CN114896844B - Arch bridge back buckling cable tension data processing method, system and storage medium - Google Patents
Arch bridge back buckling cable tension data processing method, system and storage medium Download PDFInfo
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Abstract
The invention discloses a method, a system and a storage medium for processing arch bridge back-buckling cable tension data, which can be widely applied to the field of bridge construction. According to the invention, the influence matrixes of displacement of arch rib control nodes and inhaul cable force in different construction stages are extracted; based on the displacement influence matrix, acquiring actual displacement of the arch rib control node after closure rope loosening; and the sum of squares of actual displacement and target displacement difference of arch rib control points at each hoisting construction stage is taken as an objective function to restrain the linearity of the upstream arch rib, the downstream arch rib, the linear shape of the large mileage, and the like, and solve the back cable force of the arch bridge, thereby improving the linear error control precision.
Description
Technical Field
The invention relates to the technical field of bridges, in particular to a method, a system and a storage medium for processing back cable force data of an arch bridge buckle.
Background
The arch bridge has the advantages of beautiful shape, economical manufacturing cost, good durability, strong earthquake resistance, wind resistance and bearing capacity, rapid development and wide application in mountain areas in China. The arch bridge can be divided into a bracket method, an integral hoisting method, a swivel construction method, a cable-stayed buckling cantilever method and the like according to different construction methods. For the mountain large-span arch bridge, the cable-stayed buckling cantilever method is a construction method which is widely applied to the construction of the large-span arch bridge, wherein buckling towers are arranged on two sides of the large-span arch bridge, and the buckling towers are assembled and poured through buckling cables and cable-stayed components. Along with the continuous innovation and development of arch bridge technology, the span of the arch bridge is continuously increased, and the construction difficulty is also increased, so that the requirements on the linear control and the cable force uniformity of the structure in the construction process of the cable-stayed buckling and hanging are higher.
The existing method generally takes the deviation of the displacement of each control node and the target linear displacement after closure and cable loosening as a constraint condition, takes the vector norm of the displacement of each control point and the target displacement difference of each hoisting construction stage as an optimization objective function, combines an influence matrix method to establish an optimal calculation theory of 'process optimal and result controllable' cantilever assembly construction, strictly controls the actual linear shape and the target linear shape of each construction hoisting stage, ensures that the pre-lifting value of each control node is gentle in change, the cable force uniformity is good, the stress concentration phenomenon of the material in the construction process can not occur, and the constraint condition is less.
The method is characterized in that the tower deviation is taken as an assumption, the influence of the tower deviation in the calculation process is not considered when the back cable force is calculated, the back cable force value is iterated according to the horizontal component force balance principle of the horizontal angle between the back cable and the buckle cable on the buckle tower after the buckle cable force is calculated, the back cable force is calculated and is brought into the finite element model, whether the calculated tower deviation result is zero is used as a standard to judge whether the back cable force meets the requirement, all the cable force can be obtained after multiple adjustments, a certain cable adjusting experience is needed in the process when the back cable force is automatically corrected when the tower deviation result in the finite element model is not zero in the back cable calculation process, and the calculated back cable force is applied to the actual installation process to have linear deviation.
Disclosure of Invention
The invention aims to at least solve one of the technical problems in the prior art, and provides a method, a system and a storage medium for processing arch bridge back cable force data, which improve the control precision of linear errors.
In one aspect, an embodiment of the present invention provides a radar ranging apparatus based on phase tracking, including:
s100, extracting at least one displacement influence matrix and at least one cable force influence matrix based on the coupling effect of a first variable on the displacement of arch rib control nodes and the cable force of a cable, wherein the first variable comprises constant load and unit cable tension in different construction stages;
s200, acquiring actual displacement of the arch rib control node after closure rope loosening based on the displacement influence matrix, the rope force influence matrix and a second variable, wherein the second variable is arch bridge back rope buckling force;
s300, solving the second variable, so that the difference value between the actual displacement of the arch rib control node and the target displacement after closure and loosening under the action of the arch bridge back rope force is within a first threshold value, the actual displacement of the forefront arch rib control node with the same mileage and the actual displacement of the upstream and downstream arch rib control nodes are equal when the closure section is erected under the action of the released arch bridge back rope force, and the released arch bridge back rope force is within a preset range.
In some embodiments, step S100 is preceded by: and establishing a space finite element model of the arch bridge structure according to the arch bridge structure parameters, and determining at least one of the number of arch rib control nodes, the number of unknown loads in the second variable, the first threshold value and a preset range of back buckling cable force.
