Hybrid method and apparatus for space cable lofting

Abstract

The application discloses a kind of spatial cable form-finding hybrid method and device, it is related to suspension bridge design field, the method includes the vertical coordinate target value of span midpoint is calculated to obtain;Iterative main cable line shape, the unstressed length of each cable segment and the unstressed length of sling;Establish the first finite element model to calculate the space cable coordinates of each node of main cable;Based on the space cable coordinates of each node of main cable calculated by the first finite element model, establish the second finite element model;Superimpose the coordinate of span midpoint before main cable deformation, obtain the new span midpoint coordinate after deformation;Again, the new span midpoint coordinate after deformation is calculated;Based on the new span midpoint coordinate after deformation calculated again, the new span midpoint coordinate after deformation is calculated once more;According to the new span midpoint coordinate after deformation calculated again, and the new span midpoint coordinate after deformation calculated once more, to judge whether to suspend calculation.This application can handle large rotation and multi-directional rotation coupling problem without simplification.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of suspension bridge design, in particular to a hybrid method and device for spatial cable form finding. BACKGROUND

[0002] In the design of a suspension bridge, the main cable form finding should be carried out first, otherwise the subsequent work cannot be carried out. Through the form finding, the main cable bridge line (i.e. the coordinates of each point), the unstressed length of each cable segment of the main cable and the unstressed length parameters of each suspension cable can be determined, and the subsequent construction stage analysis, live load calculation, self-vibration characteristic analysis and the like are based on these parameters. It can be seen that the accurate form finding of the main cable in the bridge state is very important. For a large-span spatial cable suspension bridge, due to the force requirement, the diameter of the main cable is often large, reaching more than 1 m. The large-diameter section has a certain torsional and bending stiffness. On the other hand, the main cable of the spatial cable suspension bridge is in the vertical plane in the air cable state, and gradually deforms laterally during the process of suspending the beam, and forms a spatial form. In this process, the torsional and bending stiffness of the main cable acts simultaneously, so that the actual main cable line after the bridge cannot reach the theoretical line shape calculated by ignoring the torsional and bending stiffness. At present, for the main cable form finding of a large-diameter spatial cable suspension bridge, the traditional pure analytical method is usually used as for the plane cable.

[0003] However, the traditional pure analytical form finding method has the following problems:

[0004] 1. In order to be able to solve analytically, the main cable must be simplified and assumed as a catenary flexible cable, which can only be in tension. The improved analytical method can only consider the in-plane bending, cannot consider the bending in and out of the plane at the same time, and cannot consider the torsion for three-dimensional bending-torsion coupling analysis.

[0005] 2. For a large-diameter spatial cable, if the torsional and bending stiffness of the main cable cannot be considered at the same time, the line shape after the bridge will be deviated, especially in the vicinity of the left and right sides of the main cable. The transverse inclination angle of the long suspension cable and the installation angle of the cable clamp will be deviated, and according to the installation angle, the cable clamp will have an additional bending moment, and the stress will change from axial tension to tension-bending coupling, which is more prone to fatigue failure. The line shape deviation will also cause the change of the suspension cable force, especially for the long cable, the cable force will be reduced, and even fail. SUMMARY

[0006] In view of the defects in the prior art, the purpose of the present application is to provide a hybrid method and device for spatial cable form finding, which can handle the large rotation and multi-directional rotation coupling problem without simplification.

[0007] To achieve the above purpose, the hybrid method for spatial cable form finding provided by the present application specifically comprises the following steps:

[0008] Calculate the vertical coordinate target value of the midspan point based on the left node coordinates of the main cable, the right node coordinates of the main cable, and the given rise-span ratio;

[0009] Use the analytical method to perform the bridge formation of the cable system, and iteratively obtain the main cable line shape, the unstressed length of each cable segment, and the unstressed length of the sling according to the given rise-span ratio;

[0010] According to the calculated main cable line shape and the unstressed length of each cable segment, establish a first finite element model to calculate the empty cable coordinates of each node of the main cable;

[0011] Based on the empty cable coordinates of each node of the main cable calculated by the first finite element model, establish a second finite element model;

[0012] Perform nonlinear calculation on the second finite element model to obtain the displacement of the midspan point, and superimpose the coordinates of the midspan point before the deformation of the main cable to obtain the new coordinates of the midspan point after the deformation;

[0013] Calculate the new rise-span ratio based on the new midspan point coordinates, and repeat the calculation again according to the new rise-span ratio to obtain the new midspan point coordinates after the deformation again;

[0014] Based on the new midspan point coordinates after the deformation obtained by the calculation again, calculate the new rise-span ratio again, and repeat the calculation again according to the new rise-span ratio obtained by the calculation again to obtain the new midspan point coordinates after the deformation again;

[0015] According to the new midspan point coordinates after the deformation obtained by the calculation again, and the new midspan point coordinates after the deformation obtained by the calculation again, determine whether to terminate the calculation.

[0016] On the basis of the above technical scheme, the vertical coordinate target value of the midspan point is calculated in the following specific manner:

[0017] Y c =(Y k-1 +Y0) / 2-(X k-1 -X0)λ

[0018] Wherein, Y c represents the vertical coordinate target value of the midspan point, λ represents the given rise-span ratio, the left node coordinates of the main cable are (X0, Y0, Z0), the right node coordinates of the main cable are (X k-1 , Y k-1 , Z k-1 ), and k represents the total number of main cable nodes.

[0019] On the basis of the above technical scheme, the bridge formation of the cable system is performed by using the analytical method, and the main cable line shape, the unstressed length of each cable segment, and the unstressed length of the sling are iteratively obtained according to the given rise-span ratio, wherein the specific steps of iteration include:

[0020] Let λ0= λ, the new target value of the vertical coordinate across the midpoint is calculated, and the calculation method is:

[0021] Y c0 = (Y k-1 + Y0) / 2 - (X k-1 - X0) λ0;

[0022] According to the longitudinal force F XL , the vertical force F YL , the horizontal force F ZL of the left end of the main cable, and the projection length L0 of the main cable in the horizontal plane, the height difference H0 between the left and right points of the first cable segment of the main cable and the unstressed cable length S are obtained by the plane catenary equation and using Newton's method iteration, wherein the projection length L0 of the main cable in the horizontal plane The longitudinal force F XL of the left end of the main cable is P Z / λ / 8, the vertical force F YL of the left end of the main cable is P Z / 2, and the horizontal force F ZL of the left end of the main cable is F XL (Z b - Z0) / (X b - X0), P Z represents the total vertical force of the sling lower end, Z b represents the horizontal coordinate of the main beam at the lower end of the sling across the midpoint, and X b represents the vertical coordinate of the main beam at the lower end of the sling across the midpoint.

