CN116757024A - Mixing method and device for space cable shape finding - Google Patents

Mixing method and device for space cable shape finding Download PDF

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CN116757024A
CN116757024A CN202310669510.7A CN202310669510A CN116757024A CN 116757024 A CN116757024 A CN 116757024A CN 202310669510 A CN202310669510 A CN 202310669510A CN 116757024 A CN116757024 A CN 116757024A
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main cable
cable
coordinates
span
mid
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霍学晋
陈宇
罗莉
汪珍
杨明芳
陈佳
王东绪
苑仁安
韩若愚
王哲尧
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China Railway Major Bridge Reconnaissance and Design Institute Co Ltd
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Abstract

The invention discloses a mixing method and a device for space cable shape finding, and relates to the field of suspension bridge design, wherein the method comprises the steps of calculating to obtain a cross-midpoint vertical coordinate target value; iterating to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling; establishing a first finite element model 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 obtained by calculation of the first finite element model; superposing the mid-span point coordinates before the main cable is deformed to obtain new mid-span point coordinates after the main cable is deformed; calculating again to obtain the deformed new mid-span point coordinates; based on the new deformed mid-span point coordinates obtained by the re-calculation, obtaining the new deformed mid-span point coordinates by the re-calculation; and judging whether to stop the calculation according to the new deformed mid-span point coordinate obtained by the calculation again and the new deformed mid-span point coordinate obtained by the calculation again. The invention can deal with the large rotation and multidirectional rotation coupling problem without simplification.

Description

Mixing method and device for space cable shape finding
Technical Field
The invention relates to the field of suspension bridge design, in particular to a mixing method and device for space cable shape finding.
Background
When the suspension bridge is designed, the main cable should be formed into a bridge to find the shape, otherwise, the follow-up work cannot be carried out. By bridge formation and shape finding, the bridge formation line shape (namely coordinates of each point) of the main cable, the unstressed length of each cable section of the main cable and the unstressed length parameters of each sling can be determined, and the accurate shape finding of the bridge formation state of the main cable is very important based on the parameters in the subsequent construction stage analysis, live load calculation, self-vibration characteristic analysis and the like. For a large-span space cable suspension bridge, the diameter of a main cable is often larger to be more than 1m due to stress requirements, and a large-diameter section has certain torsional rigidity and bending rigidity. On the other hand, when the space cable suspension bridge is in an empty cable state, the main cable is in a vertical plane, and is gradually deformed transversely along with the suspension beam process to be stretched into a space form, and in the process, the torsion resistance and the bending stiffness of the main cable simultaneously act, so that the main cable line shape after the actual bridge formation cannot reach a theoretical line shape for neglecting the calculation of the torsion resistance and the bending stiffness. Currently, for main cable shape finding of large-diameter space cable suspension bridges, a traditional pure resolution method is generally adopted, as is still the flat cable.
However, the following problems exist in the conventional purely analytic shape finding method:
1. In order to be able to carry out analytical solution, the main cable must be simplified, the main cable is assumed to be a catenary flexible cable, the cable can only be pulled, the improved analytical method can only consider in-plane bending resistance, can not consider out-of-plane bending at the same time, and can not consider torsion resistance any more, so that three-way bending-torsion coupling analysis is carried out;
2. for a large-diameter space cable, if torsion resistance and bending stiffness of the main cable cannot be considered at the same time, errors of the line shape after bridging are caused, particularly, the calculation of the transverse inclination angle of a long sling and the installation angle of a cable clamp in the area near the left side and the right side of the main cable is deviated, and after the cable is installed according to the angle, an additional bending moment is generated in the cable clamp, and the stress of the cable clamp is changed into stretch bending coupling from shaft tension, so that fatigue damage is more likely to occur; the linear deviations can also cause variations in sling forces, especially long ropes, which can decrease and even fail.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a mixing method and a device for space cable shape finding, which can solve the problems of large rotation and multi-directional rotation coupling without simplification.
In order to achieve the above purpose, the invention provides a mixing method for spatial cable shape finding, which specifically comprises the following steps:
Calculating to obtain a vertical coordinate target value crossing a midpoint based on the left node coordinate of the main cable, the right node coordinate of the main cable and a given sagittal ratio;
performing bridge forming and shape finding of the cable system by adopting an analytic method, and iterating to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling according to a given sagittal ratio;
according to the calculated main cable line shape and the unstressed length of each cable section, 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 obtained by calculation of the first finite element model;
performing nonlinear calculation on the second finite element model to obtain displacement of a cross-midpoint, and superposing cross-midpoint coordinates before the main cable is deformed to obtain new cross-midpoint coordinates after the main cable is deformed;
calculating to obtain a new mid-span ratio based on the new mid-span point coordinates, and repeatedly calculating again according to the new mid-span ratio to obtain deformed new mid-span point coordinates again;
based on the new mid-span point coordinate after deformation obtained by recalculation, recalculating to obtain a new mid-span ratio, and recalculating according to the new mid-span ratio obtained by recalculation, and obtaining the new mid-span point coordinate after deformation by recalculation;
And judging whether to stop the calculation according to the new deformed mid-span point coordinate obtained by the calculation again and the new deformed mid-span point coordinate obtained by the calculation again.
On the basis of the technical scheme, the calculation is performed to obtain a cross-midpoint vertical coordinate target value, and the specific calculation mode is as follows:
Y c ＝(Y k-1 +Y 0 )/2-(X k-1 -X 0 )λ
wherein Y is c Represents a target value of vertical coordinates crossing the midpoint, lambda represents a given sagittal ratio, and the coordinates of the left node of the main cable are (X 0 、Y 0 、Z 0 ) The coordinates of the right node of the main cable are (X) k-1 、Y k-1 、Z k-1 ) K represents the total number of main cable nodes.