In some embodiments, extracting the influence matrix in step S100 using the finite element model includes:
during the construction process, obtainMatrix D of influence of tension unit cable force on displacement of arch rib control node f And a cable force influence matrix F of the tension unit cable force on the inhaul cable f ；
In the process of detaching the cable, obtaining a displacement influence matrix D of the detaching unit cable force on the arch rib control node dc ；
Obtaining a displacement influence matrix b of constant load on the arch rib control node 0 And a cable force influence matrix b of the constant load on the inhaul cable 1 。
In some embodiments, obtaining the actual displacement of the rib control node after closure release in step S200 includes:
based on the displacement influence matrix, the cable force influence matrix and a second variable T i Acquiring actual displacement u of cantilever end control node corresponding to currently installed arch rib section and tensioned buckling rope 1 (T i ) The actual displacement u of the cantilever end control node corresponding to the transverse connection of the currently installed arch ring 2 (T i ) Wherein u is 1 (T i )＝D f ·T i +b 0 ′+D dc ·(F f ·T i +b 1 )，u 2 (T i )＝D f ·T i +b 0 ″+D dc ·(F f ·T i +b 1 ) B when the constant load is the self weight of the arch rib 0 ' is a displacement influence matrix of the constant load on the arch rib control node, and b is when the constant load is arch rib dead weight and wind bracing 0 "is the displacement influence matrix of the constant load on the arch rib control node, and the actual displacement uh (T i ) Wherein uh (T) i )＝αu 1 (T i )+βu 2 (T i ) Alpha and beta are set values.
In some embodiments, solving the second variable in step S300 comprises:
taking the sum of squares of the actual displacement and the target displacement difference of arch rib control points at each hoisting construction stage as an objective function F, wherein
n is the unknown load number in the second variable, b 2 Is the target displacement;
solving the second variable to enable the objective function to be a global minimum value so as to ensure the linear stability of the arch rib control node in the construction process.
In some embodiments, the actual displacement equality of the front-end arch rib control nodes of the mileage when the closure segments are erected under the action of the solved back-bridge buckle cable in step S300 includes:
obtaining a large and small mileage cable force displacement matrix difference Aeq, aeq = [ E ] of a forefront control node in a maximum cantilever state before closure 1 ·(D f +D dc ·F f )-E 2 ·(D f +D dc ·F f )]Wherein E is 1 ，E 2 Is a preset matrix;
acquiring a fixed load displacement vector difference beq, beq =e of the size mileage of the front-end control node in the maximum cantilever state before closure 2 ·(b 0 +D dc ·b 1 )-E 1 ·(b 0 +D dc ·b 1 )；
The practical displacement of the control nodes of the forefront arch ribs with the same size mileage during the erection of the closure section is taken as a constraint condition, aeq.T i = beq, where T i And selecting the back cable force of the arch bridge buckle for the second variable to control the elevation of the arch rib after closure and loosening to be equal.
In some embodiments, the equality of the actual displacements of the upstream and downstream arch rib control nodes under the action of the unbuckled back cable in step S300 comprises:
the actual displacement u1_S of the control node at the upstream of the arch rib in the hoisting construction stage is obtained,
acquiring actual displacement u1_S of a downstream control node of an arch rib in a hoisting construction stage;
taking the maximum absolute value of the actual displacement difference value of the upstream and downstream control nodes of the arch rib in the hoisting construction stage as a nonlinear inequality constraint condition within a minimum range, and max (abs (u1_S-u1_X)) +.χ, wherein χ is a preset value, and selecting the back cable force of the arch bridge buckle to ensure the equality of the line shapes of the upstream and downstream arch rib control nodes.
In some embodiments, a mathematical model is constructed based on the constraint conditions and the objective function, the influence matrix is substituted into the mathematical model, and the back buckling cable force of the cable-stayed buckling construction arch bridge is solved.
On the other hand, the embodiment of the invention also provides a data processing system for the back cable force of the arch bridge buckle, which is characterized by comprising the following steps:
the first module is used for extracting at least one displacement influence matrix and at least one cable force influence matrix based on the coupling effect of a first variable on the displacement of the arch rib control node and the cable force of the cable, wherein the first variable comprises constant load and unit cable tension in different construction stages;
the second module is used for acquiring the actual displacement of the arch rib control node after closure rope loosening based on the displacement influence matrix, the rope force influence matrix and a second variable, wherein the second variable is the arch bridge back rope buckling force;
and the third module is used for solving the second variable so that the difference value between the actual displacement of the arch rib control node and the target displacement after closure and loosening are performed under the action of the arch bridge back-buckling cable force is within a first threshold value, the actual displacement of the foremost arch rib control node with the same size mileage and the actual displacement of the upstream and downstream arch rib control nodes are equal when the closure section is erected under the action of the closure of the opened arch bridge back-buckling cable force, and the opened arch bridge back-buckling cable force is within a preset range.
In yet another aspect, an embodiment of the present invention further provides a computer readable storage medium, where a computer program is stored, where the computer program when executed by a processor implements the method steps of any of the above embodiments.
The beneficial effects of the invention are as follows: taking the force of each back buckling cable as an unknown quantity, fully considering the influence of each variable load and fixed load on arch rib line shape and the mutual influence between the variable load and the fixed load to obtain a related influence matrix, extracting the corresponding influence matrix through finite element software, and substituting the corresponding influence matrix into a mathematical model to perform one-time solution of all the back buckling cable forces; the problems that the upstream and downstream buckling ropes are asymmetric in the longitudinal bridge direction, the heights of arch ribs after closure and loosening are unequal and the like are fully considered, the upstream and downstream rope force is considered separately, the contour constraint is carried out on the upstream and downstream arch rib line shape, and the line shape of the large mileage is constrained when the closure section is erected, so that the calculated back buckling rope force is almost consistent with the target line in the actual installation process.
