Form finding method and system for elliptical plane cable truss structure

Abstract

The invention provides a shape finding method and system for an elliptical plane cable truss structure, and the method comprises the steps: calculating the prestress of an inner ring cable of the elliptical plane cable truss structure, the prestress of an upper chord cable, the prestress of a lower chord cable, and the vertical coordinates of a lower chord cable node, if the change value of the vertical coordinates of the lower chord cable node and a support node meets the precision requirement, determining the shape finding of the elliptical plane cable truss structure; and finishing the shape finding analysis of the cable truss structure. According to the method, professional form-finding analysis software is not needed, the method can be completed by adopting a simple calculation table, the influence of the self-weight of the structure can be considered, and the prestress and the geometrical shape of the elliptical plane cable truss structure under the action of the self-weight of the structure can be efficiently and accurately determined.

Description

Technical Field

[0001] This invention relates to the field of large-span spatial structure design in building engineering, specifically to a form-finding method and system for an elliptical planar cable truss structure. Background Technology

[0002] Cable trusses originated from the concept of tensioned monolithic structures. Due to their advantages such as light weight, high structural efficiency, and ease of construction, they are widely used worldwide as roof structures for large stadiums. In engineering applications, depending on the stadium's shape requirements, there are two types: circular and elliptical, with the elliptical being more common. A cable truss structure consists of upper and lower cable nets, and intermediate members (vertical members or suspension cables). During construction, the cables need to be tensioned to achieve the prestress level and geometry designed by the engineer. At this point, the entire cable truss structure possesses the stiffness to withstand various external loads. Therefore, the most crucial issue in cable truss structure design is determining the structural prestress and corresponding geometry, i.e., form-finding analysis.

[0003] Common methods for form-finding analysis of cable trusses include force density method, dynamic relaxation method, singular value decomposition method, and finite element method. However, these methods typically require large commercial software, hindering their widespread adoption. When using singular value decomposition, the influence of the structure's self-weight on the geometry cannot be considered, leading to discrepancies between the form-finding results and the actual shape. Furthermore, some simplified algorithms are primarily designed for circular planar cable trusses and are not suitable for elliptical planar cable trusses.

[0004] Therefore, a scheme is needed to efficiently and accurately determine the prestress and geometry of an elliptical plane cable truss structure considering its own weight. Summary of the Invention

[0005] One objective of this application is to provide a form-finding method and system for elliptical planar cable truss structures, in order to solve the problem that, in the prior art, there is a deviation between the form-finding result and the actual shape when considering the influence of the structure's self-weight on the geometry of cable truss structures.

[0006] To achieve the above objectives, some embodiments of this application provide a form-finding method for an elliptical planar cable truss structure, the method comprising the following steps:

[0007] Step 1: Set the prestress of the first inner ring cable to H1, and the angle between the first inner ring cable and the horizontal plane to be... Calculate the prestress H of the inner ring cable in other sections. i Then calculate the equivalent nodal load F of the inner ring cable node along the radial and vertical directions. ri and F zi ;

[0008] Step 2: Without considering the self-weight of the structure, calculate the prestress distribution of the cable truss. According to the prestress distribution, determine the section specifications for the cables and rods, distribute the weights of the cables and rods to the two end nodes of the members, and calculate the equivalent nodal loads F ik and F ik ';

[0009] Step 3: Calculate the prestress T ik of the upper chord cables and the prestress V ik of the vertical members in the cable truss structure;

[0010] Step 4: Calculate the horizontal angle β ik of the lower chord cables and the prestress B ik of the lower chord cables in the cable truss structure, and calculate the vertical coordinates Z ij' of the support nodes of the lower chord cables and the coordinate change value ΔZ ij' , as well as the other node coordinates Z ik' and the coordinate change value ΔZ ik' ;

[0011] Among them, after the first form-finding is completed, if the values of ΔZ ij' and ΔZ ik' do not meet the accuracy requirements, adjust the angle β i1 between the lower chord cable and the horizontal plane under the initial conditions, adjust each cable truss and update the equivalent nodal loads of the cables and rods, and return to Step 3 to recalculate until the accuracy meets the requirements.

