A method for applying moving loads to a non-uniformly discretized finite element model

Abstract

This application relates to a method for applying moving loads to a non-uniformly discretized finite element model, comprising: constructing a non-uniformly discretized finite element model, determining the node number and corresponding spatial coordinates of each finite element node, wherein the element length of the moving load is non-uniformly distributed; calculating the length of the element subjected to the moving load; and calculating the length of the moving load. i The time step j The spatial location of the moving load; determine the first i The time step j For each moving load element, the node number of the left node of the element at that time step is obtained and defined as a trajectory matrix. The distance between the moving load and the left node at that time step is calculated and defined as a distance matrix. This process is repeated to obtain the trajectory matrix and distance matrix of all moving loads within the total time steps. The equivalent nodal forces borne by the left and right nodes of the element when the moving load acts on it are calculated. This application dynamically tracks and precisely locates moving loads for accurate application throughout the entire time-history analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of dynamic time history analysis, and particularly relates to a method for applying moving load to a non-uniform discretized finite element model. BACKGROUND

[0002] In dynamic time history analysis, when the time history size and position of an external dynamic load (such as a moving load generated by a running train) are known (representing the relationship between the amplitude and the spatial position and time), a key technical challenge is how to accurately load the dynamically changing load onto the discretized finite element model.

[0003] In related technologies, the load needs to be applied to a specific spatial position of the finite element model, and the model node number and spatial coordinates corresponding to the load instantaneous action point are usually determined first, but this is only applicable to static or simple cases of loading the load based on the nodes. In a non-uniform discretized finite element model, such as a case where the element longitudinal column length is inconsistent or the node number has no regularity, for a distributed load with continuous moving characteristics (such as a moving wheel-rail force), the load action position often changes with time and space, that is, it crosses different finite element units over time, and the instantaneous action point is generally located inside the unit and cannot directly correspond to the existing finite element node, and there is no accurate loading method. SUMMARY

[0004] The present application provides a method for applying moving load to a non-uniform discretized finite element model, which solves the technical problem in related technologies that there is no accurate method for applying moving load to a non-uniform discretized finite element model.

[0005] The present application provides a method for applying moving load to a non-uniform discretized finite element model, which includes the following steps:

[0006] Step S1, constructing a non-uniform discretized finite element model , determining the node number of each finite element node coord_Node and the corresponding spatial coordinates coord_Bri , The element length of the moving load is non-uniformly distributed;

[0007] Step S2, calculating the spatial position of the i moving load in the non-uniform discretized finite element model j at the time step ;

[0008] Step S3, determining whether the i moving load in the non-uniform discretized finite element model jFor each cell containing a moving load, the node number of the left node of that cell at that time step is obtained and defined as the trajectory matrix. track_N Calculate the distance between the moving load and the left node at that time step, and define it as a distance matrix. LN ;

[0009] Repeat steps S2 and S3 to obtain the trajectory matrix of all moving loads within the total time step. track_N Sum Distance Matrix LN ;

[0010] Step S4: Based on the trajectory matrix track_N Sum Distance Matrix LN Calculate the equivalent nodal forces borne by the left and right nodes of the element when the moving load is applied to the element.

[0011] In one implementation, step S3, determining the first i The time step j For each cell containing a moving load, the node number of the left node of that cell at that time step is obtained and defined as the trajectory matrix. track_N Calculate the distance between the moving load and the left node at that time step, and define it as a distance matrix. LN include:

[0012] Step S31: Based on the spatial location of the moving load, determine the first... i The time step j For each cell containing a moving load, the node number of the left node of that cell at that time step is obtained and defined as the trajectory matrix. track_N ;

[0013] Step S32: Calculate the distance between the moving load and the left node of the element where the moving load is located at the current time step based on the spatial location of the moving load and the spatial coordinates of the left node of the element where the moving load is located, and define it as a distance matrix. LN .

[0014] In one implementation, the determination condition in step S31 is:

[0015] like ,but track_N ;

[0016] in, h Number the nodes.