[0023] The three-directional forces (F XR , F YR , F ZR ) at the right end of the first cable segment of the main cable are calculated from the force balance condition, and the coordinates (X1, Y1, Z1) of the right end of the first cable segment of the main cable are calculated from the height difference H0 and the included angle β L , wherein:

[0024] F XR = -F XL

[0025] F YR = -F YL + Sω

[0026] F ZR = -F ZL

[0027] β L = arctan (F ZR / F XR )

[0028] Wherein, ω represents the weight per meter of the main cable material.

[0029] Based on the coordinates (X1, Y1, Z1) of the right end point of the first cable segment of the main cable, and the known coordinates (X d , Y d , Z d ) of the lower end point of the sling and the vertical force Q of the sling end, the unstressed length S d of the sling is obtained by using the flexible iteration method, and the three-directional forces (F Xd , F Yd , F Zd ) of the upper end of the sling are obtained from the force balance condition;

[0030] The three-directional forces (F XR , F YR , F ZR ) at the right end point of the first cable segment of the main cable and the three-directional forces (F Xd , F Yd , F Zd ) of the upper end of the sling are superimposed, (F XL , F YL , F ZL ) is updated, and then the iteration of the next cable segment is performed until the calculation of all cable segments is completed, the vertical coordinate Y mR and the horizontal coordinate Z mR of the rightmost node of the main cable are obtained, and the vertical coordinate Y mc of the mid-span point of the main cable is obtained;

[0031] Based on the difference between the obtained vertical coordinate Y mR and the horizontal coordinate Z mR of the rightmost node of the main cable and the target value, and the vertical coordinate Y mc of the mid-span point of the main cable, if the accuracy condition is not met, the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the vertical coordinate of the mid-span point of the main cable are calculated again, and an influence matrix is obtained;

[0032] Based on the influence matrix, the three-directional forces at the left end point of the first cable segment of the main cable are corrected, and then the rightmost node coordinate of the main cable and the vertical coordinate of the mid-span point of the main cable are calculated until the accuracy condition is met;

[0033] Based on the node coordinates of the main cable, the main cable profile is determined, and the unstressed lengths of the cable segments and the slings of the main cable are obtained.

[0034] On the basis of the above technical scheme, based on the difference between the obtained vertical coordinate Y mR and the horizontal coordinate Z mR of the rightmost node of the main cable and the target value, and the vertical coordinate Y mc of the mid-span point of the main cable, if the accuracy condition is not met, the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the vertical coordinate of the mid-span point of the main cable are calculated again, and an influence matrix is obtained, and the specific steps include:

[0035] Based on the calculated vertical coordinate Y of the rightmost node of the main cable mR and the horizontal coordinate Z mR , and the vertical coordinate Y of the main cable mid-span mc The difference between the target value and the target value, namely ΔY mR =Y mR -Y k-1 , ΔZ mR =Z mR -Z k-1 , ΔY mc =Y mc -Y c0 :

[0036] like If it is less than the given limit, it ends;

[0037] like If the three-axis force (F xL 、F yL 、F zL ), and the three-direction forces at the left end point of the first section of the main cable are taken as (F xL +1, F yL 、F zL )、(F xL 、F yL +1, F zL )、(F xL 、F yL 、F zL +1), calculate again the vertical coordinate and horizontal coordinate of the rightmost node of the main cable, and the vertical coordinate of the mid-span point of the main cable, and get three new results, which are (Y mR1 , Z mR1 , Z mc1 )、(Y mR2 , Z mR2 , Z mc2 )、(Y mR3 , Z mR3 , Z mc3 ), and then the influence matrix is ​​obtained;

[0038] Among them, the influence matrix is ​​expressed as:

[0039]

[0040] On the basis of the above technical solution, the three-dimensional force at the left end point of the first section of the main cable is corrected based on the influence matrix, and then the coordinates of the rightmost node of the main cable and the vertical coordinates of the mid-span point of the main cable are calculated until the accuracy conditions are met, specifically:

[0041] The influence matrix is ​​used to correct the three-dimensional forces at the left end point of the first section of the main cable, namely:

[0042]

[0043] wherein, (ΔF xL , ΔF yL , ΔF zL ) represents the three-directional force at the left end point of the first cable segment of the main cable after correction;

[0044] F xL + ΔF xL , F yL + ΔF yL , F zL + ΔF zL are obtained as new initial values of iteration, and then the vertical coordinate and horizontal coordinate of the rightmost node of the main cable and the vertical coordinate of the mid-point of the main cable are continuously calculated until is less than a given limit value, the iteration is terminated.

[0045] On the basis of the above technical solution, the first finite element model is established according to the calculated main cable line shape and the unstressed length of each cable segment to calculate the coordinates of each node of the main cable in the air, and the specific steps include:

[0046] According to the calculated coordinates of each node of the main cable and the unstressed length of each cable segment, the first finite element model is established, wherein each node of the main cable is taken as the node of the finite element model, the cable segment is taken as the unit of the finite element model, the catenary cable unit is adopted, the corresponding unstressed length value is given, and only the main cable is in the first finite element model without the suspension cable, the two ends of the main cable are fixed, and the air cable line shape of the main cable, i.e. the coordinates of each node of the main cable in the air, is calculated through the first finite element model.

[0047] On the basis of the above technical solution, the second finite element model is established based on the coordinates of each node of the main cable in the air calculated by the first finite element model, and the specific steps include:

[0048] According to the coordinates of each node of the main cable in the air calculated by the first finite element model, the coordinates of each node of the main cable are updated to obtain the coordinates of each node of the main cable after deformation of the first finite element model, i.e. the coordinates of the main cable under the air cable, and the second finite element model is established according to the coordinates, the catenary cable unit is adopted to establish the main cable unit in the second finite element model, and the corresponding unstressed length is given;

[0049] The suspension cable unit is established, and the corresponding unstressed length is given;

[0050] The main cable beam unit is established, the main cable beam unit and the main cable unit are overlapped to obtain the superimposed double unit, the cross-sectional area of the superimposed double unit is given a very small value, the torsional inertia and the bending inertia are calculated according to the circular cross-section of the main cable, and the main cable beam unit is given.

