CN110110387A - A kind of Cable Structure finite element form finding analysis method - Google Patents
A kind of Cable Structure finite element form finding analysis method Download PDFInfo
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Abstract
The present invention relates to a kind of Cable Structure finite element form finding analysis methods, the following steps are included: establishing the Cable Structure finite element model of fold-line-shaped, apply load on the break of finite element model, solves initial equilibrium conditions solution of the Cable Structure under prestressing force and the load；It is taken off in the initial equilibrium conditions, continues superposition self weight and/or external loads, solve the working condition solution that Cable Structure is superimposed after the self weight and/or external loads；The load is eliminated, end-state solution is solved, determines Cable Structure form.The present invention is modeled using broken line, the modeling of Cable Structure can be made more convenient, and the initial equilibrium conditions solution under the obtained Concentrated load of the finite element model based on broken line, it can make the more efficient simplicity of solution of Cable Structure initial equilibrium conditions solution, it is transitioned into working condition solution from obtained initial balance solution is solved, is more convenient for calculating the malformation under self weight and/or external loads.
Description
Technical field
The present invention relates to Cable Structures to look for shape technical field, more particularly, to a kind of Cable Structure finite element form finding analysis side
Method.
Background technique
Rope or rope net play critically important role in Structural Engineering, such as cableway, suspended-cable structure, slant-pull structure, Suo Qiong
Roof construction, cable-truss structure etc..A kind of large deformation flexible structure of Suo Zuowei, force analysis belongs to GEOMETRICALLY NONLINEAR, not
It is that rigidity, rope shape are not geometrically unstable systems when application tension, and initial geometric shape has with prestress distribution
It closes.Therefore the most crucial problem analyzed for rope and rope net is exactly form finding analysis.Currently used form finding analysis method is effectively close
Degree method, Dynamic Relaxation and node balance method based on finite element analysis and support lift method etc..
These above-mentioned methods or there are the building of rope net archetype is complicated；Complex steps, it is computationally intensive, when calculating
Between it is long；There are numerical value convergence, the problems such as computational accuracy is insufficient；And it is required to iterative calculation repeatedly, it is unfavorable for engineering
Application.
Summary of the invention
The present invention is directed to overcome at least one defect (deficiency) of the above-mentioned prior art, a kind of Cable Structure finite element is provided and is looked for
Conformal analysis method can make the model foundation of Cable Structure more convenient, and the solution of Cable Structure initial equilibrium conditions solution is more efficient
It is easy.
The technical solution adopted by the present invention is that:
A kind of Cable Structure finite element form finding analysis method, comprising the following steps:
S1. the Cable Structure finite element model for establishing fold-line-shaped applies load on the break of finite element model, solves hitch
Initial equilibrium conditions solution of the structure under prestressing force and the load；
S2. it is taken off in the initial equilibrium conditions, continues to be superimposed self weight and/or external loads, it is described certainly to solve Cable Structure superposition
Working condition solution after weight and/or external loads；
S3. the load is eliminated, end-state solution is solved, determines Cable Structure form.
The finite element model of fold-line-shaped is established, a large amount of cable-truss is not necessarily to, so that the foundation of finite element model is simpler
Just, and rate and accuracy rate that model calculates analysis are improved.Using the suspension cable geometric modeling under load as suspension cable knot
The initial balance solution of structure, can make the solution procedure of initial balance solution more rapidly restrain, so that initial balance be more easily accomplished
The solution of state solution.It is transitioned into working condition solution from obtained initial balance solution is solved, is more convenient for calculating in self weight and/or outside
Malformation under load finally eliminates the load initially applied, and obtained end-state solution is the rope to be looked for
Structural form.
Further, in the step S2, the work for solving Cable Structure and being superimposed after the self weight and/or external loads
State solution, specifically includes: solving the working condition after Cable Structure is superimposed the self weight and/or external loads by iterative analysis
Solution.
It is transitioned into working condition by initial equilibrium conditions by iterative analysis, the iteration convergence when solving working condition solution
Speed is faster.
Further, rope length of the Cable Structure described in the Suo Changyu of the finite element model under no-load is equal.
Further, described that the Cable Structure superposition self weight and/or outside are solved by iterative analysis in the step S2
Working condition solution after load, specifically includes:
S21. initial stiffness matrix [K is formed according to initial equilibrium conditions solutionT]0, load is formed according to self weight and/or external loads
Matrix [R] solves equation [KT]0{ δ }={ R }, is displaced { δ1And internal force { F1, enable i=1；
S22. displacement { δ is generated in finite element modeliIn the case where, form stiffness matrix [KT]i；
S23. new nodal force { F (δ is calculatedi)=[KT]i{δi}；
S24. out-of-balance force { Δ P is calculatedi}={ R }-{ F (δi)}；
S25. equation [K is solvedT]i{Δδi}={ Δ Pi, obtain displacement increment { Δ δi, calculate displacement { δi+1}={ Δ δi}+
{δi}；
S26. judge whether to restrain, if i=i+1 and return step S22 are otherwise enabled, if terminating.
