阅读说明：本技术 拱桥成桥最优索力计算方法、装置、设备及可读存储介质 (Method, device and equipment for calculating optimal cable force of arch bridge forming bridge and readable storage medium ) 是由 陈涛 柯卫峰 王吉 薛其林 吕宏奎 余飞 袁建新 何祖发 于 2021-07-02 设计创作，主要内容包括：本发明公开了一种拱桥成桥最优索力计算方法、装置、设备及可读存储介质,涉及桥梁施工技术领域,所述计算方法包括：步骤S1,获取拱桥的各个吊杆与系梁连接点在其预设初始索力作用下的初始位移；步骤S2,根据各个初始位移与预设目标位移计算得到各个初始索力增量,并根据各个初始索力增量和预设初始索力计算得到各个第二索力；步骤S3,以各个第二索力增量为变量建立位移偏差函数,根据预设边界条件迭代计算得到位移偏差函数的最优解,并根据最优解和各个第二索力计算得到拱桥成桥时各个吊杆与系梁连接点的最优索力。本发明能保证成桥状态下索力符合设计要求,计算方法简捷高效。(The invention discloses a method, a device, equipment and a readable storage medium for calculating optimal cable force of an arch bridge, which relate to the technical field of bridge construction, wherein the calculation method comprises the following steps: step S1, acquiring the initial displacement of each suspender of the arch bridge and the tie beam connection point under the action of the preset initial cable force; step S2, calculating to obtain each initial cable force increment according to each initial displacement and a preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and a preset initial cable force; and step S3, establishing a displacement deviation function by taking each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspender and the tie beam when the arch bridge is formed according to the optimal solution and each second cable force. The invention can ensure that the cable force in the bridge-forming state meets the design requirement, and the calculation method is simple and efficient.)

1. An optimal cable force calculation method for an arch bridge to form a bridge is characterized by comprising the following steps:

acquiring initial displacement of each suspender of the arch bridge and a tie beam connecting point under the action of a preset initial cable force;

calculating to obtain each initial cable force increment according to each initial displacement and a preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and a preset initial cable force;

and establishing a displacement deviation function by taking each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspender and the tie beam when the arch bridge is bridged according to the optimal solution and each second cable force.

2. The method for calculating the optimal cable force for bridging an arch bridge according to claim 1, wherein the obtaining of the initial displacement of each connecting point of the suspension rod and the tie beam of the arch bridge under the action of the preset initial cable force comprises:

establishing a suspender cable force vector { T } - [ T ]₁ T₂ … T_m]^TAnd a displacement vector (u) of a connecting point of the suspension rod and the tie beam is [ u ] }₁ u₂… u_m]^TWherein m is the number of the suspender;

will preset the initial cable force vector T¹Substituting the displacement vector into an arch bridge finite element model, and calculating to obtain an initial displacement vector (u)¹}。

3. The method for calculating the optimal cable force for bridging the arch bridge according to claim 2, wherein the calculating to obtain each initial cable force increment according to each initial displacement and the preset target displacement and to obtain each second cable force according to each initial cable force increment and the preset initial cable force comprises:

according to a preset initial cable force vector { T¹Taking m groups of cable force vectors, and substituting the m groups of cable force vectors into an arch bridge finite element model respectively to calculate to obtain m groups of displacement vectors;

calculating a rigidity matrix { K } of the cable force vector { T } and the displacement vector { u } according to the m groups of cable force vectors and the m groups of displacement vectors;

establishing a relational expression among the cable force increment vector, the rigidity matrix and the displacement vector, and according to the rigidity matrix { K }, the initial displacement vector { u }¹And a preset target displacement vector u⁰And calculating to obtain an initial cable force increment vector (delta T)¹}；

According to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²}。

4. The arch bridge bridging optimal cable force calculation method according to claim 3, wherein the calculation method further comprises:

according to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²After that, for the second cable force vector { T }²And correcting.

