Train loading method and device for calculating dynamic response of train passing over bridge

Abstract

The application discloses a train loading method and device for calculating train bridge dynamic response, and relates to the technical field of bridge dynamic analysis. The method comprises the following steps: based on an established bridge finite element analysis model, setting a train load loading node interval, and forming a dynamic loading node sequence; a virtual beam unit is established between the dynamic loading node sequence, and the length of the virtual beam unit before and after each dynamic loading node is calculated; the time when the train head reaches each dynamic loading node is calculated; the equivalent node force of the train uniform load and the concentrated force is calculated, and the equivalent node force of the dynamic loading node is obtained; the equivalent node concentrated force loading time function is obtained; the input file of the finite element software is generated according to the equivalent node concentrated force loading time function corresponding to each dynamic loading node and the train head arrival time, and is led to the finite element software, so that the train dynamic load moving loading is realized. The application reduces the node loading data, and greatly shortens the calculation time.

Description

Technical Field

[0001] This invention relates to the field of bridge dynamic analysis technology, specifically to a train loading method and apparatus for calculating the dynamic response of a train crossing a bridge. Background Technology

[0002] With economic and technological development, the construction of ultra-long-span railway cable-stayed bridges has progressed rapidly, and train speeds have continued to increase. Meanwhile, operational experience with large-span railway cable-stayed and suspension bridges completed and opened to traffic in recent years shows that the longitudinal displacement at the beam ends caused by trains crossing the bridge cannot be ignored. Commonly used static analysis methods cannot account for the influence of viscous dampers and bearing friction on the bridge's dynamic response; therefore, accurate simulation of the dynamic loading process of trains crossing the bridge is necessary.

[0003] For simulating train dynamic loads, existing finite element software uses a triangular pulse load equivalent method for train dynamic loading. This method's technical characteristics are: the load diagram of uniformly distributed force + concentrated force of the railway train is equivalent to several concentrated forces; the magnitude and duration of the triangular pulse load are determined based on the magnitude of the concentrated forces and the spacing between lane loading nodes; each concentrated force arriving at a lane node results in one pulse load being applied; and the entire dynamic loading process of the train crossing the bridge is formed based on the arrival time of each concentrated force at the lane node. However, this triangular pulse equivalent load has the following drawbacks: the concentrated force equivalence of the train loading diagram cannot accurately simulate the train loading diagram in relevant railway bridge and culvert design specifications; and several triangular pulse loads are required for each lane loading node, leading to reduced efficiency in dynamic analysis calculations. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a train loading method and apparatus for calculating the dynamic response of a train crossing a bridge, thereby reducing the amount of node loading data and significantly shortening the calculation time.

[0005] To achieve the above objectives, the present invention provides a train loading method for calculating the dynamic response of a train crossing a bridge, specifically including the following steps:

[0006] Based on the established bridge finite element analysis model, the spacing between train load loading nodes is set to filter track nodes, forming a dynamic loading node sequence.

[0007] Virtual beam elements are established between the dynamic loading node sequences, and the lengths of the virtual beam elements before and after each dynamic loading node are calculated.

[0008] Based on the distance between the dynamic loading node and the starting end of the bridge, and the train speed, the time it takes for the train head to reach each dynamic loading node is calculated.

[0009] Based on the railway train load diagram, the train loading method is obtained, and the equivalent nodal force of the uniformly distributed load and concentrated force of the train is calculated, thus obtaining the equivalent nodal force of the dynamic loading node.

[0010] The equivalent nodal force of the concentrated force and the equivalent nodal force of the uniformly distributed load are superimposed to obtain the loading time history function of the equivalent nodal concentrated force.

[0011] The input file for the finite element software is generated based on the equivalent node concentrated force loading time history function corresponding to each dynamic loading node and the arrival time of the train head, and then imported into the finite element software to realize the moving loading of the train dynamic load.

[0012] Based on the above technical solution, the step of setting the spacing between train load loading nodes to filter track nodes and form a dynamic loading node sequence based on the established bridge finite element analysis model specifically includes the following steps:

[0013] Based on the bridge design drawings, a finite element analysis model of the bridge was established, and the coordinates of the bridge train track nodes were extracted.

[0014] Set the spacing between train load loading nodes, and filter track nodes according to the set spacing to form a dynamic loading node sequence.