[0012] Further, in Step 1, calculate the prestress H i of the inner ring cables in the other segments, and the calculation formula is as follows:

[0013] When 1 < i ≤ m / 2,

[0014]

[0015] When i = m / 2 + 1,

[0016]

[0017] When m / 2 + 1 < i ≤ m / 2 + n / 2,

[0018]

[0019] The calculation of the equivalent nodal loads F ri and F zi of the inner ring cable nodes along the radial and vertical directions, and the calculation formula is as follows:

[0020] When i = 1,

[0021]

[0022]

[0023] When 1 < i ≤ m / 2,

[0024]

[0025]

[0026] When i = m / 2 + 1,

[0027]

[0028]

[0029] When m / 2 + 1 < i ≤ m / 2 + n / 2,

[0030]

[0031]

[0032] When i = m / 2 + n / 2 + 1,

[0033]

[0034]

[0035] In the formula, θ1 and θ2 are the central angles of the small sector and the large sector respectively, m and n are the number of equal parts of the small sector and the large sector respectively, is the angle between the inner cable and the horizontal plane; among which, the vertical equivalent nodal load F zi is positive when the load direction is downward, and vice versa when the load direction is upward.

[0036] Furthermore, in step 2, calculating the self - weight equivalent nodal loads F ik and F ik ', their calculation formulas are as follows:

[0037] F ik = ∑G ik / 2

[0038] F ik' = ∑G ik' / 2

[0039] In the formula, G ik is the weight of all cables and rods at node ik, and G ik’ is the weight of all cables and rods at node ik'.

[0040] Furthermore, in step 3, the prestress T of the upper chord of the inner cable truss structure is calculated. ik and vertical prestressed V ik The calculation formula is as follows:

[0041] When i = 1:

[0042]

[0043]

[0044] When i≥2:

[0045] T ik =T i(k-1) cosa i(k-1) / cosa ik

[0046] V ik =T ik sina ik -T i(k-1) sina i(k-1) -F ik

[0047] In the formula, T ik B i1 Let V represent the prestress of the upper chord and the lower chord under initial conditions, respectively, where i represents the i-th cable truss; α and β represent the angles between the upper and lower chords and the horizontal plane, respectively; V ik Indicates the prestress in the vertical members; α i The quantity is known.

[0048] Furthermore, in step 4, the horizontal angle β of the lower chord of the inner cable truss structure is calculated. ik and lower chord prestress B ik The calculation formula is as follows:

[0049]

[0050]

[0051] Furthermore, in step 4, the vertical coordinate Z of the lower chord support node is calculated. ij' and coordinate change value ΔZ ij' and the coordinates Z of other nodes ik' and coordinate change value ΔZ ik' ;

[0052]

[0053]

[0054] ΔZ ij’=|Z ij’ (n)-Z ij’ (0)|

[0055] ΔZ ik’ =||Z ik’ (n)-Z ik’ (n-1)|

[0056] In the formula, Z i Let Δl be the vertical coordinate of node i in the inner loop. ik Z is the horizontal distance between the lower chord node k' and (k+1)' of the i-th cable truss; where Z ik' (n) represents the vertical coordinate of node ik' calculated in the nth iteration.

[0057] Furthermore, in step 4, ΔZ ij' and ΔZ ik' The condition for a value to satisfy the required precision is:

[0058] ΔZ ij’ =|Z ij’ (n)-Z ij’ (0)|≤0.001m

[0059] ΔZ ik’ =|Z ik’ (n)-Z ik’ (n-1)|≤0.001m.

[0060] Furthermore, in step 4, the angle β between the lower chord and the horizontal plane under the initial conditions is adjusted. i1 Where Z ij' (n)>Z ij' (0), increase β i1 Conversely, decrease β i1 .