Further, in the step S26, judge whether to restrain, specifically include: judging whether to meet Δ δi/δ1≤ ε, ε
To set permissible value.
Further, in the step S1, the break of the finite element model is located on the node of suspension cable.
Compared with prior art, the invention has the benefit that
(1) present invention can model Cable Structure using broken line, and modeling is convenient, and it is long equal to suspension cable original only to meet broken line overall length,
Without using a large amount of cable-truss, rate and accuracy rate that model calculates analysis are improved；
(2) other methods, the initial balance under the Concentrated load obtained the present invention is based on the finite element model of broken line are compared
State solution is easy to that the incipient stability solution is calculated in finite element software, and other methods commonly look for shape such as gravity load,
Need constantly in finite element cycle calculations it is tens of it is time even more can just obtain corresponding rope shape, and the present invention need to only have
It is calculated in limit member once, is not necessarily to cycle calculations, and convergence is good, calculating speed is fast, and precision is high；
(3) apply self weight and external work load again on the basis of incipient stability solution, be also easy to count in finite element software
Calculate the working condition solution after obtaining applying self weight and external work load.
Detailed description of the invention
Fig. 1 is that the finite element model of the embodiment of the present invention establishes schematic diagram.
Fig. 2 is the example schematic diagram of the embodiment of the present invention.
Fig. 3 is another example schematic diagram of the embodiment of the present invention
Specific embodiment
Attached drawing of the present invention only for illustration, is not considered as limiting the invention.It is following in order to more preferably illustrate
Embodiment, the certain components of attached drawing have omission, zoom in or out, and do not represent the size of actual product；For art technology
For personnel, the omitting of some known structures and their instructions in the attached drawings are understandable.
Embodiment
The present embodiment provides a kind of Cable Structure finite element form finding analysis methods, comprising the following steps:
S1. the Cable Structure finite element model for establishing fold-line-shaped, applies several loads on the break of finite element model, asks
Solve initial equilibrium conditions solution of the Cable Structure under prestressing force and the load；
S2. it is taken off in the initial equilibrium conditions, continues to be superimposed self weight and/or external loads, it is described certainly to solve Cable Structure superposition
Working condition solution after weight and/or external loads；
S3. the load is eliminated, end-state solution is solved, determines Cable Structure form.
The finite element model of fold-line-shaped is established, a large amount of cable-truss is not necessarily to, so that the foundation of finite element model is simpler
Just, and rate and accuracy rate that model calculates analysis are improved.It can be taken under the equally distributed self weight of span length under normal circumstances
Initial balance solution of the suspension cable geometric modeling as suspended-cable structure, and the present embodiment is made using the suspension cable geometric modeling under load
For the initial balance solution of suspended-cable structure, the solution procedure of initial balance solution can be made more rapidly to restrain, to be more easily accomplished
The solution of initial equilibrium conditions solution.It is transitioned into working condition solution from obtained initial balance solution is solved, is more convenient for calculating and be self-possessed
And/or the malformation under external loads, finally the load initially applied is eliminated, obtained end-state solution is institute
The Cable Structure form to be looked for.
Method provided by the present embodiment has adaptivity, without meeting Suo Li and loading the requirement of dynamic balance.
In specific implementation process, the break of finite element model can be located at any position on Cable Structure suspension cable, and can
Think multiple.It can first determine the load position to be applied, according to deformation of the anticipation suspension cable after by load, really
Determine the position of break.
Preferably, the break is one, and load is one, can so be reduced in finite element model analysis
Constraint condition improves convergence efficiency.
Preferably, the value of the opposite self weight of the value of the load and/or external loads is smaller.Load takes
Value is smaller relative to the value of self weight and/or external loads, and the iterative convergence speed for solving initial equilibrium conditions solution can be faster.
In the present embodiment, in the step S2, after the solution Cable Structure is superimposed the self weight and/or external loads
Working condition solution, specifically includes: solving the work shape after Cable Structure is superimposed the self weight and/or external loads by iterative analysis
State solution.
It is transitioned into working condition by initial equilibrium conditions by iterative analysis, the iteration convergence when solving working condition solution
Speed is faster.
In the present embodiment, rope length of the Cable Structure described in the Suo Changyu of the finite element model under no-load is equal.
Increase constraint condition when the fold-line-shaped finite element model of foundation --- Cable Structure described in the Suo Changyu of finite element model
Rope length under no-load is equal, finite element model can be made more to meet reality.
