Railway pier digital twin non-node external load equivalent force calculation method

Abstract

The application discloses a railway bridge pier digital twin non-node external load equivalent force calculation method, which comprises the following steps: inputting overall size information of the bridge pier; inputting external load information acting on the bridge pier; dividing the bridge pier unit and nodes, and digitizing information of each unit and node; calculating a general formula of equivalent node force under the action of non-node concentrated load; calculating a general formula of equivalent node force under the action of non-node distributed load; converting the general formula of equivalent node force into a general complete solution format; and composing a general complete solution of equivalent node force of the bridge pier under the action of any load. Based on the mechanical equivalent principle, the application deduces the equivalent node force expression of the concentrated load and the distributed load, and through equivalent replacement of boundary conditions of each load working condition and the Heaviside function, the general complete solution of the equivalent node force of the bridge pier unit under the action of any form of concentrated load or distributed load is obtained, and then the railway bridge pier non-node external load equivalent node force calculation technology is established.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology in the transportation industry, specifically relating to a method for calculating the equivalent effect of non-node external loads on railway bridge piers using digital twins. Background Technology

[0002] In recent years, the national "eight vertical and eight horizontal" high-speed rail backbone network has been rapidly taking shape. In most high-speed rail projects, bridges account for over 50%, with simply supported standard beams being the most common. High-speed rail places extremely high demands on the safety of trains traveling on bridges and the comfort of passengers. Pier settlement, weak foundations, shrinkage and creep, and beam end displacement can all cause irreversible damage to the geometry of the track on the bridge, thus threatening the safety of high-speed rail operations. Pier stiffness and pier top displacement under external loads are crucial indicators affecting train operation safety during the design phase. The design phase must fully consider all construction and maintenance conditions, focusing on improving the calculation accuracy of external forces and deformations in the pier foundations to better maintain millimeter-level track smoothness from a design perspective.

[0003] To obtain high-precision calculation results, the finite element method (FEM) is often used, along with strategies to improve element accuracy. However, FEM modeling is not suitable for large-scale high-speed railway bridge design processes. Existing pier design manuals and software use the unit force method based on elastic assumptions, considering the elastic stiffness of the pier itself. However, the unit force modeling method cannot accurately handle concentrated and distributed loads acting on non-nodes, resulting in lower calculation accuracy when faced with distributed loads such as wind and earth pressure acting on the piers, or when multiple types of loads act together.

[0004] To address the aforementioned issues, it is essential to develop a method for calculating the equivalent effect of non-nodal external loads on railway bridge piers using digital twins. This method would systematically solve the problem of accurately calculating the external loads on railway bridge piers in a real-world environment using twin models. Summary of the Invention

[0005] This invention is proposed to solve the problems existing in the prior art, and its purpose is to provide a method for calculating the equivalent effect of non-node external loads of railway bridge piers using digital twins.

[0006] The technical solution of this invention is: a method for calculating the equivalent effect of non-nodal external loads on railway bridge piers using digital twins, comprising the following steps:

[0007] A. Obtain the overall dimensions of the bridge piers;

[0008] B. Obtain information on external loads acting on the bridge piers;

[0009] C. Based on the overall dimensions of the piers, divide the piers into units and nodes, and digitize the information of each unit and node;

[0010] D. Based on the pier unit and external load information, calculate the general formula for the equivalent nodal force under non-nodal concentrated load;

[0011] E. Based on the pier unit and external load information, divide the actual stress conditions and calculate the general formula for the equivalent nodal force under non-nodal distributed loads.

[0012] F. Convert the general formulas for the equivalent nodal forces in the above two steps into a general complete solution format;

[0013] G. Based on the general complete solution format, the general complete solution of the equivalent nodal force of the bridge pier under any load is obtained.

[0014] Step A: Obtain the overall size information of the bridge pier. The overall size information is derived from the physical entity model of the railway bridge pier and includes the height of the bridge pier, the coordinates and outline dimensions of the top and bottom of the pier, and the geometric shape information from the top to the bottom of the pier.

[0015] In step B, the external load information acting on the bridge pier is obtained. The external load information includes concentrated loads and distributed loads acting on the bridge pier.

