Bridge double-support-column associated stress analysis method

Abstract

The invention, which relates to the technical field of stress analysis, discloses a bridge double-support-column associated stress analysis method comprising the following steps: initializing the stress state of a bridge double-support column, and initializing the particle vector of a particle swarm algorithm model according to the stress state; the stress distribution of the bridge supporting columns is optimized; solving a stress state and performance associated with the double support columns; and inversely deducing the size and arrangement of the optimal support column, and carrying out analogue simulation to obtain specific data. The joint stress problem of the double support columns of the bridge is optimized by combining the particle swarm optimization (PSO), so that the bridge floor support force of the bridge can be maximized under the condition of limited support column structures, the optimal bridge structure is obtained, the optimal solution can be searched in the multi-dimensional design space through the particle swarm optimization, and the design efficiency is improved. The safety, the stability and the economical efficiency of the bridge under the load effect are ensured.

Description

Technical Field

[0001] The invention relates to the technical field of force analysis, and in particular to a method for analyzing the associated force of double supporting columns of a bridge. Background Art

[0002] As an important infrastructure, bridges undertake multiple functions such as transportation and logistics. The safety of their design, construction and operation directly affects the safety of people's lives and property. In the design and analysis of bridges, the support system is a crucial part. The support system of the bridge not only bears the direct effects from the bridge deck and traffic loads, but is also affected by environmental factors (such as temperature changes, wind, earthquakes, etc.) and wear and fatigue during long-term use. Among the many bridge support structures, double support columns (or double bearing support systems) are a common structural form, especially in bridges across large spans or bridges with special environmental conditions. Double support columns usually refer to a structural form in which two support columns are supported at both ends or in the middle of the bridge. These support columns work together to share the longitudinal, transverse and vertical loads of the bridge.

[0003] In the prior art, the double support column structure of a bridge usually involves the bridge deck and main beam bearing loads through the support columns, and the support columns may be under the influence of uneven loads, temperature changes or settlement. Traditional force analysis methods rely on analytical formulas, finite element methods or influence line methods, which may not be able to directly solve optimization problems with complex constraints and objective functions, especially when it comes to factors such as the size of the support columns, load distribution, and structural stability. Summary of the invention

[0004] The technical problem solved by the present invention is that traditional force analysis methods rely on analytical formulas, finite element method or influence line method, which may not be able to directly solve optimization problems with complex constraints and objective functions, especially when it comes to factors such as the size of the support column, load distribution, structural stability, etc.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions: a method for analyzing the associated forces of double supporting columns of a bridge, comprising the following steps: Step S1: Initialize the stress state of the double support columns of the bridge, and initialize the particle vector of the particle swarm algorithm model according to the stress state; Step S2: Optimizing the force distribution of the bridge support column; Step S3: solving the stress state and performance associated with the double support columns; Step S4: reversely infer the size and arrangement of the optimal support column and perform simulation to obtain specific data; The step S1 comprises: Collecting historical information on the size, stiffness and load distribution coefficient of each support column of the bridge respectively, wherein the size of the support column is represented by the weighted product of the cross-sectional area and the height of the support column, and the load distribution coefficient is represented by the proportion of the load borne by the support column; Collect the displacement and bending moment change data of the front and rear piles of the bridge support column, calculate the slope residual thrust and pile side geotechnical resistance of the entire bridge according to the physical formula, calculate the lateral connection force of the double support columns according to the front and rear pile displacement, bending moment change data, slope residual thrust and pile side geotechnical resistance, use the lateral connection force as the particle vector of the particle swarm algorithm, and use the front and rear pile displacement and bending moment change data as the target parameter; The mathematical expression for calculating the residual thrust of the slope is: ; in, is the residual thrust on the slope, is the mass of the double support column, is the acceleration due to gravity, is the inclination angle of the bridge slope; The mathematical expression for calculating the pile side geotechnical resistance is: ; in, is the rock and soil resistance of the pile side, is the resistance coefficient of the rock and soil at the current detection point, for h The lateral displacement of the bridge support column corresponding to the underground buried point of meters; The mathematical expression of the front and rear pile displacement is: ; in, is the displacement of the supporting column and main beam, is the displacement difference of the supporting column and main beam in a unit time period, and |·| is the absolute value calculation; The mathematical expression of the bending moment change data is: ; in, is the bending moment change data, is the difference in the bending moment change per unit time of one of the supporting columns, is the difference in the bending moment change per unit time of another supporting column; The mathematical expression for calculating the lateral connection force of the double support column is: ; in, For the lateral connection force, is the total number of steel main beam grids supporting the columns, is the total number of steel sub-beam grids supporting the column, is the lateral distance from the nth beam grid to the central axis of the supporting column section, is the sum of the squares of the transverse distances from the steel main beam grid to the center axis of the supporting column section, It is the sum of the squares of the transverse distances from the steel sub-beam grid to the center axis of the supporting column section.