5. The arch bridge bridging optimal cable force calculation method of claim 4, wherein the pair of second cable force vectors { T } T²Correcting, including:

when in useOrWhen it is used, order

6. The method for calculating the optimal cable force of the arch bridge bridging according to claim 3, wherein the establishing a displacement deviation function by using each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspension rod and the tie beam when the arch bridge is bridged according to the optimal solution and each second cable force, comprises:

construction of the Displacement deviation function f (Δ T)_i ²) Wherein the second cable force increment Δ T_i ²∈[a,b]I is 1, …, m;

iterative computation starting from a with a varying step c, with f (Δ T)_i ²) K is less than or equal to the preset boundary condition, and a displacement deviation function f (delta T) is obtained by calculation_i ²) Is best solution of (Δ T)²}；

According to the optimal solution [ Delta T ]²A second cable force vector { T }²And the formula { T }³}＝{T²}+{ΔT²And calculating to obtain an optimal cable force vector { T }of the finished bridge³}；

Wherein a, b, c and k are preset values.

7. The method for calculating the optimal cable force for forming the arch bridge according to claim 2, wherein the step of obtaining the initial displacement of each connecting point of the suspension rod and the tie beam of the arch bridge under the action of the preset initial cable force comprises the following steps:

establishing an arch bridge finite element model which comprises a main bridge structure and a temporary structure, and correcting the weight of each structure.

8. An arch bridge bridging optimal cable force calculation device, comprising:

the system comprises an acquisition unit, a control unit and a control unit, wherein the acquisition unit is used for acquiring the initial displacement of each connecting point of a suspender and a tie beam of the arch bridge under the action of a preset initial cable force;

the first calculation unit is used for calculating to obtain each initial cable force increment according to each initial displacement and a preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and a preset initial cable force;

and the first calculation unit is used for establishing a displacement deviation function by taking each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspender and the tie beam when the arch bridge is formed according to the optimal solution and each second cable force.

9. A computer device, comprising: a memory and a processor, the memory having stored therein at least one instruction, the at least one instruction being loaded and executed by the processor to implement the arch bridge-to-bridge optimal cable force calculation method of any one of claims 1 to 7.

10. A computer-readable storage medium characterized by: the computer storage medium stores computer instructions that, when executed by a computer, cause the computer to perform the arch bridge-to-bridge optimal cable force calculation method of any one of claims 1 to 7.

Technical Field

The invention relates to the technical field of bridge construction, in particular to a method, a device, equipment and a readable storage medium for calculating optimal cable force of an arch bridge to form a bridge.

Background

The stress mode of the basket tied arch bridge is that the dead weight of the bridge deck structure and the load of a travelling crane are transmitted to the arch ribs through the suspenders, the horizontal force generated by the arch ribs is born by the bridge deck tie beams, and the arch ribs and the tie beams bear all the load together through the suspenders, so the suspenders are important components of the arch bridge. The hanger rods are usually installed and tensioned one by one after the installation of the arch ribs and the tie beams, the cable force for firstly completing tensioning always changes along with the construction of the bridge behind, but the full-bridge hanger rods have a set of bridge forming cable force during the final bridge forming, different bridge forming cable forces correspond to different bridge forming states, and how to determine a set of optimal bridge forming cable force to ensure that the bridge forming state meets the design is one of the keys of the bridge construction.

The existing finite element software usually has a bridge cable force calculation function, and the calculation result can meet the requirement for a simple bridge structure. However, when the bridge structure model is complex, according to the calculation result of the bridge forming cable force of the existing finite element software, a certain deviation exists between the bridge forming state and the expected state, if the deviation cannot be accepted, the cable force needs to be adjusted manually, for the bridge with more cables, the manual adjustment is time-consuming and labor-consuming, and sometimes even cannot be adjusted to an ideal result. Therefore, it is needed to provide an optimal cable force calculation method for an arch bridge to solve the technical problem of large deviation of calculation results of the cable force of the existing finite element software for bridging.

Disclosure of Invention

The embodiment of the invention provides a method, a device, equipment and a readable storage medium for calculating optimal cable force of an arch bridge, which can solve the technical problem that the deviation of the calculation result of the cable force of the existing finite element software for forming the bridge is large.

In a first aspect, a method for calculating optimal cable force of an arch bridge in bridging is provided, which comprises the following steps:

acquiring initial displacement of each suspender of the arch bridge and a tie beam connecting point under the action of a preset initial cable force;

calculating to obtain each initial cable force increment according to each initial displacement and a preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and a preset initial cable force;

and establishing a displacement deviation function by taking each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspender and the tie beam when the arch bridge is bridged according to the optimal solution and each second cable force.