[0016] Step C involves dividing the piers into units and nodes based on their overall dimensions, and digitizing the information of each unit and node. The specific process is as follows:

[0017] First, the bridge piers are divided into segments along their height to obtain the bridge pier elements and their corresponding nodes;

[0018] Then, the height of each pier unit, the cross-sectional profile information of the upper and lower ends of the pier unit, and the variation law within the height range are calculated.

[0019] Then, the coordinates of each node are calculated.

[0020] Step D: Based on the pier element and external load information, calculate the general formula for the equivalent nodal force under non-nodal concentrated loads. The specific process is as follows:

[0021] First, the specific location of the non-node concentrated load acting on the pier element is determined by combining the external load information and the element node information.

[0022] Then, based on the resultant force and moment balance equations, the equivalent nodal forces acting on the upper and lower nodes of the corresponding pier element are solved.

[0023] Step E involves dividing the actual stress conditions based on the pier elements and external load information, and calculating the general formula for the equivalent nodal force under non-nodal distributed loads. The specific process is as follows:

[0024] First, based on the distribution range and relative position of the distributed load and the pier unit, four actual stress conditions are identified.

[0025] Then, the height of the overlapping part of the two is calculated based on the geometric relationship between the distributed loads under each working condition and the pier unit.

[0026] Then, based on the mechanical similarity triangles, the upper and lower boundary loads, the center of bending moment, and their graphical area of ​​the overlapping loads are solved.

[0027] Then, based on the force and moment balance relationship, the equivalent nodal forces acting on the upper and lower nodes of the corresponding pier element are solved.

[0028] Step F transforms the general formulas for the equivalent nodal forces from the above two steps into a universal complete solution scheme. The specific process is as follows:

[0029] First, establish the relationship between the boundary conditions of non-nodal concentrated loads and distributed loads for each calculation case and the Headside function;

[0030] Then, the general formulas of the equivalent nodal forces for the corresponding working conditions obtained in steps D and E are converted into a general complete solution format based on the Headside function.

[0031] Then, by superimposing the universal complete solution for all possible working conditions, the corresponding equivalent nodal forces are obtained.

[0032] Step G, based on the general complete solution format, yields the general complete solution of the equivalent nodal forces of the bridge pier under any load. The specific process is as follows:

[0033] First, each arbitrary load acting on the pier unit is classified as either a concentrated load or a distributed load.

[0034] Then, the relevant parameter information for each arbitrary load is digitized;

[0035] Then, the equivalent nodal load expression under arbitrary loads is obtained by using the general complete solution based on the Headside function calculated in step F.

[0036] The beneficial effects of this invention are as follows:

[0037] This invention addresses the problem of calculating the equivalent nodal forces of non-nodal external loads in the digital twin simulation model of railway bridge piers. Based on the principle of mechanical equivalence, it derives the equivalent nodal force expressions for concentrated and distributed loads. By equivalently replacing the boundary conditions of each load case with the Heaviside function, it obtains a general and complete solution for the equivalent nodal forces of pier elements under any form of concentrated or distributed load, thus establishing a technology for calculating the equivalent nodal forces of non-nodal external loads on railway bridge piers.

[0038] This invention can accurately simulate non-node concentrated loads and distributed loads in digital twin simulation models of bridge piers with constant or variable cross sections in the transportation field, thus solving the accuracy problem of digital twin models. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the steps of the present invention;

[0040] Figure 2 This is a schematic diagram of the concentrated load acting on the pier unit in this invention;

[0041] Figure 3 This is a schematic diagram of the distributed load acting on the pier unit in this invention;

[0042] Figure 4 This is a schematic diagram of six working conditions of distributed load in this invention;

[0043] Figure 5 This is a schematic diagram of the equivalent load calculation for distributed load case 2 in this invention;

[0044] Figure 6 This is a schematic diagram of the equivalent load calculation for distributed load case 3 in this invention;

[0045] Figure 7 This is a schematic diagram of the equivalent load calculation for distributed load case 4 in this invention;

[0046] Figure 8 This is a schematic diagram of the equivalent load calculation for distributed load case 6 in this invention;

[0047] Figure 9 This is a schematic diagram of the bridge pier unit bearing various external loads in this invention;

[0048] Figure 10 This is a diagram showing the Midas calculation model and calculation results under unit force in an embodiment of the present invention;

[0049] Figure 11 This is a diagram of the input interface of the present invention under unit force.

