 represents 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 the n-1th step, 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 respectively, 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, thereby improving modeling efficiency.

[0091] Example 2

[0092] In view of the increasingly prominent defects of the line-bridge interaction coupling analysis model, such as complex modeling, one bridge for one analysis model, and low efficiency of simulation calculation, a decoupled iterative calculation method for line-bridge interaction analysis is proposed in this embodiment 2. 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 respectively 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 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 ballasted track, ballastless track and bridge finite element models, and proposes a setting method for the track model boundary conditions. The influence of material nonlinearity and structural nonlinearity such as the ballast bed and fastener resistance can be fully considered.

[0095] Taking the finite element model of ballasted track as an example, the rails are simulated as continuous point-supported beam units; the longitudinal resistance and vertical support of the fasteners are simulated as nonlinear spring actions; the sleepers are simulated as beam units based on their force characteristics; the longitudinal resistance and vertical support stiffness of the ballast bed are simulated as spring units; the ballast bed spring unit of the bridge section has one end node connected to the sleepers, and the other end node is laterally constrained, and the longitudinal and vertical forced displacements of the bridge are applied longitudinally and vertically; the ballast bed spring unit of the roadbed section has one end node connected to the sleepers, and the other end node is fully constrained; taking the CRTSIII slab track as an example, the rails in the model are simulated by beam units, the track plate and self-compacting concrete are used as composite plate structures, and the two are combined and considered to be simulated using shell units; the base plate is simulated by shell units, and since the base plate is connected to the bridge through a sleeve, the sleeve is simulated as a spring unit 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 on the bridge.

[0096] The decoupled iterative calculation method for line-bridge interaction analysis proposed in this embodiment uses the 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 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) The 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

[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, in order to ensure that the bridge force and bridge displacement can accurately act on the bridge model and the track model during the iteration process, when the grid size of the bridge structure is inconsistent with the grid size of the track structure, the bridge force and bridge displacement 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 force and bridge forced displacement can accurately act on the two sub-models, it is necessary to process the bridge force and bridge forced displacement respectively by means of node force equivalence and spline interpolation. When the bridge mesh size is larger than the track mesh 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 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 consistent with the unit size of the bridge model, it is still recommended that the bridge be divided according to the size of the track structure when dividing the mesh, so as to facilitate the extraction and application of node forces and node displacements, and avoid the work of node 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] In order to accelerate iterative convergence, avoid iterative oscillation, and reduce the number of iterations, it is proposed to use an iterative acceleration factor to accelerate iteration. That is, when performing displacement calculation, 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 this 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 the nth step; X n-1 , Y n-1 represents 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 the n-1th step, α is the iteration acceleration factor, 0<α<1, and its value has a certain relationship with the span of the bridge. After many trials, when α is 0.25-0.3, the convergence of the iterative algorithm is better 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, and the longitudinal force and vertical force transmitted to the bridge by the roadbed under complex conditions such as complex temperature, deflection, and braking are calculated. (2) The bridge force is applied to the finite element model of the bridge, 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 as boundary conditions in the form of forced displacement 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 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. 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 sub-model and bridge sub-model are shown in Figure 2. The decoupled track sub-model needs to impose reasonable constraints on the nodes of the ballast bed spring. Taking the finite element model of ballasted track as an example, one end of the ballast bed spring unit is connected to the sleeper, and the other end node applies the longitudinal and vertical forced displacement of the bridge in the longitudinal and vertical directions. When the ballasted ballast bed is located in the roadbed section, one end of the spring unit is connected to the sleeper, and the other end node is fully constrained. The decoupled bridge sub-model needs to apply the bridge force transmitted to the bridge by the ballast bed, which is divided into two directions: longitudinal and vertical.

[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 F 1 and F 2 , where F 1 The distance from point A is a 1 , the distance from point B is b 1 , F 2 The distance from point A is a 2 , the distance from point B is b 2 , where: the spacing between fasteners is a 2 and a 1 The equivalent nodal axial force F at A and B is A and F B As shown below:

[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 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 vertical forces acting on the bridge are F 1 and F 2 , where F 1 The distance from point A is a 1 , the distance from point B is b 1 , F 2 The distance from point A is a 2 , the distance from point B is b 2 , where: the spacing between fasteners is a 2 and a 1 The difference between A and B is: A 、F B , equivalent node bending moment M A 、M B As shown below:

[0118]

[0119] In order to verify the correctness of the decoupled iterative calculation method, a 5-span 32m simply supported beam bridge with ballasted track seamless line is considered, the roadbed on both sides is 150m long, the longitudinal stiffness of the abutment is 3000kN / cm, the longitudinal stiffness of the pier is 500kN / cm, and the iteration factor is 0.25. Two methods are used to calculate the line-bridge interaction under expansion and contraction and braking conditions respectively. Figure 6-Figure 8 They are respectively the longitudinal force of the rail, the relative displacement of the beam and the longitudinal force of the pier under the telescopic condition calculated in this example; Figure 9-11 They are respectively the longitudinal force of the rail, the relative displacement of the beam and the longitudinal force of the pier under the braking condition calculated in this example. The solid line is the result of the decoupling iteration method, and the dotted line is the result of the spatial coupling model. It can be seen from the figure that the results calculated by the two methods are basically completely coincident. Table 1 shows the peak values ​​and their errors calculated by the two methods. It can be seen from the table that the peak values ​​of the calculation results corresponding to the two methods are slightly different, and the corresponding errors are within 2%, indicating 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 condition

[0121]

[0122] In order to verify the versatility of the decoupled iterative calculation method, a 3×24m simply supported beam bridge + (72+128+72)m continuous beam bridge + 3×24m simply supported beam bridge with 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 and braking conditions respectively. Figure 12-Figure 14 They are respectively the longitudinal force of the rail, the relative displacement of the beam and the longitudinal force of the pier under the telescopic condition calculated in this example; Figure 15-17 They are respectively the longitudinal force of the rail, the relative displacement of the beam and the longitudinal force of the pier under the braking condition calculated in this example. The solid line is the result of the decoupling iteration method, and the dotted line is the result of the spatial coupling model. It can be seen from the figure that the results calculated by the two methods are basically completely coincident. Table 2 shows the peak values ​​and their errors calculated by the two methods. It can be seen from the table that the peak values ​​of the calculation results corresponding to the two methods are slightly different, and the corresponding errors are all within 1%, which shows the adaptability of the decoupling iteration algorithm to continuous beam bridges.