On the basis of the technical scheme, the bridge forming and shape finding of the cable system are carried out by adopting an analytic method, and the main cable line shape, the unstressed length of each cable section and the unstressed length of the sling are obtained through iteration according to a given sagittal ratio, wherein the specific steps of iteration comprise:
let lambda get 0 =λ, a new target value of the vertical coordinate across the midpoint is calculated in the following manner:
Y c0 ＝(Y k-1 +Y 0 )/2-(X k-1 -X 0 )λ 0 ；
according to the longitudinal component F of the left end of the main cable XL Vertical component force F YL Transverse component F ZL And the main cable is horizontalIn-plane projection length L 0 The plane catenary equation and Newton method are adopted to iterate to obtain the height difference H between the right two points of the main cable head joint Duan Zuo 0 And a stress-free cable length S, wherein the projected length of the main cable in the horizontal plane Longitudinal component F of left end of main cable XL ＝P Z Lambda/8, vertical component F at the left end of the main cable YL ＝P Z Transverse component F at left end of main cable ZL ＝F XL (Z b -Z 0 )/(X b -X 0 )，P Z Represents the sum of vertical forces at the lower end of the sling, Z b X represents the abscissa of the main beam at the lower end of the mid-span sling b Representing the ordinate of the main girder at the lower end of the mid-span sling;
the three-way force (F) at the right end point of the main cable head section is calculated according to the force balance condition XR 、F YR 、F ZR ) And is formed by height difference H 0 And an included angle beta L Calculating to obtain the coordinate (X) of the right end point of the main cable head section 1 、Y 1 、Z 1 ) Wherein:
F XR ＝-F XL
F YR ＝-F YL +Sω
F ZR ＝-F ZL
β L ＝arctan(F ZR /F XR )
wherein ω represents the weight per linear meter of the main cable material;
based on the coordinates (X) of the right end point of the main cable head section 1 、Y 1 、Z 1 ) And the known sling lower end point coordinates (X d 、Y d 、Z d ) And the vertical force Q at the sling end, and obtaining the stress-free length S of the sling by adopting a flexible iteration method d The three-way force (F) at the upper end of the sling is obtained from the balance of forces Xd 、F Yd 、F Zd )；
The three-way force (F XR 、F YR 、F ZR ) And the three-way force at the upper end of the sling (F Xd 、F Yd 、F Zd ) Superposition, update (F XL 、F YL 、F ZL ) Then iterating the next cable segment until all cable segments are calculated to obtain the vertical coordinate Y of the rightmost node of the main cable mR And the abscissa Z mR And main cable cross-midpoint vertical coordinate Y mc ；
Vertical coordinate Y based on obtained rightmost node of main cable mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc If the difference value between the main cable and the target value does not meet the precision condition, calculating again to obtain the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable, and obtaining an influence matrix;
correcting the three-way force at the left end point of the main cable head section based on the influence matrix, and then continuing to calculate to obtain the rightmost node coordinate of the main cable and the midpoint-crossing vertical coordinate of the main cable until the precision condition is met;
and determining the line shape of the main cable based on the coordinates of each node of the main cable, and obtaining the stress-free length of each cable section and each sling of the main cable.
On the basis of the technical scheme, the vertical coordinate Y based on the obtained rightmost node of the main cable mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc If the difference value between the main cable and the target value does not meet the precision condition, the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable are calculated again, and an influence matrix is obtained, and the specific steps comprise:
vertical coordinate Y of rightmost node of main cable based on calculation mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc The difference from the target value, i.e. DeltaY mR ＝Y mR -Y k-1 ，ΔZ mR ＝Z mR -Z k-1 ，ΔY mc ＝Y mc -Y c0 ：
If it isIf the value is smaller than the given limit value, ending;
if it isNot less than a given limit, for the three-way force (F xL 、F yL 、F zL ) Sequentially taking the three-directional force at the left end point of the head section of the main cable as (F xL +1、F yL 、F zL )、(F xL 、F yL +1、F zL )、(F xL 、F yL 、F zL +1), calculating again to obtain the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable, and obtaining 3 groups of new results, namely (Y mR1 、Z mR1 、Z mc1 )、(Y mR2 、Z mR2 、Z mc2 )、(Y mR3 、Z mR3 、Z mc3 ) Thereby obtaining an influence matrix;
wherein the impact matrix is expressed as:
on the basis of the technical scheme, the three-way force at the left end point of the head section of the main cable is corrected based on the influence matrix, and then the right-most node coordinate of the main cable and the midpoint-crossing vertical coordinate of the main cable are continuously calculated until the precision condition is met, specifically:
correcting the three-way force at the left end point of the main cable head section by adopting an influence matrix, namely:
wherein (ΔF) xL 、ΔF yL 、ΔF zL ) Representing the three-way force at the left end point of the modified main cable head section;
obtaining F xL +ΔF xL 、F yL +ΔF yL 、F zL +ΔF zL As new iteration initial value, then continuously calculating to obtain the vertical coordinate and horizontal coordinate of the rightmost node of the main cable, and the cross-midpoint vertical coordinate of the main cable, and directlyTo the point ofLess than a given limit, the iteration is terminated.
On the basis of the technical scheme, according to the calculated main cable shape and the unstressed length of each cable section, a first finite element model is built to calculate the empty cable coordinates of each node of the main cable, and the specific steps include:
According to the calculated coordinates of all nodes of the main cable and the unstressed length of all cable sections, a first finite element model is built, wherein all nodes of the main cable are used as nodes of the finite element model, the cable sections are used as units of the finite element model, the units adopt catenary cable units, corresponding unstressed length values are given to the units, only the main cable does not have slings in the first finite element model, two ends of the main cable are fixedly connected, and the empty cable line shape of the main cable, namely the empty cable coordinates of all nodes of the main cable, is calculated through the first finite element model.
On the basis of the technical scheme, the empty cable coordinates of each node of the main cable calculated based on the first finite element model are used for establishing a second finite element model, and the method specifically comprises the following steps:
updating the coordinates of each node of the main cable according to the empty cable coordinates of each node of the main cable calculated by the first finite element model, so as to obtain the deformed coordinates of the first finite element model, namely the coordinates of the main cable under the empty cable, establishing a second finite element model according to the coordinates, establishing a main cable unit in the second finite element model by adopting a catenary cable clue unit, and endowing the main cable unit with a corresponding stress-free length;
building sling units and giving corresponding stress-free lengths;
the method comprises the steps of establishing a main cable beam unit, overlapping the main cable beam unit and the main cable unit to obtain an overlapped double unit, giving a minimum value to the sectional area of the overlapped double unit, calculating torsional inertia and bending moment according to the circular section of the main cable, and giving the main cable beam unit.
