Steel cable position optimization method for replacing suspended dome structure with CFRP cable

Abstract

The invention discloses a method for optimizing the position of a steel cable for replacing a suspended dome structure with a CFRP cable. The method comprises the following steps that cable replacement parameters of the suspended dome structure are determined; calculating the number of cables needing to be replaced; determining a cable replacement position; comparing the size of A with the size of M1, if Alt; if A is larger than or equal to M1, all the CFRP is evenly and symmetrically arranged on the inner ring radial cables, if A is larger than or equal to M1, all the inner ring radial cables are replaced with CFRP, and when the remaining A-M1lt is larger than or equal to M1, all the CFRP is replaced with CFRP; when A-M1 is larger than or equal to M2, the A-M1 pieces are evenly and symmetrically arranged on the second circle of radial cables, when the remaining A-M1 is larger than or equal to M2, the inner circle and the second circle of radial cables are all replaced with CFRP, the remaining A-(M1 + M2) pieces are arranged on the third circle of radial cables, and so on; and replacing the corresponding steel cable with the CFRP by adopting an equal-rigidity replacement principle to finish the position optimization of replacing the steel cable with the CFRP. According to the method, the relative optimal cable replacement scheme of the CFRP cable can be obtained according to different radial cable replacement proportion requirements, and the high-performance stress characteristic of the suspended dome structure can be brought into full play.

Description

Technical Field

[0001] The invention relates to the technical field of building structure design, and in particular to a method for optimizing the position of steel cables in a chord-dome structure in which CFRP cables are replaced. Background Art

[0002] Compared with steel, CFRP materials have the advantages of light weight, high strength and good corrosion resistance. They are widely used in the field of civil engineering, especially in bridge structures, but are less used in large-span spatial structural systems. Replacing some steel cables in the suspensory dome structure with CFRP cables can not only significantly improve its corrosion resistance, but also reduce the deadweight of the structure to a certain extent, and reduce the adverse effects of temperature changes on the prestress of the cables, which helps to give full play to the high-performance stress characteristics of the suspensory dome structure system and make the application and development prospects of large-span spatial structures broader.

[0003] At present, CFRP is combined with the suspend-dome structure. When replacing cables, all cables are considered. Although CFRP has many advantages over steel cables, it also has some disadvantages, such as its anisotropy, low temperature expansion coefficient, low elongation and easy brittle fracture. Therefore, replacing all cables in the suspend-dome structure with CFRP may introduce safety hazards.

[0004] The cables in the suspension-dome structure are divided into circumferential cables and radial cables. The circumferential cables bear a large prestress and are the main load-bearing components in the suspension-dome structure, so they are not suitable for replacement. Considering replacing some radial cables in the suspension-dome structure with CFRP cables, there are many rods in the suspension-dome structure system, and there are many ways to replace the radial cables in the structure with CFRP cables to improve the static performance of the structure. Replacing them one by one is labor-intensive and it is difficult to find the relatively optimal cable replacement method. Summary of the invention

[0005] In view of the defects of the existing method of replacing the position of steel cables in a suspend-dome structure with CFRP, the present invention provides a method for replacing the steel cables in a suspend-dome structure with CFRP cables and optimizing the CFRP cable replacement position, which can solve the above technical problems.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions: a method for replacing the position of the steel cable of the suspensory dome structure with a CFRP cable, comprising the following steps:

[0007] Step S1: Determine cable replacement parameters of the suspensory dome structure.

[0008] Step S2: Calculate the required number of cable changes.

[0009] Step S3: Determine the cable changing position.

[0010] Step S4: Complete CFRP cable replacement.

[0011] Compared with the traditional large-span space structure, the present invention combines the lightweight and high-strength CFRP material with the suspensory dome structure, and provides a method of replacing part of the radial cables in the suspensory dome structure with CFRP cables. Compared with the previous method of replacing all the steel cables in the suspensory dome structure with CFRP materials, this cable replacement method can quickly obtain the relatively optimal cable replacement scheme of CFRP cables according to different radial cable replacement ratio requirements. The static performance of the suspensory dome structure after combining with CFRP and optimizing the position is improved, which helps to give full play to the high-performance force characteristics of the suspensory dome structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a schematic diagram of the method flow of the present invention.

[0013] Figure 2 Schematic diagram of the suspensory dome structure in the embodiment.

[0014] Figure 3 Schematic diagram of radial cable distribution in the cable-rod system of the embodiment.

[0015] Figure 4 FIG. 1 is a diagram showing the locations of the CFRP replacement cables determined in the embodiment.

[0016] Figure 5 It is a distribution diagram of the Pareto optimal solution in the solution space in the embodiment.