[0050] Figure 12 This is a diagram showing the Midas calculation model and calculation results under lateral wind force in an embodiment of the present invention;

[0051] Figure 13 This is a diagram of the input interface of the present invention under lateral wind force. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings and embodiments:

[0053] like Figures 1 to 13As shown, a method for calculating the equivalent effect of non-nodal external loads on railway bridge piers using digital twins includes the following steps:

[0054] A. Obtain the overall dimensions of the bridge piers;

[0055] B. Obtain information on external loads acting on the bridge piers;

[0056] C. Based on the overall dimensions of the piers, divide the piers into units and nodes, and digitize the information of each unit and node;

[0057] D. Based on the pier unit and external load information, calculate the general formula for the equivalent nodal force under non-nodal concentrated load;

[0058] E. Based on the pier unit and external load information, divide the actual stress conditions and calculate the general formula for the equivalent nodal force under non-nodal distributed loads.

[0059] F. Convert the general formulas for the equivalent nodal forces in the above two steps into a general complete solution format;

[0060] G. Based on the general complete solution format, the general complete solution of the equivalent nodal force of the bridge pier under any load is obtained.

[0061] Step A: Obtain the overall size information of the bridge pier. The overall size information is derived from the physical entity model of the railway bridge pier and includes the height of the bridge pier, the coordinates and outline dimensions of the top and bottom of the pier, and the geometric shape information from the top to the bottom of the pier.

[0062] like Figure 2 , Figure 3 As shown, in step B, the external load information acting on the bridge pier is obtained. The external load information includes concentrated loads and distributed loads acting on the bridge pier.

[0063] Step C involves dividing the piers into units and nodes based on their overall dimensions, and digitizing the information of each unit and node. The specific process is as follows:

[0064] First, the bridge piers are divided into segments along their height to obtain the bridge pier elements and their corresponding nodes;

[0065] Then, the height of each pier unit, the cross-sectional profile information of the upper and lower ends of the pier unit, and the variation law within the height range are calculated.

[0066] Then, the coordinates of each node are calculated.

[0067] like Figure 2 As shown, step D calculates the general formula for the equivalent nodal force under non-nodal concentrated loads based on the pier element and external load information. The specific process is as follows:

[0068] First, the specific location of the non-node concentrated load acting on the pier element is determined by combining the external load information and the element node information.

[0069] Then, based on the resultant force and moment balance equations, the equivalent nodal forces acting on the upper and lower nodes of the corresponding pier element are solved.

[0070] like Figures 3-8 As shown, step E involves dividing the actual stress conditions based on the pier elements and external load information, and calculating the general formula for the equivalent nodal force under non-nodal distributed loads. The specific process is as follows:

[0071] First, based on the distribution range and relative position of the distributed load and the pier unit, four actual stress conditions are identified.

[0072] Then, the height of the overlapping part of the two is calculated based on the geometric relationship between the distributed loads under each working condition and the pier unit.

[0073] Then, based on the mechanical similarity triangles, the upper and lower boundary loads, the center of bending moment, and their graphical area of ​​the overlapping loads are solved.

[0074] Then, based on the force and moment balance relationship, the equivalent nodal forces acting on the upper and lower nodes of the corresponding pier element are solved.

[0075] Step F transforms the general formulas for the equivalent nodal forces from the above two steps into a universal complete solution scheme. The specific process is as follows:

[0076] First, establish the relationship between the boundary conditions of non-nodal concentrated loads and distributed loads for each calculation case and the Headside function;

[0077] Then, the general formulas of the equivalent nodal forces for the corresponding working conditions obtained in steps D and E are converted into a general complete solution format based on the Headside function.

[0078] Then, by superimposing the universal complete solution for all possible working conditions, the corresponding equivalent nodal forces are obtained.