[0006] Preferably, step S2 comprises: The optimization objective function expression of the particle swarm algorithm is: ; Among them, F To optimize the objective function, is the lateral force, s is the front and rear pile displacement, and r is the bending moment change.

[0007] Preferably, the mathematical expression of the particle vector is: ; in, For the particle vector, , and are respectively the size, stiffness and load distribution coefficient of the support column, and the size, stiffness and load distribution coefficient of the support column are respectively the design parameters for particle optimization.

[0008] Preferably, the particle vector is updated with a speed in the particle swarm model optimization process, and the mathematical expression of the speed update is: ; in, For the The particle vector in The speed of updating time of each dimension, For the The particle vector in The speed of the dimension, is the inertia weight, which is used to control the influence of the historical change speed of the particle vector on the current change speed. and is the acceleration constant, which controls the speed at which the particle vector moves toward the local optimal solution and the global optimal solution respectively. and is a random number, the random number range is [0, 1], For the The particle vector in The historical optimal position of the dimension, For the The particle vector in The global optimal position in each dimension.

[0009] Preferably, the particle vector is subjected to a design parameter update of the particle swarm model optimization process, and the mathematical expression for the design parameter update is: ; in, For the The particle vector in Design parameters in three dimensions.

[0010] Preferably, the finite element analysis method is used to calculate the stress and deformation results of the bridge under the design parameters to obtain the corresponding fitness value. The mathematical expression of the fitness function is: ; in, is the fitness function, and R is the total displacement of the supporting column and the bridge body.

[0011] Preferably, according to the mathematical formulas for updating the velocity of the particle vector and the design parameters, the optimal solution for the design parameter combination of the particle vector is iteratively calculated, and when the fitness value reaches a preset fitness threshold, the final result of the particle swarm algorithm is output, and the final result represents the optimal global solution.

[0012] Preferably, the global optimal solution is adjusted to obtain the optimal size and arrangement of the support columns through an inverse particle swarm algorithm.

[0013] Preferably, the bridge is simulated by using Matlab, the bridge parameters are adjusted, and specific data of the optimal stress state of the double support columns under the bridge parameters corresponding to different bridges are obtained; The bridge parameters include the size, stiffness and load distribution coefficient of each supporting column of the bridge.

[0014] The beneficial effects of the present invention are as follows: the particle swarm algorithm (PSO) is combined to optimize the joint force problem of the double support columns of the bridge, so that the bridge deck support force can be maximized under the condition of limited support column structure, and the optimal bridge structure can be obtained. Through the particle swarm algorithm, the optimal solution can be searched in the multi-dimensional design space to ensure the safety, stability and economy of the bridge under load. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A schematic diagram of the basic flow of a method for analyzing the associated forces of double supporting columns of a bridge provided by an embodiment of the present invention.

[0016] Figure 2 A schematic cross-sectional view of a double support column of a bridge provided in accordance with an embodiment of the present invention. DETAILED DESCRIPTION

[0017] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, but not all of the embodiments.