In some embodiments, obtaining the initial displacement of each boom-to-tie-beam connection point of the arch bridge under the action of the preset initial cable force comprises:

establishing a suspender cable force vector { T } - [ T ]₁ T₂ … T_m]^TAnd a displacement vector (u) of a connecting point of the suspension rod and the tie beam is [ u ] }₁u₂ … u_m]^TWherein m is the number of the suspender;

will preset the initial cable force vector T¹Substituting the displacement vector into an arch bridge finite element model, and calculating to obtain an initial displacement vector (u)¹}。

In some embodiments, the calculating to obtain each initial cable force increment according to each initial displacement and the preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and the preset initial cable force includes:

according to a preset initial cable force vector { T¹Taking m groups of cable force vectors, and substituting the m groups of cable force vectors into an arch bridge finite element model respectively to calculate to obtain m groups of displacement vectors;

calculating a rigidity matrix { K } of the cable force vector { T } and the displacement vector { u } according to the m groups of cable force vectors and the m groups of displacement vectors;

establishing a relational expression among the cable force increment vector, the rigidity matrix and the displacement vector, and according to the rigidity matrix { K }, the initial displacement vector { u }¹And a preset target displacement vector u⁰And calculating to obtain an initial cable force increment vector (delta T)¹}；

According to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²}。

In some embodiments, the computing method further comprises:

according to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²After that, for the second cable force vector { T }²And correcting.

In some embodiments, the pair of second cable force vectors { T²Correcting, including:

when in useOrWhen it is used, order

In some embodiments, the establishing a displacement deviation function with each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative computation according to a preset boundary condition, and obtaining an optimal cable force of each connecting point of the hanger rod and the tie beam when the arch bridge is bridged according to the optimal solution and each second cable force, includes:

construction of the Displacement deviation function f (Δ T)_i ²) Wherein the second cable force increment Δ T_i ²∈[a,b]I is 1, …, m;

iterative computation starting from a with a varying step c, with f (Δ T)_i ²) K is less than or equal to the preset boundary condition, and a displacement deviation function f (delta T) is obtained by calculation_i ²) Is best solution of (Δ T)²}；

According to the optimal solution [ Delta T ]²A second cable force vector { T }²And the formula { T }³}＝{T²}+{ΔT²And calculating to obtain an optimal cable force vector { T }of the finished bridge³}；

Wherein a, b, c and k are preset values.

In some embodiments, before the initial displacement of each boom-to-tie-beam connection point of the arch bridge under the action of the preset initial cable force, the method comprises:

establishing an arch bridge finite element model which comprises a main bridge structure and a temporary structure, and correcting the weight of each structure.

In a second aspect, an arch bridge bridging optimal cable force calculation device is provided, which includes:

the system comprises an acquisition unit, a control unit and a control unit, wherein the acquisition unit is used for acquiring the initial displacement of each connecting point of a suspender and a tie beam of the arch bridge under the action of a preset initial cable force;

the first calculation unit is used for calculating to obtain each initial cable force increment according to each initial displacement and a preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and a preset initial cable force;

and the first calculation unit is used for establishing a displacement deviation function by taking each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspender and the tie beam when the arch bridge is formed according to the optimal solution and each second cable force.

In a third aspect, a computer device is provided, comprising: the device comprises a memory and a processor, wherein at least one instruction is stored in the memory, and is loaded and executed by the processor to realize the method for calculating the optimal cable force of the arch bridge in the bridge formation.

In a fourth aspect, a computer-readable storage medium is provided, which stores computer instructions that, when executed by a computer, cause the computer to perform the foregoing arch bridge bridging optimal cable force calculation method.

The technical scheme provided by the invention has the beneficial effects that:

the embodiment of the invention provides a method, a device, equipment and a readable storage medium for calculating the optimal cable force of an arch bridge finished bridge, wherein a displacement deviation function taking each second cable force increment as a variable is established, and the cable force of each connecting point of a suspender and a tie beam in a finished bridge state is determined through a preset boundary condition.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

Fig. 1 is a flowchart of a method for calculating an optimal cable force of an arch bridge bridging according to an embodiment of the present invention;

fig. 2 is a structural diagram of an optimal cable force calculation device for an arch bridge bridging according to an embodiment of the present invention;

fig. 3 is a schematic structural diagram of a computer device according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.