[0079] like Figure 9 As shown, step G, based on the general complete solution format, yields the general complete solution of the equivalent nodal forces of the bridge pier under any load. The specific process is as follows:

[0080] First, each arbitrary load acting on the pier unit is classified as either a concentrated load or a distributed load.

[0081] Then, the relevant parameter information for each arbitrary load is digitized;

[0082] Then, the equivalent nodal load expression under arbitrary loads is obtained by using the general complete solution based on the Headside function calculated in step F.

[0083] Specifically, the concentrated load information acting on the bridge pier obtained in step B includes the magnitude of the concentrated load, the point of application, and the distance of the application location from the origin of the coordinate system.

[0084] Specifically, the distributed load information acting on the bridge pier obtained in step B includes the magnitude of the upper and lower boundary loads of the distributed load, the height of the distributed load, the moment center of the distributed load, and the variation law of the distributed load along the distribution range.

[0085] Specifically, step D requires calculating the general formula for the equivalent nodal force under non-nodal concentrated loads. The specific process is as follows:

[0086] like Figure 2 As shown, by listing the equations for the resultant force and moment equilibrium, we can obtain:

[0087] (1)

[0088] Therefore, we can conclude that:

[0089] (2)

[0090] In the diagram and expression, F k , F k+1 They are nodes k , k +1 requires solving for the equivalent nodal forces of the concentrated load; for the pier element, its two end nodes are k , k +1, its distance from the coordinate axis y The distances are respectively x k , x k+1 ; l k Let be the geometric length of the pier element; the magnitude of the concentrated force acting on the pier element is . C k Distance from node k The distance is l c Distance from coordinate axis y The distance is x ck .

[0091] Specifically, step E calculates the general formula for the equivalent nodal force under non-nodal distributed loads, and the specific process is as follows:

[0092] For distributed loads, such as Figure 3 As shown, let the upper and lower boundary sizes of the distributed load be... p 1.p 2; Distributed load along the coordinate axes x The size is p ( x The height of the distributed load is... l p ;point c The moment center of the distributed load; x c This is the distance from the center of the load moment to the upper edge of the distributed load; x pe , x ps These represent the distances from the upper and lower boundaries of the distributed load to the coordinate axes, respectively. y The distance is the same as before, and the other variables are the same as before.

[0093] Based on the equilibrium condition of force and torque, the following calculation equation can be obtained:

[0094] (3)

[0095] In the formula, S This represents the area of ​​the distributed loads in the diagram.

[0096] Furthermore, because the distributed load and the pier element have their own distribution range and relative positional relationship, the specific expression of formula (3) will differ. Figure 3 The coordinate relationship shown can be obtained through distributed load boundary parameters. x pe , x ps Boundary parameters of bridge pier elements x k , x k+1 Based on the relationship, the stress conditions of the bridge pier unit are divided into the following categories of working conditions, and the correspondence between different working conditions and each parameter is shown in Table 1.

[0097]

[0098] Table 1 lists the operating conditions corresponding to operating conditions 1 through 6. Each operating condition is shown in Table 1. Figure 4 From the relative positional relationship between the distributed force and the pier element in the figure, it can be seen that there is no load transfer relationship between working conditions 1 and 5. The other four working conditions all require equivalent conversion of the distributed load. The general formulas for the four working conditions are derived below.

[0099] First, derive the general formula for the equivalent load in load case 2.

[0100] like Figure 5 As shown, the distributed load is assumed to be trapezoidal, with the load magnitudes at its upper and lower boundaries being... p 1. p2; The loads corresponding to the upper and lower boundaries of the overlapping portion of the distributed load and the pier unit are the overlapping loads. The overlapping loads are respectively p k , p k+1 The center of bending moment of overlapping loads is denoted as ck Its distance to the upper boundary of the overlapping load is x ck The height of the overlapping load is l pk The meanings of the remaining parameters are the same as those above.

[0101] Depend on Figure 5 The geometric relationship can be used to obtain the height of the overlapping load.

[0102] (4)

[0103] The upper and lower boundary loads of the overlapping load are obtained from the diagram and mechanical similarity triangles, and their expressions are as follows:

[0104] (5)

[0105] Center of bending moment of overlapping load x ck and its graph area S for:

[0106] (6)

[0107] Substituting formulas (5) and (6) into formula (3), we obtain the equivalent nodal force as follows:

[0108] (7)

[0109] During the calculation, the center of the bending moment of the overlapping load x ck That is, formula (3) x c .

