CN118133373A - Suspension bridge cable force optimization method - Google Patents
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Abstract
The invention relates to a suspension bridge cable force optimization method, which comprises the steps of firstly establishing an integral analysis model of a suspension bridge by utilizing finite element analysis software and verifying the accuracy of bridge formation of the model. Then in the calculation model diagram, the suspender is cut off, the main beam is divided into discrete units, and the main beam displacement and the main cable displacement are controlled linearly to be used as optimization solving targets, so that an objective function is established. And (3) symmetrically tensioning the full bridge, and tensioning the suspenders sequentially from the midspan to the two ends. And establishing a relation between the displacement state of the previous tensioning and the displacement state of the current boom tensioning during each tensioning. And (3) establishing an index function by using a dynamic programming method, substituting the target function and the relation established during each tensioning into the index function, and solving to obtain the tensioning force of the suspender in each construction stage. The invention aims at controlling the cable force once through dynamic planning construction, and solves the recurrence relation in stages in the construction process through controlling the objective function, thereby shortening the construction period, saving the construction cost and obtaining the optimal and reasonable bridge formation state.
Description
Technical Field
The invention relates to a bridge construction technology, in particular to a suspension bridge cable force optimization method.
Background
In recent years, suspension bridges have been favored by people in terms of their elegant line shape, flexible adaptability and economy, and the number of such bridges to be built has also been increasing and has been advancing toward larger spans. At present, for the cable force problem in the process of erecting a large-span suspension bridge structure, many scholars have studied, but the following three methods are mainly focused on:
The first method is the "parabolic method": the primary and secondary constant loads are assumed to be uniformly distributed in the span range and are borne by the main cable, so that the main cable is parabolic in a bridge-forming state, the stiffening girder does not bear bending moment, and based on the parabolic main cable, each erection parameter is calculated in a reverse thrust mode. The calculation method belongs to an approximation method, and can determine the line shape and the internal force of the main cable under the constant load effect under the condition of small span, but when the span is large, the error of the result obtained by the method is large.
The second method is the "segmented catenary method": the method takes the empty cable state as the initial state of calculation, at the moment, the main cable is a catenary, the weight equivalent of the primary constant load and the secondary constant load except the main cable is that a plurality of concentrated forces act on the hypothesized catenary to carry out nonlinear calculation, the hypothesized catenary is modified under the condition that the precision requirement is not met by comparing the calculated values with the design parameters of the bridge forming state, the calculation is repeated, the relation is established between each span through the condition that the horizontal forces of the axial force of the main cable are equal, the line shape and the internal force of the structure of the main cable of the bridge forming state are finally obtained, and the erection parameters are reversely pushed based on the relation. The method is used for calculating the erection parameters of the Forth Road bridge and the Severm bridge respectively. The method has the advantages that the influence of non-uniformity of constant load distribution and partial geometrical nonlinearity factors is considered, and the calculation is simpler. However, because the deflection of the saddle and the secondary constant load are not considered, the main cable and the stiffening girder bear the same factors, and the weights of the stiffening girder and the suspender are simply reduced to a series of vertical concentrated force loads which directly act on the free cable to perform approximate calculation, the device has access to the actual situation.
The third method is the "finite element method": firstly, according to the known structural geometric control parameters when the bridge is designed, such as bridge deck design line shape, boom position, saddle center position, main cable sag and other control parameters, an ideal initial state of construction is assumed, then a period of constant load is applied to the cable tower structure in the actual construction process (namely, the weights of stiffening girders and slings are equalized to be centralized force to act on the cable clamp position), and the structural analysis is carried out by adopting nonlinear finite elements, so that the geometric shape and internal force under the action of the constant load in the period are obtained. And on the basis, the steel connection of the stiffening girder and the application of the second-stage constant load are carried out, so that the geometric shape and the internal force of the structure under the action of all constant loads are obtained. And then comparing the parameter values with the geometric control parameters designed to be in a bridge state, if the error is larger, correcting the parameter values of the ideal initial state of the construction, repeating the steps, continuously correcting until the precision requirement is met, and finally outputting the erection parameters. However, the actual construction process is simulated to have a certain error in the final result due to the fact that the actual structure (saddle, tower, stiffening beam, sling system) is accessed by the practice of applying the weight of the stiffening beam, sling, etc. to the cable tower structure as a concentrated force.
Disclosure of Invention
The invention aims to provide a suspension bridge cable force optimization method, which aims to solve the problem of large cable force calculation result error in the erection process of the existing large-span suspension bridge structure.