On the basis of the technical proposal, the method comprises the following steps,
the nonlinear calculation is carried out on the second finite element model to obtain the displacement of the cross-midpoint, and the cross-midpoint coordinates before the deformation of the main cable are overlapped to obtain the deformed main cableThe new mid-point coordinate is specifically obtained by performing nonlinear calculation on the second finite element model to obtain the mid-point displacementAnd superposing the mid-span point coordinates before the deformation of the main cable to obtain new mid-span point coordinates after the deformation
The new mid-span point coordinate is calculated to obtain a new mid-span ratio, and the calculation is repeated again according to the new mid-span ratio to obtain the deformed new mid-span point coordinate, specifically, the new mid-span ratio lambda is calculated based on the new mid-span point coordinate 1 And repeating the calculation again according to the new sagittal ratio, and calculating again to obtain the deformed new mid-span point coordinatesWherein the method comprises the steps of
On the basis of the technical proposal, the method comprises the following steps,
the new mid-span point coordinates after deformation based on the recalculation are recalculated to obtain new mid-span ratios, and the new mid-span point coordinates after deformation are calculated again according to the new mid-span ratios obtained by the recalculation, specifically:
based on the new mid-span point coordinates after deformation obtained by recalculation, recalculating to obtain a new sagittal-span ratio lambda 2 And repeatedly calculating again according to the new sagittal ratio obtained by the recalculation, and obtaining the deformed new mid-span point coordinates by the calculation againWherein the method comprises the steps of
The step of judging whether to stop calculation according to the deformed new mid-span point coordinate obtained by calculation again and the deformed new mid-span point coordinate obtained by calculation again comprises the following steps:
if it isIf the value is smaller than the given limit value, the condition is met, and the calculation is terminated;
if it isAnd if the vector cross ratio is not smaller than the given limit value, continuing to calculate the vector cross ratio and the mid-point coordinate until the condition is met.
The invention provides a mixing device for space cable shape finding, which comprises:
the calculation module is used for calculating a cross-midpoint vertical coordinate target value based on the left node coordinate of the main cable, the right node coordinate of the main cable and a given sagittal ratio;
the iteration module is used for carrying out bridge forming and shape finding on the cable system by adopting an analytic method, and iteration is carried out according to a given sagittal ratio to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling;
the first building module is used for building a first finite element model according to the calculated main cable line shape and the unstressed length of each cable section so as to calculate the empty cable coordinates of each node of the main cable;
The second building module is used for building a second finite element model based on the empty cable coordinates of each node of the main cable obtained by calculation of the first finite element model;
the superposition module is used for carrying out nonlinear calculation on the second finite element model to obtain displacement of a cross-midpoint, and superposing the cross-midpoint coordinates before the main cable is deformed to obtain new cross-midpoint coordinates after the main cable is deformed;
the first execution module is used for calculating to obtain a new mid-span ratio based on the new mid-span point coordinates, repeatedly calculating again according to the new mid-span ratio, and calculating again to obtain deformed new mid-span point coordinates;
the second execution module is used for recalculating to obtain a new mid-span ratio based on the new mid-span point coordinates after the deformation obtained by recalculation, recalculating according to the new mid-span ratio obtained by recalculation, and obtaining the new mid-span point coordinates after the deformation by recalculation;
and the judging module is used for judging whether to stop calculation according to the deformed new mid-span point coordinate obtained by calculation again and the deformed new mid-span point coordinate obtained by calculation again.
Compared with the prior art, the invention has the advantages that:
(1) The analytic method is still a traditional method based on a catenary equation, a plurality of assumptions are not required to be set for introducing bending stiffness, and complex deduction is not required, but the finite element method is based on a finite displacement theory, so that the problems of large rotation and multi-directional rotation coupling can be solved without simplification, and the three-way coupling effect of torsion resistance and bidirectional bending resistance can be accurately considered;
(2) According to the application, by constructing an outer layer loop iteration and mixing an analytic method and a finite element method, influence factors are decomposed, respective advantages of the two methods are exerted, the axial rigidity and the sag effect of the main cable are considered in the analytic method, the torsional rigidity and the bending rigidity of the main cable are considered in the finite element method, and the main cable shape meeting a target value and simultaneously considering the torsional rigidity and the bidirectional bending rigidity can be obtained;
(3) According to the application, the inclination angle of the transverse sling and the installation angle of the cable clamp can be accurately calculated, the cable clamp can still maintain an axial tension state when being bridged, the risk of stretch bending fatigue damage is reduced, and the sling force can not fail and redistribute.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a hybrid method of space cable shaping in an embodiment of the application;
FIG. 2 is a schematic structural view of a bridge;
FIG. 3 is an elevational projection of a space cable system;
FIG. 4 is a plan view of a space cable system;
fig. 5 is a schematic diagram of a bridged wire shape and a blank wire shape.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application.
Referring to fig. 1, the method for mixing the shape of the space cable provided by the embodiment of the application specifically includes the following steps:
s1: calculating to obtain a vertical coordinate target value crossing a midpoint based on the left node coordinate of the main cable, the right node coordinate of the main cable and a given sagittal ratio; see fig. 2 for a bridge construction in the present application.
In the application, a vertical coordinate target value crossing the middle point is obtained by calculation, and the specific calculation mode is as follows:
Y c ＝(Y k-1 +Y 0 )/2-(X k-1 -X 0 )λ
wherein Y is c Represents a target value of vertical coordinates crossing the midpoint, lambda represents a given sagittal ratio, and the coordinates of the left node of the main cable are (X 0 、Y 0 、Z 0 ) The coordinates of the right node of the main cable are (X) k-1 、Y k-1 、Z k-1 ) K represents the total number of main cable nodes.