[0110] Then, the general formula for the equivalent load in load case 3 is derived.

[0111] Figure 6 The calculation diagram for load case 3 is given. Unlike load case 2, the upper boundary of the overlapping load is determined by the pier element. k The location of the nodes determines the physical meaning of each parameter in the figure, which is the same as in case 2. The calculation process for solving the equivalent load is given below.

[0112] Height of overlapping load

[0113] (8)

[0114] The boundary load corresponding to the overlapping load is

[0115] (9)

[0116] Center of bending moment of overlapping load x ck and its graph area S The calculation formula is the same as formula (6).

[0117] The equivalent nodal force is:

[0118] (10).

[0119] Then, the general formula for the equivalent load of load case 4 is derived.

[0120] Figure 7 The calculation diagram for load case 4 is given. Unlike load case 3, the lower boundary position of the overlapping load is determined by the lower boundary position of the distributed load. The physical meaning of each parameter in the diagram is the same as that of the previous load cases. The calculation process for solving the equivalent load is given below.

[0121] Height of overlapping load

[0122] (11)

[0123] The boundary load corresponding to the overlapping load is

[0124] (12)

[0125] Center of bending moment of overlapping load x ck and its graph area S The calculation formula is the same as formula (6); the expression for the equivalent nodal force is the same as formula (10).

[0126] Finally, the general formula for the equivalent load in load case 6 is derived.

[0127] Figure 8 The calculation diagram for load case 6 is given. In this case, the upper and lower boundaries of the overlapping load are the same as the upper and lower boundaries of the distributed load. The physical meaning of each parameter in the diagram is the same as that of the previous load case. The calculation process for solving the equivalent load is given below.

[0128] Height of overlapping load

[0129] (13)

[0130] The boundary load corresponding to the overlapping load is

[0131] (14)

[0132] Center of bending moment of overlapping load xck and its graph area S The calculation formula is the same as formula (6); the expression for the equivalent nodal force is the same as formula (7).

[0133] Specifically, step F transforms the general formula for equivalent nodal forces into a universal complete solution scheme. The specific process is as follows:

[0134] The introduced Heavside function has the following expression:

[0135] (15)

[0136] For example Figure 2 The concentrated load shown in the equation holds true under the condition that the concentrated load is within the range of the pier element, that is, it satisfies the condition that... x k ≤ x ck ≤ x k+1 The boundary conditions are required. These boundary conditions can be expressed using the Heavyside function as follows: H ( x ck－ x k ) H ( x k+1－ x ck Therefore, the complete solution formula for the equivalent nodal forces of a bridge pier element after any concentrated load is obtained as follows:

[0137] (16).

[0138] Correspondingly, for the six working conditions under which distributed loads act on the bridge piers, the equivalent transformation relationship between each boundary condition and the Heaviside function can be shown in Table 2.

[0139]

[0140] Based on this equivalent transformation relationship, the six working conditions of distributed load can be superimposed to obtain a general complete solution of the equivalent nodal force of distributed load.

[0141] For simplicity, the equivalent nodal forces corresponding to working conditions 2, 3, 4, and 6 are represented by subscripts ",". i ( i= "2,3,4,6)" means, for example F k,2 Indicates the equivalent nodal force in working condition 2 F k , F k+1,6 Indicates the equivalent nodal force for load case 6.F k+1 .

[0142] By combining the boundary conditions corresponding to each working condition, the expressions based on the Heaviside function for working conditions 2, 3, 4, and 6 can be obtained. The specific solution process is as follows:

[0143] As shown in Table 1, operating condition 2 requires simultaneous fulfillment of ( x k+1 ≤ x pe ≤ x k )∪( x ps < x k+1 The corresponding expression for the Heavside function is: H ( x k－ x pe ) × H ( x pe－ x k+1 )× H ( x k+1－ x ps If ), then the equivalent nodal force can be written as

[0144] (17).

