CN111666615A - Suspension bridge space cable form finding method based on finite elements - Google Patents

Suspension bridge space cable form finding method based on finite elements Download PDF

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CN111666615A
CN111666615A CN202010406229.0A CN202010406229A CN111666615A CN 111666615 A CN111666615 A CN 111666615A CN 202010406229 A CN202010406229 A CN 202010406229A CN 111666615 A CN111666615 A CN 111666615A
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许福友
马召宇
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Dalian University of Technology
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Abstract

The invention belongs to the technical field of bridge engineering, and provides a suspension bridge space cable form finding method based on finite elements, which comprises the following steps: 1) establishing an initial finite element model containing a main cable and a suspender, wherein the suspender only restrains longitudinal and vertical freedom degrees at a lifting point of a main beam, releases transverse restraint, and applies a design value of transverse tension of the suspender to ensure that the tension of the suspender is always a design requirement value after each step of iterative calculation, 2) updating the finite element model after determining the initial values of space cable alignment and internal force by applying a small elastic modulus technology, 3) expanding iterative calculation through nested circulation, updating the cable alignment and the internal force by internal circulation, ensuring that the internal force of the suspender of a convergence result is the design requirement value, correcting the node coordinates of the main cable by external circulation, ensuring that the control point coordinates of the main cable of the convergence result are the design value, and alternately iterating the internal and external circulation until the convergence requirement is met, and 4) outputting the result. The method has the advantages of simple operation, stable convergence, high precision, high speed, strong universality and convenience for engineering application and popularization.

Description

Suspension bridge space cable form finding method based on finite elements
Technical Field
The invention belongs to the technical field of bridge engineering, and relates to a suspension bridge cable shape finding method, in particular to a suspension bridge space cable shape finding method based on finite elements.
Background
When engineering personnel design a suspension bridge, in order to improve the mechanical property and the aesthetic effect, cables with spatial cable surfaces are usually adopted, such as a korean Yongzon large bridge (main span 300m) and an old san francisco Oakland Bay new bridge (main span 385m) in the united states adopt spatial main cables to improve the transverse rigidity and the torsional rigidity of the structure, and space wind cables are adopted to improve the wind resistance of the structure, such as a Shanyi-Dong Monshan pedestrian suspension bridge (span 420m), a Switzerls-Kunan pedestrian truss bridge (span 494m), a Huanghe Wanjia Zhu hydraulic engineering pedestrian bridge (span 500m), and the like, wherein a wind cable suspension rod of the Huanghe Wanjia hydraulic engineering pedestrian bridge is more in an arrangement form of being inclined along the bridge direction, and the design and the construction difficulty of the suspension bridge are greatly increased by a complex cable form.
The shape finding of the cable is a key problem in the design and construction of the suspension bridge. Different from the traditional suspension bridge, the main cable and the suspender of the spatial cable suspension bridge are coupled, namely the linear shape of the main cable determines the linear shape of the suspender, and the linear shape of the suspender determines the magnitude of each component of the suspender force acting on the main cable; for the spatial cable with the suspension rods obliquely arranged along the bridge direction, the suspension rods are coupled with the main cable, and the two adjacent oblique suspension rods are also coupled, so that the difficulty in finding the shape of the spatial cable surface suspension bridge cable is greatly improved.
Finite element methods and Segmented Catenary Methods (SCM) are common methods for cable form finding in suspension bridges. At present, more scholars use a sectional catenary method for finding shape of a planar cable for reference, and a spatial analysis model is adopted to provide the sectional catenary method for finding shape of the spatial cable, and the method has the following defects:
(1) the method needs programming to solve a complex nonlinear equation set, and is inconvenient for application and popularization of engineers;
(2) the method has poor convergence stability, needs to introduce a proper relaxation factor or an artificial intervention initial value, and has higher operation difficulty for designers lacking engineering experience.
(3) The method can be used for finding the shape of the spatial cable of a parallel suspender system, but cannot be used for solving the more complicated spatial cable with the suspenders obliquely arranged along the bridge direction.
