CN105243185B - A kind of tension integral structure based on Monte Carlo method looks for shape method - Google Patents
A kind of tension integral structure based on Monte Carlo method looks for shape method Download PDFInfo
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Abstract
A kind of tension integral structure based on Monte Carlo method looks for shape method, belongs to tension integral structure statics Analysis field.For the problem that lacking corresponding program, calculating speed is relatively low and lacks for the definition of basic conception and the processing method of special circumstances, and the present invention takes following method：Step 1: setting primary condition；Step 2: initial configuration is generated at random；Step 3: new configuration is generated at random and judges whether to receive；Step 4: whether check system balances；Step 5: it obtains looking for shape result.The present invention solves the special circumstances looked in shape calculating and technical problem of tension integral structure, so as to accelerate the speed that shape is looked for calculate；Monte Carlo method is realized using MATLAB programmings, shape calculating process is looked for tension integral structure, can quick and precisely obtain its self-balancing configuration, significant effect.
Description
Technical field
The invention belongs to tension integral structure statics Analysis fields, and be related to a kind of tension integral structure looks for shape method.
Background technology
The seif-citing rate cable net structure that tension integral structure is made of continuous stay cable and individual stamp, concept earliest by
Fuller is proposed, due to having graceful shape, and is taken full advantage of the characteristic of material, can mitigate weight and is saved material,
Get the attention and rapidly develop in recent years, and civil engineering, aircraft deployable mechanism, biological cell engineering and
Many fields such as materialogy, which achieve, to be widely applied.
After the topological structure and element length of tension integral structure are designated, it is thus necessary to determine that its self-balancing knot
Structure is known as looking for shape.Can shape be looked for be related to structure work normally, particularly significant for the research of tension integral structure.Research
Persons look for shape method to carry out a large amount of research to tension integral structure, whole for the simple tensioning with high symmetry
Structure can carry out looking for shape using analytic method.However for more generally structure, need to use numerical method.Force density method,
Dynamic Relaxation, evolution algorithm, genetic algorithm etc. are seen in report.Nevertheless, still lack it is more flexible, more powerful, can
To be used for irregularly and in the form of asymmetric tension integral structure carrying out the method for looking for shape to large-size or geometry.For
This, researchers propose looks for shape by Monte Carlo method introducing tension integral structure.
But there is no the methods realized using specific procedure to it for these researchs, and therefore, it is difficult in the practical calculating of engineering
In be applied and and guide the solution of technical problem.Meanwhile method still has relatively low calculating speed, while lacks some bases
The definition of this concept and the processing method to special circumstances in calculating process.
Invention content
For lacking corresponding program, calculating speed is relatively low and lacks definition for basic conception and special circumstances
The problem of processing method, the present invention proposes a kind of tension integral structure based on Monte Carlo method and looks for shape method, whole to tensioning
Body structure carries out that shape is looked for calculate, so as to obtain self-balance structure in engineering.
The purpose of the present invention is what is be achieved through the following technical solutions：
A kind of tension integral structure based on Monte Carlo method looks for shape method, includes the following steps：
Step 1: setting primary condition：
The geometric configuration of tension integral structure and material properties are set in a program, the rigidity of unit is counted
It calculates, while proposes the concept of connection matrix and the unit order of connection is provided；
Step 2: initial configuration is generated at random：
Initial configuration is generated at random using program, obtains the coordinate vector matrix of each unit, then calculate the energy of configuration, and
Set node random file radius；
Step 3: new configuration is generated at random and judges whether to receive：
First node or the last one node are fixed, shape result is looked for so as to improve efficiency and not influence.Random choosing again
A fixed node, using selected node as the centre of sphere, r is the new position for setting the node in the ball of radius at random, new so as to generate
Configuration.Drag-line is constantly judged whether there is in the process relaxation occur and deal with to it, is carried out if without cable slack new
The calculating of configuration energy retightens node if having cable slack and carries out next round calculating.
The energy of new configuration is calculated, receives new configuration if less than the energy of previous step configuration, and original is replaced with new configuration
Come configuration, if more than previous step energy then without replace, carry out next round calculating.
When iterations have reached 100 integral multiple, then the ratio for receiving new configuration in this 100 step is calculated, if ratio
It is relatively low, then reduce radius.
Step 4: whether check system balances：
Whether the balance of system balance to judge by node, if meet each unit internal force be 0 if system balancing.It is real
More iterations are just needed since error is wanted to reach complete equipilibrium on border, and with the increase modal displacement of iterations
Radius is gradually reduced, and more iterations are just without too big practical significance.Therefore can the limits of error be set according to error, if
Determine approximate equilibrium condition.