[0015] Based on the above technical solution, the length of the virtual beam element before and after each dynamic loading node is calculated, and the specific calculation method is as follows:

[0016] L j =x i -x i-1

[0017] L j+1 =x i+1 -x i

[0018] Among them, L j x represents the length of the virtual beam element j before the i-th dynamic loading node. i Let x represent the coordinates of the i-th dynamic loading node. i-1 L represents the coordinates of the (i-1)th dynamic loading node. j+1 x represents the length of the virtual beam element j+1 after the i-th dynamic loading node. i+1 This represents the coordinates of the (i+1)th dynamic loading node.

[0019] Based on the above technical solution, the calculation of the time for the train head to reach each power loading node is specifically performed as follows:

[0020] t i =S i-1 / v

[0021] Among them, t i S represents the time it takes for the train's locomotive to reach the i-th power loading node. i-1 represents the distance from the (i-1)th dynamic loading node to the starting end of the bridge, and v represents the train speed.

[0022] Based on the above technical solution, the specific calculation method for the equivalent nodal force of the dynamically loaded node is as follows:

[0023] F i =F i j +F i j+1

[0024] Among them, F i F represents the equivalent nodal force at the i-th dynamic loading node. i j F represents the force distributed at the i-th dynamically loaded node when the load passes through the virtual beam element j. i j+1 This represents the force distributed at the i-th dynamic loading node when the load passes through the virtual beam element j+1.

[0025] Based on the above technical solution, the equivalent nodal force distribution method for the uniformly distributed load in the train load diagram is as follows:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] Among them, [N] T F represents the transpose of the shape function matrix of the virtual beam element. i1 M represents the equivalent nodal force at the first point of the virtual beam element before or after the i-th dynamic loading node. i1 F represents the equivalent nodal bending moment at the first point of the virtual beam element before or after the i-th dynamic loading node. i2 M represents the equivalent nodal force at the second point of the virtual beam element before or after the i-th dynamic loading node. i2The equivalent nodal bending moment at the second point of the virtual beam element before or after the i-th dynamic loading node is represented by the length direction of the virtual beam element as the x-axis. x0 represents the distance from the end of the uniformly distributed force to the first point of the virtual beam element, x1 represents the distance from the front end of the uniformly distributed force to the first point of the virtual beam element, q represents the magnitude of the uniformly distributed load in the train load diagram, and e represents the virtual beam element number.

[0032] Based on the above technical solution, the equivalent nodal force distribution method of the concentrated force in the train load diagram is as follows:

[0033]

[0034]

[0035] Among them, a j The distance to the (i-1)th dynamic loading node of the concentrated moment of the train is represented by p, where p represents the concentrated force in the train load diagram, and a j+1 This represents the distance to the i-th power loading node of the train's concentrated torque.

[0036] The present invention provides a train loading device for calculating the dynamic response of a train crossing a bridge, comprising:

[0037] The setting module is used to set the spacing between train load loading nodes based on the established bridge finite element analysis model to filter track nodes and form a dynamic loading node sequence.

[0038] A module is established to create virtual beam elements between dynamic loading node sequences and to calculate the length of the virtual beam elements before and after each dynamic loading node.

[0039] The first calculation module is used to calculate the time it takes for the train head to reach each dynamic loading node based on the distance between the dynamic loading node and the starting end of the bridge, and the train speed.

[0040] The second calculation module is used to obtain the train loading method based on the railway train load diagram, calculate the equivalent nodal force of the uniformly distributed load and concentrated force of the train, and obtain the equivalent nodal force of the dynamic loading node.

[0041] The superposition module is used to superimpose the equivalent nodal forces of concentrated forces and the equivalent nodal forces of uniformly distributed loads to obtain the loading time history function of equivalent nodal concentrated forces.

[0042] The execution module is used to generate input files for the finite element software based on the equivalent node concentrated force loading time history function corresponding to each dynamic loading node and the arrival time of the train head, and then import them into the finite element software to realize the moving loading of the train dynamic load.

[0043] Based on the above technical solution, the process of setting the spacing between train load loading nodes to filter track nodes and forming a dynamic loading node sequence based on the established bridge finite element analysis model includes the following steps:

[0044] Based on the bridge design drawings, a finite element analysis model of the bridge was established, and the coordinates of the bridge train track nodes were extracted.