In order to solve the above problems, a space cable shape-finding method which is convenient for designers to implement, has good convergence stability and strong universality needs to be invented, and a finite element rule becomes the best choice for solving the above problems.
Disclosure of Invention
The invention provides a quick, convenient and stable space cable form-finding method according to the design requirements of the space cable.
The technical scheme of the invention is as follows:
a suspension bridge space cable shape finding method based on finite elements adopts finite element software ANSYS to find the shape of a space cable, and comprises the following steps:
step 1, establishing an initial finite element model of space cable linear iterative computation through APDL, namely a main cable A0、AnPoint-fixed, boom B1～Bn-1The hoisting point only restrains the directions x and z, releases the restraint in the direction y and applies the design value F of the tensile force in the transverse bridge direction1y～F(n-1)y；
Step 2, setting initial elastic modulus of the main cable and the suspender unit;
step 3, setting the initial strain of the main cable and the suspender unit, wherein the initial strain and the initial strain of the main cable and the suspender unit are the same;
step 4, carrying out one-step nonlinear finite element solution on the initial finite element model;
step 5, calculating a main cable control point AiY coordinate of (a) and design value yiDeviation of (a)1If Δ1>Δcon1-1Returning to the step 3 to correct the initial strain value; if Δ1<Δcon1-1Outputting the internal force of the main cable and the suspender unit, the y and z coordinates of the main cable node and the z coordinate of the suspender node, and entering the next step;
step 6, updating the initial strain of each unit, updating the y and z coordinates of the main cable node and the z coordinate of the suspender node, and recovering the actual elastic modulus of the cable unit;
step 7, nonlinear solution is carried out, and the internal force of the main cable and the suspender unit, the y and z coordinates of the main cable node and the suspender node and the z coordinate of the suspender node are output;
step 8, correcting the y coordinate of the main cable node to ensure the main cable control point AiHas a y coordinate ofEvaluating yi；
Step 9, updating the initial strain of each unit, and updating the y and z coordinates of the main cable node and the z coordinate of the suspender node;
step 10, nonlinear solving, and outputting the internal force of the main cable and the suspender unit, the y and z coordinates of the main cable node and the suspender node;
step 11, obtaining B1～Bn-1Node y-direction displacement delta2If Δ2>Δcon2Then go back to step 9, if Δ2<Δcon2Entering the next step;
step 12, calculating a main cable control point AiY coordinate of (a) and design value yiDeviation of (a)1If Δ1>Δcon1-2Then go back to step 8, if Δ1<Δcon1-2And ending the iteration and outputting the result.
The invention has the beneficial effects that:
(1) the invention adopts the general finite element software ANSYS to realize the shape finding of the suspension bridge space cable, is simple and quick and is convenient for the application and popularization of engineering personnel;
(2) the invention establishes a finite element model containing a main cable and a suspender, analyzes the shape of the space cable, and releases the model B1～Bn-1The hoisting point is restrained in the y direction, and the design tension force in the transverse bridge direction of the suspender is applied, so that the internal force of the suspender in each step of iteration result is effectively ensured to be a design required value;
(3) the invention adopts the small elastic modulus technology to determine the linearity of the main cable and the suspender, and the initial value and the target value of the internal force are closer, thereby effectively ensuring the convergence of iterative calculation;
(4) the method adopts nested loop iterative computation, the convergence process is stable and quick, the internal loop updates the linear shape and the internal force of the cable rope, the internal force of a convergence result suspender is ensured to be a design required value, the external loop corrects the y coordinate of a main cable node, and the convergence result main cable control point A is ensurediIs the design value yi；
(5) The invention can analyze the shape of the spatial cable obliquely arranged along the bridge direction of the suspender, and has strong universality.
Drawings
FIG. 1 is a flowchart of an iterative finite element-based spatial cable shape finding calculation according to the present invention.
Fig. 2 is a schematic view of a spatial cable according to the present invention.
FIG. 3 is a schematic diagram of an iterative initial finite element model according to the present invention.
Fig. 4 is a schematic diagram of correcting y-coordinates of a main cable node in step 8 according to the present invention.