Step 5: it obtains looking for shape result：
Output looks for shape as a result, i.e. each node coordinate, and draws tension integral structure self-balancing configuration according to coordinate.
The present invention has the following advantages：
1st, the special circumstances looked in shape calculating and technical problem of tension integral structure are solved, so as to accelerate
The speed that shape is looked for calculate；
2nd, it realizes Monte Carlo method using MATLAB programmings and shape calculating process is looked for tension integral structure, it can be quick
Accurately obtain its self-balancing configuration, significant effect.
Description of the drawings
Fig. 1 is the flow chart that Monte Carlo method looks for shape to calculate；
Fig. 2 is that T prisms look for shape calculating process energy curves figure；
Fig. 3 is that T prisms look for the initial configuration generated in shape calculating process；
Fig. 4 is that T prisms look for the configuration obtained after the calculating of 10000 steps in shape calculating process；
Fig. 5 is that T prisms look for the configuration obtained after the calculating of 30000 steps in shape calculating process；
Fig. 6 is the final configuration for meeting the setting of approximate equilibrium condition that T prisms look for that shape is calculated.
Specific embodiment
Technical scheme of the present invention is further described below in conjunction with the accompanying drawings, however, it is not limited to this, every to this
Inventive technique scheme is modified or replaced equivalently, and without departing from the spirit and scope of technical solution of the present invention, should all be covered
In protection scope of the present invention.
Specific embodiment one：Present embodiments provide for a kind of tension integral structures based on Monte Carlo method to look for shape side
The parameter definition and setting method of method, as shown in Figure 1, specifically comprising the following steps：
Step 1: setting primary condition, can be divided into the following steps progress：
1.1st, note unit sum is m, and number of nodes n, compression bar number is eb, drag-line number is es, wherein eb+es=m.
1.2nd, material properties：Needing sectional area A of the material properties set including unit, (compression bar and drag-line are denoted as respectively
Ab、As) and unit elastic modulus E (Eb、Es, the material all same of general homogeneous unit) and unit the long L of originalo(Lob、Los,
The long matrix L of original of row input cell is distinguished if the length difference of each unito)。
1.3rd, the rigidity S of computing unit：The rigidity of k-th of unit is according to formula Sk=Ek·Ak/LokIt calculates.
1.4th, the connection matrix C of unit：Can be according to from down to up for beginning and end, mode counterclockwise provides list
The order of connection of member, starting point 1, terminal are -1.
Step 2: generating initial configuration at random, the following steps progress can be divided into：
2.1st, initial configuration P is generated at random：P is the coordinates matrix of a node, and dimension is n × 3, then the coordinate of each unit
Vector matrix g is g=Cp.
2.2nd, the ENERGY E of configuration is calculated：Gross energy is according to formulaIt calculates, wherein, Sk, lk, lokRespectively
K-th of element stiffness is represented, length and original are grown.
2.3rd, setting node random file radius r：It is chosen to be the half of longest unit in structure.
Step 3: generating new configuration at random and judging whether to receive, the following steps progress can be divided into：
3.1st, a node (such as first node or the last one node) is fixed to improve computational efficiency and not influence to look for
Shape result.
3.2nd, a certain node is selected at random, and using selected node as the centre of sphere, r is to set the node at random in the ball of radius
New position, so as to generate new configuration P '.
3.3rd, it judges whether there is drag-line to relax, step 3.1 is repeated if having, if carrying out 3.4 without cable slack.
3.4th, the ENERGY E of new configuration P ' is calculated ', receive new configuration if E ' ＜ E, and original configuration is replaced with new configuration
That is P=P ', E=E '；Without replacing if E ' >=E, and repeat step 3.1.
If the 3.5, iterations have reached 100 integral multiple, the ratio for receiving new configuration in this 100 step is calculated, if than
Example then reduces radius and enables r=0.95r less than 50%, if ratio is not less than 50%, radius is constant.
Step 4: whether check system balances.
Whether the balance of system balance to judge by node, and the internal force of each unit is fk=Sk(lk-lok), then force density
qkForIf meetThen system balancing.Equilibrium equation can be rewritten as according to connection matrix C by CTdiag
(q) CP=0.
The suitable limits of error ε of one smaller and numerical value is set according to scantling and property in the range of 10~100N to obtain
Approximate equilibrium condition, can be by limiting the maximum value F of out-of-balance force matrix in result of calculation on the left of equilibrium equation equationmaxCome
Judge whether system balances, if Fmax＜ ε then carry out step 5, if Fmax＞ ε then carry out step 3.