S2: performing bridge forming and shape finding of the cable system by adopting an analytic method, and iterating to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling according to a given sagittal ratio;
In the invention, an analytic method is adopted to carry out bridge forming and shape finding of a cable system, and the main cable line shape, the unstressed length of each cable section and the unstressed length of a sling are obtained through iteration according to a given sagittal ratio, wherein the specific steps of iteration comprise:
a: let lambda get 0 =λ, a new target value of the vertical coordinate across the midpoint is calculated in the following manner:
Y c0 ＝(Y k-1 +Y 0 )/2-(X k-1 -X 0 )λ 0 ；
b: according to the longitudinal component F of the left end of the main cable XL Vertical component force F YL Transverse component F ZL And the projection length L of the main cable in the horizontal plane 0 The plane catenary equation and Newton method are adopted to iterate to obtain the height difference H between the right two points of the main cable head joint Duan Zuo 0 And a stress-free cable length S, wherein the projected length of the main cable in the horizontal planeLongitudinal component F of left end of main cable XL ＝P Z Lambda/8, vertical component F at the left end of the main cable YL ＝P Z Transverse component F at left end of main cable ZL ＝F XL (Z b -Z 0 )/(X b -X 0 )，P Z Represents the sum of vertical forces at the lower end of the sling, Z b X represents the abscissa of the main beam at the lower end of the mid-span sling b Representing the ordinate of the main girder at the lower end of the mid-span sling;
c: the three-way force (F) at the right end point of the main cable head section is calculated according to the force balance condition XR 、F YR 、F ZR ) And is formed by height difference H 0 And an included angle beta L Calculating to obtain the coordinate (X) of the right end point of the main cable head section 1 、Y 1 、Z 1 ) Wherein:
F XR ＝-F XL
F YR ＝-F YL +Sω
F ZR ＝-F ZL
β L ＝arctan(F ZR /F XR )；
wherein ω represents the weight per linear meter of the main cable material;
d: sling for carrying outThe upper end point of the sling is the right end point of the cable section of the sling, specifically, the upper end point is based on the coordinate (X 1 、Y 1 、Z 1 ) And the known sling lower end point coordinates (X d 、Y d 、Z d ) And the vertical force Q at the sling end, and obtaining the stress-free length S of the sling by adopting a flexible iteration method d The three-way force (F) at the upper end of the sling is obtained from the balance of forces Xd 、F Yd 、F Zd )；
e: the three-way force (F XR 、F YR 、F ZR ) And the three-way force at the upper end of the sling (F Xd 、F Yd 、F Zd ) Superposition, update (F XL 、F YL 、F ZL ) And then returning to the step b, and iterating the next cable segment until all cable segments are calculated to obtain the vertical coordinate Y of the rightmost node of the main cable mR And the abscissa Z mR And main cable cross-midpoint vertical coordinate Y mc ；
f: vertical coordinate Y based on obtained rightmost node of main cable mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc If the difference value between the main cable and the target value does not meet the precision condition, calculating again to obtain the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable, and obtaining an influence matrix;
in the invention, the vertical coordinate Y of the rightmost node of the main cable is obtained mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc If the difference value between the main cable and the target value does not meet the precision condition, the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable are calculated again, and an influence matrix is obtained, and the specific steps comprise:
Vertical coordinate Y of rightmost node of main cable based on calculation mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc The difference from the target value, i.e. DeltaY mR ＝Y mR -Y k-1 ，ΔZ mR ＝Z mR -Z k-1 ，ΔY mc ＝Y mc -Y c0 ：
If it isIf the value is smaller than the given limit value, ending;
if it isNot less than a given limit, for the three-way force (F xL 、F yL 、F zL ) Sequentially taking the three-directional force at the left end point of the head section of the main cable as (F xL +1、F yL 、F zL )、(F xL 、F yL +1、F zL )、(F xL 、F yL 、F zL +1), circularly executing the steps b-e, and calculating again to obtain the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable, and obtaining 3 groups of new results, namely (Y) mR1 、Z mR1 、Z mc1 )、(Y mR2 、Z mR2 、Z mc2 )、(Y mR3 、Z mR3 、Z mc3 ) Thereby obtaining an influence matrix;
wherein the impact matrix is expressed as:
g: correcting the three-way force at the left end point of the main cable head section based on the influence matrix, and then continuing to calculate to obtain the rightmost node coordinate of the main cable and the midpoint-crossing vertical coordinate of the main cable until the precision condition is met;
in the invention, the three-way force at the left end point of the head section of the main cable is corrected based on the influence matrix, and then the right-most node coordinate of the main cable and the midpoint-crossing vertical coordinate of the main cable are continuously calculated until the precision condition is met, specifically:
a: correcting the three-way force at the left end point of the main cable head section by adopting an influence matrix, namely:
Wherein (ΔF) xL 、ΔF yL 、ΔF zL ) Representing the three-way force at the left end point of the modified main cable head section;
b: obtaining F xL +ΔF xL 、F yL +ΔF yL 、F zL +ΔF zL B, as a new iteration initial value, circularly executing the steps b-e, and then continuously calculating to obtain the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable untilLess than a given limit, the iteration is terminated.
C: and determining the line shape of the main cable based on the coordinates of each node of the main cable, and obtaining the stress-free length of each cable section and each sling of the main cable. And in the result of the last iteration step, the coordinates of each node of the main cable determine the line shape, namely the space state, of the main cable.
S3: according to the calculated main cable line shape and the unstressed length of each cable section, a first finite element model is established 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 section, the invention establishes a first finite element model to calculate the empty cable coordinates of each node of the main cable, and the specific steps comprise:
according to the calculated coordinates of all nodes of the main cable and the unstressed length of all cable sections, a first finite element model is built, wherein all nodes of the main cable are used as nodes of the finite element model, the cable sections are used as units of the finite element model, the units adopt catenary cable units, corresponding unstressed length values are given to the units, only the main cable does not have slings in the first finite element model, two ends of the main cable are fixedly connected, and the empty cable line shape of the main cable, namely the empty cable coordinates of all nodes of the main cable, is calculated through the first finite element model.
The main differences between this step and the conventional method are: a first finite element model is built, the space cable line shape is calculated, and preparation is made for stacking the beam units in the space cable state in step S4 (the stacked beam units must be built in the space cable shape, and thus the first finite element model needs to be built).
S4: establishing a second finite element model based on the empty cable coordinates of each node of the main cable obtained by calculation of the first finite element model;
in the invention, 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, and the specific steps comprise:
s401: updating the coordinates of each node of the main cable according to the empty cable coordinates of each node of the main cable calculated by the first finite element model to obtain the deformed coordinates of the first finite element model, namely the coordinates of the main cable under the empty cable, establishing a second finite element model according to the coordinates, establishing a main cable unit in the second finite element model by adopting a catenary clue unit, and endowing the main cable unit with a corresponding unstressed length (obtained by an analysis method in the step S2);
s402: building sling units and giving corresponding stress-free lengths (obtained by an analysis method in the step S2);
s403: a main cable beam unit is established, the main cable beam unit and the main cable unit are overlapped to obtain an overlapped double unit, and the cross section area of the overlapped double unit is given a minimum value (such as 10 -8 ) And the torsional inertia and the bending inertia are calculated according to the circular section of the main cable and are endowed to the main cable beam unit.
For boundary conditions: the two ends of the main cable are fixedly connected, the lower end of the sling is loosened in vertical freedom degree, and the rest degrees of freedom are fixed. Load: considering the dead weight of the main cable and the sling, a vertical force acts on the lower end of the sling, and the vertical force is the weight for supporting the main girder. The finite element model is characterized by comprising a main cable and a sling unit, wherein the main cable unit is simulated by adopting a superposition double unit, the cable unit is a beam unit, the cable unit considers the axial rigidity and the sagging effect of the main cable, and the beam unit considers the torsional rigidity and the bending rigidity of the main cable.