[0045] Set the spacing between train load loading nodes, and filter track nodes according to the set spacing to form a dynamic loading node sequence.

[0046] Based on the above technical solution, the length of the virtual beam element before and after each dynamic loading node is calculated, and the specific calculation method is as follows:

[0047] L j =x i -x i-1

[0048] L j+1 =x i+1 -x i

[0049] Among them, L j x represents the length of the virtual beam element j before the i-th dynamic loading node. i Let x represent the coordinates of the i-th dynamic loading node. i-1 L represents the coordinates of the (i-1)th dynamic loading node. j+1 x represents the length of the virtual beam element j+1 after the i-th dynamic loading node. i+1 This represents the coordinates of the (i+1)th dynamic loading node.

[0050] Compared with existing technologies, the advantages of this invention are as follows: By establishing virtual beam elements between dynamic loading nodes, and distributing the uniformly distributed loads and concentrated forces moving to the virtual beam elements to the loading nodes through the principle of equivalent nodal forces, the equivalent nodal concentrated force loading time history function is obtained by superposition. Then, based on the principle that the lengths of the virtual beam elements before and after the dynamic loading node are equal, the same equivalent nodal concentrated force loading time history functions are grouped into one type to reduce the equivalent nodal concentrated force loading time history function. The dynamic loading effect of the train is achieved by corresponding the dynamic loading node number, the equivalent nodal concentrated force loading time history function and the arrival time of the train head. That is, this invention establishes a dynamic loading method based on the principle of equivalent nodal forces, and accurately applies the train loading pattern load to each dynamic loading node through the principle of equivalent nodal forces. Compared with the traditional triangular time history function loading, the nodal loading data is reduced, which greatly shortens the calculation time. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a flowchart of a train loading method for calculating the dynamic response of a train crossing a bridge, as described in an embodiment of the present invention.

[0053] Figure 2 This is an elevation view of the suspension bridge.

[0054] Figure 3 This is a diagram showing the train load.

[0055] Figure 4 This is a diagram of a virtual beam element.

[0056] Figure 5 A diagram illustrating the equivalent principle calculation for a dynamically loaded node;

[0057] Figure 6 The time history function of the equivalent nodal concentrated force loading is illustrated.

[0058] Figure 7 The diagram shows the time history function of a triangular pulse load. Detailed Implementation

[0059] This invention provides a train loading method for calculating the dynamic response of a train crossing a bridge. Virtual beam elements are established between dynamic loading nodes, and the uniformly distributed load and concentrated force moving to the virtual beam elements are distributed to the loading nodes using the principle of equivalent nodal forces. The equivalent nodal concentrated force loading time history function is obtained by superposition. Then, based on the principle that the lengths of the virtual beam elements before and after the dynamic loading node are equal, the same equivalent nodal concentrated force loading time history functions are grouped together to reduce the number of equivalent nodal concentrated force loading time history functions. The dynamic loading effect is achieved by corresponding the dynamic loading node number, the equivalent nodal concentrated force loading time history function, and the train head arrival time. In other words, this invention establishes a dynamic loading method based on the principle of equivalent nodal forces, accurately equating the train loading pattern load to each dynamic loading node. Compared to traditional triangular time history function loading, the nodal loading data is reduced, significantly shortening the calculation time. This invention also provides a train loading device for calculating the dynamic response of a train crossing a bridge.

[0060] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this application, but not all embodiments.

[0061] See Figure 1 As shown in the figure, this invention provides a train loading method for calculating the dynamic response of a train crossing a bridge, which can accurately and efficiently calculate the longitudinal displacement of a train crossing the bridge end of a long-span bridge. The method specifically includes the following steps:

[0062] S1: Based on the established bridge finite element analysis model, the spacing between train load loading nodes is set to filter track nodes and form a dynamic loading node sequence;

[0063] In this invention, based on the established bridge finite element analysis model, the spacing between train load loading nodes is set to filter track nodes, forming a dynamic loading node sequence, specifically including the following steps:

[0064] S101: Based on the bridge design drawings, establish a finite element analysis model of the bridge and extract the coordinates of the bridge train track nodes;

[0065] S102: Set the spacing between train load loading nodes, and filter track nodes according to the set spacing between train load loading nodes to form a dynamic loading node sequence.