Drawings
Fig. 1 is a flowchart of a method for processing data of back cable force of an arch bridge according to an embodiment of the present invention.
Fig. 2 is a schematic view of an arch bridge according to an embodiment of the present invention.
Fig. 3 is a flowchart illustrating a method for processing data of back cable force of an arch bridge according to an embodiment of the present invention.
Fig. 4 is a diagram illustrating an iterative calculation process of the back cable force of the arch bridge according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of the values of the back-buckling cable force after iterative convergence according to an embodiment of the present invention.
Fig. 6 is a schematic diagram of deformation values of an upstream control node at different stages of construction according to an embodiment of the present invention.
Fig. 7 is a schematic diagram showing deformation values of a downstream control node at different construction stages according to an embodiment of the present invention.
Fig. 8 is a schematic diagram showing deformation values of an upstream and a downstream control nodes according to an embodiment of the present invention.
Fig. 9 is a block diagram of an arch bridge back cable force data processing system according to an embodiment of the invention.
Detailed Description
Reference will now be made in detail to the present embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the accompanying drawings are used to supplement the description of the written description so that one can intuitively and intuitively understand each technical feature and overall technical scheme of the present invention, but not to limit the scope of the present invention.
In the description of the present invention, unless explicitly defined otherwise, terms such as arrangement and the like should be construed broadly, and those skilled in the art can reasonably determine the specific meaning of the terms in the present invention in combination with the specific contents of the technical scheme.
The invention utilizes finite element analysis software to carry out space finite element analysis on the mechanical property of a main span bridge section, specifically, establishes a space finite element model of an arch bridge structure according to arch bridge structure parameters, and determines at least one of the number of arch rib control nodes, the number of unknown loads in arch bridge back buckling cable force, a first threshold value and a preset range of back buckling cable force. Wherein the number of arch rib control nodes is marked as m, the number of unknown loads in the arch bridge back-buckling cable force is marked as n, and the ith unknown load is marked as T i The first threshold is noted as x and the preset range of the back-buckling cable force is noted as (lb, ub). Further, the fixed load is denoted t.
As shown in fig. 1, the method for processing the data of the back cable force of the arch bridge buckle provided by the embodiment of the invention comprises the following steps:
s100, extracting at least one displacement influence matrix and at least one cable force influence matrix based on the coupling effect of a first variable on the displacement of arch rib control nodes and the cable force of a cable, wherein the first variable comprises constant load and unit cable tension in different construction stages;
specifically, extracting the influence matrix in step S100 by using the finite element model includes: in the construction process, a displacement influence matrix D of the tension unit cable force on arch rib control nodes is obtained f And a cable force influence matrix F of the tension unit cable force on the inhaul cable f The method comprises the steps of carrying out a first treatment on the surface of the In the process of detaching the cable, obtaining a displacement influence matrix D of the detaching unit cable force on the arch rib control node dc The method comprises the steps of carrying out a first treatment on the surface of the Obtaining a displacement influence matrix b of constant load on arch rib control nodes 0 And a constant load cable force influence matrix b for the inhaul cable 1 。
S110, in the construction process, a matrix D is formed by influencing the displacement of arch rib control nodes by the tension unit cable force f As shown in formula (1).
D f Alpha is the element of the middle element jk (j=1, 2, …, m; k=1, 2, …, n) is the displacement influence of the tension unit cable force of the kth cable on the jth control node during construction;
s120, in the construction process, a cable force influence matrix F of the tension unit cable force on the inhaul cable f As shown in equation (2).
F f Intermediate element beta kl (k=1, 2, …, n; l=1, 2, …, n) is the influence of the tension unit cable force of the kth cable on the cable force of the first cable during construction;
s130, in the process of detaching the cable, acquiring a displacement influence matrix D of the detaching unit cable force on the arch rib control node dc As shown in equation (3).
D dc Middle element gamma jk (j=1, 2, …, m; k=1, 2, …, n) is the displacement influence of the tension unit cable force of the kth cable on the jth control node after arch rib closure;
s140, obtaining a displacement influence matrix b of constant load on arch rib control nodes 0 ：
1. B when the constant load is the self weight of the arch rib 0 The displacement influence matrix of the constant load on the arch rib control node is shown in formula (4).
b 0 ' element lambda in jk (j=1, 2, …, m; k=1, 2, …, n) is the displacement influence of the dead weight of the kth cable on the jth control node;
2. b when constant load is arch rib dead weight and wind bracing 0 "constantThe displacement influence matrix of the load pair arch rib control nodes is shown in formula (5).
b 0 "Medium element phi rj (j=1, 2, …, m; r=1, 2, …, t) is the displacement influence of the (r) th fixed load on the (j) th control node during construction;
s150, a constant load cable force influence matrix b of the inhaul cable 1 As shown in equation (6).
b 1 Medium element eta lr (l=1, 2, …, n; r=1, 2, …, t) is the effect of the (r) th fixed load on the (i) th cable force during construction.