[0145] Operating condition 3 requires simultaneous fulfillment of ( x pe > x k )∪( x ps < x k+1 The corresponding expression for the Heavside function is: H ( x pe－ x k )× H ( x k+1－ x ps If ), then the equivalent nodal force can be written as

[0146] (18).

[0147] Operating condition 4 requires simultaneous fulfillment of ( x pe > x k)∪( x k+1 ≤ x ps ≤ x k The corresponding expression for the Heavside function is: H ( x pe－ x k )× H ( x k－ x ps ) H ( x ps－ x k+1 If ), then the equivalent nodal force can be written as

[0148] (19).

[0149] Operating condition 6 requires simultaneous fulfillment of ( x k+1 ≤ x pe ≤ x k )∪( x k+1 ≤ x ps ≤ x k The corresponding expression for the Heavside function is: H ( x k－ x pe ) H ( x pe－ x k+1 )× H ( x k－ x ps ) H ( x ps－ x k+1 If ), then the equivalent nodal force can be written as

[0150] (20).

[0151] By superimposing the equivalent nodal force expressions for load cases 2, 3, 4, and 6, the complete solution formula for the equivalent nodal force of the pier element after any distributed load is obtained as follows:

[0152] (twenty one)

[0153] Specifically, step G, based on the general complete solution scheme, yields the general complete solution of the equivalent nodal forces of the bridge pier under any load. The specific process is as follows:

[0154] for Figure 9 In the case of multiple concentrated loads and multiple distributed loads acting on the same pier element, it is only necessary to substitute the properties of each concentrated load into formula (16) and the properties of each distributed load into formula (21), and then superimpose them to obtain the equivalent nodal force after the combined action of these loads.

[0155] Example 1

[0156] This invention was used to verify the displacement of the pier top of a hollow variable cross-section bridge pier under two test conditions: concentrated force and distributed force. During the test, the algorithm of this invention was incorporated into the self-designed software.

[0157] The pier of the round-ended hollow variable cross section is 50m high. The bottom of the abutment is fixed. The pier body is divided into three sections along the pier height. The information of each section of the abutment is shown in Table 3.

[0158]

[0159] Test condition 1 involves applying a unit force along the bridge direction at the pier top. Figure 10 The model is for the corresponding commercial finite element software MIDAS Civil. Figure 11 To design the input interface for the software independently.

[0160] Test condition 2 involves applying a longitudinal wind load to the side of the bridge pier, with a basic wind pressure of 0.6 kPa. The relevant wind load parameters are as follows: K 1 = 1.1, K 2=1, K 3=1, calculate the displacement of the pier top caused by wind force. Figure 12 The model is for the corresponding commercial finite element software MIDAS Civil. Figure 13 To design the input interface for the software independently.

[0161] The calculation results for the two test conditions were extracted with the same precision and listed in Table 4.

[0162]

[0163] As shown in Table 4, the maximum error between the calculation results derived by the present invention and the calculation results of MIDAS Civil software is 0.19%, which is no more than 0.2%.

[0164] Therefore, it can be seen that the method for calculating the equivalent effect of non-node external loads in the digital twin of railway bridge piers described in this invention meets the requirements of digital twin simulation in actual engineering.

[0165] This invention addresses the problem of calculating the equivalent nodal forces of non-nodal external loads in the digital twin simulation model of railway bridge piers. Based on the principle of mechanical equivalence, it derives the equivalent nodal force expressions for concentrated and distributed loads. By equivalently replacing the boundary conditions of each load case with the Heaviside function, it obtains a general and complete solution for the equivalent nodal forces of pier elements under any form of concentrated or distributed load, thus establishing a technology for calculating the equivalent nodal forces of non-nodal external loads on railway bridge piers.

[0166] This invention can accurately simulate non-node concentrated loads and distributed loads in digital twin simulation models of bridge piers with constant or variable cross sections in the transportation field, thus solving the accuracy problem of digital twin models.