[0017] Figure 6 These are the first four CFRP cable replacement schemes in the Pareto optimal solution in the embodiment. DETAILED DESCRIPTION

[0018] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example

[0020] like Figure 1 As shown, a method for optimizing the position of a chord-dome structure steel cable replaced by a CFRP cable comprises the following steps:

[0021] S1. Determine the cable replacement parameters of the suspension-dome structure, specifically, determine the number of radial cables from the inner circle to the outer circle of the suspension-dome structure, denoted as M1, M2…Mn respectively. Determine the ratio of CFRP cables to replace radial steel cables, denoted as V.

[0022] S2. Calculate the number of cables to be replaced A = (M1 + M2 + ... + Mn) × V;

[0023] S3. Determine the cable replacement positions. Compare the magnitudes of A and M1. If A < M1, arrange all the CFRP symmetrically and evenly on the inner-ring radial cables. If A ≥ M1, replace all the inner-ring radial cables with CFRP. When the remaining A - M1 < M2, arrange A - M1 symmetrically and evenly on the second-ring radial cables. When the remaining A - M1 ≥ M2, replace all the inner-ring and second-ring radial cables with CFRP, and arrange the remaining A - (M1 + M2) on the third-ring radial cables, and so on.

[0024] S4. Complete the cable replacement with CFRP. Adopt the principle of equal stiffness replacement, and replace the corresponding steel cables with CFRP. The steel cables replaced by CFRP are denoted as C1, C2, C3, … Complete the optimization of the positions of the steel cables replaced by CFRP.

[0025] In this embodiment, the above technical solution is applied. Taking a cable-supported dome structure as an example Figure 2 as shown, a method for replacing some steel cables in the cable-supported dome structure with CFRP cables and optimizing the cable replacement positions. The main process includes:

[0026] The first step is to determine the cable replacement parameters of the cable-supported dome structure. As Figure 3 shown, in this embodiment, the number of inner-ring radial cables in the cable-supported dome structure is 12, the number of outer-ring radial cables is 24, the proportion of steel cables replaced by CFRP cables is taken as 40%, M1 = 12, M2 = 24, and V = 40%.

[0027] The second step is to calculate the required number of cables to be replaced A = (M1 + M2) × V = 14.4, that is, A = 14.

[0028] The third step is to determine the cable replacement positions. A = 14, M1 = 12, A > M1, that is, all the inner-ring radial cables are replaced with CFRP, and A - M1 = 2. Two radial cables in the outer-ring are symmetrically replaced with CFRP.

[0029] The fourth step is to adopt the principle of equal stiffness replacement, and replace the cable replacement positions determined in the third step with CFRP. The steel cables replaced by CFRP are denoted as C1, C2, C3, … C14. As Figure 4 shown, complete the optimization of the positions of the steel cables replaced by CFRP.

[0030] Now, use the ANSYS finite element program and Matlab to verify the present invention. Establish a cable-supported dome model in ANSYS. In the embodiment, the diameter is 70.6 m, the rise is 7.06 m. The upper part of the structure adopts a Kiewitt - United Square single-layer reticulated shell, with a total of 6 rings; the lower structure is a cable-bracing system, with 2 prestressed circular cables arranged, and there are radial cables connecting between the circular cables, and they are connected to the upper reticulated shell with struts. The single-layer reticulated shell uses building steel sections, and the specifications of the single-layer reticulated shell members are The specifications of the struts are The specifications of the cable materials are and Under gravity load, the prestressing force of the hoop cable is 100kN and 800kN from inside to outside. The height of the support rod is 3.988m, 5.573m and 6.799m from inside to outside. The single-layer lattice shell uses cast steel nodes to connect the rods, which are simplified to rigid connections, and the remaining connections are simplified to hinged connections. The supports use rubber bearings, which are radially released and fully constrained in the annular and vertical directions. Loads are applied to the upper lattice nodes of the suspensory dome structure, and the load combination is taken as the following formula: 1.0 dead load + 1.0 live load, where the dead load is 0.85kN / m 2 , live load is 0.5kN / m 2 The lattice shell adopts Beam188 beam unit, the vertical brace and radial cable adopt Link180 bar unit, and the ring cable adopts Link10 unit.

[0031] The improved genetic algorithm (NSGAII) is used in Matlab to optimize the position of the CFRP replacement part of the radial cable of the suspensory dome structure. The proportion of CFRP replacement of radial cables is set to 40%. The outer ring cable tension, support reaction and structural stiffness (flexibility index) of the suspensory dome structure are taken as the optimization targets. The crossover probability of the NSGAII genetic algorithm is set to 0.8, the mutation probability is 0.05, the population size is 500, and the number of iterations is 20. Matlab programming is used to obtain the Pareto solution set. Each point in the Pareto optimal solution set corresponds to an optimization scheme, such as Figure 5 As shown. Take the first four cable replacement schemes in the Pareto optimal solution set as Figure 6 shown.