S200, acquiring actual displacement of arch rib control nodes after closure rope loosening based on a displacement influence matrix, a rope force influence matrix and a second variable, wherein the second variable is the back rope force of the arch bridge buckle;
specifically, based on the displacement influence matrix, the cable force influence matrix and the second variable T i Acquiring actual displacement u of cantilever end control node corresponding to currently installed arch rib section and tensioned buckling rope 1 (T i ) The actual displacement u of the cantilever end control node corresponding to the transverse connection of the currently installed arch ring 2 (T i ) Wherein u is 1 (T i )＝D f ·T i +b 0 ′+D dc ·(F f ·T i +b 1 )，u 2 (T i )＝D f ·T i +b 0 ″+D dc ·(F f ·T i +b 1 ) B when the constant load is the self weight of the arch rib 0 ' is a displacement influence matrix of constant load on arch rib control nodes, and when the constant load is arch rib dead weight and wind bracing, b 0 "is the displacement influence matrix of constant load to arch rib control node, actual displacement uh (T i ) Wherein uh (T) i )＝αu 1 (T i )-βu 2 (T i ) The invention sets a, β as the set value, the invention sets a, β as the empirical value 0.5, i.e. a=β=0.5, uh (T i )＝0.5·[u 1 (T i )-u 2 (T i )]。
S300, solving a second variable, so that the difference value between the actual displacement and the target displacement of the arch rib control node after closure and cable loosening under the action of the arch bridge back cable force is within a first threshold value, the actual displacement of the foremost arch rib control node with the same size mileage when the closure section is erected under the action of the solved arch bridge back cable force is equal, and the actual displacement of the upstream and downstream arch rib control nodes is equal, wherein the solved arch bridge back cable force is within a preset range.
Specifically, taking the sum of squares of actual displacement and target displacement difference of arch rib control points at each hoisting construction stage as an objective function F, wherein
n is the unknown load number in the second variable, b 2 Is the target displacement;
solving the second variable to make the objective function be the global minimum value so as to ensure the linear stability of the arch rib control node in the construction process.
S310, in the step S300, the difference value between the actual displacement of the arch rib control node and the target displacement after closure and loosening under the action of the arch bridge back cable force is within a first threshold value, and the constraint condition can be expressed as shown in a formula (7) by using a linear inequality.
abs(D f ·T i +b 0 +D dc ·(F f ·T i +b 1 )－b 2 )<△x (7)
The influence of the fixed load on the control node is a constant value, and the constant load influences the displacement influence matrix b 0 Usable b 0 ＝(ψ 1 ,....,ψ m ) T A representation; the influence of the fixed load on the cable force of the cable is also a fixed value, and the constant load influences the cable force of the cable by the matrix b 1 Usable b 1 ＝(ζ 1 ,...,ζ n ) T In the formula b 2 ＝(μ 1 ,...,μ m ) T For the displacement vector of the ideal bare arch of the control node, deltax=epsilon is the tolerance deviation between the control node line shape and the ideal bare arch in the bare arch state;
s320, the actual displacement equality of the forefront arch rib control nodes of the mileage when the closure section is erected under the action of the cable force of the unbuckled arch bridge back cable in the step S300 comprises the following steps:
s321, acquiring a size mileage cable force displacement matrix difference Aeq, aeq = [ E ] of a forefront control node in a maximum cantilever state before closure 1 ·(D f +D dc ·F f )-E 2 ·(D f +D dc ·F f )]Wherein E is 1 ，E 2 For a preset matrix, where E 1 ，E 2 As shown in equations (8-9).
S322, obtaining a fixed load displacement vector difference beq, beq =E of the size mileage of the front-end control node in the maximum cantilever state before closure 2 ·(b 0 +D dc ·b 1 )-E 1 ·(b 0 +D dc ·b 1 )；
S323, taking the actual displacement equality of the control nodes of the arch ribs at the forefront end of the large mileage during the erection of the closure section as a constraint condition, selecting the back cable buckling force of the arch bridge so as to control the elevation equality of the arch ribs after closure releasing. The above constraint is as shown in formula (10).