The embodiment of the invention provides a method for calculating optimal cable force of an arch bridge to form a bridge, which can solve the technical problem that the deviation of the calculation result of the cable force of the existing finite element software to form the bridge is large.

Referring to fig. 1, the method for calculating the optimal cable force for forming the arch bridge comprises the following steps:

and step S1, acquiring the initial displacement of each connecting point of the suspension rod and the tie beam of the arch bridge under the action of the preset initial cable force.

Specifically, the acquiring of the initial displacement of each boom and tie beam connection point of the arch bridge under the action of the preset initial cable force includes:

establishing a suspender cable force vector { T } - [ T ]₁ T₂ … T_m]^TAnd a displacement vector (u) of a connecting point of the suspension rod and the tie beam is [ u ] }₁u₂ … u_m]^TWherein m is the boom number;

will preset the initial cable force vector T¹Substituting the displacement vector into an arch bridge finite element model, and calculating to obtain an initial displacement vector (u)¹}。

For example, if the force applied to each boom by the facility is 100kN, the initial cable force vector is presetSubstituting into the arch bridge finite element model, and calculating to obtain an initial displacement vector

And step S2, calculating to obtain each initial cable force increment according to each initial displacement and the preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and the preset initial cable force.

Specifically, the calculating according to each initial displacement and the preset target displacement to obtain each initial cable force increment, and calculating according to each initial cable force increment and the preset initial cable force to obtain each second cable force includes:

according to a preset initial cable force vector { T¹And taking m groups of cable force vectors, and substituting the m groups of cable force vectors into the arch bridge finite element model respectively to calculate to obtain m groups of displacement vectors. For example, the m sets of cable force vectors may be { Δ T₁}＝[100 0 … 0]^T，{ΔT₂}＝[0 100 … 0]^T，…，{ΔT_m}＝[0 0 … 100]^TAnd respectively substituting the calculation results into the finite element model calculation of the arch bridge.

And calculating a rigidity matrix { K } of the cable force vector { T } and the displacement vector { u } according to the m groups of cable force vectors and the m groups of displacement vectors. Wherein the stiffness matrix K may be represented as:

establishing a relational expression among the cable force increment vector, the rigidity matrix and the displacement vector, and according to the rigidity matrix { K }, the initial displacement vector { u }¹And a preset target displacement vector u⁰And calculating to obtain an initial cable force increment vector (delta T)¹}. Specifically, the relationship among the cable force increment vector, the stiffness matrix and the displacement vector is as follows:

{K}·{ΔT¹}＝{u¹}-{u⁰}

according to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²}. Specifically, { T²}＝{T¹}+{ΔT¹}。

And step S3, establishing a displacement deviation function by taking each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspender and the tie beam when the arch bridge is formed according to the optimal solution and each second cable force.

Specifically, the establishing a displacement deviation function by using each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining an optimal cable force of each connecting point of the hanger rod and the tie beam when the arch bridge is bridged according to the optimal solution and each second cable force calculation, includes:

construction of the Displacement deviation function f (Δ T)_i ²) Wherein the second cable force increment Δ T_i ²∈[a,b]I is 1, …, m.

Wherein{u³}＝{K}·({T³}-{T¹})+{u¹}。

Iterative computation starting from a with a varying step c, with f (Δ T)_i ²) K is less than or equal to the preset boundary condition, and a displacement deviation function f (delta T) is obtained by calculation_i ²) Is best solution of (Δ T)²}. Wherein a, b, c and k are preset values.

According to the optimal solution [ Delta T ]²A second cable force vector { T }²And the formula { T }³}＝{T²}+{ΔT²And calculating to obtain an optimal cable force vector { T }of the finished bridge³}。

The optimal cable force calculation method for the arch bridge to form the bridge in the embodiment of the invention establishes the displacement deviation function taking each second cable force increment as a variable, and determines the cable force of each connecting point of the suspender and the tie beam in the bridge forming state through the preset boundary condition.

As an optional implementation manner, in the embodiment of the present invention, the method for calculating the optimal cable force of the arch bridge in bridging further includes:

according to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²After that, for the second cable force vector { T }²And correcting.

