Arch bridge negative angle vertical rotation whole process continuous calculation method and system

Abstract

The present disclosure provides a continuous calculation method and system for the whole process of negative angle vertical rotation of an arch bridge, which is applied to the technical field of bridge structure construction and comprises the following steps: constructing an arch bridge vertical rotation model based on the design parameters of the arch bridge vertical rotation structure, wherein the arch bridge vertical rotation model comprises a cable simulation unit, and the cable simulation unit comprises a plurality of straight rod units; inputting the arch bridge design parameters and the unstressed length in the initial state into the arch bridge vertical rotation model, simulating the construction process by using the arch bridge vertical rotation model, inputting the sub-variation of the calculated unstressed length in sequence, and simulating and calculating the cable force and control parameters of the cable component in different states until the vertical rotation process is completed; the present disclosure is simple, flexible and high-precision, can truly reflect the changes of the cable quality and stiffness, and is suitable for scenes such as steep valleys and busy traffic lines.

Description

Technical Field

[0001] This disclosure relates to the field of bridge structure construction technology, and in particular to a method and system for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge. Background Technology

[0002] Bridge rotation is a construction method that involves rotating a bridge structure into position in a vertical plane. Depending on the direction of rotation, it can be divided into two types: positive angle rotation and negative angle rotation. Positive angle rotation, due to clearance requirements under the bridge, is easily constrained by terrain, waterways, or existing facilities, often requiring the erection of tall temporary towers and the provision of significant lifting force. In contrast, negative angle rotation uses a "lowering" lowering method, effectively overcoming these limitations. It offers advantages such as no need for temporary under-bridge supports, lower lifting force requirements, better economic efficiency, and less interference with activities under the bridge, making it suitable for arch bridge construction in steep valleys, busy traffic routes, and other similar scenarios.

[0003] However, during the negative-angle vertical rotation of the arch bridge, the structure is in a complex dynamic equilibrium state. After the vertical rotation construction begins, there is initially a traction phase, where rotation is achieved by tensioning the cables, followed by a lowering phase. At this point, the structure's gravity becomes a crucial factor in inducing dynamic rotation. Improper control during either the traction or lowering phase can easily lead to safety accidents. To ensure lowering speed, morphological accuracy, and structural stability, construction calculations must possess high precision, dynamic continuity, and adaptability to construction deviations.

[0004] Currently, the construction calculation for bridge vertical rotation generally adopts the discrete static simulation method, that is, establishing independent finite element models for static analysis under multiple preset vertical rotation angles. This method has significant limitations:

[0005] First, its essence is to discretize the continuous large displacement geometric nonlinear calculation process into multiple isolated static postures, which cannot simulate the continuous deformation of the structure. Second, there is a lack of parameterized correlation between the models. When deviations occur during construction, all subsequent models need to be manually rebuilt and recalculated one by one. The manpower and time costs are high and the cycle is long. It is difficult to achieve real-time tracking and predictive control of the construction process, and it cannot meet the fine control requirements of negative angle vertical rotation.

[0006] Therefore, there is an urgent need for a new calculation method that can realistically simulate the entire process of the negative angle vertical rotation of an arch bridge, so as to achieve full-process, dynamic, and continuous simulation from the start of the rotation to the positioning, and to have parametric modeling capabilities, so that the entire analysis process can be more efficient and convenient while ensuring high accuracy, in order to cope with complex actual construction conditions. Summary of the Invention

[0007] This disclosure provides a method and system for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge, which solves the problems that traditional methods cannot simulate continuous structural deformation, lack parameter correlation between models, and require a large amount of work to modify the model when adjusting the construction plan during negative angle vertical rotation.

[0008] According to a first aspect of this disclosure, a method for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge is provided. The method includes:

[0009] An arch bridge vertical rotation model is constructed based on the design parameters of the arch bridge vertical rotation structure. The arch bridge vertical rotation model includes a cable simulation unit, which includes multiple straight bar units.

[0010] The arch bridge design parameters and the stress-free length in the initial state are input into the arch bridge vertical rotation model. The construction process is simulated using the arch bridge vertical rotation model. The sub-variables of the calculated stress-free length are input sequentially to simulate and calculate the cable force and control parameters of the cable members under different states until the vertical rotation process is completed.

[0011] The sub-variable is obtained by dividing the total variable into N-1 groups. The total variable is based on the stress-free length of the cable member in the initial state and the stress-free length in the final state in the vertical rotation structure of the arch bridge. N is a natural number greater than 1.

[0012] The calculation process for the stress-free length in the initial state specifically includes:

[0013] Based on the initial state of the arch bridge before the vertical rotation of the structure is started, an initial state calculation model is established by combining the arch rib coordinates and cable positions, and the initial cable force corresponding to the cable member in this state is solved.

[0014] The stress-free length in the initial state is calculated based on the correlation between the initial cable force, the actual stressed length of the cable member, the elastic elongation induced by the cable force, and the sag correction length; among which,

[0015] The sag correction length is used to compensate for the sag effect caused by the self-weight of the cable component, and the elastic elongation is used to reflect the material deformation characteristics of the cable component under the action of cable force.

[0016] The calculation process for the stress-free length in the final state is the same as that for the stress-free length in the initial state.