Aeq·T i ＝beq (10)
S330, the actual displacement equality of the upstream and downstream arch rib control nodes under the action of the cable force of the unbuckled arch bridge back cable in the step S300 comprises:
s331, acquiring actual displacement u1_S of an arch rib upstream control node in a hoisting construction stage,
s332, acquiring actual displacement u1_S of a downstream control node of the arch rib in the hoisting construction stage;
s333, taking the maximum absolute value of the actual displacement difference value of the arch rib upstream and downstream control nodes in the hoisting construction stage as a nonlinear inequality constraint condition within a minimum range, and max (abs (u1_S-u1_X)) +.χ, wherein χ is a preset value, and selecting arch bridge back cable force to ensure that the control nodes of the upstream and downstream arch ribs are equal in line shape. For example, when the preset value χ is 0.001, the constraint inequality condition is as shown in the formula (11).
max(abs(u1_S-u1_X))-0.001≤0 (11)
S340, the back cable force of the arch bridge buckle obtained in the step S300 is within a preset range and comprises the following steps:
and the maximum breaking force of the back buckling rope force is taken as a minimum boundary constraint condition, and the constraint inequality condition is shown as a formula (12).
lb<T i <ub (12)
Wherein lb is a lower limit of the cable force, ub is an upper limit of the cable force, lb and ub can be selected according to specific specifications in construction, and a preset range of the back-buckling cable force is recorded as (lb and ub);
based on the above constraint conditions such as formula (7), formula (10), formulas (11-12) and objective function
And constructing a mathematical model, substituting the influence matrix into the mathematical model, and solving the back buckling cable force of the cable-stayed buckling construction arch bridge.
As shown in FIG. 2, the embodiment of the invention is exemplified by a steel truss arch bridge-a roqueur Shui He super bridge with a net span of 290 m. The arch axis uses catenary, and the theoretical catenary parameters are shown in table 1.
TABLE 1 theoretical catenary parameters
The arch rib axis is a part of a theoretical catenary, and the horizontal distance from the starting point of the arch axis to the theoretical arch axis is designed: preferably, the shore side is 28m, the shore side of the cross section of the main arch rib is 0m, the total section of the main arch rib is equal in height, and the vertical distance from the center line of the upper chord to the center line of the lower chord is 7.5m. The center distance of the two transverse arch rib trusses is 27m, the two arch rib trusses are connected through the wind brace, and the full-bridge wind brace is of a decimeter type and a K type. The upper chord member and the lower chord member of the arch rib are all in box-shaped cross sections, the web members are in box-shaped cross sections, the upper flat joint and the lower flat joint of the air brace and the diagonal brace are in box-shaped cross sections, and the web members of the air brace are in H-shaped cross sections. The bridge arch rib sections are 22, preferably 10 construction sections are arranged on the shore side, 12 construction sections are arranged on the shore side of the bridge arch rib, each construction section is divided into an upstream construction section and a downstream construction section, and a cantilever splicing method is adopted for construction. Assuming a total of m=88 rib control nodes, there are n=88 variable loads to affect 88 rib control nodes, no. 1-22 upstream rib control nodes, no. 23-44 upstream main tower control nodes, no. 45-66 downstream rib control nodes, no. 67-88 downstream main tower control nodes, in this embodiment the number of rib construction erection stages is 26, so there are t=26 fixed loads, the rib linear deviation is set, i.e. the first threshold x=2 cm, and the cable force tolerance is the breaking force of the cable, as shown in table 2.
Table 2 structural parameters of arch bridge
Aiming at the asymmetric cable force caused by the upstream and downstream asymmetric cables of the arch bridge, the conventional method needs to solve each cable independently, the cable force of the cables is solved by taking the arch rib line shape as a control target, and the cable force of the back cables is solved by taking the tower deflection line shape as a control target. All the cable force of the inhaul cable can be obtained after multiple adjustments, a certain cable adjusting experience is needed in the process of automatically correcting the cable force of the back cable when the tower deviation result in the finite element model is not zero in the process of calculating the back cable, and the calculated back cable buckling force cannot be really realized under the condition of actual engineering due to cable force tensioning deviation when the calculated back cable buckling force is applied to the actual process.
As shown in fig. 3, the embodiment of the invention constructs a finite element model based on the geometric parameters, material parameters, boundary conditions and load conditions of the arch bridge; root of Chinese characterDetermining a construction stage structure group, a boundary value and a load group according to engineering construction working conditions to establish a construction stage model; determining the number of unknown loads by combining the influence matrix principle, and deriving an influence matrix D corresponding to the unknown loads f ，D dc ，F f ，b 0 ，b 1 . In the present embodiment, D f ，D dc ，F f ，b 0 ，b 1 The result of (2) is calculated by combining finite element software such as midas/civil structure analysis software, and the solution adopts mathematical engineering optimization software such as MATLAB; determining control nodes, variable load number, fixed load number, and standard requirement arch rib linear deviation value, cable force tolerance value and other parameters, then introducing the influence matrix data and the parameter values into a mathematical model constructed by programming software, solving the back buckling cable force, and carrying out iterative calculation by a computer, wherein the convergence process is shown in fig. 4, and the back buckling cable calculation process is rapid and does not need to carry out manual calculation and repeated cable adjustment as can be known from fig. 4; as shown in fig. 5, the calculation result of the cable force is shown in fig. 5, and the overall change of the cable force of each buckle cable is relatively gentle, the cable force difference between two adjacent buckle cables is relatively small, no cable force mutation exists, and the uniformity of the cable force is good. Fig. 6 is a deformation condition of an upstream control node in the installation process, and fig. 7 is a deformation condition of a downstream control node in the installation process, as can be seen from fig. 6 and 7, displacement changes of cantilever end control nodes of different sections in the construction process are more gentle under the condition of considering the integral influence of a buckling rope and a back rope, the continuity of construction linearity is better, in addition, the elevation and ideal linearity errors of all control points after closure and release of the rope are 20mm, and the elevation and ideal linearity errors of all control points in the hoisting construction stage are not more than 30mm; the data show that the calculation method of the invention not only can control the line shape of the structure after closure and loosening, but also can control the line shape of each arch rib hoisting construction stage with high precision, and is simple and convenient in process, and the calculation method of the arch bridge back buckling cable force data processing is unnecessary to consider calculation separately. As can be seen from fig. 8, when all the upstream and downstream cable forces are considered, the control accuracy of the linear error of the corresponding control node is extremely high, and the error value is basically zero.