Claims

1. A method for optimizing the position of steel cables in a chord-dome structure by replacing them with CFRP cables, characterized in that: It includes the following steps: S1. Determine the cable replacement parameters of the cable-supported dome structure, specifically, determine the number of radial cables from the inner ring to the outer ring of the cable-supported dome structure, denoted as M1, M2…Mn respectively; determine the proportion of CFRP cables replacing the radial steel cables, denoted as V; S2. Calculate the required number of cables to be replaced A = (M1 + M2 + … + Mn) × V; S3. Determine the cable replacement positions; compare the magnitudes of A and M1. If A < M1, arrange all the CFRP cables symmetrically and evenly on the inner-ring radial cables. If A ≥ M1, replace all the inner-ring radial cables with CFRP. When the remaining A - M1 < M2, arrange A - M1 cables symmetrically and evenly on the second-ring radial cables. When the remaining A - M1 ≥ M2, replace all the inner-ring and second-ring radial cables with CFRP, and arrange the remaining A - (M1 + M2) on the third-ring radial cables, and so on; S4. Complete the CFRP cable replacement. Use the equal stiffness replacement principle to replace the corresponding steel cables with CFRP. The steel cables replaced by CFRP are denoted as C1, C2, C3, ... Completed CFRP replacement cable position optimization.

2. The method for optimizing the position of a suspensory dome structure using CFRP cables to replace steel cables according to claim 1, characterized in that: Step 1. Determine the cable replacement parameters of the cable-supported dome structure. The number of inner-ring radial cables of the cable-supported dome structure is 12, the number of outer-ring radial cables is 24, and the proportion of CFRP cables replacing the steel cables is taken as 40%. M1 = 12, M2 = 24, V = 40%; Step 2. Calculate the required number of cables to be replaced A = (M1 + M2) × V = 14.4, that is, A = 14; Step 3. Determine the cable replacement positions; A = 14, M1 = 12, A > M1, that is, replace all the inner-ring radial cables with CFRP, A - M1 = 2, and symmetrically and evenly replace 2 radial cables of the outer-ring radial cables with CFRP; Step 4. Adopt the principle of equal stiffness replacement, and replace the cable replacement positions determined in Step 3 with CFRP. The steel cables replaced by CFRP are denoted as C1, C2, C3, …C14, and complete the optimization of the positions of the steel cables replaced by CFRP.

3. The method for optimizing the position of a suspense-dome structure using CFRP cables to replace steel cables according to claim 2, characterized in that: The ANSYS finite element program and Matlab verification were used. A suspensory dome model was established in ANSYS with a diameter of 70.6m and a rise of 7.06m. The upper part of the structure adopts a single-layer lattice shell of the Kvit-Lianfang type, with a total of 6 rings. The lower structure is a cable-supported system with 2 prestressed ring cables, which are connected by radial cables and connected to the upper lattice shell with struts. The single-layer lattice shell adopts architectural steel, and the specifications of the single-layer lattice shell rods are The specifications of the support rod are Cable specifications: and Under gravity load, the prestressing force of the hoop cable is 100kN and 800kN from inside to outside respectively; the height of the strut is 3.988m, 5.573m and 6.799m from inside to outside; the connection of each bar of the single-layer lattice shell adopts cast steel nodes, which are simplified to rigid connection, and the other connections are simplified to hinged connection; the support adopts rubber support, which is radially released and fully constrained in the annular and vertical directions; the load is applied to the upper lattice node of the suspensory dome structure, and the load combination is taken as follows: 1.0 dead load + 1.0 live load, where the dead load is 0.85kN / m 2 , live load is 0.5kN / m 2 ; The lattice shell adopts Beam188 beam unit, the vertical struts and radial cables adopt Link180 rod unit, and the ring cable adopts Link10 unit; In Matlab, use the improved genetic algorithm NSGAII to optimize the positions of the CFRP replacing some of the radial cables of the cable-supported dome structure. Take the proportion of CFRP replacing the radial cables as 40%. Take the tension of the outer-ring cables, the support reaction force and the structural stiffness of the cable-supported dome structure as the optimization objectives. Set the crossover probability of the NSGAII genetic algorithm to 0.8, the mutation probability to 0.05, the population size to 500, and the number of iterations to 20; use Matlab programming to obtain the Pareto solution set, and each point in the Pareto optimal solution set corresponds to an optimization scheme.

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