[0066] S2: Establish virtual beam elements between the dynamic loading node sequences and calculate the length of the virtual beam elements before and after each dynamic loading node;

[0067] In this invention, the length of the virtual beam element before and after each dynamic loading node is calculated. The specific calculation method is as follows:

[0068] L j =x i -x i-1

[0069] L j+1 =x i+1 -x i

[0070] Among them, L j x represents the length of the virtual beam element j before the i-th dynamic loading node. i Let x represent the coordinates of the i-th dynamic loading node. i-1 L represents the coordinates of the (i-1)th dynamic loading node. j+1 x represents the length of the virtual beam element j+1 after the i-th dynamic loading node. i+1 This represents the coordinates of the (i+1)th dynamic loading node.

[0071] S3: Based on the distance between the dynamic loading node and the starting end of the bridge, and the train speed, the time it takes for the train head to reach each dynamic loading node is calculated.

[0072] In this invention, the time it takes for the train head to reach each power loading node is calculated. The specific calculation method is as follows:

[0073] t i =S i-1 / v

[0074] Among them, t i S represents the time it takes for the train's locomotive to reach the i-th power loading node. i-1 represents the distance from the (i-1)th dynamic loading node to the starting end of the bridge, and v represents the train speed.

[0075] S4: Based on the railway train load diagram, the train loading method is obtained, and the equivalent nodal force of the uniformly distributed load and concentrated force of the train is calculated to obtain the equivalent nodal force of the dynamic loading node; specifically, the train loading method is obtained based on the railway train load diagram in the "Railway Bridge and Culvert Design Code" TB10002-2017 version.

[0076] In this invention, the equivalent nodal force of the dynamically loaded node is calculated as follows:

[0077] F i =F i j +F i j+1

[0078] Among them, F i F represents the equivalent nodal force at the i-th dynamic loading node. i j F represents the force distributed at the i-th dynamically loaded node when the load passes through the virtual beam element j. i j+1 This represents the force distributed at the i-th dynamic loading node when the load passes through the virtual beam element j+1.

[0079] In this invention, the equivalent nodal force distribution method for uniformly distributed loads in the train load diagram is as follows:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] Among them, [N] T F represents the transpose of the shape function matrix of the virtual beam element. i1M represents the equivalent nodal force at the first point of the virtual beam element before or after the i-th dynamic loading node. i1 F represents the equivalent nodal bending moment at the first point of the virtual beam element before or after the i-th dynamic loading node. i2 M represents the equivalent nodal force at the second point of the virtual beam element before or after the i-th dynamic loading node. i2 The equivalent nodal bending moment at the second point of the virtual beam element before or after the i-th dynamic loading node is represented by the length direction of the virtual beam element as the x-axis. x0 represents the distance from the end of the uniformly distributed force to the first point of the virtual beam element, x1 represents the distance from the front end of the uniformly distributed force to the first point of the virtual beam element, q represents the magnitude of the uniformly distributed load in the train load diagram, and e represents the virtual beam element number.

[0086] In this invention, the equivalent nodal force distribution method for the concentrated forces in the train load diagram is as follows:

[0087]

[0088]

[0089] Among them, a j The distance to the (i-1)th dynamic loading node of the concentrated moment of the train is represented by p, where p represents the concentrated force in the train load diagram, and a j+1 This represents the distance to the i-th power loading node of the train's concentrated torque.

[0090] S5: Superimpose the equivalent nodal forces of the concentrated force and the equivalent nodal forces of the uniformly distributed load to obtain the loading time history function of the equivalent nodal concentrated force. Since the time history curves are exactly the same when the lengths of the virtual beam elements before and after the dynamic loading node are exactly the same, the loading time history function of the equivalent nodal concentrated force is classified according to the lengths of the virtual beam elements before and after the dynamic loading node in order to reduce the number of loading time history functions of the equivalent nodal concentrated force and improve the calculation efficiency.

[0091] S6: Generate the input file for the finite element software based on the equivalent node concentrated force loading time history function corresponding to each dynamic loading node and the arrival time of the train head, and import it into the finite element software to realize the moving loading of the train dynamic load.