[0061] On the other hand, embodiments of this application provide a form-finding system for an elliptical planar cable truss structure. The system includes a memory for storing computer program instructions and a processor for executing the program instructions. When the computer program instructions are executed by the processor, the system is triggered to execute the aforementioned form-finding method for the elliptical planar cable truss structure. Attached Figure Description

[0062] Figure 1(a) and Figure 1(b) are three-dimensional schematic diagrams of the first and second types of elliptical planar cable truss structures of the present invention, respectively;

[0063] Figure 2(a), (b) and (c) are respectively the plan view, side view and three-dimensional view of the inner ring cable prestress calculation model of the present invention;

[0064] Figure 3(a) and (b) are calculation model diagrams of the first and second types of internal cable truss structures of the present invention, respectively;

[0065] Figure 4 This is a flowchart of the elliptical planar cable truss structure form-finding method of the present invention;

[0066] Figure 5(a), (b) and (c) show the three-dimensional view, plan view and geometric dimensions and member numbers of the elliptical planar cable truss structure of the present invention, respectively.

[0067] Figure 6 This is a schematic diagram of the initial equilibrium state of the elliptical plane cable truss structure of the present invention, considering the structure's self-weight. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0070] This application proposes a form-finding method and system for elliptical planar cable truss structures. This method does not require specialized form-finding analysis software; it can be completed using simple calculation tables and can take into account the influence of the structure's self-weight. This method can efficiently and accurately determine the prestress and geometry of elliptical planar cable truss structures considering their self-weight.

[0071] In some embodiments, the form-finding method proposed in this application is mainly aimed at two types of elliptical planar cable truss structures, where the inner ring of the cable truss consists of a single ring cable, and the outer ring is connected to the support. Specifically: As shown in Figure 1(a), the upper chord of the first type of cable truss has negative curvature, and the lower chord has positive curvature; therefore, the intermediate vertical members need to be vertical rods, generally circular steel pipes. As shown in Figure 1(b), the upper chord of the second type of cable truss has positive curvature, and the lower chord has negative curvature; therefore, the intermediate vertical members need to be suspension cables.

[0072] The form-finding process for an elliptical planar cable truss structure is divided into two main parts:

[0073] (1) Calculation of prestress in inner ring cable

[0074] Exemplarily, the elliptical plane is constructed by the four-center circle method. As shown in Figure 2, where (a), (b), and (c) in Figure 2 are respectively the plan view, side view, and three-dimensional view of the prestress calculation model of the inner ring cable of this solution. Taking this elliptical inner ring cable as an example, the prestress calculation of the elliptical inner ring cable is described. The inner ring cable can be a plane curve in space or a space curve such as a hyperbolic parabola. Considering the symmetry of the ellipse, 1 / 4 of the ellipse is selected for analysis. θ1 and θ2 are respectively the central angles of the small sector and the large sector, m and n are respectively the equal division numbers of the small sector and the large sector, the prestress of the first segment of the inner ring cable is H1, and the angle between the first segment of the inner ring cable and the horizontal plane is The prestress H of other segments of the inner ring cable i , is the angle between the inner ring cable and the horizontal plane. By performing a mechanical equilibrium analysis on the inner ring cable along the circumferential direction, the relationship of the prestress of the inner ring cable can be obtained as follows:

[0075] When 1 < i ≤ m / 2,

[0076]

[0077] When i = m / 2 + 1,

[0078]

[0079] When m / 2 + 1 < i ≤ m / 2 + n / 2,

[0080]

[0081] The equivalent nodal loads F along the radial and vertical directions of the inner ring cable nodes 1 to m / 2 + n / 2 + 1 ri and F zi The calculation formulas are:

[0082] When i = 1,

[0083]

[0084] When 1 < i ≤ m / 2,

[0085]

[0086]

[0087] When i = m / 2 + 1,

[0088]

[0089]

[0090] When m / 2 + 1 < i ≤ m / 2 + n / 2,

[0091]

[0092]

[0093] When i = m / 2 + n / 2 + 1

[0094]

[0095]

[0096] Wherein: Vertical equivalent nodal load F zi A positive value indicates that the load is directed downwards, while a negative value indicates that the load is directed upwards.