[0017] Furthermore, the construction process is simulated using the arch bridge vertical rotation model. Corresponding sub-variables are input, and the cable forces and control parameters of the cable-stayed components are calculated until the vertical rotation process is completed, including:

[0018] Entering the current construction phase;

[0019] Determine whether the current construction stage is the first stage. If so, the stress-free length sub-change obtained by the cable simulation unit is 0, and the next construction stage is taken as the current construction stage, and the previous step is entered. If not, the stress-free length sub-change obtained by the cable simulation unit for the corresponding construction stage is superimposed to calculate the stress-free length corresponding to the cable simulation unit for the current construction stage.

[0020] Based on the stress-free length of the cable simulation unit at the current construction stage, the tangent stiffness matrix and load array are calculated.

[0021] Large displacement nonlinear calculations are performed in the vertical rotation model of the arch bridge, and convergence is determined by the unbalanced force criterion. The cable force and control parameters of the cable members in the current construction stage are output.

[0022] Determine whether the vertical rotation process is complete. If yes, end the process; otherwise, proceed to the next construction stage and return to step one.

[0023] Furthermore, the calculation process of the tangent stiffness matrix specifically includes the following steps:

[0024] Construct a structural coordinate system and a co-rotating coordinate system, and determine the relationship between the displacement vector of the cable simulation element and the nodal coordinates;

[0025] The elongation of the straight bar element under load at different times and the corresponding element attitude angle are determined based on the relationship between the displacement vector and the nodal coordinates.

[0026] Based on the unit attitude angle and elongation, the rod end force vectors corresponding to the straight rod unit in the co-rotation coordinate system and the structural coordinate system are calculated.

[0027] Differentiating the rod end force in the co-rotation coordinate system yields the correlation between the rod end force increment and the axial deformation increment; differentiating the rod end force in the structural coordinate system yields the correlation between the rod end force increment and the angle change increment; based on the element attitude angle and elongation, the correlation between the axial deformation increment and the nodal displacement increment is calculated.

[0028] The tangent stiffness matrix is ​​calculated based on the correlation between the increment of bar end force and the increment of axial deformation, the correlation between the increment of bar end force and the increment of angle change, and the correlation between the increment of axial deformation and the increment of nodal displacement.

[0029] Furthermore, the tangent stiffness matrix is ​​obtained by adding the linear stiffness matrix and the geometric stiffness matrix;

[0030] The linear stiffness matrix is ​​calculated based on the elastic modulus, cross-sectional area, stress-free length in the initial state, and element orientation angle of the cable member.

[0031] The geometric stiffness matrix is ​​calculated based on the axial deformation of the cable member and the angle of the element orientation.

[0032] Furthermore, large displacement nonlinear calculations are performed in the vertical rotation model of the arch bridge, and convergence is determined using the unbalanced force criterion, including:

[0033] Obtain the tangent stiffness matrix of the cable simulation element from the previous iteration, and calculate the displacement vector and displacement increment for the current iteration.

[0034] The tangent stiffness matrix of the current iteration is calculated based on the displacement vector of the current iteration. The internal force vector of the current iteration is calculated based on the tangent stiffness matrix of the current iteration and the displacement increment of the current iteration. The unbalanced load of the current iteration is calculated based on the internal force vector of the current iteration.

[0035] Determine if the unbalanced load of the current iteration is less than the preset tolerance. If so, the calculation ends; otherwise, apply the unbalanced load of the current iteration back to the cable simulation element and calculate the load increment of the current iteration caused by the unbalanced load.

[0036] The displacement vector for the next iteration is calculated based on the load increment of the current iteration, and the displacement vector of the next iteration is used as the displacement vector of the current iteration and substituted back into the first step for iterative processing.

[0037] Furthermore, the sub-variables are obtained by dividing the total variable into N-1 groups, including:

[0038] The total change is divided into sub-changes according to the vertical rotation start-up phase, vertical rotation maintenance phase, and vertical rotation end phase.

[0039] Among them, the sub-changes in the vertical rotation start-up stage and the vertical rotation end stage are smaller than the sub-changes in the vertical rotation maintenance stage, and each sub-change is a multiple of the jack stroke.

[0040] According to a second aspect of this disclosure, a continuous calculation system for the entire process of negative angle vertical rotation of an arch bridge is provided, comprising:

[0041] The data processing module is used to obtain the total change based on the stress-free length of the cable members in the initial and final states of the vertical rotation structure of the arch bridge. The sub-changes are obtained by dividing the total change into N-1 groups; N is a natural number greater than 1.

[0042] The model building module, connected to the data processing module, is used to build an arch bridge vertical rotation model based on the design parameters of the arch bridge vertical rotation structure. The arch bridge vertical rotation model includes a cable simulation unit, which includes multiple straight bar units.

[0043] The construction simulation module, connected to the model building module, is used to input the arch bridge design parameters and the stress-free length in the initial state into the arch bridge vertical rotation model. The construction process is simulated using the arch bridge vertical rotation model. The calculated sub-variables of the stress-free length are input sequentially to simulate and calculate the cable force and control parameters of the cable members under different states until the vertical rotation process is completed.

[0044] According to a third aspect of this disclosure, an electronic device is provided, including a memory, a processor, and a computer program; wherein the computer program is stored in the memory and configured to be executed by the processor to implement a continuous calculation method for the entire process of the negative angle vertical rotation of an arch bridge.

[0045] According to a fourth aspect of this disclosure, a computer-readable storage medium is provided having a computer program stored thereon; the computer program is executed by a processor to implement a method for continuous calculation of the entire process of the negative angle vertical rotation of an arch bridge.