[0051] On the basis of the above technical solution,

[0052] The second finite element model is calculated non-linearly to obtain the displacement of the midspan, and the midspan coordinate before deformation of the main cable is superimposed to obtain new midspan coordinates after deformation, specifically, the second finite element model is calculated non-linearly to obtain the displacement of the midspan And the midspan coordinate before deformation of the main cable is superimposed to obtain new midspan coordinates after deformation

[0053] The new rise-span ratio is calculated based on the new midspan coordinates, and the new rise-span ratio is calculated again based on the new rise-span ratio, and the new midspan coordinates after deformation are calculated again, specifically, the new rise-span ratio λ1 is calculated based on the new midspan coordinates, and the new rise-span ratio is calculated again based on the new rise-span ratio, and the new midspan coordinates after deformation are calculated again Wherein

[0054]

[0055] On the basis of the above technical solutions,

[0056] The new rise-span ratio is calculated based on the new midspan coordinates after deformation calculated again, and the new rise-span ratio is calculated again based on the new rise-span ratio calculated again, and the new midspan coordinates after deformation are calculated again, specifically:

[0057] The new rise-span ratio λ2 is calculated based on the new midspan coordinates after deformation calculated again, and the new rise-span ratio is calculated again based on the new rise-span ratio calculated again, and the new midspan coordinates after deformation are calculated again Wherein

[0058]

[0059] The new midspan coordinates after deformation calculated again and the new midspan coordinates after deformation calculated again are used to judge whether to stop calculation, specifically:

[0060] If Less than a given limit value, indicating that the condition is met, and the calculation is terminated;

[0061] If Not less than a given limit value, the calculation of the rise-span ratio and the midspan coordinate is continued until the condition is met.

[0062] The application provides a kind of hybrid device of space cable form finding, comprising:

[0063] The calculation module is used to calculate the vertical coordinate target value of the midspan based on the left node coordinate of the main cable, the right node coordinate of the main cable and the given rise-span ratio;

[0064] An iteration module is configured to adopt an analytical method to perform bridge-forming of the cable system, and to obtain the main cable line shape, the unstressed length of each cable segment and the unstressed length of the sling according to a given rise-span ratio;

[0065] A first establishing module is configured to establish a first finite element model according to the main cable line shape and the unstressed length of each cable segment to calculate the empty cable coordinates of each node of the main cable;

[0066] A second establishing module is configured to establish a second finite element model based on the empty cable coordinates of each node of the main cable calculated by the first finite element model;

[0067] A superposition module is configured to perform nonlinear calculation on the second finite element model to obtain the displacement of the mid-span point, and to superimpose the mid-span point coordinates before the deformation of the main cable to obtain new mid-span point coordinates after the deformation;

[0068] A first executing module is configured to calculate a new rise-span ratio based on the new mid-span point coordinates, and to repeatedly calculate again according to the new rise-span ratio to obtain new mid-span point coordinates after the deformation again;

[0069] A second executing module is configured to calculate a new rise-span ratio again based on the new mid-span point coordinates after the deformation calculated again, and to repeatedly calculate again according to the new rise-span ratio calculated again to obtain new mid-span point coordinates after the deformation once more;

[0070] A judging module is configured to judge whether to stop the calculation according to the new mid-span point coordinates after the deformation calculated again and the new mid-span point coordinates after the deformation calculated once more.

[0071] Compared with the prior art, the present application has the following advantages:

[0072] (1) The analytical method in the present application is still the traditional method based on the catenary equation, without setting many assumptions for introducing the bending stiffness, and without complex derivation, while the finite element method based on the finite displacement theory can handle large rotation and multi-directional rotation coupling problems without simplification, and can accurately consider the three-way coupling effects of torsion resistance and two-way bending resistance;

[0073] (2) The present application constructs an outer loop iteration, and mixes the use of analytical method and finite element method to decompose the influencing factors, and to exert the respective advantages of the two methods, the analytical method considers the axial stiffness and sag effect of the main cable, and the finite element method considers the torsion resistance and bending stiffness of the main cable, so that the main cable line shape meeting the target value and considering the torsion resistance and two-way bending stiffness can be obtained;

[0074] (3) The present application can accurately calculate the transverse cable inclination angle and the cable clamp installation angle, and the cable clamp can maintain the axial tension state when the bridge is formed, thereby reducing the risk of tension bending fatigue damage, and the cable force will not fail and redistribute. BRIEF DESCRIPTION OF DRAWINGS

[0075] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0076] Figure 1 The flowchart of the hybrid method for spatial cable shape finding in the embodiments of the present application;

[0077] Figure 2 The structural schematic diagram of the bridge;

[0078] Figure 3 The elevation projection diagram of the spatial cable system;

[0079] Figure 4 The horizontal projection diagram of the spatial cable system;

[0080] Figure 5 The bridge line and the spatial cable line schematic diagram. DETAILED DESCRIPTION

[0081] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments.

[0082] Referring to Figure 1 The hybrid method for spatial cable shape finding provided by the embodiments of the present application specifically includes the following steps:

[0083] S1: based on the left node coordinates of the main cable, the right node coordinates of the main cable and the given rise-span ratio, the vertical coordinate target value of the midspan point is calculated; for the bridge structure in the present application, please refer to Figure 2 .

[0084] In the present application, the vertical coordinate target value of the midspan point is calculated, and the specific calculation method is as follows:

[0085] Y c =(Y k-1 +Y0) / 2-(X k-1 -X0)λ

[0086] Yc represents the vertical coordinate target value across the midpoint, λ represents a given rise-span ratio, the left node coordinate of the main cable is (X0, Y0, Z0), the right node coordinate of the main cable is (X k-1 , Y k-1 , Z k-1 ), and k represents the total number of main cable nodes.

[0087] S2: the bridge forming and shaping of the cable system is carried out by using an analytical method, the main cable line shape, the unstressed length of each cable segment and the unstressed length of the sling are obtained by iteration according to a given rise-span ratio;

[0088] In the application, the bridge forming and shaping of the cable system is carried out by using an analytical method, the main cable line shape, the unstressed length of each cable segment and the unstressed length of the sling are obtained by iteration according to a given rise-span ratio, wherein the specific steps of iteration include:

[0089] a: let λ0= λ, the vertical coordinate new target value across the midpoint is calculated, and the calculation method is:

[0090] Y c0 =(Y k-1 +Y0) / 2-(X k-1 -X0)λ0;

[0091] b: according to the longitudinal component F XL , the vertical component F YL , the horizontal component F ZL of the left end of the main cable and the horizontal projection length L0 of the main cable, the height difference H0 between the left and right points of the first cable segment of the main cable and the unstressed cable length S are obtained by the plane catenary equation and by using the Newton method for iteration, wherein the horizontal projection length L0 of the main cable is The longitudinal component F XL of the left end of the main cable is P Z / λ / 8, the vertical component F YL of the left end of the main cable is P Z / 2, and the horizontal component F ZL of the left end of the main cable is F XL (Z b -Z0) / (X b -X0), P Z represents the total vertical force of the sling lower end, Z b represents the horizontal coordinate of the main beam at the lower end of the sling across the midpoint, and X b represents the longitudinal coordinate of the main beam at the lower end of the sling across the midpoint.