[0017] In one implementation, in step S32, the formula for calculating the distance matrix is: ;

[0018] in, the unit length corresponding to the unit where the mobile load acts.

[0019] In an embodiment, the step S4, calculating the equivalent nodal forces borne by the left and right nodes of the unit when the mobile load acts on the unit, further comprises: LN and the distance matrix track_N In an embodiment, the equivalent nodal forces borne by the left and right nodes of the unit when the mobile load acts on the unit are calculated according to the trajectory matrix

[0020] When a single mobile load acts on a unit, the equivalent nodal forces borne by the left and right nodes of the unit in a time step are calculated according to the trajectory matrix LN and the distance matrix track_N of the mobile load in the time step.

[0021] In an embodiment, the calculation formula is: ;

[0022] wherein, A is the left node of the unit, B is the right node of the unit, F is the force of the mobile load, a is the distance matrix of the mobile load, b is the distance of the mobile load from the right node, is the unit length corresponding to the unit where the mobile load acts.

[0023] In an embodiment, the step S4, calculating the equivalent nodal forces borne by the left and right nodes of the unit when the mobile load acts on the unit, further comprises: LN and the distance matrix track_N In an embodiment, the equivalent nodal forces borne by the left and right nodes of the unit when the mobile load acts on the unit are calculated according to the trajectory matrix

[0024] When multiple mobile loads act on a unit, the equivalent nodal forces borne by the left / right nodes of the unit when each mobile load acts on the unit are calculated according to the trajectory matrix LN and the distance matrix track_N of each mobile load in the same time step;

[0025] The equivalent nodal forces borne by the left / right nodes of the unit when each mobile load acts on the unit are superimposed to form the equivalent resultant force of the nodes.

[0026] In an embodiment, the step S4, calculating the equivalent nodal forces borne by the left and right nodes of the unit when the mobile load acts on the unit, further comprises: calculating the equivalent moments borne by the left and right nodes of the unit. LN and the distance matrix track_N In an embodiment, the equivalent nodal forces borne by the left and right nodes of the unit when the mobile load acts on the unit are calculated according to the trajectory matrix

[0027] In an embodiment, the calculation formula is: .

[0028] In one embodiment, in step S2, the spatial position of the first moving load in the non-uniformly discretized finite element model at the first time step is calculated according to the geometric distance and moving speed between the moving loads. i j .

[0029] The technical scheme provided by the embodiments of the present application has the following beneficial effects:

[0030] The present application provides a moving load application method for a non-uniformly discretized finite element model, which dynamically tracks and accurately locates the spatial position of a moving load and the finite element unit to which the action position of the moving load belongs and the corresponding node set (i.e. node number) and spatial coordinates of the node set within the full-time analysis range based on the given moving load and the unit column information of the non-uniformly discretized finite element model to be loaded, and synchronously determines the size (amplitude) of the equivalent moving load value acting on the nodes and the time-varying history of the equivalent moving load value, and accurately applies the moving load with different unit lengths and node numbers. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical scheme in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0032] LN The figure is a step flow chart of the moving load application method for a non-uniformly discretized finite element model in an embodiment of the present application.

[0033] Fig. 1 The figure is a schematic diagram of a single moving load acting on a unit in an embodiment of the present application. DETAILED DESCRIPTION

[0034] In order to enable those skilled in the art to better understand the technical scheme of the present application, the technical scheme in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0035] ​​​The embodiment of the application provides a mobile load application method for a non-uniform discretization finite element model, which can solve the technical problem that there is no accurate mobile load application method for the non-uniform discretization finite element model in the prior art.

[0036] As shown in Fig. 2 , Fig. 1 The step flow chart of the mobile load application method for the non-uniform discretization finite element model in the embodiment of the application is shown.