As shown in Figure 1, endpoint O, B are the position of known support, break A is any position on suspension cable, according to endpoint
O, the position of B and the position of break A can establish out the Cable Structure finite element model of fold-line-shaped.The length of broken line OAB and outstanding
Rope length of the rope under unstress state is equal.After applying load F on break A, in prestressing force and load F
The lower initial equilibrium conditions solution for solving Cable Structure.In order to facilitate the foundation and analytical calculation of finite element model, coordinate system can be with
Choose OX ' Y '.
In the present embodiment, in the step S2, superposition self weight and/or the external loads on finite element model are gone forward side by side
Working condition solution described in row iteration analysis and solution, specifically includes:
S21. initial stiffness matrix [K is formed according to initial equilibrium conditions solutionT]0, load is formed according to self weight and/or external loads
Matrix [R] solves equation [KT]0{ δ }={ R }, is displaced { δ1And internal force { F1, enable i=1；
S22. displacement { δ is generated in finite element modeliIn the case where, form stiffness matrix [KT]i；
S23. new nodal force { F (δ is calculatedi)=[KT]i{δi}；
S24. out-of-balance force { Δ P is calculatedi}={ R }-{ F (δi)}；
S25. equation [K is solvedT]i{Δδi}={ Δ Pi, obtain displacement increment { Δ δi, calculate displacement { δi+1}={ Δ δi}+
{δi}
S26. judge whether to restrain, if i=i+1 and return step S22 are otherwise enabled, if terminating.
In the present embodiment, in the step S26, judge whether to restrain, specifically include: judging whether to meet Δ δi/δ1≤
ε, ε are setting permissible value.
Self weight and/or external loads are disposably added in Cable Structure, are displaced according to initial stiffness matrix calculate node, so
Bitter end power is acquired according to the deformed Structure Calculation rigidity of structure afterwards.Since deformation front-end geometry rigidity is different, node is generated not
Equilibrium load is applied on node using these unbalanced load loads as joint load, calculates to meet node balance
Relative to deformed modal displacement amount, this iterative process, sets permissible value until unbalanced load is less than repeatedly.
In the present embodiment, in the step S1, the break of the finite element model be can choose on the node of suspension cable.
It is illustrated in figure 2 the fixed Cable Structure in both ends for bearing multiple loads (unit: kN), suspension cable cross section face
Product A=5.48 × 10-4m2, elastic modulus E=1.54 × 10 of suspension cable material5MPa, the self weight of suspension cable are 47.03N/m, suspension cable
The long S of original under unstress state0=312.85m, the sag of the Cable Structure original state are fc=35.25m.
In document " Cable Structure static analysis method and Research on Accuracy " (highway and automotive, 2008 (3): 148-152), adopt
Form finding analysis is carried out to Cable Structure as shown in Figure 2 with segmental correlation rope method, the Y-direction coordinate value of each node is calculated,
Its calculated result counts in table 1.
Form finding analysis is carried out to Cable Structure as shown in Figure 2 using method provided by the present embodiment, is equally calculated
The Y-direction coordinate value of each node, calculated result also count in table 1.
The Y-direction coordinate value (unit: m) of each node of 1 Cable Structure of table
| Node serial number | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| The stretched wire clue method of document 2 | -9.615 | -18.538 | -26.848 | -34.612 | -30.145 | -25.211 | -19.779 | -13.805 | -7.235 |
| The method that embodiment provides | -9.441 | -18.427 | -26.961 | -35.045 | -30.399 | -25.275 | -19.675 | -13.598 | -7.042 |
| Error/% | 1.8 | 0.6 | 0.4 | 1.3 | 0.8 | 0.3 | 0.5 | 1.5 | 2.6 |
As shown in table 1, the calculated result difference of two methods is smaller, shows method calculated result provided by the present embodiment
It is substantially accurately.
It is illustrated in figure 3 an Orthogonal Cable-Net Structures, cross-sectional area A=1.4645 × 10 of each rope section-4m2, suspension cable material
Elastic modulus E=8.2737 × 10 of material4MPa, the former a length of 30.419m of the rope section of number 3,4,8,11, number 1,2,5,
6, the former a length of 31.76m of 7,9,10,12 rope section.4., 5., 8., 9. node above acts on the vertical load of 35.56kN, gravity load
Q=1.46 × 10-3kN/m。
In " the Shape finding of incomplete cable-strut assemblies containing of document 2
slack and prestressed elements》(Computers&Structures,2005,83(21-22):1767-
1779) in, form finding analysis is carried out to cable net structure as shown in Figure 3 using the method for document 2, it is 5 that node serial number, which is calculated,
Nodes X, Y, Z-direction coordinate value, calculated result count in table 2.