[0092] c: the three-way force (F XR , F YR , F ZR ) at the right end point of the first cable segment of the main cable is calculated according to the force balance condition, and the height difference H0 and the included angle β L, the coordinates (X1, Y1, Z1) of the right end point of the first cable segment of the main cable are calculated, wherein:

[0093] F XR = -F XL

[0094] F YR = -F YL +Sω

[0095] F ZR = -F ZL

[0096] β L = arctan (F ZR / F XR ) ;

[0097] wherein ω represents the weight per meter of the main cable material;

[0098] d: iteration of the sling, the upper end point of the sling being the right end point of the cable segment where the sling is located, specifically, based on the coordinates (X1, Y1, Z1) of the right end point of the first cable segment of the main cable, and the known coordinates (X d , Y d , Z d ) of the lower end point of the sling and the vertical force Q of the end of the sling, the unstressed length S d of the sling is obtained by using the flexible iteration method, and the three-directional forces (F Xd , F Yd , F Zd ) of the upper end of the sling are obtained from the force balance condition;

[0099] e: superimposing the three-directional forces (F XR , F YR , F ZR ) at the right end point of the first cable segment of the main cable and the three-directional forces (F Xd , F Yd , F Zd ) of the upper end of the sling, updating (F XL , F YL , F ZL ), and then returning to step b to perform iteration of the next cable segment until the iteration of all cable segments is completed, to obtain the vertical coordinate Y mR and the horizontal coordinate Z mR of the rightmost node of the main cable, and the vertical coordinate Y mc of the mid-span point of the main cable;

[0100] f: based on the obtained vertical coordinate Y mR and horizontal coordinate Z mR of the rightmost node of the main cable, and the vertical coordinate Y mcThe difference between the target value and the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the vertical coordinate of the mid-point of the main cable span are calculated again if the accuracy condition is not met, and an influence matrix is obtained;

[0101] In the present application, based on the vertical coordinate Y mR and the horizontal coordinate Z mR of the rightmost node of the main cable and the vertical coordinate Y mc of the mid-point of the main cable span obtained, the difference between the target value and the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the vertical coordinate of the mid-point of the main cable span are calculated again if the accuracy condition is not met, and an influence matrix is obtained, and the specific steps include:

[0102] Based on the vertical coordinate Y mR and the horizontal coordinate Z mR of the rightmost node of the main cable and the vertical coordinate Y mc of the mid-point of the main cable span obtained, the difference between the target value and the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the vertical coordinate of the mid-point of the main cable span, i.e. ΔY mR =Y mR -Y k-1 , ΔZ mR =Z mR -Z k-1 , ΔY mc =Y mc -Y c0 :

[0103] If is less than the given limit value, the process is ended;

[0104] If is not less than the given limit value, for the three-directional force (F xL , F yL , F zL ) at the left end point of the first cable segment of the main cable, the three-directional force at the left end point of the first cable segment of the main cable is sequentially taken as (F xL +1, F yL , F zL ), (F xL , F yL +1, F zL ), (F xL , F yL , F zL +1), and steps b-e are executed in a loop to calculate again the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the vertical coordinate of the mid-point of the main cable span, and obtain three new results, which are (Y mR1 , Z mR1 , Z mc1 ), (Y mR2 , Z mR2 , Z mc2 ), (Y mR3 , Z mR3 , Z mc3), and then the influence matrix is obtained;

[0105] The influence matrix is represented as:

[0106]

[0107] g: the three-direction forces at the left end point of the first cable segment of the main cable are corrected based on the influence matrix, and then the rightmost node coordinate of the main cable and the vertical coordinate of the mid-span point of the main cable are calculated until the precision condition is met;

[0108] In the application, the three-direction forces at the left end point of the first cable segment of the main cable are corrected based on the influence matrix, and then the rightmost node coordinate of the main cable and the vertical coordinate of the mid-span point of the main cable are calculated until the precision condition is met, and the specific steps are as follows:

[0109] A: the three-direction forces at the left end point of the first cable segment of the main cable are corrected based on the influence matrix, that is:

[0110]

[0111] wherein (ΔF xL , ΔF yL , ΔF zL ) represent the corrected three-direction forces at the left end point of the first cable segment of the main cable;

[0112] B: F xL +ΔF xL , F yL +ΔF yL , F zL +ΔF zL are obtained as new iteration initial values, steps b-e are executed in a loop, and then the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the vertical coordinate of the mid-span point of the main cable are calculated until is less than a given limit value, and the iteration is terminated.

[0113] C: the main cable shape is determined based on the node coordinates of the main cable, and the unstressed lengths of the cable segments and the hangers of the main cable are obtained. In the result of the last iteration step, the node coordinates of the main cable determine the main cable shape, that is, the spatial state.

[0114] S3: a first finite element model is established based on the calculated main cable shape and the unstressed lengths of the cable segments to calculate the empty cable coordinates of the nodes of the main cable.

[0115] In the application, a first finite element model is established based on the calculated main cable shape and the unstressed lengths of the cable segments to calculate the empty cable coordinates of the nodes of the main cable, and the specific steps include:

[0116] According to the calculated coordinates of each node of the main cable and the unstressed length of each cable section, a first finite element model is established, wherein each node of the main cable is taken as a node of the finite element model, and each cable section is taken as an element of the finite element model, the element is a catenary element, and the corresponding unstressed length value is assigned, only the main cable is included in the first finite element model without the suspension cable, the two ends of the main cable are fixed, and the empty cable line shape of the main cable, i.e., the empty cable coordinates of each node of the main cable, is calculated through the first finite element model.

[0117] The main difference between this step and the traditional method is that the first finite element model is established, and the empty cable line shape is calculated, so as to prepare for the superposed beam element in the empty cable state (the superposed beam element must be established in the empty cable line shape, and therefore the first finite element model needs to be established).

[0118] S4: based on the empty cable coordinates of each node of the main cable calculated by the first finite element model, a second finite element model is established.

[0119] In the application, the second finite element model is established based on the empty cable coordinates of each node of the main cable calculated by the first finite element model, and the specific steps include:

[0120] S401: according to the empty cable coordinates of each node of the main cable calculated by the first finite element model, the coordinates of each node of the main cable are updated to obtain the coordinates of the first finite element model after deformation, i.e., the coordinates of the main cable in the empty cable state, and the second finite element model is established according to the coordinates, the catenary element is used to establish the main cable element in the second finite element model, and the corresponding unstressed length (obtained by the analytical method in step S2) is assigned.

[0121] S402: the cable element is established, and the corresponding unstressed length (obtained by the analytical method in step S2) is assigned.

[0122] S403: the main cable beam element is established, the main cable beam element and the main cable element are superposed to obtain a superposed double element, a very small value (such as 10 -8 ) is assigned to the cross-sectional area of the superposed double element, the torsional inertia and the bending inertia are calculated according to the circular cross section of the main cable, and the main cable beam element is assigned.