[0037] The embodiment of the application provides a mobile load application method for a non-uniform discretization finite element model, which includes the following steps:

[0038] Step S1, constructing a non-uniform discretization finite element model , determining the node number of each finite element node Fig. 1 and the corresponding spatial coordinates coord_Node , The unit length of the action of the mobile load presents a non-uniform distribution;

[0039] Step S2, calculating the spatial position of the first mobile load in the non-uniform discretization finite element model i at the first time step j ; Step S3, determining the unit in which the first mobile load is located at the first time step , obtaining the node number of the left node of the unit in which the mobile load is located at the time step, and defining the node number as a trajectory matrix

[0040] , calculating the distance of the mobile load from the left node at the time step, and defining the distance as a distance matrix i ; j coord_Bri Repeating step S2 and step S3 to obtain the trajectory matrix track_N and the distance matrix of all mobile loads in the total time step;

[0041] LN Step S4, according to the trajectory matrix track_N and the distance matrix , calculating the equivalent node force borne by the left node and the right node of the unit when the mobile load acts on the unit.

[0042] LN track_N

[0043] ​​​This embodiment provides a method for applying moving loads to a non-uniformly discretized finite element model. Based on the given moving load and the column information of the elements to be loaded in the non-uniformly discretized finite element model, the method dynamically tracks and accurately locates the spatial position of the moving load, as well as the finite element to which the moving load is applied and its corresponding set of nodes (i.e., node numbers) and spatial coordinates, within the entire time history analysis range. Simultaneously, the method determines the magnitude (amplitude) of the equivalent moving load acting on these nodes and its change history over time. With different element lengths and node numbers, the moving load is accurately applied, laying the foundation for the subsequent efficient and accurate assembly of the overall time history load vector.

[0044] The following provides a detailed explanation of each step.

[0045] In step S1, a non-uniform discretized finite element model is first constructed. The model consists of a series of finite element nodes and elements, and the node number of each finite element node is determined. LN and their corresponding spatial coordinates coord_Node This facilitates accurate loading in the subsequent finite element model; furthermore, node numbering... coord_Bri Its function is as a locator, establishing a mapping between the unique identifier of each node in the model and its specific location (coordinates) in space. Spatial coordinates coord_Node Its function is to be an ordered array containing the spatial locations of all nodes, which can be arranged according to the node number order or some spatial order, and serve as the direct data basis for executing the half-open and half-closed criterion of the coordinate interval. A moving load The length of the active element { } is a set that exhibits a non-uniform distribution, and is related to the non-uniform discretized finite element model. It is related to the spatial coordinates of the nodes.

[0046] In one embodiment, in step S2, the first... i The time step j A moving load in a non-uniformly discretized finite element model spatial location .

[0047] Specifically, spatial location The dimension is related to the number of time steps and the number of moving loads. Here, we assume the total number of time steps is... t num The number of moving loads is .

[0048] In one embodiment, step S3, determining the first i The time step jFor each cell containing a moving load, the node number of the left node of that cell at that time step is obtained and defined as the trajectory matrix. coord_Bri Calculate the distance between the moving load and the left node at that time step, and define it as a distance matrix. track_N include:

[0049] Step S31: Determine the first load based on its spatial location. i The time step j For each cell containing a moving load, the node number of the left node of that cell at that time step is obtained and defined as the trajectory matrix. LN ;

[0050] In one embodiment, in step S31, the determination condition is:

[0051] like ,but track_N ;

[0052] in, h Number the nodes.

[0053] Step S32: Calculate the distance between the moving load and the left node of the element where the moving load is located at the current time step based on the spatial location of the moving load and the spatial coordinates of the left node of the element where the moving load is located, and define it as a distance matrix. track_N .

[0054] In one embodiment, in step S32, the formula for calculating the distance matrix is: ;

[0055] in, The element length corresponding to the element subjected to the moving load.

[0056] The above scheme accurately determines the point of application of moving loads, iteratively searches and calculates spatial relationships for several load sources (furthermore, considering the case where a single element acts on multiple loads, iterative determination can be performed on all moving loads), and after identifying the element to which the moving load belongs, automatically extracts the adjacent node numbers and their reference coordinates associated with that element, instantly determining the specific finite element node (trajectory matrix) where the load point is currently located and its corresponding distance (distance matrix). Essentially, it records the element paths traversed by all moving loads throughout the entire time history, enabling each moving load at each time step to achieve a precise geometric association with the finite element model, thus jointly realizing the accurate mapping of dynamic loads.