Further, the pair of second cable force vectors { T }²Correcting, including:

when in useOrWhen it is used, order

Calculating a second cable force vector { T) according to a relational expression among the cable force increment vector, the rigidity matrix and the displacement vector²There may be a force imbalance by applying a second cable force vector T²Correcting for the second cable force vector { T }²Force is balanced.

As an optional implementation manner, the method for calculating the optimal cable force of the arch bridge in the embodiment of the present invention, before acquiring the initial displacement of the connecting point of each boom and the tie beam of the arch bridge under the action of the preset initial cable force, includes:

and establishing an arch bridge finite element model which comprises a main bridge structure and a temporary structure, and correcting the weight of each structure to ensure the accuracy of a subsequent calculation result.

In the following, taking an arch bridge 213m long as an example, assuming that the number of bridge suspenders is 32, 32 groups of { Δ T }_iAnd calculating a bridge rigidity matrix { K }, and presetting a target displacement vector { u } at the moment⁰Solving the { delta T by using a cable force increment vector and displacement vector equation when the } is 0¹Get the second cable force vector { T }²2388, 2197, 1459, 1505, … 1489, 2138, 1192 for { T }²Performing imbalance correction to obtain { T }²-1500, 1500, 1459, 1505, … 1489, 1500, 1192} let Δ T_i ²∈[-40,40]Changing the step pitch to 1, k 50mm into f (Δ T)_i ²) Circularly calculating to judge the composite f (delta T)_i ²) Under the condition of less than or equal to k, solving out { delta T²30, 27, 26, 35, … 15, 21, 24, according to the optimal solution Δ T²A second cable force vector { T }²And the formula { T }³}＝{T²}+{ΔT²And calculating to obtain an optimal cable force vector { T }of the finished bridge³}。

Referring to fig. 2, an embodiment of the present application further provides an arch bridge bridging optimal cable force calculation apparatus, including: the device comprises an acquisition unit, a first calculation unit and a second calculation unit.

The acquisition unit is used for acquiring the initial displacement of each connecting point of the suspension rod and the tie beam of the arch bridge under the action of the preset initial cable force.

The first calculation unit is used for calculating to obtain each initial cable force increment according to each initial displacement and a preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and a preset initial cable force.

The second calculation unit is used for establishing a displacement deviation function by taking each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspension rod and the tie beam when the arch bridge forms the bridge through calculation according to the optimal solution and each second cable force.

Specifically, the acquiring of the initial displacement of each boom and tie beam connection point of the arch bridge under the action of the preset initial cable force includes:

establishing a suspender cable force vector { T } - [ T ]₁ T₂ … T_m]^TAnd a displacement vector (u) of a connecting point of the suspension rod and the tie beam is [ u ] }₁u₂ … u_m]^TWherein m is the boom number;

will preset the initial cable force vector T¹Substituting the displacement vector into an arch bridge finite element model, and calculating to obtain an initial displacement vector (u)¹}。

For example, if the force applied to each boom by the facility is 100kN, the initial cable force vector is presetSubstituting into the arch bridge finite element model, and calculating to obtain an initial displacement vector

Specifically, the first calculating unit is configured to calculate each initial cable force increment according to each initial displacement and a preset target displacement, and calculate each second cable force according to each initial cable force increment and a preset initial cable force, and includes:

according to a preset initial cable force vector { T¹And taking m groups of cable force vectors, and substituting the m groups of cable force vectors into the arch bridge finite element model respectively to calculate to obtain m groups of displacement vectors. For example, the m sets of cable force vectors may be { Δ T₁}＝[100 0 … 0]^T，{ΔT₂}＝[0 100 … 0]^T，…，{ΔT_m}＝[0 0 … 100]^TAnd respectively substituting the calculation results into the finite element model calculation of the arch bridge.