[0123] For the boundary condition, the two ends of the main cable are fixed, the lower end of the suspension cable is loosened in the vertical degree of freedom, and the remaining degrees of freedom are fixed. The load: the self-weight of the main cable and the suspension cable is considered, and a vertical force is applied to the lower end of the suspension cable, which is the weight of the supporting beam. The characteristic of the finite element model is that the main cable and the cable element are included, the main cable element is simulated by the superposed double element, the cable element and the beam element, the axial stiffness and the sag effect of the main cable are considered in the cable element, and the torsional and bending stiffness of the main cable are considered in the beam element.

[0124] The main difference of this step from the traditional method is that the simulation of the main cable uses the superposition unit, the spatial cable unit and the spatial beam unit, the special processing of assigning a minimum value to the cross-sectional area of the beam unit is only considered the torsional and bidirectional bending stiffness, and the spatial beam unit is used to consider the bending-torsional coupling effect of the spatial main cable.

[0125] S5: Nonlinear calculation is performed on the second finite element model to obtain the displacement of the midspan point, and the new midspan point coordinates after deformation are obtained by superimposing the midspan point coordinates before deformation of the main cable.

[0126] That is, nonlinear calculation is performed on the second finite element model to obtain the displacement of the midspan point and the new midspan point coordinates after deformation are obtained by superimposing the midspan point coordinates before deformation of the main cable

[0127] S6: The new rise-span ratio is calculated based on the new midspan point coordinates, and the calculation is repeated again according to the new rise-span ratio, and the new midspan point coordinates after deformation are calculated again.

[0128] That is, the new rise-span ratio λ1 is calculated based on the new midspan point coordinates, and the calculation is repeated again according to the new rise-span ratio (i.e., returning to step S2 and executing steps S2-S5), and the new midspan point coordinates after deformation are calculated again Wherein

[0129]

[0130] S7: The new rise-span ratio is calculated again based on the new midspan point coordinates after deformation calculated again, and the calculation is repeated again according to the new rise-span ratio calculated again, and the new midspan point coordinates after deformation are calculated again.

[0131] In the present application, the new rise-span ratio is calculated again based on the new midspan point coordinates after deformation calculated again, and the calculation is repeated again according to the new rise-span ratio calculated again, and the new midspan point coordinates after deformation are calculated again, which is specifically:

[0132] The new rise-span ratio λ2 is calculated again based on the new midspan point coordinates after deformation calculated again, and the calculation is repeated again according to the new rise-span ratio calculated again (i.e., returning to step S2 and executing steps S2-S5), and the new midspan point coordinates after deformation are calculated again Wherein

[0133]

[0134] S8: According to the new midspan point coordinates after deformation calculated again and the new midspan point coordinates after deformation calculated again, it is judged whether to stop the calculation.

[0135] In the present application, according to the new mid-span point coordinate after deformation obtained by re-computation and the new mid-span point coordinate after deformation obtained by re-computation, whether to suspend the computation is judged, and specifically, if

[0136] If is less than a given limit value (such as 10 -3 , set according to the requirement), it indicates that the condition is met, and the computation is terminated.

[0137] If is not less than the given limit value, let λ0=λ1, λ1=λ2, repeat steps S1-S8, and continue the computation of the rise-span ratio and the mid-span point coordinate until the condition is met.

[0138] The main difference between this step and the traditional method is that the outer loop iteration is constructed, the analytical method and the finite element method are simultaneously included in the iteration process, and the mixed loop is used to give full play to their respective advantages. The analytical method considers the axial stiffness and sag effect of the main cable, and the finite element method considers the torsional and bidirectional bending stiffness of the main cable.

[0139] The present application is specifically described below by taking the form-finding of a large-diameter spatial cable system with a span of 1000m or more as an example.

[0140] Known conditions: the coordinates of the two end points of the main cable are (8, 208.1, 200.25) (1152, 208.1, 200.25), the elastic modulus is 2.0e 8 kPa, the cross-sectional area is 0.32m 2 , the material bulk density is 82.3kN / m 3 , the torsional moment of inertia of the circular cross-section of the main cable is 1.6298e -4 , the in-plane and out-of-plane bending moments of inertia are both 8.1487e -3 , 75 sub-points are set, the target rise-span ratio is 1 / 9, each main cable sub-point is connected to a suspension cable, and there are 75 suspension cables. The longitudinal coordinates of the lower end points of the suspension cables are the same as those of the upper end main cable sub-points, the vertical coordinates are all 77.5m, and the horizontal coordinates are all 13.25m (differing from the horizontal coordinates of the two end points of the main cable by 187m, and the spatial opening amount is large). The vertical bearing forces of the lower ends of the suspension cables are all -2000kN. The elastic modulus of the suspension cable material is 1.95e 8 kPa, the cross-sectional area is 0.00428m 2 , and the material bulk density is 86.24kN / m 3 . The spatial cable system is shown in Figure 3 and Figure 4 . According to the horizontal plane projection, it can be seen that the spatial effect of the cable system is more obvious.

[0141] The specific steps are as follows:

[0142] (1) The vertical coordinate target value of the midspan of the main cable is calculated as 80.9889 m, the initial three-way force (F xL , F yL , F zL ) of the left end of the main cable is calculated, the horizontal projection length L0 of the entire main cable is 1144 m, the vertical force sum F yL of the lower end of the sling is -84375 kN, the initial lateral force F zL is 55168.3 kN, and the analytical iteration is performed to obtain the main cable line shape, the unstressed length of each cable segment, and the unstressed length of the sling.

[0143] (2) According to the node coordinates of the main cable in the completed bridge state and the unstressed length of the cable segment in step (1), a first finite element model is established, only including the main cable and only having the load of the self weight of the main cable, the empty cable state is calculated, and see Figure 5 It can be seen from the figure that the empty cable line shape is lower than the completed bridge line shape, which is because the spatial cable swings to the vertical direction.

[0144] (3) On the basis of the deformed empty cable line shape, a second finite element model is established according to the empty cable coordinates, a catenary cable element is used to establish the main cable element, and the unstressed length value is given (obtained from step (1)); a catenary cable element is used to establish the sling element, and the unstressed length is given (obtained from step (1)); a main cable beam element is established, which is completely coincided with the main cable element, the cross-sectional area is given as a small value 10 -8 , the torsional moment of inertia is 1.6298e -4 , and the bending moment of inertia is 8.1487e -3 ; the two ends of the main cable are fixed, the vertical degree of freedom of the lower end of the sling is released, the remaining degrees of freedom are fixed, and the vertical concentrated force -2000 kN is applied to the lower end of the sling. The nonlinear calculation is performed on the second finite element model, the vertical displacement of the midspan is 85.3419 m, the vertical coordinate of the midspan before deformation is superimposed when modeling, the vertical coordinate of the midspan after deformation is obtained as 80.9598 m, and the target value of the vertical coordinate of the midspan is 80.9889 m, the difference is 2.9099 cm. This is because the influence of the torsional and bending stiffness of the main cable is considered, and if this is not considered, the difference should be 0.