[0092] The technical principle of this invention is as follows: When the train moves across the bridge, virtual beam elements are established between the dynamic loading nodes. The uniformly distributed load and concentrated force moving to the virtual beam elements are distributed to the loading nodes through the principle of equivalent nodal force. The equivalent nodal concentrated force loading time history function is obtained by superposition. Then, according to the principle that the length of the virtual beam elements before and after the dynamic loading node is equal, the same equivalent nodal concentrated force loading time history function is grouped into one type to reduce the equivalent nodal concentrated force loading time history function. The dynamic loading effect of the train is achieved by corresponding the dynamic loading node number, the equivalent nodal concentrated force loading time history function and the arrival time of the train head. This invention establishes a dynamic loading method based on the principle of equivalent nodal force.

[0093] The train loading method for calculating the dynamic response of a train crossing a bridge according to the present invention will be specifically described below with reference to examples.

[0094] The invention is described in detail using a double-tower, five-span railway suspension bridge as an example. The span arrangement of this suspension bridge is (84+84+1092+84+84)m, and the total length of the bridge is 1428m. The bridge facade layout is as follows: Figure 2 As shown. The train loading diagram selects the ZK load from the "Railway Bridge and Culvert Design Code," with a loading length of 550m, a uniformly distributed force of 64kN / m, a concentrated force of 200kN, a spacing of 1.6m between the four concentrated forces, a spacing of 0.8m between the concentrated force and the uniformly distributed force, and a train speed of 200km / h. The train loading diagram is as follows. Figure 3 As shown. According to Figure 1 The train loading method shown is as follows:

[0095] Step 1: Based on Figure 2 A finite element model of the bridge was established, and the train track node numbers and dynamic loading node coordinates were extracted. The spacing between train load loading nodes was set to 14m. Based on the set train load loading node spacing, the sequence {X} of track nodes subject to loading was selected, which included the dynamic loading node numbers and coordinates.

[0096] Step 2: Create virtual beam elements between the dynamically loaded node sequence {X}, such as... Figure 4 As shown, the length of the virtual beam element before and after each dynamic loading node is calculated. In this example, the track node spacing is equal, therefore the length L of the virtual beam element before and after all dynamic loading nodes is... j and L j+1 Both are 14m. Since the starting dynamic loading node has no front virtual beam element and the ending dynamic loading node has no rear virtual beam element, the lengths of the front and rear virtual beam elements of the starting and ending dynamic loading nodes are approximately the same.

[0097] Step 3: Calculate the time it takes for the train head to reach each power loading node. Specifically, the time t it takes for the train head to reach the i-th power loading node. i =S i-1 / v,S i-1 =14×(i-1), v=200×1000 / 3600(m / s).

[0098] Step 4: Based on Figure 3 The train load diagram is used to calculate the equivalent nodal forces of all dynamic loading node sequences {X} under a uniformly distributed load of 64 kN / m and a concentrated load of 200 kN. Taking the i-th dynamic loading node as an example, based on the principle of nodal force equivalence, the uniformly distributed load is... Figure 4 There are four cases for virtual beam elements, see Figure 5In situations ① to ④, concentration is achieved through... Figure 4 There are two cases for virtual beam elements, see Figure 5 Situation ⑤⑥. Figure 5 The equivalent node force of the i-th node under the six loading conditions shown is:

[0099] Equivalent nodal force of uniformly distributed force:

[0100]

[0101] In the formulas for cases ① and ②:

[0102]

[0103] Case ①F i =F i2 Case ②F i =448+F i1 ;

[0104] In cases ③ and ④:

[0105]

[0106] Case ③F i =448+F i2 Situation ④F i =F i1 ;

[0107] Concentrated force equivalent nodal force:

[0108] Situation 5

[0109] Situation ⑥

[0110] Step 5: Obtain the equivalent nodal concentrated force loading time history function. Since the length of the virtual beam element before and after all dynamic loading nodes is 14m, the equivalent nodal concentrated force loading time history function is reduced to one, such as... Figure 6 As shown.

[0111] Step 6: Generate the equivalent node concentrated force loading time history function and the train head arrival time corresponding to each dynamic loading node into the finite element software input file, and import it into the finite element software to realize the moving loading of train dynamic load.

[0112] The time history functions of the dynamic loading method and the triangular pulse load loading method of this invention are shown below. Figure 6 and Figure 7This paper analyzes the train crossing the bridge problem in this example. Both loading methods calculate the beam end displacement the same. The calculation time for the dynamic loading method proposed in this invention is 0.3 hours, while the calculation time for the triangular pulse load is 2.75 hours. Therefore, the dynamic loading method proposed in this invention has higher calculation efficiency.