[0057] In one embodiment, step S4, based on the trajectory matrix LN Sum Distance Matrix track_NWhen the moving load acts on the element, the equivalent node force borne by the left node and the right node of the element includes:

[0058] When a single moving load acts on a certain element, according to the trajectory matrix LN and the distance matrix track_N of the moving load at a certain time step, the equivalent node force borne by the left node and the right node of the element at the time step is calculated.

[0059] In an embodiment, the calculation formula is:

[0060] wherein, A the left node of the element is, B the right node of the element is, F the acting force of the moving load is, a the distance matrix of the moving load is, b the distance of the moving load from the right node is, the element length corresponding to the element on which the moving load acts is.

[0061] In an embodiment, step S4, according to the trajectory matrix LN and the distance matrix track_N of the moving load, the equivalent node force borne by the left node and the right node of the element when the moving load acts on the element further includes:

[0062] When multiple moving loads act on a certain element, according to the trajectory matrix LN and the distance matrix track_N of each moving load at the same time step, the equivalent node force borne by the left node / right node of the element when each moving load acts on the element is calculated.

[0063] The equivalent node forces borne by the left node / right node of the element when each moving load acts on the element are superimposed to form the equivalent resultant force of the nodes.

[0064] In an embodiment, step S4, according to the trajectory matrix LN and the distance matrix coord_Node of the moving load, the equivalent node force borne by the left node and the right node of the element when the moving load acts on the element further includes: calculating the equivalent moment borne by the left node and the right node of the element.

[0065] In an embodiment, the calculation formula is: .

[0066] Through the above scheme, the distributed load aggregation strategy is adopted to realize the equivalent superposition of multiple loads.

[0067] The following is described and explained through a specific embodiment.

[0068] ​This embodiment provides a method for applying moving loads to a non-uniformly discretized finite element model, which includes the following steps:

[0069] Step S1: In this embodiment, a simply supported beam model with a span of 150m is constructed. A non-uniform discretized element strategy is used to accurately simulate the geometric characteristics of the real bridge structure, thus constructing a non-uniform discretized finite element model. Node number coord_Bri =[11;2;301;45;5;76;72;8;94;100;10;], employing a non-continuous numbering strategy to simulate the heterogeneity of node IDs in actual engineering, reflecting the versatility of the modeling system. Its discrete non-uniform unit spatial coordinates are located as follows: track_N =[0;10;30;40;50;75;89;105;115;132;150;], defines the precise position of the nodes in the global coordinate system, where the first and last nodes (0m, 150m) correspond to the beam end support points. From this, the element length { }=[10;20;10;10;25;14;16;10;17;18;]. This simply supported beam model can simulate the case of non-uniform discrete elements.

[0070] Assume a train traveling at V = 100 km / h passes over a simply supported beam. The force exerted by the train on the bridge can be simplified as follows: n w =4 moving wheel and rail forces The negative sign indicates the vertical pressure load, measured in Newtons. Assuming each step represents 1.5 meters of movement from the moment the wheel-rail system enters the bridge to the moment it exits, the total time is calculated in steps. t num =101 time steps.

[0071] Step S2: Based on the spatial coordinates of the bridge's non-uniform discretized finite element model and the train's geometry, define four wheel-rail force position vectors at the initial time (t1) of the moving wheel-rail forces: =[0 -2.5 -18 -20.5], The dimension is t num *n w It can be seen that the first moving wheel-rail force is located exactly at the coordinates of the upper bridge node at the initial moment. The progress of the moving load with time step is shown in Table 1.

[0072] Table 1. Progression of moving load over time step

[0073]

[0074] Step S3: When the moving load, i.e., the four moving wheel-rail forces, begins to move on the model, taking the 20th time step as an example, the four moving wheel-rail forces on the model... The position in the middle is =[28.5 26 10.5 8], determine the first... i The time step j The trajectory matrix of the moving load at that time step is obtained by determining the cell where the moving load is located. LN Sum Distance Matrix track_N .