[0018] Reference Figure 1 , as an embodiment of the present invention, provides a method for analyzing the associated forces of double supporting columns of a bridge, comprising the following steps: Step S1: Initialize the stress state of the double support columns of the bridge, and initialize the particle vector of the particle swarm algorithm model according to the stress state; Step S2: Optimizing the force distribution of the bridge support column; Step S3: solving the stress state and performance associated with the double support columns; Step S4: Reversely infer the size and arrangement of the optimal support columns and perform simulation to obtain specific data.

[0019] The step S1 comprises: Collect historical information on the size, stiffness and load distribution coefficient of each support column of the bridge respectively, wherein the size of the support column is represented by the weighted product of the cross-sectional area and the height of the support column, and the load distribution coefficient is represented by the ratio of the load borne by the support column, which is usually close to 1; Collect the displacement and bending moment change data of the front and rear piles of the bridge support column, calculate the slope residual thrust and pile side geotechnical resistance of the entire bridge according to the physical formula, calculate the lateral connection force of the double support columns according to the front and rear pile displacement, bending moment change data, slope residual thrust and pile side geotechnical resistance, use the lateral connection force as the particle vector of the particle swarm algorithm, and use the front and rear pile displacement and bending moment change data as the target parameter; The mathematical expression for calculating the residual thrust of the slope is: ; in, is the residual thrust on the slope, is the mass of the double support column, is the acceleration due to gravity, is the inclination angle of the bridge slope; The mathematical expression for calculating the pile side geotechnical resistance is: ; in, is the rock and soil resistance of the pile side, is the resistance coefficient of the rock and soil at the current detection point, for h The lateral displacement of the bridge support column corresponding to the underground buried point of meters; The mathematical expression of the front and rear pile displacement is: ; in, is the displacement of the supporting column and main beam, is the displacement difference of the supporting column and main beam in a unit time period, and |·| is the absolute value calculation; The mathematical expression of the bending moment change data is: ; in, is the bending moment change data, is the difference in the bending moment change per unit time of one of the supporting columns, is the difference in the bending moment change per unit time of another supporting column; The mathematical expression for calculating the lateral connection force of the double support column is: ; in, For the lateral connection force, is the total number of steel main beam grids supporting the columns, is the total number of steel sub-beam grids supporting the column, is the lateral distance from the nth beam grid to the central axis of the supporting column section, is the sum of the squares of the transverse distances from the steel main beam grid to the center axis of the supporting column section, is the sum of the squares of the lateral distances from the steel auxiliary beam grid to the central axis of the support column section, and the optimal distribution of the slope residual thrust, pile side rock and soil resistance and lateral connection force to the pile foundation displacement and internal driving force is solved.

[0020] The step S2 comprises: The optimization objective function expression of the particle swarm algorithm is: ; Among them, F To optimize the objective function, is the lateral force, s is the front and rear pile displacement, and r is the bending moment change.

[0021] In bridge force analysis, each particle can be represented as a vector, where each component corresponds to a parameter in bridge design; The mathematical expression of the particle vector is: ; in, For the particle vector, , and are respectively the size, stiffness and load distribution coefficient of the support column, and the size, stiffness and load distribution coefficient of the support column are respectively the design parameters for particle optimization.

[0022] The particle vector is updated with the speed of the particle swarm model optimization process. The mathematical expression of the speed update is: ; in, For the The particle vector in The speed of updating time of each dimension, For the The particle vector in The speed of the dimension, is the inertia weight, which is used to control the influence of the historical change speed of the particle vector on the current change speed. and is the acceleration constant, which controls the speed at which the particle vector moves toward the local optimal solution and the global optimal solution respectively. and is a random number, the random number range is [0, 1], For the The particle vector is at the historical optimal position in the dimension, For the The particle vector in The global optimal position in each dimension.

[0023] The design parameters of the particle swarm model optimization process are updated for the particle vector. The mathematical expression for the design parameter update is: ; in, For the The particle vector in Design parameters in three dimensions.

[0024] The finite element analysis method is used to calculate the stress and deformation results of the bridge under the design parameters, and the corresponding fitness value is obtained. The mathematical expression of the fitness function is: ; in, is the fitness function, and R is the total displacement of the supporting column and the bridge body.