[0046] The beneficial effects of this disclosure are:

[0047] This disclosure determines the stress-free length and total change of the cable component in the initial and final states. The total change is divided according to the principle of refining the vertical rotation stage and adapting to the jack stroke. Then, a straight bar unit that supports direct input of stress-free length and dynamic change during construction is constructed. Multi-segment straight bar units are used to simulate the cable structure and establish an arch bridge vertical rotation model. Finally, the stress-free length and other data of the cable are updated stage by stage through iterative calculations during the construction stage.

[0048] This disclosure requires only a single finite element model to achieve dynamic and continuous simulation of the entire process of vertical rotation of an arch bridge. The calculation is simple, flexible, and more accurate, and can truly reflect the changes in cable mass and stiffness. It is suitable for negative angle vertical rotation construction of arch bridges in scenarios such as steep valleys and busy traffic lines.

[0049] It should be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of this disclosure, nor is it intended to restrict the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0050] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. The drawings are provided for a better understanding of the invention and are not intended to limit the scope of this disclosure. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0051] Figure 1 A flowchart is shown below illustrating a method for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge, as provided in an embodiment of this disclosure.

[0052] Figure 2 This diagram illustrates the state change of the straight rod unit from the initial time to time t, as provided in an embodiment of this disclosure.

[0053] Figure 3 This diagram illustrates the state of the straight rod unit at the initial moment according to an embodiment of the present disclosure.

[0054] Figure 4 This diagram illustrates the state of the straight rod unit at time t according to an embodiment of the present disclosure.

[0055] Figure 5 This diagram illustrates a framework diagram of a continuous calculation system for the entire process of negative angle vertical rotation of an arch bridge, provided by an embodiment of this disclosure.

[0056] Figure 6 A block diagram of an electronic device provided according to an embodiment of the present disclosure is shown. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0058] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0059] This disclosure provides a method for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge, which first involves the following preprocessing:

[0060] Based on the stress-free length of the cable members in the initial state and the stress-free length in the final state of the vertical rotation structure of the arch bridge, the total change in stress-free length is calculated and divided into N-1 sub-changes; N is a natural number greater than 1.

[0061] Based on the initial state of the arch bridge before the vertical rotation of the structure, an initial state calculation model is constructed according to the coordinates of the arch ribs and the positions of the cables on the arch bridge. Analysis and calculation are then performed to obtain the cable forces of the cable members in the initial state, i.e., the initial cable forces. .

[0062] The calculation process for the stress-free length in the initial state specifically includes:

[0063] Based on the initial state of the arch bridge before the vertical rotation of the structure is started, an initial state calculation model is established by combining the arch rib coordinates and cable positions, and the initial cable force corresponding to the cable member in this state is solved.

[0064] The stress-free length in the initial state is calculated based on the correlation between the initial cable force, the actual stressed length of the cable member, the elastic elongation induced by the cable force, and the sag correction length; among which,

[0065] The sag correction length is used to compensate for the sag effect caused by the self-weight of the cable component, and the elastic elongation is used to reflect the material deformation characteristics of the cable component under the action of cable force.

[0066] The calculation process for the stress-free length in the initial state and the stress-free length in the final state is the same.

[0067] Specifically, based on the initial cable force Calculate the stress-free length of the cable member in its initial state. The specific calculation is performed using the following formula:

[0068] ,

[0069] ,

[0070] ,

[0071] ,

[0072] Where L represents the length of the cable member after it is subjected to force; This represents the elastic elongation caused by the cable force in the cable member; Indicates the sag correction length. and The coordinates of the two ends of the cable member are represented respectively; E represents the elastic modulus of the cable member; A represents the cross-sectional area of ​​the cable member. The value of q represents the weight per unit length of the cable member; q represents the self-weight intensity of the cable member. The x represents the angle between the cable member and the horizontal plane, where x represents 0 to 1. Any value between.

[0073] This disclosure introduces a sag correction length. To compensate for the sag effect caused by the self-weight of the cable members, the calculation error was reduced; elastic elongation It reflects the material deformation characteristics of cable components under cable force.

[0074] Stress-free length in the final state of vertical rotation The stress-free length of the cable member in its initial state The calculation process is consistent, so I will not go into too much detail here.

[0075] The total change in stress-free length can be calculated using the following formula. :

[0076] .

[0077] To meet the requirements of on-site construction control and vertical rotation safety, the total change in stress-free length is divided into N-1 sub-changes. (i=1, 2, ..., N-1), the partitioning principles specifically include:

[0078] (1) The total change in stress-free length is further subdivided into the vertical rotation start-up stage and the vertical rotation end stage. With smaller values, the structural attitude is unstable and the safety risk is high during these two stages. Small adjustments are made to ensure attitude accuracy and construction safety.

[0079] (2) The cable force of the cable member is applied by jacks. The single-step stroke of the jacks is limited. In order to facilitate the tensioning implementation and control on the construction site, the sub-variable of the cable member at each construction stage is determined. All of these are multiples of the jack stroke H to ensure precise control during on-site tensioning.

[0080] In conclusion, Satisfy the following formula:

[0081] ;

[0082] The construction phase is specifically divided into N stages. The first construction stage is the stress-free length under the calculated initial state. The second construction stage is based on the first construction stage and involves the following steps. The changes, the third stage, occur based on the second construction stage. The changes occur sequentially.