[0075] The judgment criteria are:

[0076] like ,

[0077] but LN , ;in, h Number the nodes. The element length corresponding to the element subjected to the moving load.

[0078] The forces on the four moving wheels and rails are determined according to the node number. track_N The process is repeated to determine whether the wheel-rail force is within a certain unit.

[0079] Repeat steps S2 and S3 to obtain the trajectory matrix of all moving loads within the total time step. LN Sum Distance Matrix track_N All dimensions t num *n w .

[0080] Step S4: Based on the trajectory matrix LN Sum Distance Matrix track_N Calculate the equivalent nodal forces borne by the left and right nodes of the element when a moving load is applied to it.

[0081] like LN As shown, taking the vertical force of the wheel and rail as an example (the principles of lateral and vertical forces are similar, only differing in direction), according to the principles of structural dynamics, we know that:

[0082] When a single moving load acts on a certain element, the nodal bending moment and nodal shear force borne by segments A and B are:

[0083] ;

[0084] ;

[0085] in, A The left node of the element. B The right node of the element. FFor the force of the moving load, a This is the distance matrix of the moving load. b The distance of the moving load from the right node. ( track_N LN coord_Node coord_Bri track_N LN track_N LN track_N LN track_N LN track_N LN track_N LN Fig. 2 Fig. 2 The middle is displayed as l ) represents the element length corresponding to the element subjected to the moving load.

[0086] When multiple moving loads act on different locations of a unit, each moving load is treated equivalently, and then the equivalent resultant force of the nodes is formed according to the principle of superposition of equivalent forces at the same nodes, thereby completing the equivalent superposition of multiple load sources within the same time step.

[0087] Taking the 20th time step as an example, the first, second, and third wheel-rail forces are located in the second unit, and the left and right nodes of the second unit are numbered 2 and 301, respectively. Taking the left node as the trajectory determination point for the moving wheel-rail forces, the trajectory node for the first, second, and third wheel-rail forces is 2, and the trajectory node for the fourth wheel-rail force is 301, that is... Based on the length of unit 2, the distances from the track nodes to the wheel-rail forces of units 1, 2, 3, and 4 are calculated as follows: Therefore, the orbital forces of the first, second, and third wheels need to be equivalently superimposed on the second unit.

[0088] The first round track force F1 = -132300, and the length of the assigned unit. Distance matrix , Substituting into the calculation formula, we get:

[0089] .

[0090] The second-round orbital force F2 = -132300, and the length of the assigned unit. Distance matrix , Substituting into the calculation formula, we get:

[0091] .

[0092] The third-round track force F3 = -132300, and the length of the assigned unit. Distance matrix , Substituting into the calculation formula, we get:

[0093] .

[0094] The fourth-round track force F4 = -132300, and the length of the assigned unit. Distance matrix , Substituting into the calculation formula, we get:

[0095] .

[0096] Based on the trajectory matrix of the four wheel-rail forces Then, the equivalent vertical resultant force at node 2 in the non-uniform discretized finite element model is:

[0097] .

[0098] The equivalent resultant force at node 3 is:

[0099] .

[0100] The equivalent resultant force of node 11 is:

[0101] .

[0102] The equivalent moments are similar to those above and will not be repeated here.

[0103] This allows us to obtain the equivalent resultant force of each node in the non-uniformly discretized finite element model that changes with the time step, thus enabling the accurate loading of the moving load onto the non-uniformly discretized finite element model.

[0104] It should be noted that the sequence numbers of the embodiments in this application are merely for descriptive purposes and do not represent the superiority or inferiority of the embodiments. The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not represent a sequential order, nor do they limit "first," "second," and "third" to different types.