[0097] (2) Form-finding calculation of cable truss structure

[0098] The calculation models for the two types of cable truss structures can be simplified to planar cable trusses, as shown in Figure 3. Figure 3(a) and (b) show the calculation models for the first and second types of internal cable truss structures in this scheme, respectively. In Figure 3, T... ik B ik F represents the prestress of the upper and lower chords, respectively; ik and F ik ' represents the equivalent nodal load of the cable's self-weight, where i represents the i-th cable truss; α and β represent the angles between the upper and lower chords and the horizontal plane, respectively; V ik This indicates the prestress in the vertical members.

[0099] Distribute the weight of the cable and rod equally to the nodes at both ends of the rod, and calculate the equivalent nodal load F of the cable and rod's self-weight. ik and F ik The calculation formula is:

[0100] F ik =∑G ik / 2

[0101] F ik' =∑G ik' / 2

[0102] In the formula, G ik G is the weight of all cables and rods at node ik. ik’ Let ik' be the weight of all cables and rods at node ik'.

[0103] Based on the node equilibrium relationship, two equilibrium equations, one horizontal and one vertical, are established for each node to solve for the cable prestress.

[0104] When i = 1:

[0105]

[0106] When i≥2:

[0107]

[0108] When calculating the prestress and geometry of a cable truss structure, the geometry of the upper chord remains unchanged, i.e., α. i Given a known quantity, in addition, β i1 It is also used as an initial known condition.

[0109] After shape-finding calculation, the vertical coordinate Z of the lower chord node is... ij' and Z ik’ The calculation is performed using the following formula:

[0110]

[0111]

[0112] Where: Z i Let Δl be the vertical coordinate of node i in the inner loop. ik Let k' be the horizontal distance between the lower chord node k' and (k+1)' of the i-th cable truss.

[0113] The vertical coordinate Z of the following cable support node ij' ij' As a control value, β is adjusted iteratively. i1 Make Z ij' The change value ΔZ ij’ Not exceeding 0.001m. Furthermore, during iterative adjustment of β... i1 During the process, it is also necessary to ensure the change value ΔZ of the vertical coordinates of other nodes ik' of the lower chord. ik’ Not exceeding 0.001m, which is expressed as:

[0114]

[0115] Where: Z ik' (n) represents the vertical coordinate of node ik' calculated in the nth iteration.

[0116] Adjusting β i1 During the process, due to changes in the shape of the lower chord and the length of the vertical members, the weight of the cables and members was recalculated, and the weight of the cables and members was evenly distributed to the nodes. The equivalent nodal load F of the self-weight of the upper and lower chords was then updated. ik and F ik '.

[0117] Some embodiments of this application are based on the above-described form-finding method for elliptical planar cable truss structures, such as... Figure 4 As shown, its shape-finding process includes the following steps:

[0118] Step 1: Set the prestress of the first inner ring cable to H1, and calculate the prestress H of the inner ring cable based on geometric relationships.i Then calculate the equivalent nodal load F of the inner ring cable node along the radial and vertical directions. ri and F zi .

[0119] Step 2: Ignoring the structure's self-weight, calculate the prestress distribution of the cable truss. Based on the prestress distribution, determine the cross-sectional specifications for the cables and rods, ensuring that the stress in the cables and rods meets relevant code requirements. Distribute the weight of the cables and rods evenly to the nodes at both ends of the members, and calculate the equivalent nodal load F of the self-weight of the cables and rods. ik and F ik '.

[0120] Step 3: Calculate the prestress of the upper chord and vertical members of the cable truss structure, based on F. ri F zi α i ,β i1 and F ik Calculate the prestress T of the upper chord cable ik and vertical prestressed V ik .