[0083] See Figures 1 to 4 This disclosure provides a method for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge, which specifically includes the following steps:

[0084] S1. Construct an arch bridge vertical rotation model based on the design parameters of the arch bridge vertical rotation structure. The arch bridge vertical rotation model includes a cable simulation unit, which includes multiple straight bar units.

[0085] The arch bridge vertical rotation model is a finite element calculation model. It is constructed based on the design parameters of the arch bridge vertical rotation structure, and specifically includes arch bridge simulation elements and cable simulation elements.

[0086] The arch bridge simulation unit includes arch ribs, supports, etc., and is generally simulated using beam elements. Existing beam elements can be used for simulation.

[0087] The simulation methods for cable-stayed structures in cable simulation elements mainly include straight bar elements, catenary elements, and multi-segment straight bar elements. Among these, straight bar elements cannot account for the sag effect of the cable structure, resulting in significant errors. Therefore, they are only suitable for cases with very small sag. However, during vertical rotation, the sag of the cable is very large, and the computational error generated by using straight bar elements cannot be ignored. Catenary elements can accurately describe the true mechanical behavior of cable-stayed structures, but the calculation formulas are complex, the computation time is long, and the convergence is poor in complex nonlinear analyses. Multi-segment straight bar elements, consisting of several straight bar elements, can better reflect the sag effect of cable-stayed structures, avoid the complex formation process of the tangent stiffness matrix of catenary elements, and have the advantages of high computational efficiency and good convergence.

[0088] This disclosure derives a straight bar element model based on a multi-segment straight bar element simulation method, which supports direct input of stress-free length and can be continuously updated during the construction process.

[0089] When simulating cable-stayed members, a single cable-stayed member is discretized into M equal parts, where M∈[5,15]. Each part is modeled and represented using straight bar elements, and the initial stress-free length is... / M, a cable-stayed structure is simulated using multiple straight bar elements, which are connected end-to-end through nodes to reflect the sag of the cable-stayed structure under gravity. The multi-segment straight bar element consists of M straight bar elements to support dynamic adjustment of the stress-free length.

[0090] In summary, the method disclosed herein can achieve continuous calculation of the entire vertical rotation process by continuously modifying the stress-free length of the cable simulation element. Using the catenary wire element will result in a slow calculation process and poor convergence.

[0091] S2. Input the arch bridge design parameters and the stress-free length in the initial state into the arch bridge vertical rotation model. Use the arch bridge vertical rotation model to simulate the construction process. Input the sub-variables of the calculated stress-free length in sequence to simulate and calculate the cable force and control parameters of the cable members in different states until the vertical rotation process is completed.

[0092] The design parameters of the arch bridge vertical rotation structure are input into the arch bridge vertical rotation model. The design parameters include input materials, boundaries, load characteristics, etc., and the stress-free length of the initial state obtained by the above calculation is input into the cable element, thereby transforming the actual arch bridge vertical rotation structure into a numerical model that can be used for mechanical analysis.

[0093] During the construction phase simulation, activation and deactivation groups for the structure, boundaries, and loads of each construction phase are established, and the stress-free length variation of the straight bar elements in each construction phase is assigned. / M(i=1,2,……,N-1), to obtain the calculation model of the entire process of the negative angle vertical rotation of the bridge structure.

[0094] Specifically, it includes the following:

[0095] S21. Enter the current construction stage i (i=1, 2, ..., N), each construction stage corresponds to each sub-variable;

[0096] S22. Determine if the current construction stage is the first stage, i.e., determine if i=1. If i=1, the stress-free length sub-change obtained by the cable simulation unit is 0, and the next construction stage is taken as the current construction stage, proceeding to the previous step; if i≠1, the stress-free length sub-change obtained by the cable simulation unit for the corresponding construction stage is... / M(i=i-1), the stress-free length corresponding to the current construction stage is obtained by superposition calculation;

[0097] S23. Based on the stress-free length of the cable simulation unit at the current construction stage (including structure, boundary, load, etc.), calculate the tangent stiffness matrix and load array.

[0098] In this disclosure, the sub-variation of the stress-free length is used as an input parameter for the vertical rotation model of the arch bridge, causing a corresponding change in the stress-free length of the cable simulation element. The structural change of the cable member can be calculated by solving the tangent stiffness matrix.

[0099] As the construction phase changes, the cable simulation unit is updated according to the calculated change in stress-free length. However, the actual shape and internal forces of the corresponding structure do not match the updated stress-free state, and the entire system is in an unbalanced state. Therefore, it is necessary to calculate the corresponding structural form so that all units can achieve internal force balance under the new form.

[0100] This disclosure employs an iterative method. After each tentative adjustment of the structural form, a scale is needed to measure the relationship between unbalanced forces and restoring forces, namely the tangent stiffness matrix.

[0101] The load array is the equivalent nodal force vector composed of gravity, external loads, etc. of the cable simulation element, and is used to calculate unbalanced forces and subsequent iterative solutions.

[0102] The calculation process of the tangent stiffness matrix is ​​summarized as follows:

[0103] Construct a structural coordinate system and a co-rotating coordinate system, and determine the relationship between the displacement vector of the cable simulation element and the nodal coordinates;

[0104] The elongation of the straight bar element under load at different times and the corresponding element attitude angle are determined based on the relationship between the displacement vector and the nodal coordinates.