[0105] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0106] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0107] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish the different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0108] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for applying moving loads to a non-uniformly discretized finite element model, characterized in that, It includes the following steps: Step S1, constructing a non-uniform discretized finite element model , determining the node number of each finite element node coord Node and its corresponding spatial coordinates coord_Bri , unit length of the action of the mobile load presents a non-uniform distribution; Step S2, calculating the spatial position of the first moving load at the first time step in the non-uniformly discretized finite element model i j ;​​​ Step S3, determine the first i The time step j For each cell containing a moving load, the node number of the left node of that cell at that time step is obtained and defined as the trajectory matrix. track_N Calculate the distance between the moving load and the left node at that time step, and define it as a distance matrix. LN ; Steps S2 and S3 are repeated to obtain trajectory matrices of all moving loads in total time steps track_N and distance matrices LN ; Step S4, calculating the equivalent node force of the left node and the right node of the unit when the moving load acts on the unit according to the trajectory matrix track_N and the distance matrix LN of the unit when the moving load acts on the unit The step S3 comprises: i The step S3 comprises: j The step S3 comprises: track_N The step S3 comprises: LN The step S3 comprises: Step S31, determining the cell where the mobile load is located at the first time step under the condition of the spatial position of the mobile load, obtaining the node number of the left node of the cell where the mobile load is located at the time step, and defining it as a trajectory matrix i . j . Step S32, determining the cell where the mobile load is located at the second time step under the condition of the spatial position of the mobile load, obtaining the node number of the left node of the cell where the mobile load is located at the time step, and defining it as a trajectory matrix track_N . Step S32, according to the time step of the mobile load space position and the mobile load left node of the unit space coordinates of the time step of the mobile load distance from the left node, defined as the distance matrix LN .

2. The method for applying moving loads to a non-uniformly discretized finite element model of claim 1, wherein, In step S31, the determination condition is: If then track_N=h ; wherein h is the node number.

3. The method for applying moving loads to a non-uniformly discretized finite element model of claim 2, wherein, In step S32, the distance matrix is calculated according to the following formula: ; wherein, The node number of the unit subjected to the moving load is h the corresponding unit length.

4. The method for applying moving loads to a non-uniformly discretized finite element model of claim 1, wherein, The step S4, according to the trajectory matrix track_N and distance matrix LN When the moving load acts on the unit, the equivalent node force borne by the left node and the right node of the unit comprises: When a single moving load acts on a certain element, the trajectory matrix of the moving load at a certain time step is used to calculate the equivalent nodal forces on the left and right nodes of the element at the time step track_N and the distance matrix LN The equivalent nodal forces on the left and right nodes of the element at the time step are calculated.

5. The method for applying moving loads to a non-uniformly discretized finite element model of claim 4, wherein, The calculation formula is: ; wherein, A is the left node of the element, B is the right node of the element, F is the force of the moving load, a is the distance matrix of the moving load, b is the distance of the moving load from the right node, is the element length corresponding to the element on which the moving load acts.

6. The method for applying moving loads to a non-uniformly discretized finite element model of claim 4, wherein, The step S4, according to the trajectory matrix track_N and distance matrix LN When the moving load acts on the unit, the equivalent node force borne by the left node and the right node of the unit also includes: When multiple moving loads act on a unit, the equivalent node force borne by the left node or the right node of the unit when each moving load acts on the unit is calculated according to the trajectory matrix of each moving load under the same time step and the distance matrix track N and the distance matrix LN When multiple moving loads act on a unit, the equivalent node force borne by the left node or the right node of the unit when each moving load acts on the unit is calculated according to the trajectory matrix of each moving load under the same time step and the distance matrix The equivalent node forces borne by the left node or the right node when each mobile load acts on the unit are superposed to form a node equivalent resultant force.

7. The method for applying moving loads to a non-uniformly discretized finite element model of claim 5, wherein, The step S4, according to the trajectory matrix track_N and distance matrix LN When the moving load acts on the element, the equivalent node forces borne by the left node and the right node of the element also include: calculating the equivalent moments borne by the left node and the right node of the element.

8. The method for applying moving loads to a non-uniformly discretized finite element model of claim 7, wherein, The calculation formula is: .

9. The method for applying moving loads to a non-uniformly discretized finite element model of claim 1, wherein, In step S2, the spatial position of the first moving load in the non-uniformly discretized finite element model at the first time step is calculated according to the geometric distance and moving speed between the moving loads. i j ​​​​

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