FIG. 5 is a graph showing the displacement of the shape finding result of example 1 under the action of its own weight.
FIG. 6 is a schematic diagram of the spatial cable of the hanger rod of the embodiment 2 arranged obliquely along the bridge direction.
FIG. 7 is a graph showing the displacement of the shape finding result of example 2 under the action of its own weight.
Detailed Description
The finite element-based spatial cable form finding method of the present invention is further explained in detail with reference to the following embodiments.
Taking the form finding of the pedestrian suspension bridge wind cable as an example, as shown in fig. 2, the known design conditions are as follows:
1) the elasticity modulus, the section area, the material density and other parameters of the main cable and the suspender;
2) main cable A0、AnTwo anchor points x, y, z coordinates, A1～An-1X coordinate of the hoisting point, control point AiY-coordinate of (a);
3) hanging rod on main beam hanging point B1～Bn-1X, y, z coordinates of (a);
4)B1～Bn-1design value F of y-direction component of lifting rod force at lifting point1y～F(n-1)y。
The method comprises the following specific steps:
step 1, as shown in fig. 3, establishing an initial finite element model of space cable linear iterative computation through APDL, namely a main cable A0、AnPoint-fixed, boom B1～Bn-1The hoisting point only restrains the directions x and z, releases the restraint in the direction y and applies the design value F of the tensile force in the transverse bridge direction1y～F(n-1)y；
Step 2, the main cable and the suspender unit are assigned with a smaller initial elastic modulus (generally smaller than an actual value by 3 orders of magnitude);
step 3, the main cable and the suspender unit are assigned with a same and larger initial strain;
step 4, solving nonlinear finite elements;
step 5, calculating a main cable control point AiY coordinate of (a) and design value yiDeviation of (a)1If Δ1>Δcon1-1Then go back to step 3 to correct the initial strain value, if delta1<Δcon1-1Outputting the internal force of the main cable and the suspender unit, the y and z coordinates of the main cable node and the z coordinate of the suspender node, and entering the next step, wherein the output result of the step is only used for updating the model of the step 6, only the convergence of the nonlinear solution of the step 7 is needed to be ensured, and the precision requirement on the output result is not high, so that the convergence allowable value delta is limitedcon1-1The value can be selected within the range of 0.1-1 m;
step 6, updating the finite element model, wherein the x coordinate of each node of the main cable and the x and y coordinates of each node of the suspender are specified according to the known design conditions, the y and z coordinates of each node of the main cable and the z coordinate of each node of the suspender are updated according to the calculation result of the step 5, and the initial strain of each unit is calculated and determined according to the formula 1:
Figure BDA0002491408650000051
wherein, the initial strain value of each unit, E is the real elastic modulus of the cable unit, A is the area of the cable unit, and F is the internal force of each unit in the calculation result of the step 5;
step 7, nonlinear solution is carried out, and the internal force of the main cable and the suspender unit, y and z coordinates of a main cable node and a suspender node and z coordinates of the suspender node are obtained;
step 8, as shown in FIG. 4, according to the wind cable control point AiY coordinate design requirement value yiCorrecting the y coordinate of the wind cable obtained by the last calculation, wherein a is the y coordinate of each node of the wind cable obtained by the last calculation and is set as A0、(xi，Δ1)、AnC, a parabola b of the three points is obtained, and the parabola b is subtracted from the parabola a to obtain a corrected y coordinate c of the wind cable;
step 9, updating the initial strain of each unit according to the formula 1, and updating the y and z coordinates of the main cable node and the z coordinate of the suspender node;
step 10, nonlinear solving to obtain the internal force of the main cable and the suspender unit, the y and z coordinates of the main cable node and the suspender node;
step 11, obtaining B1～Bn-1Node y-direction displacement delta2If Δ2>Δcon2Then returning to step 9 to continue updating the internal circulation linearity and internal force, if delta is2<Δcon2Proceed to the next step in which the tolerance value Δ is convergedcon2Generally having a value of 10-6m；
Step 12, calculating a main cable control point AiY coordinate of (a) and design value yiDeviation of (a)1If Δ1>Δcon1-2Returning to the step 8 to correct the y coordinate of the outer circulation main cable node, and if delta is obtained1<Δcon1-2Then the iteration is ended and the iteration result is output, wherein the convergence tolerance value deltacon1-2Generally having a value of 10-6m。
The above-mentioned step flow chart is shown in fig. 1, and the present invention is described in more detail below by combining specific examples:
example 1: as shown in figure 1, the coordinates of two anchoring points of the wind cable are A respectively0(-100, 0, 0) m and A15(80, 25, 20) m, boom point B1(-65, 100, 60) m and B14(65, 100, 60) m, control Point A8Has a y-coordinate of 60m, a boom spacing of 10m in the x-direction, and a boom at B1～B14The design tensile force of the point in the y direction is 45 kN. The sectional area, the elastic modulus and the linear density of the wind cable and the hanger rod are respectively 62.80cm2158Gpa, 528.78N/m and 5.22cm2165Gpa, 45.21N/m, determining the line shape and internal forces of the space cable.