[0025] According to the mathematical formulas for updating the speed of the particle vector and the design parameter, the optimal solution of the design parameter combination of the particle vector is iteratively calculated. When the fitness value reaches a preset fitness threshold, the final result of the particle swarm algorithm is output, and the final result represents the optimal global solution.

[0026] The particle swarm algorithm has global search capabilities and can avoid the dilemma of local optimal solutions. It is suitable for complex, nonlinear, and large-scale optimization problems and can handle complex loads and constraints in the double-support column structure of bridges.

[0027] The global optimal solution is manually adjusted, and the size and arrangement of the optimal support columns are obtained through the reverse particle swarm algorithm.

[0028] The bridge is simulated by using Matlab, the bridge parameters are adjusted, and specific data of the optimal stress state of the double support columns under the bridge parameters corresponding to different bridges are obtained; The bridge parameters include the size, stiffness and load distribution coefficient of each supporting column of the bridge.

[0029] The particle swarm algorithm (PSO) is combined with the particle swarm algorithm to optimize the joint force problem of the double support columns of the bridge, so that the bridge deck support force can be maximized under the condition of limited support column structure and the optimal bridge structure can be obtained. Through the particle swarm algorithm, the optimal solution can be searched in the multi-dimensional design space to ensure the safety, stability and economy of the bridge under load.

[0030] Reference Figure 2 In one of the embodiments, an arch ring 1 is set on the ground, there are two arch rings 1, the tops of the two arch rings 1 are fixedly connected to a first support column 2 and a second support column 3 respectively, the first support column 2 and the second support column 3 together constitute a double support column, and the bridge deck 4 is located on the top of the first support column 2 and the second support column 3.

[0031] The arch ring 1 adopts a box-shaped section, which not only reduces the deadweight of the arch ring, but also facilitates the construction of the bridge. By collecting the historical information of the size, stiffness and load distribution coefficient of the first support column 2 and the second support column 3, The slope residual thrust of the arch ring 1, the first support column 2, the second support column 3 and the bridge deck 4 as a whole, the rock and soil resistance on the pile side and the lateral connection force of the double support columns are collected, and the lateral force of the lateral connection force on the double support columns is obtained according to the physical formula. The lateral force is used as the particle vector of the particle swarm algorithm, and the displacement and bending moment change data of the front and rear piles are used as the target parameters for force analysis.

[0032] It should be understood by those skilled in the art that the embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware aspects. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program codes. Among them, the storage medium may be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (Static Random Access Memory, referred to as SRAM), electrically erasable programmable read-only memory (Electrically Erasable Programmable Read-Only Memory, referred to as EEPROM), erasable programmable read-only memory (Erasable Programmable Read Only Memory, referred to as EPROM), programmable read-only memory (Programmable Red-Only Memory, referred to as PROM), read-only memory (Read-Only Memory, referred to as ROM), magnetic memory, flash memory, magnetic disk or optical disk. These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0033] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for analyzing the associated forces of double supporting columns of a bridge, characterized in that: The following steps are involved: Step S1: Initialize the stress state of the double support columns of the bridge, and initialize the particle vector of the particle swarm algorithm model according to the stress state; Step S2: Optimizing the force distribution of the bridge support column; Step S3: solving the stress state and performance associated with the double support columns; Step S4: reversely infer the size and arrangement of the optimal support column and perform simulation to obtain specific data; The step S1 comprises: Collecting historical information on the size, stiffness and load distribution coefficient of each support column of the bridge respectively, wherein the size of the support column is represented by the weighted product of the cross-sectional area and the height of the support column, and the load distribution coefficient is represented by the proportion of the load borne by the support column; Collect the displacement and bending moment change data of the front and rear piles of the bridge support column, calculate the slope residual thrust and pile side geotechnical resistance of the entire bridge according to the physical formula, calculate the lateral connection force of the double support columns according to the front and rear pile displacement, bending moment change data, slope residual thrust and pile side geotechnical resistance, use the lateral connection force as the particle vector of the particle swarm algorithm, and use the front and rear pile displacement and bending moment change data as the target parameter; The mathematical expression for calculating the residual thrust of the slope is: ； in, is the residual thrust on the slope, is the mass of the double support column, is the acceleration due to gravity, is the inclination angle of the bridge slope; The mathematical expression for calculating the pile side geotechnical resistance is: ； in, is the rock and soil resistance of the pile side, is the resistance coefficient of the rock and soil at the current detection point, for h The lateral displacement of the bridge support column corresponding to the underground buried point of meters; The mathematical expression of the front and rear pile displacement is: ； in, is the displacement of the supporting column and main beam, is the displacement difference of the supporting column and main beam in unit time period, and |·| is the absolute value calculation; The mathematical expression of the bending moment change data is: ； in, is the bending moment change data, is the difference in the bending moment change per unit time of one of the supporting columns, is the difference in the bending moment change per unit time of another supporting column; The mathematical expression for calculating the lateral connection force of the double support column is: ； in, For the lateral connection force, is the total number of steel main beam grids supporting the columns, is the total number of steel sub-beam grids supporting the column, is the lateral distance from the nth beam grid to the central axis of the supporting column section, is the sum of the squares of the transverse distances from the steel main beam grid to the center axis of the supporting column section, It is the sum of the squares of the transverse distances from the steel sub-beam grid to the center axis of the supporting column section.