The invention is realized in the following way: a suspension bridge cable force optimization method comprises the following steps.
S1, establishing an integral analysis model of the suspension bridge by utilizing finite element analysis software.
S2, performing bridge forming cable force analysis and bridge forming linear analysis on the bridge forming state, comparing the bridge forming cable force with a disposable Cheng Qiaosuo force value, designing bridge forming linear and primary bridge forming comparison, and verifying the accuracy of the bridge forming of the model.
S3, cutting off the suspender in the calculation model diagram.
S4, dividing the main beam into discrete units, taking linear control of the displacement of the main beam and the displacement of the main cable as an optimization solving target, and establishing an objective function.
S5, tensioning the whole bridge symmetrically, and tensioning the suspenders sequentially from the midspan to the two ends, wherein each tensioning is a construction stage.
And S6, establishing a relation between the displacement state of the previous tensioning and the displacement state of the current boom tensioning during each tensioning.
And S7, applying a dynamic programming method and a Bellman optimal principle to minimize the function value of each construction stage of the objective function in the step S4 so as to establish an index function.
S8, substituting the formulas established in the step S4 and the step S6 into the index function established in the step S7 to solve, and obtaining the magnitude of the boom tension in each construction stage.
In step S4, the objective function established is:
Wherein A and B are Row of lines -order weighting matrixes, X i+1 and X i are structural displacement states of the unit beam segments before and after the hanger rod is stretched, and f i is the initial stretching force of the hanger rod.
In step S6, the established relational expression is:
Xn＝Xn-1+Gnfn
Wherein, X n and X n-1 are the displacement after the current construction stage is finished and the last construction stage is finished respectively, G n is the influence matrix of the tensioning of the suspension rod applied in the nth construction stage on the structure, and f n is the tensioning force of the suspension rod in the nth construction stage.
In step S7, for any initial state, let g n (X) be the minimum value of the objective function at the nth construction stage, to obtain an index function:
The invention establishes the suspension bridge construction cable force model by a dynamic programming method, considers geometric nonlinear factors in a dynamic programming optimization theory, optimizes the suspension bridge sling construction process in construction control, controls the influence of each sling on a main cable and a whole bridge to achieve the purpose of one-step forming in the suspension bridge construction process, and provides a practical feasible scheme for suspension bridge construction. The invention can ensure that the bridge formation line shape of the main bridge suspension bridge is basically consistent with the bridge formation target line shape expected by design on the premise of ensuring safety and reliability.
Drawings
Fig. 1 is an initial calculated overall model of a suspension bridge.
Fig. 2 is a schematic view of a first tensioned sling.
Fig. 3 is a schematic diagram of a second tensioned sling.
Fig. 4 is a schematic view of an nth tensioning sling.
FIG. 5 is a flow chart of a model bridge and empty cable state calculation.
Detailed Description
The invention provides a one-time in-place construction method for dynamically planning construction control cable force, which aims at solving the recurrence relation of the construction process in stages by controlling an objective function, has short construction period, saves construction cost and obtains the optimal reasonable bridge formation state. The invention comprises the following steps.
S1, establishing an integral analysis model of the suspension bridge by utilizing finite element analysis software.
S2, performing bridge forming cable force analysis and bridge forming linear analysis on the bridge forming state, comparing the bridge forming cable force with a disposable Cheng Qiaosuo force value, designing bridge forming linear and primary bridge forming comparison, and verifying the accuracy of the bridge forming of the model.
S3, cutting off the suspender in the calculation model diagram.
S4, dividing the main beam into discrete units, taking linear control of the displacement of the main beam and the displacement of the main cable as an optimization solving target, and establishing an objective function.
S5, tensioning the whole bridge symmetrically, and tensioning the suspenders sequentially from the midspan to the two ends, wherein each tensioning is a construction stage.
And S6, establishing a relation between the displacement state of the previous tensioning and the displacement state of the current boom tensioning during each tensioning.
And S7, applying a dynamic programming method and a Bellman optimal principle to minimize the function value of each construction stage of the objective function in the step S4 so as to establish an index function.
S8, substituting the formulas established in the step S4 and the step S6 into the index function established in the step S7 to solve, and obtaining the magnitude of the boom tension in each construction stage.
The steps of the present invention will be described in detail with reference to the accompanying drawings.
First, a global analysis model of the suspension bridge is built using finite element analysis software (e.g., midaws, ANSYS, etc.).