It can be known that the actual displacement of each control node and the target linear displacement difference after closure rope loosening are used as linear inequality constraint conditions, the maximum absolute value of the actual displacement difference of the arch rib upstream and downstream control nodes in the hoisting construction stage is used as nonlinear inequality constraint conditions in a minimum range, the maximum breaking force of the back-buckling rope force is used as minimum boundary constraint conditions, the actual displacement of the big mileage and the actual displacement difference of the front-end control node in the maximum cantilever state before closure rope are used as linear inequality constraint conditions, and the square sum of the actual displacement of the arch rib control point and the target displacement difference in each hoisting construction stage is used as an optimization objective function, so that the problems of complicated back rope calculation process, asymmetric rope force calculation and the like in the process of optimal process and controllable result are effectively solved.
As shown in fig. 9, an embodiment of the present invention further provides an arch bridge back cable force data processing system, which specifically includes:
the first module is used for extracting at least one displacement influence matrix and at least one cable force influence matrix based on the coupling effect of a first variable on the displacement of the arch rib control node and the cable force of the cable, wherein the first variable comprises constant load and unit cable tension in different construction stages;
the second module is used for acquiring the actual displacement of the arch rib control node after closure rope loosening based on the displacement influence matrix, the rope force influence matrix and a second variable, wherein the second variable is the arch bridge back rope buckling force;
and the third module is used for solving the second variable so that the difference value between the actual displacement of the arch rib control node and the target displacement after closure and loosening are performed under the action of the arch bridge back-buckling cable force is within a first threshold value, the actual displacement of the foremost arch rib control node with the same size mileage and the actual displacement of the upstream and downstream arch rib control nodes are equal when the closure section is erected under the action of the closure of the opened arch bridge back-buckling cable force, and the opened arch bridge back-buckling cable force is within a preset range.
It should be appreciated that the method steps in embodiments of the present invention may be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in non-transitory computer-readable memory. The method may use standard programming techniques. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language. Furthermore, the program can be run on a programmed application specific integrated circuit for this purpose.
Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes (or variations and/or combinations thereof) described herein may be performed under control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications), by hardware, or combinations thereof, collectively executing on one or more processors. The computer program includes a plurality of instructions executable by one or more processors.
Further, the method may be implemented in any type of computing platform operatively connected to a suitable computing platform, including, but not limited to, a personal computer, mini-computer, mainframe, workstation, network or distributed computing environment, separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, and so forth. Aspects of the invention may be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and/or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer, which when read by a computer, is operable to configure and operate the computer to perform the processes described herein. Further, the machine readable code, or portions thereof, may be transmitted over a wired or wireless network. When such media includes instructions or programs that, in conjunction with a microprocessor or other data processor, implement the steps described above, the invention described herein includes these and other different types of non-transitory computer-readable storage media. The invention also includes the computer itself when programmed according to the methods and techniques of the present invention.
The computer program can be applied to the input data to perform the functions described herein, thereby converting the input data to generate output data that is stored to the non-volatile memory. The output information may also be applied to one or more output devices such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on a display.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of one of ordinary skill in the art without departing from the spirit of the present invention.