[0121] Step 4: Calculate the prestress and shape of the lower chord of the cable truss structure, based on T ik V ik ,β i1 and F ik 'Calculate the horizontal angle β of the lower chord ik and lower chord prestress B ik Calculate the vertical coordinate Z of the lower chord support node. ij' and coordinate change value ΔZ ij' and the coordinates Z of other nodes ik' and coordinate change value ΔZ ik' .

[0122] After the first shape finding, ΔZ ij' and ΔZ ik' The value does not meet the accuracy requirements, adjust β. i1 For each cable truss, adjust and update the equivalent nodal loads of the cable and rod self-weights, then return to step 3 to recalculate until the accuracy meets the requirements. There are two adjustment methods for β. i1 The method, if Z ij' (n)>Z ij' (0), increase β i1 Conversely, decrease β i1 .

[0123] Example

[0124] Taking an elliptical planar cable truss structure as an example, this form-finding method and process are explained. The inner diameter of the small circle is 55m, and the outer diameter is 105m. The inner diameter of the large circle is 90m, and the outer diameter is 140m. The central angle of both the small and large circles is π / 2. The inner diameter of the ellipse is approximately 130.5m to 159.5m, and the outer diameter is approximately 230.5m to 359.5m. The prestress H1 of the inner ring cable is 25000kN. The example model of the elliptical planar cable truss structure is shown in Figure 5. In Figure 5, (a), (b), and (c) are the three-dimensional view, plan view, geometric dimensions, and member numbers of the example model of the elliptical planar cable truss structure of this scheme, respectively. The vertical coordinates of the initial nodes of the inner ring cable are shown in the first row of Table 3.

[0125] Considering the symmetry of the ellipse, a quarter ellipse is selected for analysis. The shape-finding analysis process is as follows:

[0126] S1. The initial prestress distribution of the inner ring cable is calculated based on the prestress H1 of the first inner ring cable. The calculation results are shown in Table 1. The cross section of the inner ring cable is determined to be 10×73φ7. Based on the prestress H1 of the inner ring cable, the equivalent nodal load F of each node of the inner ring cable is calculated. ri and F zi .

[0127] Table 1 Calculation results of prestressing of inner ring cable

[0128]

[0129] S2. Based on the prestress distribution of the inner ring cable and the equivalent nodal load, calculate the prestress distribution of the cable truss to determine the cross-sectional specifications for the cables and rods, as shown in column 2 of Table 2; distribute the weight of the cables and rods evenly to the nodes at both ends of the rods, and calculate the equivalent nodal load F of the self-weight of the cables and rods. ik and F ik '.

[0130] S3. Calculate the prestress T of the upper chord cable in the cable truss structure. ik and vertical prestressed V ik .

[0131] S4. Calculate the prestress B of the lower chord of the cable truss structure. ik The angle β between the lower chord and the horizontal plane ik ; Calculate the vertical coordinate Z of the lower chord support node. ij' and coordinate change value ΔZ ij' And the coordinates Z of other nodes of the lower chord ik' and coordinate change value ΔZ ik' .

[0132] After the first shape finding, ΔZ ij' and ΔZ ik' The value does not meet the precision requirements, according to β in the flowchart. i1The adjustment method involves adjusting each cable truss and updating the equivalent nodal loads of the cable and rod self-weights, then returning to step 3 to recalculate until the accuracy meets the requirements.

[0133] After the form finding was completed, the calculation results of the prestress of the first to 11 cable truss structures are shown in columns 3 to 13 of Table 2, and the calculation results of the vertical coordinates of the lower chord nodes of the first to 11 cable truss structures are shown in Table 3.

[0134] Table 2 shows the calculation results of cable prestress in cable trusses 1-11 when considering the structure's self-weight.

[0135]

[0136] Table 3 shows the calculation results of the vertical coordinates of the lower chord nodes of the first to eleventh cable trusses.

[0137]

[0138]

[0139] The initial prestress calculation results were verified using finite element software. Figure 6 The vertical displacement of the elliptical plane cable truss structure in its initial equilibrium state under its own weight and prestress is shown in the results. It can be seen that the vertical displacement deviates very little from the initial state, indicating that the cable truss structure maintains equilibrium under the combined action of its own weight and prestress. This proves that the form-finding method and process proposed in this invention have very high calculation accuracy.