The method comprises the following specific steps: firstly, defining a section and a material, wherein the section mainly comprises a main beam, a main tower and a cable section; then initial modeling is carried out, and the bridge and empty cable states are determined by utilizing the built-in function of accurately analyzing the initial state of the suspension bridge provided by Midasi; then applying boundary conditions, mainly comprising the following steps that an upper cross beam and a lower cross beam of a bridge tower are just connected with a side tower body, a main beam is in a single main beam form and is connected with a sling through a rigid arm, the main tower and the main beam are in rigid connection simulation, a bridge abutment and the main beam are only in pressed elastic connection, a main cable and a saddle are provided with rigid arms and the positions of the main cable and the saddle control the change of the contact points of the main cable and the saddle, and the main cable and the main beam are provided with the mutually connected upper rigid connection and the lower rigid connection for sling connection, so that the rigidity of an anchor head is realized; and finally, carrying out contrast correction on the model through modes and internal forces according to the actual structural condition.
And then, performing bridge forming cable force analysis and bridge forming line analysis on the bridge forming state: and comparing the bridge forming cable force with a disposable Cheng Qiaosuo force value, designing a bridge line shape and comparing the bridge forming cable force with a disposable bridge forming force value, and verifying the accuracy of the bridge forming of the model.
The model bridging and empty cable state calculation process is shown in fig. 5.
And after the model is established and the accuracy of the bridge formation of the model is verified, calculating according to the model.
Firstly, as shown in fig. 1, a calculation model is that the suspension rods are cut off, the cable force of each suspension rod at present (under the first-stage load) is set to be F i, the cable force direction of the suspension rod is vertical upwards for a main beam, the self weight of the main beam uniformly distributes loads q along the bridge direction, the counter forces of left and right supports are set to be F A and F B, the position coordinate of an ith suspension rod is set to be x i, the displacement of the main beam and a main cable is linearly controlled to be an optimal solving target, and an objective function is established as follows:
Wherein A and B are n-order weighting matrixes, X i+1 and X i are respectively structural displacement states of the unit beam segments at the stage before and after the hanger rod is stretched, and f i is the initial stretching force of the hanger rod.
The weighting matrix can effectively avoid the phenomenon of losing each other. The weighting coefficients may be composed of two parts: ρ=ρ 1·ρ2, wherein: ρ 1 considers the dimension of the control target value, and takes one physical quantity as a reference R 0, and if the cable force is 1, the other physical quantity, such as the physical quantity displacement R 0/Rt,R0、Rt, is the average value of the target values of the reference physical quantity and the other physical quantity, respectively. ρ 2 represents that the control target is controlled to be high or low, the general physical quantity value is 1, and the key physical quantity is selected from 1 to 10 according to the trial calculation result.
And then, symmetrically tensioning the full bridge, and tensioning the suspenders sequentially from the midspan to the two ends. If the tension of the mid-span boom is F 1 and the immediately adjacent side booms are F 2, then F 3、F4 … to F n are set in order to the bridge tower.
As shown in fig. 2, in the first tensioning, let the initial state objective function before tensioning be E 0, the boom force be f 1, the overall compliance matrix in the current stage be K 1 (directly available), and the impact matrix G 1 generated under the action of unit tensioning force satisfies at this time:
X1＝X0+G1f1
Wherein X 1 is the vertical displacement of the main beam after the 1 st construction stage is finished, X 0 is the vertical displacement of the main beam before the first construction stage, G 1 is the influence matrix of the applied unit tensile force on the vertical displacement of the main beam, and f 1 is the initial tensile force of the first suspender.
As shown in fig. 3, during the second tensioning, under the action of f 2, a corresponding G 2 is generated, and at this time, there are:
X2＝X1+G2f2
therefore, as shown in fig. 4, the displacement state of the previous tensioning and the displacement state of the current boom tensioning at each tensioning always form the following relationship:
Xn＝Xn-1+Gnfn
wherein, X n and X n-1 are the displacement after the current construction stage is finished and the last construction stage is finished respectively, G n is the influence matrix (directly available in the model) of the structure by applying the boom tensioning in the nth construction stage, and f n is the tensioning force of the boom in the nth construction stage.
At present, the matrix G n is known, the force term f is unknown, an objective function is established for solving the initial tension of each construction stage, in order to minimize the function value of each construction stage of the objective function, a dynamic programming method and a Bellman optimal principle are applied, and for any initial state, G n (X) is set as the minimum value in the construction n-stage, so as to obtain an index function:
substituting the objective function into the index function to obtain:
then substituting a relation formed by a displacement state of the previous boom stretching and a displacement state of the current boom stretching into the formula to obtain:
and (3) formulating the formula to obtain the following formula:
Wherein:
minimizing g n (X) gives:
fn＝-MnXn-Nn
Bringing the functions M n and N n into:
Wherein, X n is the displacement of the structure during the nth tensioning of the boom, and L n is the ideal vertical displacement of the main beam in each construction stage.