And calculating a rigidity matrix { K } of the cable force vector { T } and the displacement vector { u } according to the m groups of cable force vectors and the m groups of displacement vectors. Wherein the stiffness matrix K may be represented as:

establishing a relational expression among the cable force increment vector, the rigidity matrix and the displacement vector, and according to the rigidity matrix { K }, the initial displacement vector { u }¹And a preset target displacement vector u⁰And calculating to obtain an initial cable force increment vector (delta T)¹}. Specifically, the relationship among the cable force increment vector, the stiffness matrix and the displacement vector is as follows:

{K}·{ΔT¹}＝{u¹}-{u⁰}

according to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²}. Specifically, { T²}＝{T¹}+{ΔT¹}。

Specifically, the second calculating unit is configured to establish a displacement deviation function with each second cable force increment as a variable, obtain an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtain an optimal cable force of each connecting point of the hanger rod and the tie beam when the arch bridge is bridged according to the optimal solution and each second cable force, and the second calculating unit includes:

construction of the Displacement deviation function f (Δ T)_i ²) Wherein the second cable force increment Δ T_i ²∈[a,b]I is 1, …, m.

Wherein{u³}＝{K}·({T³}-{T¹})+{u¹}。

Iterative computation starting from a with a varying step c, with f (Δ T)_i ²) K is less than or equal to the preset boundary condition, and a displacement deviation function f (delta T) is obtained by calculation_i ²) Is best solution of (Δ T)²}。

According to the optimal solution [ Delta T ]²A second cable force vector { T }²And the formula { T }³}＝{T²}+{ΔT²And calculating to obtain an optimal cable force vector { T }of the finished bridge³}。

Wherein a, b, c and k are preset values.

It should be noted that, as will be clear to those skilled in the art, for convenience and brevity of description, the specific working processes of the above-described apparatus and units may refer to the corresponding processes in the foregoing embodiment of the method for calculating an optimal cable force of an arch bridge to form a bridge, and are not described herein again.

The analysis apparatus provided in the above embodiment may be implemented in the form of a computer program, which can be run on a computer device as shown in fig. 3.

An embodiment of the present application further provides a computer device, including: the system comprises a memory, a processor and a network interface which are connected through a system bus, wherein at least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor so as to realize all or part of the steps of the method for calculating the optimal cable force of the arch bridge in the bridge formation.

The network interface is used for performing network communication, such as sending distributed tasks. Those skilled in the art will appreciate that the architecture shown in fig. 3 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.

The Processor may be a CPU, other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic device, discrete hardware component, or the like. The general purpose processor may be a microprocessor or the processor may be any conventional processor or the like, the processor being the control center of the computer device and the various interfaces and lines connecting the various parts of the overall computer device.

The memory may be used to store computer programs and/or modules, and the processor may implement various functions of the computer device by executing or executing the computer programs and/or modules stored in the memory, as well as by invoking data stored in the memory. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a video playing function, an image playing function, etc.), and the like; the storage data area may store data (such as video data, image data, etc.) created according to the use of the cellular phone, etc. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), at least one magnetic disk storage device, a Flash memory device, or other volatile solid state storage device.

Wherein, in one embodiment, the processor is configured to execute a computer program stored in the memory to implement the steps of:

and step S1, acquiring the initial displacement of each connecting point of the suspension rod and the tie beam of the arch bridge under the action of the preset initial cable force.

Specifically, the acquiring of the initial displacement of each boom and tie beam connection point of the arch bridge under the action of the preset initial cable force includes:

establishing a suspender cable force vector { T } - [ T ]₁ T₂ … T_m]^TAnd a displacement vector (u) of a connecting point of the suspension rod and the tie beam is [ u ] }₁u₂ … u_m]^TWherein m is the boom number;

will preset the initial cable force vector T¹Substituting the displacement vector into an arch bridge finite element model, and calculating to obtain an initial displacement vector (u)¹}。

For example, if the force applied to each boom by the facility is 100kN, the initial cable force vector is presetSubstituting into the arch bridge finite element model, and calculating to obtain an initial displacement vector

And step S2, calculating to obtain each initial cable force increment according to each initial displacement and the preset target displacement, and calculating to obtain each second cable force according to each initial cable force increment and the preset initial cable force.

Specifically, the calculating according to each initial displacement and the preset target displacement to obtain each initial cable force increment, and calculating according to each initial cable force increment and the preset initial cable force to obtain each second cable force includes:

according to a preset initial cable force vector { T¹And taking m groups of cable force vectors, and substituting the m groups of cable force vectors into the arch bridge finite element model respectively to calculate to obtain m groups of displacement vectors. For example, the m sets of cable force vectors may be { Δ T₁}＝[100 0 … 0]^T，{ΔT₂}＝[0 100 … 0]^T，…，{ΔT_m}＝[0 0 … 100]^TAnd respectively substituting the calculation results into the finite element model calculation of the arch bridge.