The iterative algorithm of the invention is realized to calculate the calculation example by establishing a model through ANSYS parameterized language APDL. Table 1 shows the initial coordinates and the final coordinates of the wind cable node determined by the present invention. Table 2 shows the initial and calculated values of the unstressed lengths of the cable segments of the wind cable determined by the present invention. Table 3 shows B calculated according to the invention1～B14The lifting rod at the lifting point is verticalFor the convenience of comparison and verification, the calculation result of the SCM method and the calculation difference of the invention and the SCM are also given, and fig. 5 shows the displacement graph of the shape finding result of the embodiment 1 under the action of self weight, and the maximum value of the displacement is 6.8 × 10-7m, the method is high in precision and completely meets engineering requirements.
TABLE 1 wind cable alignment
Figure BDA0002491408650000071
TABLE 2 wind cable unstressed length
Figure BDA0002491408650000072
TABLE 3 boom force and unstressed Length
Figure BDA0002491408650000073
Figure BDA0002491408650000081
Example 2: as shown in FIG. 6, two anchoring points A of the wind cable0、A9Coordinates are (-100, 0, 0) m and (80, 25, 20) m, respectively, and a lifting point B1、B7Coordinates are (-65, 100, 60) m and (55, 100, 60) m, respectively, control point A5Has a y coordinate of 60m and a lifting point A1、A8The x coordinates of the suspension rods are-75 m and 65m respectively, the distance between the suspension points along the x direction is 20m, and the suspension rods are arranged at B1～B7The design tensile force of the point in the y direction is 45 kN. The sectional area, the elastic modulus and the linear density of the wind cable and the hanger rod are respectively 62.80cm2158Gpa, 528.78N/m and 5.22cm2165Gpa, 45.21N/m, trying to determine the alignment and internal forces of the spatial cable.
The iterative algorithm of the invention is realized to calculate the calculation example by establishing a model through ANSYS parameterized language APDL. Table 4 shows the initial coordinates and the final coordinates of the wind cable node determined by the present invention. Table 5 shows the results determined by the inventionInitial and calculated values of unstressed length of each cable section of the wind cable. Table 6 shows B1～B7The vertical component of the force of the boom at the suspension point and the unstressed length of the boom, fig. 7 shows the displacement diagram of the shape finding result of the present example under the action of the dead weight, and the maximum value of the displacement can be seen to be 6.0 × 10-7m。
TABLE 4 wind Cable node coordinates
Figure BDA0002491408650000082
Figure BDA0002491408650000091
TABLE 5 wind cable unstressed length
Figure BDA0002491408650000092
TABLE 6 boom force and unstressed Length
Figure BDA0002491408650000093
The parts of the present embodiment that are not described in detail are common means known in the art, and are not described here. The above-mentioned embodiments are merely illustrative, and should not be construed as limiting the scope of the invention, and any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (3)

1. A suspension bridge space cable shape finding method based on finite elements adopts finite element software ANSYS to find the shape of a space cable, and is characterized by comprising the following steps:
step 1, establishing an initial finite element model of space cable linear iterative computation through APDL, namely a main cable A0、AnPoint-fixed, boom B1～Bn-1The hoisting point only restrains the directions x and z, releases the restraint in the direction y and applies the design value F of the tensile force in the transverse bridge direction1y～F(n-1)y；
Step 2, setting initial elastic modulus of the main cable and the suspender unit;
step 3, setting the initial strain of the main cable and the suspender unit, wherein the initial strain and the initial strain of the main cable and the suspender unit are the same;