Iterating the steps to finally obtain:
Where H 1、L1, and G 1 are known, X 1 is the displacement of the structure when the boom is first tensioned. The tension force f 1 of the first boom can thereby be released.
According to the calculation process, the boom tension force of each stage can be obtained by programming and repeatedly solving step by step.
The suspension bridge body is in two parts, and the bridge body mainly generates vertical downward gravity; the suspension cable part transmits force to the bridge towers at two ends of the bridge through axial force, and the suspension cable part and the bridge towers are connected through vertical slings, so that the dynamic research analysis of the bridge body and the linear research of the main cable are very critical in the process of tensioning each sling.
The dynamic programming method is based on the measurement results of the measurement data of a plurality of distributed sensors, identifies the forces in a dynamic system state space formula in the time domain, and constructs structural response by utilizing the identified forces or the comparison results. Dynamic programming techniques essentially provide boundaries for them, which are greatly improved in recognition accuracy over existing approaches.
The method is characterized in that a dynamic programming method is used in the suspension bridge cable force optimization process, the suspension cable force optimization problem is solved by analyzing the tensioning process of each suspension cable during construction and using the dynamic programming method, the multi-step optimization problem is simplified, a calculation formula of the cable force is deduced, under the three nonlinear conditions of a large structural displacement effect, a beam-column effect and a sag effect, the change state of the bridge after the completion of tensioning of each suspension cable is analyzed by using an unknown load coefficient method in finite element software, the suspension cable construction process is optimized, and the method can be applied to suspension bridge construction control analysis.
According to the invention, a suspension bridge construction cable force model is established by a dynamic programming method, a geometric nonlinear factor is combined with a result obtained by a dynamic programming optimization theory, the suspension bridge sling construction process is optimized, the influence of each sling on a main cable and a whole bridge is controlled to achieve the purpose of one-step forming in the suspension bridge construction process, and a practical feasibility scheme is provided for suspension bridge construction. The invention can ensure that the bridge formation line shape of the main bridge suspension bridge is basically consistent with the bridge formation target line shape expected by design on the premise of ensuring safety and reliability.
Claims (4)
1. The suspension bridge cable force optimization method is characterized by comprising the following steps of:
s1, establishing an integral analysis model of a suspension bridge by utilizing finite element analysis software;
S2, performing bridge forming cable force analysis and bridge forming linear analysis on the bridge forming state, comparing the bridge forming cable force with a disposable Cheng Qiaosuo force value, designing bridge forming linear and primary bridge forming comparison, and verifying the accuracy of the bridge forming of the model;
s3, cutting off the suspender in the calculation model diagram;
s4, dividing the main beam into discrete units, taking linear control of the displacement of the main beam and the displacement of the main cable as an optimization solving target, and establishing an objective function;
S5, tensioning the whole bridge symmetrically, and tensioning the suspenders sequentially from the midspan to the two ends, wherein each tensioning is a construction stage;
S6, establishing a relation between the displacement state of the previous tensioning and the displacement state of the current boom tensioning during each tensioning;
S7, applying a dynamic programming method and a Bellman optimal principle to enable the function value of each construction stage of the objective function in the step S4 to be minimum so as to establish an index function;
s8, substituting the formulas established in the step S4 and the step S6 into the index function established in the step S7 to solve, and obtaining the magnitude of the boom tension in each construction stage.
2. The method of optimizing the suspension bridge cable force according to claim 1, characterized in that in step S4, the objective function established is:
Wherein A and B are n-order weighting matrixes, X i+1 and X i are respectively structural displacement states of the unit beam segments at the stage before and after the hanger rod is stretched, and f i is the initial stretching force of the hanger rod.
3. The method of optimizing a suspension bridge cable force according to claim 1, wherein in step S6, the established relationship is:
Xn＝Xn-1+Gnfn
Wherein, X n and X n-1 are the displacement after the current construction stage is finished and the last construction stage is finished respectively, G n is the influence matrix of the tensioning of the suspension rod applied in the nth construction stage on the structure, and f n is the tensioning force of the suspension rod in the nth construction stage.
4. The method according to claim 1, wherein in step S7, for any initial state, g n (X) is set as the minimum value of the objective function at the nth construction stage, to obtain the index function:
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