[0105] Based on the unit attitude angle and elongation, the rod end force vectors corresponding to the straight rod unit in the co-rotation coordinate system and the structural coordinate system are calculated.

[0106] Differentiating the rod end force in the co-rotation coordinate system yields the correlation between the rod end force increment and the axial deformation increment; differentiating the rod end force in the structural coordinate system yields the correlation between the rod end force increment and the angle change increment; based on the element attitude angle and elongation, the correlation between the axial deformation increment and the nodal displacement increment is calculated.

[0107] The tangent stiffness matrix is ​​calculated based on the correlation between the increment of bar end force and the increment of axial deformation, the correlation between the increment of bar end force and the increment of angle change, and the correlation between the increment of axial deformation and the increment of nodal displacement.

[0108] Specifically, see Figures 2 to 4 A structural coordinate system and a co-rotating coordinate system were constructed. The structural coordinate system is a reference system defined at the beginning of the analysis and whose position and orientation remain fixed throughout the analysis. The co-rotating coordinate system is "attached" to the straight bar element and rotates with the deformation of the straight bar element. It always takes node c of the straight bar element as the origin, the direction of the line connecting node c and node d as the X-axis, and rotates 90° counterclockwise around the X-axis as the Y-axis. The variables of the straight bar element at the initial time and time t are already defined in the structural coordinate system and the co-rotating coordinate system. Figure 2 , Figure 3 and Figure 4 Mark it.

[0109] At the initial moment, the coordinates of node c and node d of the straight bar element in the structural coordinate system are respectively , At time t, the stress-free length of the straight rod element changes and it is subjected to a load (such as the self-weight of the arch rib). At this time, its coordinates in the structural coordinate system are... , The displacement vector of the node is The displacement vector and the nodal coordinates satisfy the following formula:

[0110] ;

[0111] ;

[0112] ;

[0113] ;

[0114] The above formula establishes the correlation between the displacement deformation of the cable simulation element and the nodal displacement.

[0115] In summary, this disclosure simplifies the relevant calculations under displacement by simultaneously introducing a structural coordinate system and a co-rotating coordinate system to accurately describe the displacement and deformation during construction.

[0116] Let the lengths of the straight rod element at the initial time and at time t be respectively and They are represented by the following formulas:

[0117] ,

[0118] (1)

[0119] Elongation of the straight bar element under load from the initial time to time t It can be expressed by the following formula:

[0120] (2)

[0121] in, The formula (2) represents the change in length of the straight bar unit during the time interval from 0 to t. It is used to simulate the active and passive deformation of the cable unit. Active deformation refers to stress-free length adjustment, which is achieved by tensioning or relaxing the cable components during construction. Passive deformation refers to elastic elongation caused by load changes. Based on the distinction between active and passive deformation, the actual deformation of the cable components during vertical rotation can be accurately matched, thus minimizing simulation errors.

[0122] Let the angle between the straight rod element and the x-axis of the structural coordinate system at time t be... The unit attitude angle can be calculated using the following formula:

[0123] , (3)

[0124] in, This represents the length of the straight rod element in the horizontal direction at time t. The length of the straight rod element in the longitudinal direction is represented by the vector t. The force vector at the rod end represents the force acting on both ends of the straight rod element. In this disclosure, it is divided into two forms according to the coordinate system to reflect the force state of the straight rod element.

[0125] The force vector at the end of a straight rod element in a co-rotating coordinate system can be expressed as: ,in:

[0126] ; ;

[0127] in, This represents the axial force at node c of the straight rod element. The axial force at node d is represented by the equation. Differentiating the above equation, we get:

[0128] ; (4)

[0129] in, Let be the increment of axial deformation. The above differentiation establishes a linear relationship between the increment of rod end force and the increment of axial deformation.

[0130] The end force vector of a straight bar element in the structural coordinate system can be expressed as: ,but:

[0131] , ;

[0132] ; ;

[0133] in, This represents the horizontal component of the force at node c. This represents the vertical component of the force at node c. This represents the horizontal component of the force at node d. This represents the vertical component of the force at node d.

[0134] Differentiating both sides of the above equation, we get:

[0135] ; ;

[0136] ; (5)

[0137] in, This represents the increment of angle change, thus revealing a linear relationship between the increment of the rod end force and the increment of angle change.

[0138] The tangent stiffness matrix represents the relationship between the increment of force at the rod end and the increment of displacement at the rod end. To calculate the tangent stiffness matrix, the increment of axial deformation must first be calculated. Incremental angle change With nodal displacement increment The relationship between them.

[0139] Therefore, by differentiating both sides of formula (2) and combining formulas (1) and (3), the relationship between the axial deformation increment and the nodal displacement increment is obtained, as detailed in the following formulas:

[0140] (6)

[0141] Differentiating formula (3) and simultaneously differentiating formula (1) yields the increment of angle change. The relationship between the relationship and the nodal displacement increment is shown in the following formula:

[0142] (7)

[0143] based on , , combined and The relationship allows us to obtain the increment of the rod end force. With rod end displacement increment The relationship between them. Substituting formula (4) into formula (5), and combining formulas (6) and (7), we obtain the increment of the rod end force, as detailed in the following formulas:

[0144] ,

[0145] in, Let represent the tangent stiffness matrix of a stress-free, variable-length straight bar element, and , Represents the linear stiffness matrix. Represents the geometric stiffness matrix. and These can be expressed using the following formulas:

[0146] ,

[0147] .