[0145] (4) Because of the difference, iteration is needed, the main cable rise-span ratio is updated as 1 / 9.00206, and recalculation is performed. After two rounds of iteration cycles, the vertical coordinate of the midspan of the completed bridge line shape is 80.9889 m, which is completely consistent with the target value, and the iteration is terminated, that is, the completed bridge line shape considering the torsional and bending stiffness of the main cable is obtained.

[0146] Table 1 Main cable point coordinates

[0147]

[0148] Table 1 shows the pure analytical method of calculating the bridge line shape without considering the torsional and bending stiffness of the main cable, and the hybrid method of calculating the bridge line shape considering the torsional and bending stiffness of the main cable, and the difference between the two. As shown in Table 1, compared with the traditional pure analytical method and the method of the application, the vertical and horizontal line shapes in the bridge state are different, the maximum deviation occurs near the first sling point on both sides of the main cable, the vertical coordinate difference is 42.23 cm, the horizontal coordinate difference is 45.49 cm, the difference gradually decreases towards the midspan, and the horizontal coordinate difference is still 6.01 cm. The larger difference in the upper end point of the long sling will cause the calculation of the horizontal inclination angle of the sling to deviate, the angle of the cable clamp installation is not accurate, additional bending moment appears, the stress changes from axial tension to tension-bending coupling, and fatigue failure is more likely to occur.

[0149] In summary, for the main cable of a large-diameter spatial cable suspension bridge, the torsional and bending stiffnesses have an influence on the bridge line shape, and are coupled, and when the main cable is shaped, the influences of the torsional and bending stiffnesses should be considered. The application considers the three-way coupling effect of the torsional and bending stiffnesses, and realizes accurate shaping of the main cable.

[0150] The hybrid method of spatial cable shaping of the application uses the analytical method and the finite element method, and gives full play to their respective advantages. The analytical method considers the axial stiffness and sag effect of the main cable, the finite element method considers the three-way coupling effect of the torsional and bending stiffnesses, and the spatial cable bridge line shape meeting the target value is obtained through the cyclic iteration of the two methods. The finite element method uses the superimposed element mode, the main cable is simulated by using the cable element and the spatial beam element, and the cross-sectional area of the beam element is specially processed by assigning a minimum value. During the process of gradually forming the bridge spatial state from the vertical state of the empty cable, the torsional and bending stiffnesses of the main cable of the large-diameter spatial cable suspension bridge act simultaneously. The hybrid method considers the three-way bending-torsional coupling effect to realize shaping, can accurately calculate the spatial angle of the sling and the cable clamp, makes the cable clamp still maintain the axial tension state when the bridge is formed, and does not cause the redistribution and effectiveness of the sling force. The application can be applied to the design of a large-diameter spatial cable suspension bridge.

[0151] In a possible implementation, the embodiment of the application further provides a readable storage medium, which is located in a PLC (Programmable Logic Controller, programmable logic controller) controller, and a computer program is stored on the readable storage medium, and the program is executed by a processor to realize the steps of the hybrid method of spatial cable shaping described below:

[0152] Based on the node coordinates on the left side of the main cable, the node coordinates on the right side of the main cable, and the given rise-span ratio, the vertical coordinate target value of the midspan point is calculated;

[0153] The analytical method is used to find the shape of the cable system, the main cable linear shape, the unstressed length of each cable segment and the unstressed length of the sling are obtained by iteration according to the given rise-span ratio;

[0154] According to the calculated main cable linear shape and the unstressed length of each cable segment, a first finite element model is established to calculate the coordinates of the nodes of the main cable in the empty cable state;

[0155] Based on the coordinates of the nodes of the main cable in the empty cable state calculated by the first finite element model, a second finite element model is established;

[0156] The second finite element model is calculated in a non-linear manner to obtain the displacement of the mid-span point, and the coordinates of the new mid-span point after deformation are obtained by superimposing the coordinates of the mid-span point before deformation of the main cable;

[0157] Based on the new rise-span ratio calculated based on the new mid-span point coordinates, the new mid-span point coordinates after deformation are calculated again;

[0158] Based on the new mid-span point coordinates after deformation calculated again, the new rise-span ratio is calculated again, and the new mid-span point coordinates after deformation are calculated again according to the new rise-span ratio calculated again.

[0159] According to the new mid-span point coordinates after deformation calculated again and the new mid-span point coordinates after deformation calculated again, it is judged whether to stop the calculation.

[0160] The storage medium can adopt any combination of one or more computer readable media. The computer readable medium can be a computer readable signal medium or a computer readable storage medium. The computer readable storage medium may, for example, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or component, or any combination thereof. More specific examples (non-exhaustive list) of computer readable storage media include: electrical connections having one or more wires, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above. In this document, the computer readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device or component.

[0161] Computer readable signal media can include a propagated data signal with computer readable program code embodied therein. For example, a propagated signal can be an electromagnetic signal, an optical signal, and / or any suitable combination thereof. Computer readable program code embodied on a computer readable medium can be transmitted using any suitable medium, including, but not limited to, wireless, wire line, optical fiber cable, R.F, etc., or any suitable combination of the foregoing.

[0162] Computer program code for carrying out operations of the present application can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0163] The hybrid device for spatial cable shape finding provided by the embodiment of the present application comprises a calculation module, an iteration module, a first establishment module, a second establishment module, a superposition module, a first execution module, a second execution module and a judgment module.

[0164] The calculation module is used for calculating the vertical coordinate target value of the midspan point based on the left node coordinates of the main cable, the right node coordinates of the main cable and the given rise-span ratio;

[0165] The iteration module is used for performing bridge shape finding of the cable system by using the analytical method, and iteratively obtaining the main cable shape, the unstressed length of each cable segment and the unstressed length of the sling according to the given rise-span ratio;

[0166] The first establishment module is used for establishing a first finite element model to calculate the empty cable coordinates of each node of the main cable according to the calculated main cable shape and the unstressed length of each cable segment;

[0167] The second establishment module is used for establishing a second finite element model based on the empty cable coordinates of each node of the main cable calculated by the first finite element model;

[0168] The superposition module is used for nonlinear calculation on the second finite element model to obtain the displacement of the midspan point, and superimposes the midspan point coordinate before deformation of the main cable to obtain the new midspan point coordinate after deformation.