At document 3 " A curved element for the analysis of cable structures "
In (Computers&Structures, 1981,14 (3): 325-333), using the method for document 3 to rope net as shown in Figure 3
Structure carries out form finding analysis, and nodes X, Y, Z-direction coordinate value that node serial number is 5 is calculated, and calculated result is also counted in table 2
In.
At document 4 " Discretized initial-value analysis of cable nets "
In (International Journal of Solids&Structures, 1973,9 (11): 1403-1420), using document 4
Method form finding analysis is carried out to cable net structure as shown in Figure 3, nodes X, Y, Z-direction coordinate that node serial number is 5 is calculated
Value, calculated result also count in table 2.
X, Y, the Z-direction coordinate value (unit: m) of 2 cable net structure node 5 of table
| Direction | X | Y | Z |
| The method of document 2 | 15.2805 | 15.2805 | -9.5945 |
| The method of document 3 | 15.2802 | 15.2802 | -9.5922 |
| The method of document 4 | 15.2804 | 15.2804 | -9.5920 |
| Method provided in this embodiment | 15.28039 | 15.28039 | -9.59287 |
As shown in table 2, the calculated result difference of four kinds of methods is smaller, further demonstrates that method meter provided by the present embodiment
It calculates the result is that substantially accurately.
The present embodiment optimizes the calculation method of initial equilibrium conditions solution on the basis of satisfaction looks for shape accuracy rate, improves
The computational efficiencies of initial equilibrium conditions solutions, and the finite element model of Cable Structure is made to establish easier, finite element model
The unit of middle use is more brief, is conducive to further calculate the malformation under self weight and/or external loads.
Obviously, the above embodiment of the present invention is only intended to clearly illustrate technical solution of the present invention example, and
It is not the restriction to a specific embodiment of the invention.It is all made within the spirit and principle of claims of the present invention
Any modifications, equivalent replacements, and improvements etc., should all be included in the scope of protection of the claims of the present invention.
Claims (6)
1. a kind of Cable Structure finite element form finding analysis method, which comprises the following steps:
S1. the Cable Structure finite element model for establishing fold-line-shaped applies load on the break of finite element model, solves hitch
Initial equilibrium conditions solution of the structure under prestressing force and the load；
S2. it is taken off in the initial equilibrium conditions, continues to be superimposed self weight and/or external loads, it is described certainly to solve Cable Structure superposition
Working condition solution after weight and/or external loads；
S3. the load is eliminated, end-state solution is solved, determines Cable Structure form.
2. a kind of Cable Structure finite element form finding analysis method according to claim 1, which is characterized in that the step S2
In, the working condition solution for solving Cable Structure and being superimposed after the self weight and/or external loads specifically includes: by iteration point
Analysis solves the working condition solution that Cable Structure is superimposed after the self weight and/or external loads.
3. a kind of Cable Structure finite element form finding analysis method according to claim 2, which is characterized in that the finite element mould
Rope length of the Cable Structure described in the Suo Changyu of type under no-load is equal.
4. a kind of Cable Structure finite element form finding analysis method according to claim 2 or 3, which is characterized in that the step
It is described that working condition solution after Cable Structure is superimposed the self weight and/or external loads is solved by iterative analysis in S2, it is specific to wrap
It includes:
S21. initial stiffness matrix [K is formed according to initial equilibrium conditions solutionT]0, load is formed according to self weight and/or external loads
Matrix [R] solves equation [KT]0{ δ }={ R }, is displaced { δ1And internal force { F1, enable i=1；
S22. displacement { δ is generated in finite element modeliIn the case where, form stiffness matrix [KT]i；
S23. new nodal force { F (δ is calculatedi)=[KT]i{δi}；
S24. out-of-balance force { Δ P is calculatedi}={ R }-{ F (δi)}；
S25. equation [K is solvedT]i{Δδi}={ Δ Pi, obtain displacement increment { Δ δi, calculate displacement { δi+1}={ Δ δi}+
{δi}
S26. judge whether to restrain, if i=i+1 and return step S22 are otherwise enabled, if terminating.
5. a kind of Cable Structure finite element form finding analysis method according to claim 4, which is characterized in that the step S26
In, judge whether to restrain, specifically include: judging whether to meet Δ δi/δ1≤ ε, ε are setting permissible value.
6. a kind of Cable Structure finite element form finding analysis method according to claim 1, which is characterized in that the step S1
In, the break of the finite element model is located on the node of suspension cable.
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| CN111062072A (en) * | 2019-12-09 | 2020-04-24 | 桂林理工大学 | Cable membrane structure form finding design method based on particle swarm optimization algorithm |
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