The main differences between this step and the conventional method are: the method adopts a superposition unit mode, adopts a cable unit and a space beam unit at the same time for simulating the main cable, carries out special treatment of imparting a minimum value to the cross section area of the beam unit, only considers torsion resistance and bidirectional bending stiffness, and considers the bending-torsion coupling effect of the space main cable by using the superposition space beam unit.
S5: performing nonlinear calculation on the second finite element model to obtain displacement of a cross-midpoint, and superposing cross-midpoint coordinates before the main cable is deformed to obtain new cross-midpoint coordinates after the main cable is deformed;
namely, nonlinear calculation is carried out on the second finite element model to obtain the displacement crossing the midpoint And superposing the mid-span point coordinates before the deformation of the main cable to obtain new mid-span point coordinates after the deformation>
S6: calculating to obtain a new mid-span ratio based on the new mid-span point coordinates, and repeatedly calculating again according to the new mid-span ratio to obtain deformed new mid-span point coordinates again;
namely, a new sagittal-span ratio lambda is calculated based on the new mid-span point coordinates 1 And repeating the calculation again according to the new sagittal ratio (i.e. returning to the step S2 and executing the steps S2-S5), and calculating again to obtain the deformed new sagittal point coordinatesWherein the method comprises the steps of
S7: based on the new mid-span point coordinate after deformation obtained by recalculation, recalculating to obtain a new mid-span ratio, and recalculating according to the new mid-span ratio obtained by recalculation, and obtaining the new mid-span point coordinate after deformation by recalculation;
in the invention, based on the new mid-span point coordinates after deformation obtained by recalculation, a new mid-span ratio is obtained by recalculation, and the new mid-span point coordinates after deformation are obtained by recalculation according to the new mid-span ratio obtained by recalculation, specifically:
based on the new mid-span point coordinates after deformation obtained by recalculation, recalculating to obtain a new sagittal-span ratio lambda 2 And is calculated againRepeating the calculation of the new vector mid-point ratio again (i.e. returning to the step S2 and executing the steps S2-S5), and calculating again to obtain the deformed new mid-point coordinates Wherein the method comprises the steps of
S8: and judging whether to stop the calculation according to the new deformed mid-span point coordinate obtained by the calculation again and the new deformed mid-span point coordinate obtained by the calculation again.
In the invention, whether to stop calculation is judged according to the deformed new mid-span point coordinate obtained by calculation again and the deformed new mid-span point coordinate obtained by calculation again, specifically:
if it isLess than a given limit (e.g. 10 -3 Set as needed), the condition is satisfied, and the calculation is terminated;
if it isNot less than a given limit, let lambda 0 ＝λ 1 ，λ 1 ＝λ 2 And repeating the steps S1 to S8, and continuing to calculate the vector-span ratio and the mid-span point coordinates until the conditions are met.
The main differences between this step and the conventional method are: and constructing an outer layer loop iteration, simultaneously taking an analytic method and a finite element method into an iteration process, mixing and recycling, playing respective advantages, taking the axial rigidity and the sag effect of the main cable into consideration by the analytic method, and taking the torsion resistance and the bidirectional bending rigidity of the main cable into consideration by the finite element method.
The present invention will be specifically described below by taking the form of a large diameter space cable system having a span of 1000m or more as an example.
The conditions are known: the coordinates of the two end points of the main cable are (8,208.1 200.25) (1152, 208.1, 200.25) with an elastic modulus of 2.0e 8 kPa, cross-sectional area of 0.32m 2 The volume weight of the material is 82.3kN/m 3 The torsional moment of inertia of the circular section of the main cable is 1.6298e -4 The moment of inertia of the in-plane and out-of-plane bending resistances are 8.1487e -3 75 sub-points are arranged, the target sagittal ratio is 1/9, each main cable sub-point is connected with 75 slings, the ordinate of the lower end point of each sling is identical to the upper main cable sub-point, the vertical coordinate is 77.5m, the abscissa is 13.25m (187 m different from the abscissa of the two end points of the main cable, the space opening amount is larger), the vertical bearing force of the lower end of each sling is-2000 kN, and the elastic modulus of sling material is 1.95e 8 kPa, cross-sectional area 0.00428m 2 The volume weight of the material is 86.24kN/m 3 . Spatial cable system as illustrated in fig. 3 and 4, the spatial effect of the cable system is evident from the horizontal projection.
The method comprises the following specific steps:
(1) Calculating a target value of a vertical coordinate of a main cable crossing a midpoint to be 80.9889m, and calculating an initial three-way component force (F xL 、F yL 、F zL ) Horizontal projection length L of the whole main cable 0 1144m, sum of vertical forces F at lower end of sling yL At-84375 kN, initial value of transverse force component F zL And (5) performing analysis iteration to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling, wherein 55168.3kN is taken as the main cable shape.
(2) According to the results of the node coordinates of the main cable and the stress-free length of the cable segment in the bridge formation state in the step (1), a first finite element model is built, only the main cable is contained, the load is only the dead weight of the main cable, the empty cable state is calculated, and as can be seen in fig. 5, the empty cable line shape is lower than the bridge formation line shape because the space cable swings transversely to the vertical direction.
(3) On the basis of the deformed empty cable shape, a second finite element model is established according to empty cable coordinates, a main cable unit is established by adopting a catenary cable unit, and an unstressed length value (obtained by the step (1)) is given; building sling units, still adopting catenary cable units, and giving stress-free length (obtained by the step (1)); establishing a main cable beam unit, wherein the series of units and the main cable unit are completely overlapped, and the section of the main cable beam unit isSmall value of 10 -8 Moment of torsion of 1.6298e -4 Moment of inertia of 8.1487e -3 The method comprises the steps of carrying out a first treatment on the surface of the The two ends of the main cable are fixedly connected, the lower end of the sling is loosened in vertical degree of freedom, the other degrees of freedom are fixed, and vertical concentrated force-2000 kN acts on the lower end of the sling. And carrying out nonlinear calculation on the second finite element model to obtain a vertical displacement 85.3419m of a cross-midpoint, and superposing the vertical coordinates of the cross-midpoint before deformation during modeling to obtain a vertical coordinate 80.9598m of the cross-midpoint after deformation, wherein the target value of the vertical coordinates of the cross-midpoint is 80.9889m, and the difference is 2.9099cm. This is because the effect of torsional and bending stiffness of the main cable is taken into account, and if this is not taken into account, the difference should be 0.