[0169] The first execution module is used for calculating the new rise-span ratio based on the new midspan point coordinate, and repeatedly calculating again according to the new rise-span ratio to obtain the new midspan point coordinate after deformation again.

[0170] The second execution module is used for calculating the new rise-span ratio again based on the new midspan point coordinate after deformation obtained by the repeated calculation, and repeatedly calculating again according to the new rise-span ratio obtained by the repeated calculation to obtain the new midspan point coordinate after deformation once again.

[0171] The judging module is used for judging whether to stop the calculation according to the new midspan point coordinate after deformation obtained by the repeated calculation and the new midspan point coordinate after deformation obtained by the calculation once again.

[0172] The above description is merely specific embodiments of the present application, which enables those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

[0173] The present application is described with reference to flowcharts and / or block diagrams of the method, device (system) and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The function specified in one flow or multiple flows and / or blocks Figure 1 The device that implements the function specified in one block or multiple blocks.

Claims

1. A hybrid method for spatial cable form-finding, characterized in that: The specific steps include: Based on the coordinates of the left and right nodes of the main cable and the given rise-to-span ratio, the vertical coordinate target value of the mid-span point is calculated; The analytical method is used to find the bridge form of the cable system. Based on the given rise-span ratio, the main cable shape, the stress-free length of each cable segment and the stress-free length of the sling are iteratively obtained. Based on the calculated main cable shape and the unstressed length of each cable segment, a first finite element model is established to calculate the empty cable coordinates of each node of the main cable; Establishing a second finite element model based on the empty cable coordinates of each node of the main cable calculated by the first finite element model; Perform nonlinear calculation on the second finite element model to obtain the displacement of the mid-span point, and superimpose the mid-span point coordinates before the main cable deformation to obtain the new mid-span point coordinates after deformation; The new span-rise ratio is calculated based on the new span midpoint coordinates, and the calculation is repeated again based on the new span-rise ratio to obtain the new span midpoint coordinates after deformation; Based on the coordinates of the new mid-span point after deformation obtained by the recalculation, the new rise-to-span ratio is calculated again, and the calculation is repeated again based on the new rise-to-span ratio, and the coordinates of the new mid-span point after deformation are calculated again; Whether to terminate the calculation is determined based on the coordinates of the new mid-span point after deformation calculated again and the coordinates of the new mid-span point after deformation calculated again.

2. A hybrid method for spatial cable form-finding according to claim 1, characterized in that: The vertical coordinate target value of the mid-span point is obtained by calculation, and the specific calculation method is: Y c (Y k-1 +Y0) / 2-(X k-1 −X0)λ Among them, Y c represents the vertical coordinate target value of the mid-span point, λ represents the given span-span ratio, the coordinates of the node on the left side of the main cable are (X0, Y0, Z0), and the coordinates of the node on the right side of the main cable are (X k-1 、Y k-1 , Z k-1 ), k represents the total number of main cable nodes.

3. A hybrid method for spatial cable form-finding according to claim 2, characterized in that: The bridge form-finding of the cable system is performed using an analytical method. According to a given rise-span ratio, the main cable shape, the stress-free length of each cable segment, and the stress-free length of the sling are iteratively obtained. The specific steps of the iteration include: Let λ0 = λ, and calculate the new target value of the vertical coordinate of the mid-span point. The calculation method is: Y c0 =(Y k-1 +Y0) / 2-(X k-1 -X0)λ0; According to the longitudinal force F at the left end of the main cable XL , vertical component F YL , lateral force F ZL , and the projected length L0 of the main cable in the horizontal plane, the height difference H0 between the left and right points of the first section of the main cable and the stress-free cable length S are obtained by the plane catenary equation and Newton's method iteration. Among them, the projected length of the main cable in the horizontal plane is Longitudinal force F at the left end of the main cable XL =P Z / λ / 8, vertical component F at the left end of the main cable YL =P Z / 2, the lateral component of force F at the left end of the main cable ZL =F XL (Z b -Z0) / (X b -X0), P Z Z is the total vertical force at the lower end of the sling. b Indicates the horizontal coordinate of the main beam at the lower end of the mid-span sling, X b Indicates the vertical coordinate of the main beam at the lower end of the mid-span sling; The three-dimensional force (F XR 、F YR 、F ZR ), and the height difference H0 and the angle β L , calculate the coordinates (X1, Y1, Z1) of the right end point of the first section of the main cable, where: F XR =-F XL F YR =-F YL +Sω F ZR =-F ZL β L =arctan(F ZR / F XR ) Where, ω represents the weight of the main cable material per meter; Based on the coordinates of the right end point of the first section of the main cable (X1, Y1, Z1), and the known coordinates of the lower end point of the sling (X d 、Y d , Z d ) and the vertical force Q at the end of the sling, the stress-free length S of the sling is obtained by the flexible iteration method. d , the three-direction force (F Xd 、F Yd 、F Zd ); The three-axis force (F XR 、F YR 、F ZR ), and the three-dimensional force at the upper end of the sling (F Xd 、F Yd 、F Zd ) superposition, update (F XL 、F YL 、F ZL ), and then iterate the next cable segment until all cable segments are calculated, and obtain the vertical coordinate Y of the rightmost node of the main cable mR and the horizontal coordinate Z mR , and the vertical coordinate Y of the main cable mid-span point mc ; Based on the vertical coordinate Y of the rightmost node of the main cable mR and the horizontal coordinate Z mR , and the vertical coordinate Y of the main cable mid-span mc If the difference between the target value and the vertical coordinates is not satisfied, the vertical coordinates and horizontal coordinates of the rightmost node of the main cable and the vertical coordinates of the mid-span point of the main cable are calculated again, and the influence matrix is ​​obtained. Based on the influence matrix, the three-dimensional forces at the left end point of the first section of the main cable are corrected, and then the coordinates of the rightmost node of the main cable and the vertical coordinates of the mid-span point of the main cable are calculated until the accuracy conditions are met. The main cable shape is determined based on the coordinates of each node of the main cable, and the stress-free length of each cable segment and each sling is obtained.