Claims

1. A method for calculating the equivalent effect of non-nodal external loads on railway bridge piers using digital twins, characterized in that: Includes the following steps: (A) Obtain the overall dimensions of the bridge piers; (B) Obtain information on external loads acting on the bridge piers; (C) Based on the overall dimensions of the piers, divide the piers into units and nodes, and digitize the information of each unit and node; (D) Based on the pier unit and external load information, calculate the general formula for the equivalent nodal force under non-nodal concentrated load; (E) Based on the pier unit and external load information, divide the actual stress conditions and calculate the general formula of the equivalent nodal force under non-nodal distributed load respectively; (F) Transform the general formula for the equivalent nodal forces from the above two steps into a general complete solution scheme; (G) Based on the general complete solution format, the general complete solution of the equivalent nodal force of the bridge pier under any load is obtained; Step (E) involves dividing the actual stress conditions based on the pier elements and external load information, and calculating the general formula for the equivalent nodal force under non-nodal distributed loads. The specific process is as follows: First, based on the distribution range and relative position of the distributed load and the pier unit, four actual stress conditions are identified. Then, the height of the overlapping part of the two is calculated based on the geometric relationship between the distributed loads under each working condition and the pier unit. Then, based on the mechanical similarity triangles, the upper and lower boundary loads, the center of bending moment, and their graphical area of ​​the overlapping loads are solved. Then, based on the force and moment balance relationship, the equivalent nodal forces acting on the upper and lower nodes of the corresponding pier element are solved.

2. The method for calculating the equivalent effect of non-nodal external loads of railway bridge piers using digital twins according to claim 1, characterized in that: Step (A) Obtain the overall size information of the bridge pier. The overall size information is derived from the physical entity model of the railway bridge pier. The overall size information includes the height of the bridge pier, the coordinates and outline dimensions of the top and bottom of the pier, and the geometric shape information from the top to the bottom of the pier.

3. The method for calculating the equivalent effect of non-nodal external loads of railway bridge piers using digital twins according to claim 1, characterized in that: In step (B), the external load information acting on the bridge pier is obtained, which includes concentrated loads and distributed loads acting on the bridge pier body.

4. The method for calculating the equivalent effect of non-nodal external loads of a railway bridge pier using a digital twin as described in claim 1, characterized in that: Step (C) Based on the overall dimensions of the bridge piers, divide the piers into units and nodes, and digitize the information of each unit and node. The specific process is as follows: First, the bridge piers are divided into segments along their height to obtain the bridge pier elements and their corresponding nodes; Then, the height of each pier unit, the cross-sectional profile information of the upper and lower ends of the pier unit, and the variation law within the height range are calculated. Then, the coordinates of each node are calculated.

5. The method for calculating the equivalent effect of non-nodal external loads of railway bridge piers using digital twins according to claim 1, characterized in that: Step (D) Based on the pier element and external load information, calculate the general formula for the equivalent nodal force under non-nodal concentrated loads. The specific process is as follows: First, the specific location of the non-node concentrated load acting on the pier element is determined by combining the external load information and the element node information. Then, based on the resultant force and moment balance equations, the equivalent nodal forces acting on the upper and lower nodes of the corresponding pier element are solved.

6. The method for calculating the equivalent effect of non-nodal external loads of railway bridge piers using digital twins according to claim 1, characterized in that: Step (F) transforms the general formulas for the equivalent nodal forces from the above two steps into a general complete solution scheme. The specific process is as follows: First, establish the relationship between the boundary conditions of non-nodal concentrated loads and distributed loads for each calculation case and the Headside function; Then, the general formulas of the equivalent nodal forces for the corresponding working conditions obtained in steps (D) and (E) are converted into a general complete solution format based on the Headside function; Then, by superimposing the universal complete solution for all possible working conditions, the corresponding equivalent nodal forces are obtained.

7. The method for calculating the equivalent effect of non-nodal external loads of railway bridge piers using digital twins according to claim 1, characterized in that: Step (G) derives the general complete solution for the equivalent nodal forces of the bridge piers under any load, based on the general complete solution scheme. The specific process is as follows: First, each arbitrary load acting on the pier unit is classified as either a concentrated load or a distributed load. Then, the relevant parameter information for each arbitrary load is digitized; Then, the equivalent nodal load expression under arbitrary loads is obtained by using the general complete solution based on the Headside function calculated in step (F).

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