(4) Because of the existence of the difference value, iteration needs to be carried out, the main cable sagittal ratio is updated to be 1/9.00206, and the calculation is carried out again. And (3) through two rounds of iterative loops, the obtained bridge formation linear cross-midpoint vertical coordinate is 80.9889m, the bridge formation linear cross-midpoint vertical coordinate is completely consistent with the target value, and the iteration is terminated, so that the bridge formation linear shape taking the torsion resistance and the bending stiffness of the main cable into consideration is obtained.
TABLE 1 Main Cable Point coordinates
Table 1 shows the bridge formation calculated by a pure analytical method without considering the torsional and bending stiffness of the main cable and the bridge formation calculated by a hybrid method of the present invention with simultaneous consideration of the torsional and bending stiffness of the main cable, and gives the difference between the two. As can be seen from Table 1, compared with the results of the conventional pure analysis method and the method of the present invention, the vertical line shape and the plane line shape in the bridge formation state are different, the maximum deviation occurs at the first sling dividing point near the two sides of the main cable, the vertical coordinate is 42.23cm, the horizontal coordinate is 45.49cm, the difference gradually decreases toward the midspan, and the midspan horizontal coordinate is still 6.01cm. The larger difference of the upper end points of the long sling can cause deviation in calculation of the transverse inclination angle of the sling, the installation angle of the cable clamp is inaccurate, an additional bending moment appears, the stress of the cable clamp is changed from axial pulling to stretch bending coupling, and fatigue damage is more easy to occur.
In summary, for the main cable of the large-diameter space cable suspension bridge, the torsional rigidity and the bending rigidity of the main cable have influence on the bridge formation shape, and the main cable is coupled, and the influence of the torsional rigidity and the bending rigidity should be considered simultaneously when the main cable is shaped. The invention simultaneously considers the three-way coupling effect of torsion resistance and bidirectional bending resistance to realize the accurate shape finding of the main cable.
According to the space cable shape finding mixing method, the analytic method and the finite element method are mixed and used, the advantages of the analytic method and the finite element method are brought into play, the axial rigidity and the sag effect of the main cable are considered in the analytic method, the three-way coupling effect of torsion resistance and bidirectional bending resistance is considered in the finite element method, and the space cable bridge-forming line shape meeting the target value is obtained through the loop iteration of the two methods. The finite element method adopts a mode of overlapping units, the main cable is simultaneously simulated by adopting a cable unit and a space beam unit, and the cross section area of the beam unit is specially treated with a minimum value. The torsional rigidity and the bending rigidity of the main cable of the large-diameter space cable suspension bridge can simultaneously act in the process that the space state of the bridge is gradually Zhang Chengcheng from the vertical state of the hollow cable. The mixing method takes the three-way bending-twisting coupling effect into consideration to realize shape finding, and can accurately calculate the space angle of the sling and the cable clamp, so that the cable clamp can still maintain an axial tension state when forming a bridge, and the redistribution and the actual effect of the sling force can not be caused. The invention can be applied to the design of large-diameter space cable suspension bridges.
In a possible implementation manner, the embodiment of the present invention further provides a readable storage medium, where the readable storage medium is located in a PLC (Programmable Logic Controller ) controller, and a computer program is stored on the readable storage medium, where the program is executed by a processor to implement the following steps of the hybrid method for space cable shaping:
Calculating to obtain a vertical coordinate target value crossing a midpoint based on the left node coordinate of the main cable, the right node coordinate of the main cable and a given sagittal ratio;
performing bridge forming and shape finding of the cable system by adopting an analytic method, and iterating to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling according to a given sagittal ratio;
according to the calculated main cable line shape and the unstressed length of each cable section, 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 obtained by calculation of the first finite element model;
performing nonlinear calculation on the second finite element model to obtain displacement of a cross-midpoint, and superposing cross-midpoint coordinates before the main cable is deformed to obtain new cross-midpoint coordinates after the main cable is deformed;
calculating to obtain a new mid-span ratio based on the new mid-span point coordinates, and repeatedly calculating again according to the new mid-span ratio to obtain deformed new mid-span point coordinates again;
based on the new mid-span point coordinate after deformation obtained by recalculation, recalculating to obtain a new mid-span ratio, and recalculating according to the new mid-span ratio obtained by recalculation, and obtaining the new mid-span point coordinate after deformation by recalculation;
And judging whether to stop the calculation according to the new deformed mid-span point coordinate obtained by the calculation again and the new deformed mid-span point coordinate obtained by the calculation again.
The storage media may take the form of any combination of one or more computer-readable media. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. The computer readable storage medium may be, for example, but not limited to: an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
The computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, either in baseband or as part of a carrier wave. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination of the foregoing. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, fiber optic cable, RF, etc., or any suitable combination of the foregoing.
Computer program code for carrying out operations of the present invention may be written in one or more programming languages, including an object oriented programming language such as Java, smalltalk, C ++ and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may 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 case of a remote computer, the remote computer may be connected to the user's computer through any kind of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or may be connected to an external computer (for example, through the Internet using an Internet service provider).
The embodiment of the invention provides a mixing device for spatial cable shape finding, which 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.
The calculation module is used for calculating a vertical coordinate target value crossing the middle point based on the left node coordinate of the main cable, the right node coordinate of the main cable and a given sagittal ratio;
the iteration module is used for carrying out bridge forming and shape finding of the cable system by adopting an analytic method, and iteration is carried out according to a given sagittal ratio to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling;
the first building module is used for building a first finite element model according to the calculated main cable line shape and the unstressed length of each cable section so as to calculate the empty cable coordinates of each node of the main cable;
the second building module is used for building a second finite element model based on the empty cable coordinates of each node of the main cable obtained by calculation of the first finite element model;
the superposition module is used for carrying out nonlinear calculation on the second finite element model to obtain displacement of a cross-midpoint, and superposing the cross-midpoint coordinates before the main cable is deformed to obtain new cross-midpoint coordinates after the main cable is deformed;
the first execution module is used for calculating to obtain a new mid-span ratio based on the new mid-span point coordinates, repeatedly calculating again according to the new mid-span ratio, and calculating again to obtain deformed new mid-span point coordinates;
The second execution module is used for recalculating to obtain a new mid-span ratio based on the new mid-span point coordinates after deformation obtained by recalculation, recalculating according to the new mid-span ratio obtained by recalculation, and obtaining the new mid-span point coordinates after deformation by recalculation;
the judging module is used for judging whether to stop calculation according to the new deformed mid-span point coordinates obtained through calculation again and the new deformed mid-span point coordinates obtained through calculation again.