4. A hybrid method for spatial cable form-finding according to claim 3, characterized in that: The vertical coordinate Y of the rightmost node of the main cable is obtained mR and the horizontal coordinate Z mR , and the vertical coordinate Y of the main cable mid-span mc If the difference between the value and the target value does not meet the accuracy requirements, the vertical coordinates and horizontal coordinates of the rightmost node of the main cable and the vertical coordinates of the mid-span point of the main cable are calculated again, and the influence matrix is ​​obtained. The specific steps include: Based on the calculated vertical coordinate Y of the rightmost node of the main cable mR and the horizontal coordinate Z mR , and the vertical coordinate Y of the main cable mid-span mc The difference between the target value and the target value, namely ΔY mR =Y mR -Y k-1 , ΔZ mR =Z mR -Z k-1 , ΔY mc =Y mc -Y c0 : like If it is less than the given limit, it ends; like If the three-axis force (F xL 、F yL 、F zL ), and the three-direction forces at the left end point of the first section of the main cable are taken as (F xL +1, F yL 、F zL )、(F xL 、F yL +1, F zL )、(F xL 、F yL 、F zL +1), calculate again the vertical coordinate and horizontal coordinate of the rightmost node of the main cable, and the vertical coordinate of the mid-span point of the main cable, and get three new results, which are (Y mR1 , Z mR1 , Z mc1 )、(Y mR2 , Z mR2 , Z mc2 )、(Y mR3 , Z mR3 , Z mc3 ), and then the influence matrix is ​​obtained; Among them, the influence matrix is ​​expressed as:

5. A hybrid method for spatial cable form-finding according to claim 4, characterized in that: The three-dimensional forces at the left end point of the first section of the main cable are corrected based on the influence matrix, and then the coordinates of the rightmost node of the main cable and the vertical coordinates of the mid-span point of the main cable are calculated until the accuracy conditions are met, specifically: The influence matrix is ​​used to correct the three-dimensional forces at the left end point of the first section of the main cable, namely: Among them, (ΔF xL , ΔF yL , ΔF zL ) represents the three-dimensional force at the left end point of the first section of the main cable after correction; Get F xL +ΔF xL 、F yL +ΔF yL 、F zL +ΔF zL , as the new initial value of the iteration, and then continue to calculate the vertical coordinates and horizontal coordinates of the rightmost node of the main cable, and the vertical coordinates of the mid-span point of the main cable until If the value is less than the given limit, the iteration is terminated.

6. A hybrid method for spatial cable form-finding according to claim 5, characterized in that: The first finite element model is established based on the calculated main cable shape and the stress-free length of each cable segment to calculate the empty cable coordinates of each node of the main cable. The specific steps include: According to the calculated coordinates of each node of the main cable and the stress-free length of each cable segment, a first finite element model is established, wherein each node of the main cable is used as a node of the finite element model, and the cable segment is used as a unit of the finite element model. The unit adopts a catenary cable unit and is assigned a corresponding stress-free length value. In the first finite element model, there is only the main cable without a sling, and both ends of the main cable are consolidated. The empty cable line shape of the main cable, that is, the empty cable coordinates of each node of the main cable, is calculated through the first finite element model.

7. A hybrid method for spatial cable form-finding according to claim 6, characterized in that: The second finite element model is established based on the empty cable coordinates of each node of the main cable calculated based on the first finite element model, and the specific steps include: Based on the empty cable coordinates of each node of the main cable calculated by the first finite element model, the coordinates of each node of the main cable are updated to obtain the deformed coordinates of the first finite element model, that is, the coordinates of the main cable under the empty cable. Based on the coordinates, a second finite element model is established. In the second finite element model, the catenary cable unit is used to establish the main cable unit and the corresponding stress-free length is assigned; Establish sling units and assign corresponding stress-free lengths; The main cable beam unit is established, and the main cable beam unit and the main cable unit are overlapped to obtain a superimposed double unit. The cross-sectional area of ​​the superimposed double unit is assigned a minimum value. The torsional inertia and bending inertia are calculated according to the circular cross-section of the main cable and assigned to the main cable beam unit.

8. A hybrid method for spatial cable form-finding according to claim 7, characterized in that: The nonlinear calculation is performed on the second finite element model to obtain the displacement of the mid-span point, and the coordinates of the mid-span point before the main cable is deformed are superimposed to obtain the coordinates of the new mid-span point after deformation. Specifically, the nonlinear calculation is performed on the second finite element model to obtain the displacement of the mid-span point The coordinates of the mid-span point before the main cable deformation are superimposed to obtain the new mid-span point coordinates after deformation. The new span ratio is calculated based on the new span midpoint coordinates, and the calculation is repeated again according to the new span ratio to obtain the new span midpoint coordinates after deformation. Specifically, the new span ratio λ1 is calculated based on the new span midpoint coordinates, and the calculation is repeated again according to the new span ratio to obtain the new span midpoint coordinates after deformation. in 9. A hybrid method for spatial cable form-finding according to claim 8, characterized in that: The new span midpoint coordinates after deformation are calculated again, and the new rise-to-span ratio is calculated again. The calculation is repeated again based on the new rise-to-span ratio, and the new span midpoint coordinates after deformation are calculated again. Specifically, Based on the coordinates of the new mid-span point after deformation obtained by recalculation, the new span-ratio λ2 is calculated again, and the calculation is repeated again based on the new span-ratio obtained by recalculation, and the coordinates of the new mid-span point after deformation are calculated again. in The method of determining whether to terminate the calculation is based on the coordinates of the new mid-span point after deformation calculated again and the coordinates of the new mid-span point after deformation calculated again, specifically: like If it is less than the given limit, it means that the condition is met and the calculation is terminated; like If it is not less than the given limit, the calculation of the arrow-span ratio and the mid-span coordinates will continue until the conditions are met.

10. A hybrid device for spatial cable shape finding, characterized in that: include: A calculation module is used to calculate the vertical coordinate target value of the mid-span point based on the coordinates of the node on the left side of the main cable, the coordinates of the node on the right side of the main cable, and a given rise-to-span ratio; The iterative module is used to perform bridge form-finding of the cable system using analytical methods. Based on a given rise-to-span ratio, the main cable shape, the stress-free length of each cable segment, and the stress-free length of the sling are iteratively obtained. A first establishing module is used to establish a first finite element model based on the calculated main cable linear shape and the stress-free length of each cable segment to calculate the empty cable coordinates of each node of the main cable; A second establishing module is used to establish a second finite element model based on the empty cable coordinates of each node of the main cable calculated by the first finite element model; A superposition module is used to perform nonlinear calculation on the second finite element model to obtain the displacement of the mid-span point, and to superimpose the mid-span point coordinates before the main cable is deformed to obtain the new mid-span point coordinates after the deformation; A first execution module is configured to calculate a new rise-to-span ratio based on the new mid-span coordinates, and to repeat the calculation based on the new rise-to-span ratio to obtain the new mid-span coordinates after deformation; The second execution module is used to recalculate the new span ratio based on the new span midpoint coordinates after deformation obtained by recalculation, and repeat the calculation again based on the new span ratio obtained by recalculation to obtain the new span midpoint coordinates after deformation once again; The judgment module is used to judge whether to terminate the calculation based on the new mid-span coordinates after deformation calculated again and the new mid-span coordinates after deformation calculated again.

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