And calculating a rigidity matrix { K } of the cable force vector { T } and the displacement vector { u } according to the m groups of cable force vectors and the m groups of displacement vectors. Wherein the stiffness matrix K may be represented as:

establishing a relational expression among the cable force increment vector, the rigidity matrix and the displacement vector, and according to the rigidity matrix { K }, the initial displacement vector { u }¹And a preset target displacement vector u⁰And calculating to obtain an initial cable force increment vector (delta T)¹}. Specifically, the relationship among the cable force increment vector, the stiffness matrix and the displacement vector is as follows:

{K}·{ΔT¹}＝{u¹}-{u⁰}

according to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²}. Specifically, { T²}＝{T¹}+{ΔT¹}。

And step S3, establishing a displacement deviation function by taking each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining the optimal cable force of each connecting point of the suspender and the tie beam when the arch bridge is formed according to the optimal solution and each second cable force.

Specifically, the establishing a displacement deviation function by using each second cable force increment as a variable, obtaining an optimal solution of the displacement deviation function through iterative calculation according to a preset boundary condition, and obtaining an optimal cable force of each connecting point of the hanger rod and the tie beam when the arch bridge is bridged according to the optimal solution and each second cable force calculation, includes:

construction of the Displacement deviation function f (Δ T)_i ²) Wherein the second cable force increment Δ T_i ²∈[a,b]I is 1, …, m.

Wherein{u³}＝{K}·({T³}-{T¹})+{u¹}。

Iterative computation starting from a with a varying step c, with f (Δ T)_i ²) K is less than or equal to the preset boundary condition, and a displacement deviation function f (delta T) is obtained by calculation_i ²) Is best solution of (Δ T)²}. Wherein a, b, c and k are preset values.

According to the optimal solution [ Delta T ]²The second cableForce vector { T²And the formula { T }³}＝{T²}+{ΔT²And calculating to obtain an optimal cable force vector { T }of the finished bridge³}。

The optimal cable force calculation method for the arch bridge to form the bridge in the embodiment of the invention establishes the displacement deviation function taking each second cable force increment as a variable, and determines the cable force of each connecting point of the suspender and the tie beam in the bridge forming state through the preset boundary condition.

As an optional implementation manner, in the embodiment of the present invention, the method for calculating the optimal cable force of the arch bridge in bridging further includes:

according to the initial cable force increment vector delta T¹And a preset initial cable force vector T¹Calculating to obtain a second cable force vector (T)²After that, for the second cable force vector { T }²And correcting.

Further, the pair of second cable force vectors { T }²Correcting, including:

when in useOrWhen it is used, order

Calculating a second cable force vector { T) according to a relational expression among the cable force increment vector, the rigidity matrix and the displacement vector²There may be a force imbalance by applying a second cable force vector T²Correcting for the second cable force vector { T }²Force is balanced.

As an optional implementation manner, the method for calculating the optimal cable force of the arch bridge in the embodiment of the present invention, before acquiring the initial displacement of the connecting point of each boom and the tie beam of the arch bridge under the action of the preset initial cable force, includes:

and establishing an arch bridge finite element model which comprises a main bridge structure and a temporary structure, and correcting the weight of each structure to ensure the accuracy of a subsequent calculation result.

The embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored, where the computer program is executed by a processor to implement all or part of the steps of the foregoing method for calculating optimal cable force of an arch bridge to a bridge.

The embodiments of the present application may implement all or part of the foregoing processes, or may be implemented by a computer program to instruct related hardware, where the computer program may be stored in a computer-readable storage medium, and when the computer program is executed by a processor, the computer program may implement the steps of the foregoing methods. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer readable medium may include: any entity or device capable of carrying computer program code, recording medium, U-disk, removable hard disk, magnetic disk, optical disk, computer memory, Read-Only memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution media, and the like. It should be noted that the computer readable medium may contain other components which may be suitably increased or decreased as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, in accordance with legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunications signals.

As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, server, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.

It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or system. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or system that comprises the element.

The above-mentioned serial numbers in the embodiments of the present application are for description only and do not represent the merits of the embodiments.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The above description is merely exemplary of the present application and is presented to enable those skilled in the art to understand and practice the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.