Claims (8)
1. The arch bridge back-buckling cable force data processing method is characterized by comprising the following steps of:
s100, extracting at least one displacement influence matrix and at least one cable force influence matrix based on the coupling effect of a first variable on the displacement of arch rib control nodes and the cable force of a cable, wherein the first variable comprises constant load and unit cable tension in different construction stages;
wherein, in the construction process, a displacement influence matrix D of the tension unit cable force on the arch rib control node is obtained f And a cable force influence matrix F of the tension unit cable force on the inhaul cable f The method comprises the steps of carrying out a first treatment on the surface of the In the process of detaching the cable, obtaining a displacement influence matrix D of the detaching unit cable force on the arch rib control node dc The method comprises the steps of carrying out a first treatment on the surface of the Obtaining a displacement influence matrix b of constant load on arch rib control nodes 0 And a constant load cable force influence matrix b for the inhaul cable 1 ：
S110, in the construction process, a matrix D is formed by influencing the displacement of arch rib control nodes by the tension unit cable force f As shown in formula (1):
D f alpha is the element of the middle element jk (j＝1,2,…M; k=1, 2, …, n) is the displacement influence of the tension unit cable force of the kth cable on the jth control node in the construction process;
s120, in the construction process, a cable force influence matrix F of the tension unit cable force on the inhaul cable f As shown in formula (2):
F f intermediate element beta kl (k=1, 2, …, n; l=1, 2, …, n) is the influence of the tension unit cable force of the kth cable on the cable force of the first cable during construction;
s130, in the process of detaching the cable, acquiring a displacement influence matrix D of the detaching unit cable force on the arch rib control node dc As shown in formula (3):
D dc middle element gamma jk (j=1, 2, …, m; k=1, 2, …, n) is the displacement influence of the tension unit cable force of the kth cable on the jth control node after arch rib closure;
s140, obtaining a displacement influence matrix b of constant load on arch rib control nodes 0 ：
Wherein, b when the constant load is the self weight of the arch rib 0 The displacement influence matrix of the constant load on the arch rib control node is shown in the formula (4):
b 0 ' element lambda in jk (j=1, 2, …, m; k=1, 2, …, n) is the displacement influence of the dead weight of the kth cable on the jth control node;
wherein, b when the constant load is arch rib dead weight and wind bracing 0 The displacement influence matrix of the constant load on the arch rib control node is shown in the formula (5):
b 0 "Medium element phi rj (j=1, 2, …, m; r=1, 2, …, t) is the displacement influence of the (r) th fixed load on the (j) th control node during construction;
s150, a constant load cable force influence matrix b of the inhaul cable 1 As shown in formula (6):
b 1 medium element eta lr (l=1, 2, …, n; r=1, 2, …, t) is the effect of the (r) th fixed load on the (1) st cable force during construction;
s200, based on the displacement influence matrix, the cable force influence matrix and a second variable T i Acquiring actual displacement u of cantilever end control node corresponding to currently installed arch rib section and tensioned buckling rope 1 (T i ) The actual displacement u of the cantilever end control node corresponding to the transverse connection of the currently installed arch ring 2 (T i ) The second variable is the back cable force of the arch bridge buckle, wherein u 1 (T i )＝D f ·T i +b 0 ′+D dc ·(F f ·T i +b 1 )，u 2 (T i )＝D f ·T i +b 0 ″+D dc ·(F f ·T i +b 1 ) B when the constant load is the self weight of the arch rib 0 ' is a displacement influence matrix of the constant load on the arch rib control node, and b is when the constant load is arch rib dead weight and wind bracing 0 "is the displacement influence matrix of the constant load on the arch rib control node, and the actual displacement uh (T i ) Wherein uh (T) i )＝αu 1 (T i )+βu 2 (T i ) Alpha and beta are set values;
s300, solving the second variable, so that the difference value between the actual displacement of the arch rib control node and the target displacement after closure and loosening under the action of the arch bridge back rope force is within a first threshold value, the actual displacement of the forefront arch rib control node with the same mileage and the actual displacement of the upstream and downstream arch rib control nodes are equal when the closure section is erected under the action of the released arch bridge back rope force, and the released arch bridge back rope force is within a preset range.
2. The method for processing data of back cable force of arch bridge according to claim 1, further comprising, before step S100:
and establishing a space finite element model of the arch bridge structure according to the arch bridge structure parameters, and determining at least one of the number of arch rib control nodes, the number of unknown loads in the second variable, the first threshold value and a preset range of back buckling cable force.
3. The method of claim 2, wherein solving the second variable in step S300 comprises:
taking the sum of squares of the actual displacement and the target displacement difference of arch rib control points at each hoisting construction stage as an objective function F, wherein
n is the unknown load number in the second variable, b 2 Is the target displacement;
solving the second variable to enable the objective function to be a global minimum value so as to ensure the linear stability of the arch rib control node in the construction process.
4. The method for processing data of back-bridge buckle cable force according to claim 2, wherein the step S300 of setting up the closure segments under the action of the released back-bridge buckle cable force includes the steps of:
acquiring a big and small mileage cable force displacement matrix of a forefront control node in a maximum cantilever state before closureDifference Aeq, aeq = [ E 1 ·(D f +D dc ·F f )-E 2 ·(D f +D dc ·F f )]Wherein E is 1 ，E 2 Is a preset matrix;
acquiring a fixed load displacement vector difference beq, beq =e of the size mileage of the front-end control node in the maximum cantilever state before closure 2 ·(b 0 +D dc ·b 1 )-E 1 ·(b 0 +D dc ·b 1 )；
The practical displacement of the control nodes of the forefront arch ribs with the same size mileage during the erection of the closure section is taken as a constraint condition, aeq.T i = beq, where T i And selecting the back cable force of the arch bridge buckle for the second variable to control the elevation of the arch rib after closure and loosening to be equal.