[0113] The train loading method for calculating the dynamic response of a train crossing a bridge, as described in this invention, establishes virtual beam elements between dynamic loading nodes. Using the principle of equivalent nodal forces, it distributes the uniformly distributed load and concentrated force moving to the virtual beam elements to the loading nodes, superimposing them to obtain the equivalent nodal concentrated force loading time history function. Then, based on the principle that the lengths of the virtual beam elements before and after the dynamic loading node are equal, the same equivalent nodal concentrated force loading time history functions are grouped together to reduce the number of equivalent nodal concentrated force loading time history functions. The dynamic loading effect is achieved by corresponding the dynamic loading node number, the equivalent nodal concentrated force loading time history function, and the train head arrival time one-to-one. In other words, this invention establishes a dynamic loading method based on the principle of equivalent nodal forces, accurately equating the train loading diagram load to each dynamic loading node. Compared to traditional triangular time history function loading, the nodal loading data is reduced, significantly shortening the calculation time. In practical applications, the time can be reduced by more than 80%.

[0114] In one possible implementation, the present invention also provides a readable storage medium located in a PLC (Programmable Logic Controller) controller. The readable storage medium stores a computer program that, when executed by a processor, implements the steps of the train loading method for calculating the train's bridge-crossing dynamic response as described below:

[0115] Based on the established bridge finite element analysis model, the spacing between train load loading nodes is set to filter track nodes, forming a dynamic loading node sequence.

[0116] Virtual beam elements are established between the dynamic loading node sequences, and the lengths of the virtual beam elements before and after each dynamic loading node are calculated.

[0117] Based on the distance between the dynamic loading node and the starting end of the bridge, and the train speed, the time it takes for the train head to reach each dynamic loading node is calculated.

[0118] Based on the railway train load diagram, the train loading method is obtained, and the equivalent nodal force of the uniformly distributed load and concentrated force of the train is calculated, thus obtaining the equivalent nodal force of the dynamic loading node.

[0119] The equivalent nodal force of the concentrated force and the equivalent nodal force of the uniformly distributed load are superimposed to obtain the loading time history function of the equivalent nodal concentrated force.

[0120] The input file for the finite element software is generated based on the equivalent node concentrated force loading time history function corresponding to each dynamic loading node and the arrival time of the train head, and then imported into the finite element software to realize the moving loading of the train dynamic load.

[0121] Storage media may be any combination of one or more computer-readable media. A computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. Computer-readable storage media may be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this document, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0122] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted using any suitable medium, including but not limited to: wireless, wireline, optical fiber, RF, etc., or any suitable combination thereof.

[0123] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0124] The present invention provides a train loading device for calculating the dynamic response of a train crossing a bridge, comprising a setting module, a setting module, a first calculation module, a second calculation module, a superposition module, and an execution module.

[0125] The configuration module is used to set the spacing between train load loading nodes based on the established bridge finite element analysis model to filter track nodes and form a dynamic loading node sequence. The creation module is used to create virtual beam elements between the dynamic loading node sequences and calculate the length of the virtual beam elements before and after each dynamic loading node. The first calculation module is used to calculate the time for the train head to arrive at each dynamic loading node based on the distance of the dynamic loading node from the starting end of the bridge and the train speed. The second calculation module is used to obtain the train loading method according to the railway train load diagram, calculate the equivalent nodal force of the uniformly distributed load and concentrated force of the train, and obtain the equivalent nodal force of the dynamic loading node. The superposition module is used to superimpose the equivalent nodal force of the concentrated force and the equivalent nodal force of the uniformly distributed load to obtain the equivalent nodal concentrated force loading time history function. The execution module is used to generate the input file of the finite element software according to the equivalent nodal concentrated force loading time history function corresponding to each dynamic loading node and the arrival time of the train head, and import it into the finite element software to realize the moving loading of the train dynamic load.

[0126] In this invention, based on the established bridge finite element analysis model, the spacing between train load loading nodes is set to filter track nodes, forming a dynamic loading node sequence, specifically including the following process:

[0127] Based on the bridge design drawings, a finite element analysis model of the bridge was established, and the coordinates of the bridge train track nodes were extracted.