[0140] Some embodiments of this application also provide a form-finding system for an elliptical planar cable truss structure. The system includes a memory for storing computer program instructions and a processor for executing the program instructions. When the computer program instructions are executed by the processor, the system is triggered to execute the aforementioned form-finding method for the elliptical planar cable truss structure.

[0141] In summary, the form-finding method and system for an elliptical planar cable truss structure proposed in this application have the following advantages: 1. It keeps the geometry of the upper chord unchanged, satisfying the architect's shape requirements; 2. By adjusting the geometry of the lower chord, the support nodes of the lower chord can remain unchanged, satisfying the design requirements of the structural engineer.

[0142] Furthermore, the form-finding calculation formula is simple and does not require specialized design software; it can be completed using calculation spreadsheets such as Excel, making it convenient for engineering designers and researchers to use for modeling and mechanical performance analysis. Verification with professional software has shown that the calculation results of this form-finding method are accurate and have very high precision.

[0143] It should be noted that this application can be implemented in software and / or a combination of software and hardware, for example, using an application-specific integrated circuit (ASIC), a general-purpose computer, or any other similar hardware device. In one embodiment, the software program of this application can be executed by a processor to implement the steps or functions described above. Similarly, the software program of this application (including related data structures) can be stored in a computer-readable recording medium, such as RAM memory, magnetic or optical drives, floppy disks, and similar devices. Furthermore, some steps or functions of this application can be implemented in hardware, for example, as circuitry that cooperates with a processor to perform the various steps or functions.

[0144] In a typical configuration of this application, both the terminal and the network device include one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0145] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0146] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include non-transitory computer-readable media, such as modulated data signals and carrier waves.

[0147] Furthermore, a portion of this application can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to this application through the operation of the computer. The program instructions invoking the methods of this application may be stored in a fixed or removable recording medium, and / or transmitted via a data stream in a broadcast or other signal carrying medium, and / or stored in the working memory of a computer device operating according to the program instructions. Here, one embodiment of this application includes a device comprising a memory for storing computer program instructions and a processor for executing the program instructions, wherein, when the computer program instructions are executed by the processor, the device is triggered to run methods and / or technical solutions based on the foregoing embodiments of this application.

[0148] It will be apparent to those skilled in the art that this application is not limited to the details of the exemplary embodiments described above, and that this application can be implemented in other specific forms without departing from the spirit or essential characteristics of this application. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of this application is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be embraced within this application. No reference numerals in the claims should be construed as limiting the scope of the claims. Furthermore, it is clear that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units or devices recited in the apparatus claims may also be implemented by a single unit or device in software or hardware.

Claims

1. A method for finding the shape of an elliptical planar cable truss structure, characterized in that, Comprising the following steps: Step 1: Set the prestress of the first inner ring cable to H1, and the angle between the first inner ring cable and the horizontal plane to be... Calculate the prestress H of the inner ring cable in other sections. i Then calculate the equivalent nodal load F of the inner ring cable node along the radial and vertical directions. ri and F zi ; Step 2: Ignoring the structural self-weight, calculate the prestress distribution of the cable truss. Based on the prestress distribution, determine the cross-sectional specifications for the cables and rods. Distribute the weight of the cables and rods evenly to the nodes at both ends of the members, and calculate the equivalent nodal load F of the self-weight of the cables and rods. ik and F ik '; Step 3: Calculate the prestress T of the upper chord of the cable truss structure. ik and vertical prestressed V ik ; Step 4: Calculate the horizontal angle β of the lower chord of the cable truss structure. ik and lower chord prestress B ik And calculate the vertical coordinate Z of the lower chord support node. ij' and coordinate change value ΔZ ij' and the coordinates Z of other nodes ik' and coordinate change value ΔZ ik' ; Among them, after the first shape finding is completed, if ΔZ ij' and ΔZ ik' The value does not meet the accuracy requirements; adjust the angle β between the lower chord and the horizontal plane under the initial conditions. i1 For each cable truss, adjust and update the equivalent nodal loads of the cable and rod self-weights, then return to step 3 to recalculate until the accuracy meets the requirements.