2. The method for analyzing the associated forces of double supporting columns of a bridge according to claim 1, characterized in that: The step S2 comprises: The optimization objective function expression of the particle swarm algorithm is: ； Among them, F To optimize the objective function, is the lateral force, s is the front and rear pile displacement, and r is the bending moment change.

3. The method for analyzing the associated forces of double supporting columns of a bridge according to claim 2, characterized in that: The mathematical expression of the particle vector is: ； in, For the particle vector, , and are respectively the size, stiffness and load distribution coefficient of the support column, and the size, stiffness and load distribution coefficient of the support column are respectively the design parameters for particle optimization.

4. The method for analyzing the associated forces of double supporting columns of a bridge according to claim 3, characterized in that: The particle vector is updated with the speed of the particle swarm model optimization process. The mathematical expression of the speed update is: ； in, For the The particle vector in The speed of updating time of each dimension, For the The particle vector in The speed of the dimension, is the inertia weight, which is used to control the influence of the historical change speed of the particle vector on the current change speed. and is the acceleration constant, which controls the speed at which the particle vector moves toward the local optimal solution and the global optimal solution respectively. and is a random number, the random number range is [0, 1], For the The particle vector in The historical optimal position of the dimension, For the The particle vector in The global optimal position in each dimension.

5. The method for analyzing the associated forces of double supporting columns of a bridge according to claim 4, characterized in that: The design parameters of the particle swarm model optimization process are updated for the particle vector. The mathematical expression for the design parameter update is: ； in, For the The particle vector in Design parameters in three dimensions.

6. The method for analyzing the associated forces of double supporting columns of a bridge according to claim 5, characterized in that: The finite element analysis method is used to calculate the stress and deformation results of the bridge under the design parameters, and the corresponding fitness value is obtained. The mathematical expression of the fitness function is: ； in, is the fitness function, and R is the total displacement of the supporting column and the bridge body.

7. The method for analyzing the associated forces of double supporting columns of a bridge according to claim 6, characterized in that: According to the mathematical formulas for updating the speed of the particle vector and the design parameter, the optimal solution of the design parameter combination of the particle vector is iteratively calculated. When the fitness value reaches a preset fitness threshold, the final result of the particle swarm algorithm is output, and the final result represents the optimal global solution.

8. The method for analyzing the associated forces of double supporting columns of a bridge according to claim 7, characterized in that: The global optimal solution is adjusted, and the size and arrangement of the optimal support columns are obtained through the reverse particle swarm algorithm.

9. The method for analyzing the associated forces of double supporting columns of a bridge according to claim 1, characterized in that: The bridge is simulated by using Matlab, the bridge parameters are adjusted, and specific data of the optimal stress state of the double support columns under the bridge parameters corresponding to different bridges are obtained; The bridge parameters include the size, stiffness and load distribution coefficient of each supporting column of the bridge.

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