[0128] Set the spacing between train load loading nodes, and filter track nodes according to the set spacing to form a dynamic loading node sequence.

[0129] In this invention, the length of the virtual beam element before and after each dynamic loading node is calculated. The specific calculation method is as follows:

[0130] L j =x i -x i-1

[0131] L j+1 =x i+1 -x i

[0132] Among them, L j x represents the length of the virtual beam element j before the i-th dynamic loading node. i Let x represent the coordinates of the i-th dynamic loading node. i-1 L represents the coordinates of the (i-1)th dynamic loading node. j+1 x represents the length of the virtual beam element j+1 after the i-th dynamic loading node. i+1 This represents the coordinates of the (i+1)th dynamic loading node.

[0133] The train loading device for calculating the dynamic response of a train crossing a bridge, as described in this invention, establishes virtual beam elements between dynamic loading nodes. It then distributes the uniformly distributed load and concentrated force moving to the virtual beam elements to the loading nodes using the principle of equivalent nodal forces, superimposing these to obtain an equivalent nodal concentrated force loading time history function. Furthermore, based on the principle that the lengths of the virtual beam elements before and after the dynamic loading node are equal, identical equivalent nodal concentrated force loading time history functions are grouped together to reduce the number of equivalent nodal concentrated force loading time history functions. The dynamic loading effect is achieved by corresponding the dynamic loading node number, the equivalent nodal concentrated force loading time history function, and the train head arrival time. In other words, this invention establishes a dynamic loading method based on the principle of equivalent nodal forces, accurately equating the train loading pattern load to each dynamic loading node. Compared to traditional triangular time history function loading, this reduces the nodal loading data and significantly shortens the calculation time.

[0134] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

[0135] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

Claims

1. A train loading method for calculating the dynamic response of a train crossing a bridge, characterized in that, Specifically, the following steps are included: Based on the established bridge finite element analysis model, the spacing between train load loading nodes is set to filter track nodes, forming a dynamic loading node sequence. Virtual beam elements are established between the dynamic loading node sequences, and the lengths of the virtual beam elements before and after each dynamic loading node are calculated. Based on the distance between the dynamic loading node and the starting end of the bridge, and the train speed, the time it takes for the train head to reach each dynamic loading node is calculated. Based on the railway train load diagram, the train loading method is obtained, and the equivalent nodal force of the uniformly distributed load and concentrated force of the train is calculated, thus obtaining the equivalent nodal force of the dynamic loading node. The equivalent nodal force of the concentrated force and the equivalent nodal force of the uniformly distributed load are superimposed to obtain the loading time history function of the equivalent nodal concentrated force. The input file for the finite element software is generated based on the equivalent node concentrated force loading time history function corresponding to each dynamic loading node and the arrival time of the train head, and then imported into the finite element software to realize the moving loading of the train dynamic load.

2. The train loading method for calculating the dynamic response of a train crossing a bridge as described in claim 1, characterized in that, Based on the established bridge finite element analysis model, the spacing between train load loading nodes is set to filter track nodes and form a dynamic loading node sequence, specifically including the following steps: Based on the bridge design drawings, a finite element analysis model of the bridge was established, and the coordinates of the bridge train track nodes were extracted. Set the spacing between train load loading nodes, and filter track nodes according to the set spacing to form a dynamic loading node sequence.

3. The train loading method for calculating the dynamic response of a train crossing a bridge as described in claim 2, characterized in that, The calculation yields the length of the virtual beam element before and after each dynamically loaded node. The specific calculation method is as follows: L j =x i -x i-1 L j+1 =x i+1 -x i Among them, L j x represents the length of the virtual beam element j before the i-th dynamic loading node. i Let x represent the coordinates of the i-th dynamic loading node. i-1 L represents the coordinates of the (i-1)th dynamic loading node. j+1 x represents the length of the virtual beam element j+1 after the i-th dynamic loading node. i+1 This represents the coordinates of the (i+1)th dynamic loading node.

4. The train loading method for calculating the dynamic response of a train crossing a bridge as described in claim 3, characterized in that, The calculation yields the time it takes for the train head to reach each power loading node. The specific calculation method is as follows: t i =S i-1 / v Among them, t i S represents the time it takes for the train's locomotive to reach the i-th power loading node. i-1 represents the distance from the (i-1)th dynamic loading node to the starting end of the bridge, and v represents the train speed.