[0148] It should be noted that each straight bar element has an independent tangent stiffness matrix. The data in the tangent stiffness matrix represents the projection of the bar's axial stiffness onto the global coordinate system and the coupling terms. The tangent stiffness matrix must be accurate and reflect the change in stress-free length in order to obtain the correct structural form in subsequent convergence iterations.

[0149] By calculating the tangent stiffness matrix, both material nonlinearity and geometric nonlinearity are considered simultaneously to conform to the relevant mechanical properties during cable construction and ensure calculation accuracy.

[0150] S24. Perform large displacement nonlinear calculations in the vertical rotation model of the arch bridge and determine whether the vertical rotation model of the arch bridge converges by using the unbalanced force criterion. Output the cable force and control parameters of the cable members in the current construction stage.

[0151] Large displacement nonlinear calculations are performed using iterative methods. Finite element calculations typically do not have analytical solutions, but by setting convergence conditions, calculation results within an acceptable error range can be obtained.

[0152] Specifically, the detailed steps for large displacement nonlinear calculations are as follows:

[0153] Obtain the tangent stiffness matrix of the cable-stayed simulation element before structural deformation. The displacement vector for the first iteration is obtained using the following formula. :

[0154] ,

[0155] in, This represents the displacement increment of the first iteration, and P represents the load value of the current construction stage.

[0156] Based on the displacement vector of the first iteration The calculation formula calculates the tangent stiffness matrix after the first iteration. The internal force vector for the first iteration is calculated using the following formula. :

[0157] ,

[0158] Based on the internal force vector from the first iteration, the unbalanced load from the first iteration is calculated. Please refer to the following formula for details:

[0159] ,

[0160] Determine if the unbalanced load of the first iteration is less than the preset allowable error. If so, the calculation ends; otherwise, apply the unbalanced load of the first iteration back to the cable simulation element and calculate the load increment caused by the unbalanced load. :

[0161] ,

[0162] The displacement vector for the second iteration is obtained based on the load increment calculation. :

[0163] ,

[0164] according to Calculate the tangent stiffness matrix after the second iteration. The internal force vector for the second iteration is calculated using the following formula. :

[0165] ,

[0166] Calculate the unbalanced load in the second iteration at this point. :

[0167] ,

[0168] Determine whether the unbalanced load is less than the preset allowable error, and iterate repeatedly until convergence. The specific iterative process can be represented by the following formula:

[0169] ,

[0170] in, Indicates the first The displacement increment of the next iteration. Indicates the first The tangent stiffness matrix after the next iteration Indicates the first k Unbalanced load in the next iteration This represents the internal force vector in the k-th iteration. This represents the displacement vector in the k-th iteration. This means that the right side can be derived from the left side.

[0171] Convergence is determined using the unbalanced force criterion, and the allowable error is shown in the following formula:

[0172] ≤eps||{ }||,

[0173] in, This indicates the norm, and the iteration convergence error eps is taken as... ~ .

[0174] The nonlinear calculation of large displacements and the convergence of the unbalanced force criterion can be summarized into the following steps:

[0175] Obtain the tangent stiffness matrix of the cable simulation element from the previous iteration, and calculate the displacement vector and displacement increment for the current iteration.

[0176] The tangent stiffness matrix of the current iteration is calculated based on the displacement vector of the current iteration. The internal force vector of the current iteration is calculated based on the tangent stiffness matrix of the current iteration and the displacement increment of the current iteration. The unbalanced load of the current iteration is calculated based on the internal force vector of the current iteration.

[0177] Determine if the unbalanced load of the current iteration is less than the preset tolerance. If so, the calculation ends; otherwise, apply the unbalanced load of the current iteration back to the cable simulation element and calculate the load increment of the current iteration caused by the unbalanced load.

[0178] The displacement vector for the next iteration is calculated based on the load increment of the current iteration, and the displacement vector of the next iteration is used as the displacement vector of the current iteration and substituted back into the first step for iterative processing.

[0179] In summary, the complete solution steps can be simplified to the following:

[0180] The stress-free length is adjusted according to the sub-variable, which leads to the imbalance of internal forces and structure of the cable simulation unit. The overall tangent stiffness matrix is ​​calculated based on the current state of the straight bar unit. Nonlinear iterative solution is performed based on the tangent stiffness matrix to finally obtain the actual displacement, cable force and control parameters that satisfy the equilibrium state.

[0181] Among them, the control parameters refer to the alignment, internal forces, and structural stresses of each part of the structure during the vertical rotation construction of the arch bridge. Nonlinear iterative solutions can calculate the internal force vector and actual displacement of the structure at the current construction stage. Based on these conditions, the control parameters of each part of the structure during the vertical rotation of the arch bridge can be further calculated. For example, the alignment is the initial alignment superimposed with the actual displacements generated at each construction stage.

[0182] S25. Determine whether the vertical rotation process is complete. If yes, i.e., j=N, the calculation ends; otherwise, proceed to the next construction stage, i.e., j=j+1, and return to step S31.

[0183] This disclosure achieves cable force variation by changing the stress-free length of the cable unit, thereby enabling the rotation of the vertically rotating structure. Compared to traditional calculation methods that use initial strain or temperature loads to calculate cable force variation, this method accurately reflects the stiffness and mass changes of the cable components caused by the stress-free length variation during vertical rotation. It avoids the cumbersome calculation process of initial strain and temperature loads, and allows for dual control of the cable anchor cup pull-out amount and cable force during vertical rotation through the stress-free length variation and the output cable force.