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

[0124]

[0125] In order to verify the adaptability of the decoupled iterative calculation method to super-long-span bridges, a seamless line is laid on a (2×50+224+672+174+3×50)m double-tower cable-stayed bridge. The roadbed on both sides is 150m long 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 18-Figure 20 They are respectively the longitudinal force of the rail, the relative displacement of the beam and the vertical displacement of the bridge under the telescopic condition calculated in this example; Figure 21-24 They are respectively the longitudinal force of the rail, the relative displacement of the beam and the longitudinal force of the pier under the braking condition calculated in this example. The solid line is the result calculated by the decoupling iteration method, and the dotted line is the result calculated by the spatial coupling model. It can be seen from the figure that the results calculated by the two methods are basically completely coincident. Table 3 shows the peak values ​​and their errors calculated by the two methods. It can be seen from the table that the peak values ​​of the calculation results corresponding to the two methods are slightly different, and the corresponding errors are all within 1%, indicating that the decoupling iteration algorithm has good adaptability to cable-stayed bridges.

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

[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 0.25, and two methods are used to calculate the line-bridge interaction under expansion and braking conditions respectively. Figure 25-27 They are respectively the longitudinal force of the rail, the relative displacement of the beam and rail, and the vertical displacement of the bridge under the telescopic working condition calculated in this example; the solid line is the result calculated by the decoupling iteration method, and the dotted line is the result calculated by the spatial coupling model. It can be seen from the figure that the results calculated by the two methods are basically completely coincident. Table 4 shows the peak values ​​and their errors calculated by the two methods. It can be seen from the table that the peak values ​​of the calculation results corresponding to the two methods are slightly different, and the corresponding errors are within 1%, which shows the adaptability of the decoupling iteration algorithm to the regulator.

[0129] Table 4 Calculation results and errors of the two methods under regulator working conditions

[0130]

[0131] From the above working conditions, it can be seen that as the span of the bridge increases, the calculation errors of the decoupled 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] In order to verify the correctness of the iterative acceleration factor mentioned in the decoupled iterative calculation method, taking the condition of laying a seamless line on a 5-span simply supported beam bridge as an example, considering α to be 0.1, 0.2, 0.25, 0.3, and 0.5 respectively, and the bridge temperature to be reduced 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] It can be seen from Table 5 that with the increase of the iteration factor, the number of convergent iterations gradually decreases. It should be noted that when the iteration factor is 0.25, the iteration gradually approaches the true value from the given initial value in sequence. When it is 0.3, the iteration approaches the true value after oscillating around the true value. When the iteration factor is 0.5, the convergence of this method is poor for a 32m simply supported beam bridge, but when calculating the line-bridge interaction of a cable-stayed bridge, the number of iterations corresponding to the iteration factor of 0.5 is nearly half of that of 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 as 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, 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 so that the electronic device executes instructions for implementing the wire-bridge interaction analysis method as described above.

[0142] Although the above describes the specific implementation mode 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 without creative work on the basis of the technical solution disclosed in the present invention 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 stress 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 the basic unknown quantities, 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.

2. The line-bridge interaction analysis method according to claim 1, characterized in that: Taking the longitudinal and vertical displacements of the bridge structure as basic unknown quantities, the track sub-model and the bridge sub-model are repeatedly iterated and calculated until the displacement converges, and the rail longitudinal force, rail longitudinal displacement, bridge longitudinal and vertical displacements, and bridge pier longitudinal force are obtained, including: assuming the initial displacement of the bridge, taking it as the boundary condition of the track structure, and 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 bridge longitudinal and vertical deformation; applying the calculated bridge longitudinal and vertical deformations as boundary conditions to the line track finite element model in the form of forced displacement, and calculating the bridge force; repeatedly iterating and 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 bridge pier longitudinal force.

3. The line-bridge interaction analysis method according to claim 2, characterized in that: An iterative acceleration factor is used to reduce the number of iterations. That is, when performing displacement calculation, 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 iterative acceleration factor, and then add it to the bridge displacement applied to the track sub-model in the previous step.

4. The line-bridge interaction analysis method according to claim 3, 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 the n-1th step, α is the iteration acceleration factor, 0<α<1.

5. The line-bridge interaction analysis method according to claim 4, 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.

6. The line-bridge interaction analysis method according to claim 2, 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.

7. A line-bridge interaction analysis system, characterized in that: include: The first building module is used to establish a track finite element model, namely, a track sub-model, based on finite element theory and the nonlinear inter-layer force transmission relationship of the track structure in combination 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 take the longitudinal and vertical displacements of the bridge structure as the basic unknown quantities, and repeatedly iterate the track sub-model and the bridge sub-model until the displacement converges, so as to obtain 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.

8. 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 6 is implemented.

9. A computer device, characterized in that: It comprises a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the line-bridge interaction analysis method according to any one of claims 1-6.

10. 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 as described in any one of claims 1-6.

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