5. The train loading method for calculating the dynamic response of a train crossing a bridge as described in claim 4, characterized in that, The specific calculation method for the equivalent nodal force of the dynamically loaded node is as follows: F i =F i j +F i j+1 Among them, F i F represents the equivalent nodal force at the i-th dynamic loading node. i j F represents the force distributed at the i-th dynamically loaded node when the load passes through the virtual beam element j. i j+1 This represents the force distributed at the i-th dynamic loading node when the load passes through the virtual beam element j+1.

6. The train loading method for calculating the dynamic response of a train crossing a bridge as described in claim 5, characterized in that, The equivalent nodal force distribution method for the uniformly distributed load in the train load diagram is as follows: Among them, [N] T F represents the transpose of the shape function matrix of the virtual beam element. i1 M represents the equivalent nodal force at the first point of the virtual beam element before or after the i-th dynamic loading node. i1 F represents the equivalent nodal bending moment at the first point of the virtual beam element before or after the i-th dynamic loading node. i2 M represents the equivalent nodal force at the second point of the virtual beam element before or after the i-th dynamic loading node. i2 The equivalent nodal bending moment at the second point of the virtual beam element before or after the i-th dynamic loading node is represented by the length direction of the virtual beam element as the x-axis. x0 represents the distance from the end of the uniformly distributed force to the first point of the virtual beam element, x1 represents the distance from the front end of the uniformly distributed force to the first point of the virtual beam element, q represents the magnitude of the uniformly distributed load in the train load diagram, and e represents the virtual beam element number.

7. The train loading method for calculating the dynamic response of a train crossing a bridge as described in claim 5, characterized in that, The equivalent nodal force distribution method for the concentrated forces in the train load diagram is as follows: Among them, a j The distance to the (i-1)th dynamic loading node of the concentrated moment of the train is represented by p, where p represents the concentrated force in the train load diagram, and a j+1 This represents the distance to the i-th power loading node of the train's concentrated torque.

8. A train loading device for calculating the dynamic response of a train crossing a bridge, characterized in that, include: The setting module is used to set the spacing between train load loading nodes based on the established bridge finite element analysis model to filter track nodes and form a dynamic loading node sequence. A module is established to create virtual beam elements between dynamic loading node sequences and to calculate the length of the virtual beam elements before and after each dynamic loading node. The first calculation module is used to calculate the time it takes for the train head to reach each dynamic loading node based on the distance between the dynamic loading node and the starting end of the bridge, and the train speed. The second calculation module is used to obtain the train loading method based on the railway train load diagram, calculate the equivalent nodal force of the uniformly distributed load and concentrated force of the train, and obtain the equivalent nodal force of the dynamic loading node. The superposition module is used to superimpose the equivalent nodal forces of concentrated forces and the equivalent nodal forces of uniformly distributed loads to obtain the loading time history function of equivalent nodal concentrated forces. The execution module is used to generate input files for the finite element software based on the equivalent node concentrated force loading time history function corresponding to each dynamic loading node and the arrival time of the train head, and then import them into the finite element software to realize the moving loading of the train dynamic load.

9. A train loading device for calculating the dynamic response of a train crossing a bridge as described in claim 8, characterized in that, Based on the established bridge finite element analysis model, the spacing between train load loading nodes is set to filter track nodes and form a dynamic loading node sequence, which specifically includes the following process: Based on the bridge design drawings, a finite element analysis model of the bridge was established, and the coordinates of the bridge train track nodes were extracted. Set the spacing between train load loading nodes, and filter track nodes according to the set spacing to form a dynamic loading node sequence.

10. A train loading device for calculating the dynamic response of a train crossing a bridge as described in claim 9, characterized in that, The calculation yields the length of the virtual beam element before and after each dynamically loaded node. The specific calculation method is as follows: L j =x i -x i-1 L j+1 =x i+1 -x i Among them, L j x represents the length of the virtual beam element j before the i-th dynamic loading node. i Let x represent the coordinates of the i-th dynamic loading node. i-1 L represents the coordinates of the (i-1)th dynamic loading node. j+1 x represents the length of the virtual beam element j+1 after the i-th dynamic loading node. i+1 This represents the coordinates of the (i+1)th dynamic loading node.

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