5. A method for processing data of back arch bridge buckling and back cable force according to claim 2, wherein the step S300 of equalizing the actual displacement of the upstream and downstream arch rib control nodes under the action of the released back arch bridge buckling and back cable force comprises:
the actual displacement u1_S of the control node at the upstream of the arch rib in the hoisting construction stage is obtained,
acquiring actual displacement of a downstream control node of an arch rib in a hoisting construction stage;
taking the maximum absolute value of the actual displacement difference value of the upstream and downstream control nodes of the arch rib in the hoisting construction stage as a nonlinear inequality constraint condition within a minimum range, and max (abs (u1_S-u1_X)) +.χ, wherein χ is a preset value, and selecting the back cable force of the arch bridge buckle to ensure the equality of the line shapes of the upstream and downstream arch rib control nodes.
6. A method for processing arch bridge back-buckling cable force data according to any one of claims 1-5, wherein a mathematical model is constructed based on constraint conditions and objective functions, the influence matrix is substituted into the mathematical model, and the back-buckling cable force of the cable-stayed construction arch bridge is solved.
7. An arch bridge back lasso force data processing system, comprising:
the first module is used for extracting at least one displacement influence matrix and at least one cable force influence matrix based on the coupling effect of a first variable on the displacement of the arch rib control node and the cable force of the cable, wherein the first variable comprises constant load and unit cable tension in different construction stages;
wherein, in the construction process, a displacement influence matrix D of the tension unit cable force on the arch rib control node is obtained f And a cable force influence matrix F of the tension unit cable force on the inhaul cable f The method comprises the steps of carrying out a first treatment on the surface of the In the process of detaching the cable, obtaining a displacement influence matrix D of the detaching unit cable force on the arch rib control node dc The method comprises the steps of carrying out a first treatment on the surface of the Obtaining a displacement influence matrix b of constant load on arch rib control nodes 0 And a constant load cable force influence matrix b for the inhaul cable 1 ：
S110, in the construction process, a matrix D is formed by influencing the displacement of arch rib control nodes by the tension unit cable force f As shown in formula (1):
D f alpha is the element of the middle element jk (j=1, 2, …, m; k=1, 2, …, n) is the displacement influence of the tension unit cable force of the kth cable on the jth control node during construction;
s120, in the construction process, a cable force influence matrix F of the tension unit cable force on the inhaul cable f As shown in formula (2):
F f intermediate element beta kl (k=1, 2, …, n; l=1, 2, …, n) is the influence of the tension unit cable force of the kth cable on the cable force of the first cable during construction;
s130, in the process of detaching the cable, acquiring a displacement influence matrix D of the detaching unit cable force on the arch rib control node dc As shown in formula (3):
D dc middle element gamma jk (j=1, 2, …, m; k=1, 2, …, n) is the displacement influence of the tension unit cable force of the kth cable on the jth control node after arch rib closure;
s140, obtaining a displacement influence matrix b of constant load on arch rib control nodes 0 ：
Wherein, b when the constant load is the self weight of the arch rib 0 The displacement influence matrix of the constant load on the arch rib control node is shown in the formula (4):
b 0 ' element lambda in jk (j=1, 2, …, m; k=1, 2, …, n) is the displacement influence of the dead weight of the kth cable on the jth control node;
wherein, b when the constant load is arch rib dead weight and wind bracing 0 The displacement influence matrix of the constant load on the arch rib control node is shown in the formula (5):
b 0 "Medium element phi rj (j=1, 2, …, m; r=1, 2, …, t) is the displacement influence of the (r) th fixed load on the (j) th control node during construction;
s150, a constant load cable force influence matrix b of the inhaul cable 1 As shown in formula (6):
b 1 medium element eta lr (l=1, 2, …, n; r=1, 2, …, t) is the r fixed load pair during constructionThe influence of the first inhaul cable force;
a second module for based on the displacement influence matrix, the cable force influence matrix and a second variable T i Acquiring actual displacement u of cantilever end control node corresponding to currently installed arch rib section and tensioned buckling rope 1 (T i ) The actual displacement u of the cantilever end control node corresponding to the transverse connection of the currently installed arch ring 2 (T i ) The second variable is the back cable force of the arch bridge buckle, wherein u 1 (T i )＝D f ·T i +b 0 ′+D dc ·(F f ·T i +b 1 )，u 2 (T i )＝D f ·T i +b 0 ″+D dc ·(F f ·T i +b 1 ) B when the constant load is the self weight of the arch rib 0 ' is a displacement influence matrix of the constant load on the arch rib control node, and b is when the constant load is arch rib dead weight and wind bracing 0 "is the displacement influence matrix of the constant load on the arch rib control node, and the actual displacement uh (T i ) Wherein uh (T) i )＝αu 1 (T i )+βu 2 (T i ) Alpha and beta are set values;
and the third module is used for solving the second variable so that the difference value between the actual displacement of the arch rib control node and the target displacement after closure and loosening are performed under the action of the arch bridge back-buckling cable force is within a first threshold value, the actual displacement of the foremost arch rib control node with the same size mileage and the actual displacement of the upstream and downstream arch rib control nodes are equal when the closure section is erected under the action of the closure of the opened arch bridge back-buckling cable force, and the opened arch bridge back-buckling cable force is within a preset range.
8. A computer readable storage medium storing a computer program, characterized in that the computer program when executed by a processor implements the method steps of any of claims 1-5.
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