The foregoing is only a specific embodiment of the application to enable those skilled in the art to understand or practice the application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

Claims (10)

1. The mixing method for the shape finding of the space cable is characterized by comprising the following steps of:
calculating to obtain a vertical coordinate target value crossing a midpoint based on the left node coordinate of the main cable, the right node coordinate of the main cable and a given sagittal ratio;
performing bridge forming and shape finding of the cable system by adopting an analytic method, and iterating to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling according to a given sagittal ratio;
according to the calculated main cable line shape and the unstressed length of each cable section, 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 obtained by calculation of the first finite element model;
performing nonlinear calculation on the second finite element model to obtain displacement of a cross-midpoint, and superposing cross-midpoint coordinates before the main cable is deformed to obtain new cross-midpoint coordinates after the main cable is deformed;
calculating to obtain a new mid-span ratio based on the new mid-span point coordinates, and repeatedly calculating again according to the new mid-span ratio to obtain deformed new mid-span point coordinates again;
based on the new mid-span point coordinate after deformation obtained by recalculation, recalculating to obtain a new mid-span ratio, and recalculating according to the new mid-span ratio obtained by recalculation, and obtaining the new mid-span point coordinate after deformation by recalculation;
And judging whether to stop the calculation according to the new deformed mid-span point coordinate obtained by the calculation again and the new deformed mid-span point coordinate obtained by the calculation again.
2. The method for mixing the spatial cable shape finding according to claim 1, wherein the calculating obtains a target value of a vertical coordinate crossing a midpoint by the following specific calculating modes:
Y c ＝(Y k-1 +Y 0 )/2-(X k-1 -X 0 )λ
wherein Y is c Represents a target value of vertical coordinates crossing the midpoint, lambda represents a given sagittal ratio, and the coordinates of the left node of the main cable are (X 0 、Y 0 、Z 0 ) The coordinates of the right node of the main cable are (X) k-1 、Y k-1 、Z k-1 ) K represents the total number of main cable nodes.
3. The method for mixing the space cable shaping according to claim 2, wherein the bridge shaping of the cable system is performed by an analytic method, and the main cable line shape, the unstressed length of each cable section and the unstressed length of the sling are obtained by iteration according to a given sagittal ratio, wherein the specific steps of iteration include:
let lambda get 0 =λ, a new target value of the vertical coordinate across the midpoint is calculated in the following manner: y is Y c0 ＝(Y k-1 +Y 0 )/2-(X k-1 -X 0 )λ 0 ；
According to the longitudinal component F of the left end of the main cable XL Vertical component force F YL Transverse component F ZL And the projection length L of the main cable in the horizontal plane 0 The plane catenary equation and Newton method are adopted to iterate to obtain the height difference H between the right two points of the main cable head joint Duan Zuo 0 And a stress-free cable length S, wherein the projected length of the main cable in the horizontal planeLongitudinal component F of left end of main cable XL ＝P Z Lambda/8, vertical component F at the left end of the main cable YL ＝P Z Transverse component F at left end of main cable ZL ＝F XL (Z b -Z 0 )/(X b -X 0 )，P Z Represents the sum of vertical forces at the lower end of the sling, Z b X represents the abscissa of the main beam at the lower end of the mid-span sling b Representing the ordinate of the main girder at the lower end of the mid-span sling;
the three-way force (F) at the right end point of the main cable head section is calculated according to the force balance condition XR 、F YR 、F ZR ) And is formed by height difference H 0 And an included angle beta L Calculating to obtain the coordinate (X) of the right end point of the main cable head section 1 、Y 1 、Z 1 ) Wherein:
F XR ＝-F XL
F YR ＝-F YL +Sω
F ZR ＝-F ZL
β L ＝arctan(F ZR /F XR )
wherein ω represents the weight per linear meter of the main cable material;
based on the coordinates (X) of the right end point of the main cable head section 1 、Y 1 、Z 1 ) And the known sling lower end point coordinates (X d 、Y d 、Z d ) And the vertical force Q at the sling end, and obtaining the stress-free length S of the sling by adopting a flexible iteration method d The three-way force (F) at the upper end of the sling is obtained from the balance of forces Xd 、F Yd 、F Zd )；
The three-way force (F XR 、F YR 、F ZR ) And the three-way force at the upper end of the sling (F Xd 、F Yd 、F Zd ) Superposition, update (F XL 、F YL 、F ZL ) Then iterating the next cable segment until all cable segments are calculated to obtain the vertical coordinate Y of the rightmost node of the main cable mR And the abscissa Z mR And main cable cross-midpoint vertical coordinate Y mc ；
Vertical coordinate Y based on obtained rightmost node of main cable mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc If the difference between the target value and the target value does not meet the accuracy condition, the difference is counted againCalculating to obtain the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable, and obtaining an influence matrix;
correcting the three-way force at the left end point of the main cable head section based on the influence matrix, and then continuing to calculate to obtain the rightmost node coordinate of the main cable and the midpoint-crossing vertical coordinate of the main cable until the precision condition is met;
and determining the line shape of the main cable based on the coordinates of each node of the main cable, and obtaining the stress-free length of each cable section and each sling of the main cable.
4. A method of mixing space cable shaping according to claim 3, wherein the vertical coordinate Y based on the obtained rightmost node of the main cable mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc If the difference value between the main cable and the target value does not meet the precision condition, the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable are calculated again, and an influence matrix is obtained, and the specific steps comprise:
vertical coordinate Y of rightmost node of main cable based on calculation mR And the abscissa Z mR Main cable cross-midpoint vertical coordinate Y mc The difference from the target value, i.e. DeltaY mR ＝Y mR -Y k-1 ，ΔZ mR ＝Z mR -Z k-1 ，ΔY mc ＝Y mc -Y c0 ：
If it isIf the value is smaller than the given limit value, ending;
if it isNot less than a given limit, for the three-way force (F xL 、F yL 、F zL ) Sequentially taking the three-directional force at the left end point of the head section of the main cable as (F xL +1、F yL 、F zL )、(F xL 、F yL +1、F zL )、(F xL 、F yL 、F zL +1), calculating again to obtain the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable, and obtaining 3 groups of new results, namely (Y mR1 、Z mR1 、Z mc1 )、(Y mR2 、Z mR2 、Z mc2 )、(Y mR3 、Z mR3 、Z mc3 ) Thereby obtaining an influence matrix;
wherein the impact matrix is expressed as:
5. the method for mixing the shape of the space cable according to claim 4, wherein the three-way force at the left end point of the head section of the main cable is corrected based on the influence matrix, and then the calculation is continued to obtain the rightmost node coordinate of the main cable and the midpoint-crossing vertical coordinate of the main cable until the precision condition is met, specifically:
correcting the three-way force at the left end point of the main cable head section by adopting an influence matrix, namely:
wherein (ΔF) xL 、ΔF yL 、ΔF zL ) Representing the three-way force at the left end point of the modified main cable head section;
obtaining F xL +ΔF xL 、F yL +ΔF yL 、F zL +ΔF zL As new iteration initial value, then continuing to calculate to obtain the vertical coordinate and the horizontal coordinate of the rightmost node of the main cable and the cross-midpoint vertical coordinate of the main cable untilLess than a given limit, the iteration is terminated.