2. The method according to claim 1, characterized in that, In step 1, the prestress H of the other segments of the inner ring cable is calculated. i The calculation formula is as follows: When 1 < i ≤ m / 2, When i = m / 2 + 1, When m / 2 + 1 < i ≤ m / 2 + n / 2, The calculation of the radial and vertical equivalent nodal load F of the inner ring cable node. ri and F zi The calculation formula is as follows: When i = 1, When 1 < i ≤ m / 2, When i = m / 2 + 1, When m / 2 + 1 < i ≤ m / 2 + n / 2, When i = m / 2 + n / 2 + 1, In the formula, θ1 and θ2 are the central angles of the small and large sectors, respectively, and m and n are the equal fractions of the small and large sectors, respectively. Let F be the angle between the inner ring cable and the horizontal plane; where F is the vertical equivalent nodal load. zi A positive value indicates that the load is directed downwards, while a negative value indicates that the load is directed upwards.

3. The method according to claim 2, characterized in that, In step 2, the equivalent nodal load F of the self-weight of the cable and rod is calculated. ik and F ik The calculation formula is as follows: F ik =∑G ik / 2 F ik' =∑G ik' / 2 In the formula, G ik G is the weight of all cables and rods at node ik. ik’ Let ik' be the weight of all cables and rods at node ik'.

4. The method according to claim 3, characterized in that, In step 3, the prestress T of the upper chord of the cable truss structure is calculated. ik and vertical prestressed V ik The calculation formula is as follows: When i = 1: When i ≥ 2: T ik =T i(k-1) What i(k-1) / What ik V ik =T ik sina ik -T i(k-1) sinα i(k-1) -F ik In the formula, T ik B i1 Let V represent the prestress of the upper chord and the lower chord under initial conditions, respectively, where i represents the i-th cable truss; α and β represent the angles between the upper and lower chords and the horizontal plane, respectively; V ik Indicates the prestress in the vertical members; α i The quantity is known.

5. The method according to claim 4, characterized in that, In step 4, the horizontal angle β of the lower chord of the cable truss structure is calculated. ik and lower chord prestress B ik The calculation formula is as follows:

6. The method according to claim 5, characterized in that, In step 4, the vertical coordinate Z of the lower chord support node is calculated. ij′ and coordinate change value ΔZ ij′ and the coordinates Z of other nodes ik′ and coordinate change value ΔZ ik' ; ΔZ ij′ =|Z ij′ (n)-Z ij′ (0)| ΔZ ik′ =|Z ik′ (n)-Z ik′ (n-1)| In the formula, Z i Let Δl be the vertical coordinate of node i in the inner loop. ik Z is the horizontal distance between the lower chord node k′ and (k+1)′ of the i-th cable truss; where Z ik′ (n) represents the vertical coordinate of node ik′ calculated in the nth iteration.

7. The method according to claim 6, characterized in that, In step 4, ΔZ ij′ and ΔZ ik′ The condition for a value to satisfy the required precision is: ΔZ ij′ =|Z ij′ (n)-Z ij′ (0)|≤0.001m ΔZ ik′ =|Z ik′ (n)-Z ik′ (n-1)|≤0.001m。 8. The method according to claim 7, characterized in that, In step 4, the angle β between the lower chord and the horizontal plane under the initial conditions is adjusted. i1 Where Z ij′ (n)>Z ij′ (0), increase β i1 Conversely, decrease β i1 .

9. A form-finding system for an elliptical planar cable truss structure, the system comprising a memory for storing computer program instructions and a processor for executing the program instructions, wherein, When the computer program instructions are executed by the processor, triggering the system to execute the form-finding method of the elliptical plane cable truss structure described in any one of claims 1 to 8.

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