step 4, carrying out one-step nonlinear finite element solution on the initial finite element model;
step 5, calculating a main cable control point AiY coordinate of (a) and design value yiDeviation of (a)1If Δ1>Δcon1-1Returning to the step 3 to correct the initial strain value; if Δ1<Δcon1-1Outputting the internal force of the main cable and the suspender unit, the y and z coordinates of the main cable node and the z coordinate of the suspender node, and entering the next step;
step 6, updating the initial strain of each unit, updating the y and z coordinates of the main cable node and the z coordinate of the suspender node, and recovering the actual elastic modulus of the cable unit;
step 7, nonlinear solution is carried out, and the internal force of the main cable and the suspender unit, the y and z coordinates of the main cable node and the suspender node and the z coordinate of the suspender node are output;
step 8, correcting the y coordinate of the main cable node to ensure the main cable control point AiIs the design value yi；
Step 9, updating the initial strain of each unit, and updating the y and z coordinates of the main cable node and the z coordinate of the suspender node;
step 10, nonlinear solving, and outputting the internal force of the main cable and the suspender unit, the y and z coordinates of the main cable node and the suspender node;
step 11, obtaining B1～Bn-1Node y-direction displacement delta2If Δ2>Δcon2Then go back to step 9, if Δ2<Δcon2Entering the next step;
step 12, calculating a main cable control point AiY coordinate of (a) and design value yiDeviation of (a)1If Δ1>Δcon1-2Then go back to step 8, if Δ1<Δcon1-2And ending the iteration and outputting the result.
2. A suspension bridge space cable form-finding method based on finite elements according to claim 1,
and 3, reducing the elastic modulus of the cable unit by three orders of magnitude, and performing trial calculation to determine the initial iteration values of the linear shape and the internal force of the cable.
3. A suspension bridge space cable form-finding method based on finite elements according to claim 1,
step 8-step 12 adopt nested loop iterative computation, the convergence process is stable and rapid, the internal loop updates the cable alignment and the internal force, the internal force of the convergence result suspender is ensured to be a design required value, the external loop corrects the y coordinate of the main cable node, and the convergence result main cable control point A is ensurediIs the design value yi。
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CN113515822A (en) * 2021-01-28 2021-10-19 长春工业大学 Return-to-zero neural network-based stretching integral structure form finding method
CN114855592A (en) * 2022-04-24 2022-08-05 中铁大桥勘测设计院集团有限公司 Connecting device between stay cable and sling and parameter calculation method thereof
CN115081097A (en) * 2022-08-22 2022-09-20 中国建筑第六工程局有限公司 Method for finding shape of single-arch space cable combined structure

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Publication number Priority date Publication date Assignee Title
CN113515822A (en) * 2021-01-28 2021-10-19 长春工业大学 Return-to-zero neural network-based stretching integral structure form finding method
CN113515822B (en) * 2021-01-28 2022-11-29 长春工业大学 Return-to-zero neural network-based stretching integral structure form finding method
CN112711891A (en) * 2021-03-26 2021-04-27 上海建工集团股份有限公司 Construction control method for spatial cable suspension structure
CN114855592A (en) * 2022-04-24 2022-08-05 中铁大桥勘测设计院集团有限公司 Connecting device between stay cable and sling and parameter calculation method thereof
CN114855592B (en) * 2022-04-24 2023-11-21 中铁大桥勘测设计院集团有限公司 Parameter calculation method of connecting device between stay cable and sling
CN115081097A (en) * 2022-08-22 2022-09-20 中国建筑第六工程局有限公司 Method for finding shape of single-arch space cable combined structure

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