[0184] Based on the above technical solutions, this disclosure determines the stress-free length and total change of the cable component in the initial and final states. The total change is divided according to the principle of refining the vertical rotation stage and adapting to the jack stroke. Then, a straight bar unit that supports direct input of stress-free length and dynamic change during construction is constructed. Multi-segment straight bar units are used to simulate the cable structure and establish an arch bridge vertical rotation model. Finally, the stress-free length and other data of the cable are updated stage by stage through iterative calculations during the construction stage.

[0185] This disclosure requires only a single finite element model to achieve dynamic and continuous simulation of the entire process of vertical rotation of an arch bridge. The calculation is simple, flexible, and more accurate, and can truly reflect the changes in cable mass and stiffness. It is suitable for negative angle vertical rotation construction of arch bridges in scenarios such as steep valleys and busy traffic lines.

[0186] It should be noted that, for the foregoing embodiments, for the sake of simplicity, they are all described as a series of actions. However, those skilled in the art should understand that this disclosure is not limited to the described order of actions, because according to this disclosure, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also understand that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily essential to this disclosure.

[0187] The acquisition, storage, and application of user personal information involved in the technical solution disclosed herein comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0188] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the described module can be referred to the corresponding process in the foregoing embodiments, and will not be repeated here.

[0189] This disclosure also provides a continuous calculation system 500 for the entire process of negative angle vertical rotation of an arch bridge. See [link to system]. Figure 5 Specifically, it includes:

[0190] The data processing module 510 is used to obtain the total change based on the stress-free length of the cable member in the initial state and the stress-free length in the final state in the vertical rotation structure of the arch bridge. The sub-changes are obtained by dividing the total change into N-1 groups; N is a natural number greater than 1.

[0191] The model building module 520 is connected to the data processing module and is used to build an arch bridge vertical rotation model based on the design parameters of the arch bridge vertical rotation structure. The arch bridge vertical rotation model includes a cable simulation unit, and the cable simulation unit includes multiple straight bar units.

[0192] The construction simulation module 530 is connected to the model construction module and is used to input the arch bridge design parameters and the stress-free length in the initial state into the arch bridge vertical rotation model. The construction process is simulated using the arch bridge vertical rotation model. The calculated sub-variables of the stress-free length are input sequentially to simulate and calculate the cable force and control parameters of the cable members in different states until the vertical rotation process is completed.

[0193] Other details can be found in the previous methods section and will not be repeated here.

[0194] Figure 4A schematic block diagram of an electronic device 400 that can be used to implement embodiments of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0195] Electronic device 600 includes a computing unit 601, which can perform various appropriate actions and processes based on a computer program stored in ROM 602 or a computer program loaded into RAM 603 from storage unit 608. RAM 603 may also store various programs and data required for the operation of electronic device 600. The computing unit 601, ROM 602, and RAM 603 are interconnected via bus 604. I / O interface 605 is also connected to bus 604.

[0196] Multiple components in electronic device 600 are connected to I / O interface 605, including: input unit 605, such as keyboard, mouse, etc.; output unit 607, such as various types of displays, speakers, etc.; storage unit 608, such as disk, optical disk, etc.; and communication unit 609, such as network card, modem, wireless transceiver, etc. Communication unit 609 allows electronic device 600 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0197] The computing unit 601 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 601 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 601 performs the various processes described above. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 600 via ROM 602 and / or communication unit 609.

[0198] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0199] The program code used to implement the schemes of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0200] In the context of this disclosure, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on 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 of the foregoing.

[0201] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including voice input, speech input, or tactile input).

[0202] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0203] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.