6. The method for mixing the spatial cable shape according to claim 5, wherein the step of building 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 section comprises the following steps:
according to the calculated coordinates of all nodes of the main cable and the unstressed length of all cable sections, a first finite element model is built, wherein all nodes of the main cable are used as nodes of the finite element model, the cable sections are used as units of the finite element model, the units adopt catenary cable units, corresponding unstressed length values are given to the units, only the main cable does not have slings in the first finite element model, two ends of the main cable are fixedly connected, and the empty cable line shape of the main cable, namely the empty cable coordinates of all nodes of the main cable, is calculated through the first finite element model.
7. The method for mixing space cable shape finding according to claim 6, wherein the establishing a second finite element model based on the space cable coordinates of each node of the main cable calculated by the first finite element model comprises the following specific steps:
updating the coordinates of each node of the main cable according to the empty cable coordinates of each node of the main cable calculated by the first finite element model, so as to obtain the deformed coordinates of the first finite element model, namely the coordinates of the main cable under the empty cable, establishing a second finite element model according to the coordinates, establishing a main cable unit in the second finite element model by adopting a catenary cable clue unit, and endowing the main cable unit with a corresponding stress-free length;
Building sling units and giving corresponding stress-free lengths;
the method comprises the steps of establishing a main cable beam unit, overlapping the main cable beam unit and the main cable unit to obtain an overlapped double unit, giving a minimum value to the sectional area of the overlapped double unit, calculating torsional inertia and bending moment according to the circular section of the main cable, and giving the main cable beam unit.
8. A method of mixing spatial cable shapes as claimed in claim 7, wherein:
the nonlinear calculation is carried out on the second finite element model to obtain the displacement of the cross-midpoint, and the cross-midpoint coordinates before the deformation of the main cable are overlapped to obtainTo the deformed new mid-span point coordinate, specifically, performing nonlinear calculation on the second finite element model to obtain mid-span displacementAnd superposing the mid-span point coordinates before the deformation of the main cable to obtain new mid-span point coordinates after the deformation>
The new mid-span point coordinate is calculated to obtain a new mid-span ratio, and the calculation is repeated again according to the new mid-span ratio to obtain the deformed new mid-span point coordinate, specifically, the new mid-span ratio lambda is calculated based on the new mid-span point coordinate 1 And repeating the calculation again according to the new sagittal ratio, and calculating again to obtain the deformed new mid-span point coordinatesWherein the method comprises the steps of
9. A method of mixing spatial cable shapes as claimed in claim 8, wherein:
The new mid-span point coordinates after deformation based on the recalculation are recalculated to obtain new mid-span ratios, and the new mid-span point coordinates after deformation are calculated again according to the new mid-span ratios obtained by the recalculation, specifically:
based on the new mid-span point coordinates after deformation obtained by recalculation, recalculating to obtain a new sagittal-span ratio lambda 2 And repeatedly calculating again according to the new sagittal ratio obtained by the recalculation, and obtaining the deformed new mid-span point coordinates by the calculation againWherein the method comprises the steps of
The step of judging whether to stop calculation according to the deformed new mid-span point coordinate obtained by calculation again and the deformed new mid-span point coordinate obtained by calculation again comprises the following steps:
if it isIf the value is smaller than the given limit value, the condition is met, and the calculation is terminated;
if it isAnd if the vector cross ratio is not smaller than the given limit value, continuing to calculate the vector cross ratio and the mid-point coordinate until the condition is met.
10. A mixing device for space cable shaping, comprising:
the calculation module is used for calculating a cross-midpoint vertical coordinate target value based on the left node coordinate of the main cable, the right node coordinate of the main cable and a given sagittal ratio;
the iteration module is used for carrying out bridge forming and shape finding on the cable system by adopting an analytic method, and iteration is carried out according to a given sagittal ratio to obtain the main cable shape, the unstressed length of each cable section and the unstressed length of the sling;
The first building module is used for building a first finite element model according to the calculated main cable line shape and the unstressed length of each cable section so as to calculate the empty cable coordinates of each node of the main cable;
the second building module is used for building a second finite element model based on the empty cable coordinates of each node of the main cable obtained by calculation of the first finite element model;
the superposition module is used for carrying out nonlinear calculation on the second finite element model to obtain displacement of a cross-midpoint, and superposing the cross-midpoint coordinates before the main cable is deformed to obtain new cross-midpoint coordinates after the main cable is deformed;
the first execution module is used for calculating to obtain a new mid-span ratio based on the new mid-span point coordinates, repeatedly calculating again according to the new mid-span ratio, and calculating again to obtain deformed new mid-span point coordinates;
the second execution module is used for recalculating to obtain a new mid-span ratio based on the new mid-span point coordinates after the deformation obtained by recalculation, recalculating according to the new mid-span ratio obtained by recalculation, and obtaining the new mid-span point coordinates after the deformation by recalculation;
and the judging module is used for judging whether to stop calculation according to the deformed new mid-span point coordinate obtained by calculation again and the deformed new mid-span point coordinate obtained by calculation again.
CN202310669510.7A 2023-06-07 2023-06-07 Mixing method and device for space cable shape finding Pending CN116757024A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117993266A (en) * 2024-04-02 2024-05-07 中国十九冶集团有限公司 Cable length adjusting method based on finite element numerical model and point cloud technology

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117993266A (en) * 2024-04-02 2024-05-07 中国十九冶集团有限公司 Cable length adjusting method based on finite element numerical model and point cloud technology
CN117993266B (en) * 2024-04-02 2024-05-28 中国十九冶集团有限公司 Cable length adjusting method based on finite element numerical model and point cloud technology

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