[0204] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0205] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge, characterized in that, Includes the following steps: An arch bridge vertical rotation model is constructed based on the design parameters of the arch bridge vertical rotation structure. The arch bridge vertical rotation model includes a cable simulation unit, which includes multiple straight bar units. The design parameters of the arch bridge and the stress-free length in the initial state are input into the vertical rotation model of the arch bridge. The construction process is simulated using the vertical rotation model of the arch bridge. The sub-variables of the calculated stress-free length are input sequentially to simulate and calculate the cable force and control parameters of the cable members in different states until the vertical rotation process is completed. The sub-variable is obtained by dividing the total variable into N-1 groups. The total variable is based on the stress-free length of the cable member in the initial state and the stress-free length in the final state in the vertical rotation structure of the arch bridge. N is a natural number greater than 1. The calculation process for the stress-free length in the initial state specifically includes: Based on the initial state of the arch bridge before the vertical rotation of the structure is started, an initial state calculation model is established by combining the arch rib coordinates and cable positions, and the initial cable force corresponding to the cable member in this state is solved. The stress-free length in the initial state is calculated based on the correlation between the initial cable force, the actual stressed length of the cable member, the elastic elongation induced by the cable force, and the sag correction length; among which, The sag correction length is used to compensate for the sag effect caused by the self-weight of the cable component, and the elastic elongation is used to reflect the material deformation characteristics of the cable component under the action of cable force. The calculation process for the stress-free length in the final state is the same as that for the stress-free length in the initial state. The construction process is simulated using the arch bridge vertical rotation model. Corresponding sub-variables are input, and the cable forces and control parameters of the cable-stayed components are calculated until the vertical rotation process is completed. This includes: Entering the current construction phase; Determine whether the current construction stage is the first stage. If so, the stress-free length sub-change obtained by the cable simulation unit is 0, and the next construction stage is taken as the current construction stage, and the previous step is entered. If not, the stress-free length sub-change obtained by the cable simulation unit for the corresponding construction stage is superimposed to calculate the stress-free length corresponding to the cable simulation unit for the current construction stage. Based on the stress-free length of the cable simulation unit at the current construction stage, the tangent stiffness matrix and load array are calculated. Large displacement nonlinear calculations are performed in the vertical rotation model of the arch bridge, and convergence is determined by the unbalanced force criterion. The cable force and control parameters of the cable members in the current construction stage are output. Determine if the vertical rotation process is complete. If yes, end the process; otherwise, proceed to the next construction stage and return to step one. The calculation process of the tangent stiffness matrix specifically includes the following steps: Construct a structural coordinate system and a co-rotating coordinate system, and determine the relationship between the displacement vector of the cable simulation element and the nodal coordinates; The elongation of the straight bar element under load at different times and the corresponding element attitude angle are determined based on the relationship between the displacement vector and the nodal coordinates. Based on the unit attitude angle and elongation, the rod end force vectors corresponding to the straight rod unit in the co-rotation coordinate system and the structural coordinate system are calculated. Differentiating the rod end force in the co-rotation coordinate system yields the correlation between the rod end force increment and the axial deformation increment; differentiating the rod end force in the structural coordinate system yields the correlation between the rod end force increment and the angle change increment; based on the element attitude angle and elongation, the correlation between the axial deformation increment and the nodal displacement increment is calculated. The tangent stiffness matrix is ​​calculated based on the correlation between the increment of bar end force and the increment of axial deformation, the correlation between the increment of bar end force and the increment of angle change, and the correlation between the increment of axial deformation and the increment of nodal displacement.

2. The method for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge according to claim 1, characterized in that, The tangent stiffness matrix is ​​obtained by adding the linear stiffness matrix and the geometric stiffness matrix; The linear stiffness matrix is ​​calculated based on the elastic modulus, cross-sectional area, stress-free length in the initial state, and element orientation angle of the cable member. The geometric stiffness matrix is ​​calculated based on the axial deformation of the cable member and the angle of the element orientation.

3. The method for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge according to claim 1, characterized in that, Large displacement nonlinear calculations are performed in the vertical rotation model of the arch bridge, and convergence is determined using the unbalanced force criterion, including: Obtain the tangent stiffness matrix of the cable simulation element from the previous iteration, and calculate the displacement vector and displacement increment for the current iteration. The tangent stiffness matrix of the current iteration is calculated based on the displacement vector of the current iteration. The internal force vector of the current iteration is calculated based on the tangent stiffness matrix of the current iteration and the displacement increment of the current iteration. The unbalanced load of the current iteration is calculated based on the internal force vector of the current iteration. Determine if the unbalanced load of the current iteration is less than the preset tolerance. If so, the calculation ends; otherwise, apply the unbalanced load of the current iteration back to the cable simulation element and calculate the load increment of the current iteration caused by the unbalanced load. The displacement vector for the next iteration is calculated based on the load increment of the current iteration, and the displacement vector of the next iteration is used as the displacement vector of the current iteration and substituted back into the first step for iterative processing.

4. The method for continuous calculation of the entire process of negative angle vertical rotation of an arch bridge according to claim 1, characterized in that, The sub-variables are obtained by dividing the total variable into N-1 groups, including: The total change is divided into sub-changes according to the vertical rotation start-up phase, vertical rotation maintenance phase, and vertical rotation end phase. Among them, the sub-changes in the vertical rotation start-up stage and the vertical rotation end stage are smaller than the sub-changes in the vertical rotation maintenance stage, and each sub-change is a multiple of the jack stroke.

5. A continuous calculation system for the entire process of negative angle vertical rotation of an arch bridge, used to implement the continuous calculation method for the entire process of negative angle vertical rotation of an arch bridge as described in any one of claims 1-4, characterized in that, The system includes: The data processing module is used to obtain the total change based on the stress-free length of the cable members in the initial state and the stress-free length in the final state of the vertical rotation structure of the arch bridge. The sub-changes are obtained by dividing the total change into N-1 groups; N is a natural number greater than 1. The model building module, connected to the data processing module, is used to build an arch bridge vertical rotation model based on the design parameters of the arch bridge vertical rotation structure. The arch bridge vertical rotation model includes a cable simulation unit, which includes multiple straight bar units. The construction simulation module, connected to the model building module, is used to input the arch bridge design parameters and the stress-free length in the initial state into the arch bridge vertical rotation model. The construction process is simulated using the arch bridge vertical rotation model. The calculated sub-variables of the stress-free length are input sequentially to simulate and calculate the cable force and control parameters of the cable members under different states until the vertical rotation process is completed.

6. An electronic device, characterized in that, It includes a memory, a processor, and a computer program; wherein the computer program is stored in the memory and configured to be executed by the processor to implement a continuous calculation method for the entire process of negative angle vertical rotation of an arch bridge as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, It stores a computer program; the computer program is executed by a processor to implement a continuous calculation method for the entire process of negative angle vertical rotation of an arch bridge as described in any one of claims 1 to 4.

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