Step 5: it obtains looking for shape result.
Each node coordinate is exported, tension integral structure self-balancing configuration is drawn according to coordinate, obtains final self-balancing structure
Type, and obtain the situation of change of other process variables in calculating process.
Specific embodiment two：Present embodiments provide for a kind of T prism tension integral structures based on Monte Carlo method
The MATLAB of shape method is looked for program to realize, is included the following steps：
Step 1: setting primary condition, can be divided into the following steps progress：
1.1st, T prisms geometric parameter is set, and only provides unit number parameter setting sentence.
M=12.
1.2nd, material properties：The material properties of compression bar and drag-line are set respectively, only provide the material properties of compression bar
Setting program section.
Ab=200；
Eb=2.06e+5；
Lob=2.7806e+3.
1.3rd, the rigidity S of computing unit only provides compression bar element stiffness component (matrix the first row).
Sb=Eb*Ab/Lob；The element stiffness of % compression bars
Sr1=[Sb；Sb；Sb]；% compression bar stiffness matrix
1.4th, the connection matrix C (m rows n row) of unit, preceding eb=3 behaviors compression bar, rear es=9 behaviors drag-line (only provide
A line compression bar L1 connection matrix)：
Cr1=[1,0,0,0,0, -1]；% compression bar L1, node 1 are that starting point 6 is terminal
Step 2: generating initial configuration at random, the following steps progress can be divided into：
2.1st, initial configuration P is generated at random.
P=randi ([- 2000,2000], n, 3)；% [imin, imax] uniform random number group
G=C*P：
2.2nd, the ENERGY E of configuration is calculated.
E=1/2*sum (S.* (L '-Lo) .^2)；The gross energy of % system initial configurations
2.3rd, setting node random file radius r.
R=max (L)/2；% is set as the half of longest unit
Step 3: generating new configuration at random and judging whether to receive, the following steps progress can be divided into：
3.1st, a node is fixed.
J=randi ([1, n-1])；% selectes node 1~(n-1) at random, and node n is fixed
3.2nd, a certain node is selected at random, and using selected node as the centre of sphere, r is to set the node at random in the ball of radius
New position so as to generate new configuration T, only provides the sentence of setting X-coordinate.
T (j, 1)=2*r* (rand (1,1) -0.5)+P (j, 1)；% sets X-coordinate at random
3.3rd, drag-line is judged whether there is to relax.
if min(L(eb+1：m)′-Lo(eb+1：M)) ＜ 0
3.4th, the ENERGY E of new configuration P ' is calculated ', and decide whether to receive new configuration, provide the program segment for receiving new configuration.
W=1/2*sum (S.* (L '-Lo) .^2)；
If W ＜ E
E=W；
P=T；
3.5th, the ratio for receiving new configuration in 100 steps is calculated, judges whether to change radius according to ratio is received, only provides and connect
It is less than 50% program segment by ratio.
If k/100 ＜ 0.5
R=0.95*r；
end
Step 4: whether check system balances.
Step 5: it obtains looking for shape as a result, and drawing configuration with line orders.
Specific embodiment three：It is whole to give the tensioning based on Monte Carlo method using T prisms as example for present embodiment
Structure looks for the process of shape calculating and as a result, including the following steps：
Step 1: setting primary condition.
T prisms geometric parameter is set：Unit number is m=12, eb=3 compression bars, es=9 drag-lines, number of nodes n=6.It draws
The material properties of bar and compression bar are set.
Step 2: initial configuration is generated at random.
Random generation initial configuration P, as shown in figure 3, and calculating the ENERGY E of configuration.It is calculated in the iterative calculation of every step
The energy of acquired configuration is to understand its variation tendency, such as Fig. 2.
Step 3: new configuration is generated at random and judges whether to receive.
Calculate the ENERGY E of new configuration P ' ', and decide whether to receive new configuration.T prisms, which are looked in shape calculating process, to be passed through
The configuration that 10000 steps and 30000 steps obtain after calculating is as illustrated in figures 4-5.The ratio for receiving new configuration in every 100 step is calculated, is sentenced
It is disconnected whether to change radius.
Step 4: whether check system balances.
Step 5: it obtains looking for shape result.T prisms look for the final configuration for meeting the setting of approximate equilibrium condition that shape is calculated
As shown in Figure 6.
Claims (1)
1. a kind of tension integral structure based on Monte Carlo method looks for shape method, it is characterised in that the method step is as follows：
Step 1: setting primary condition：
(1) note unit sum is m, and number of nodes n, compression bar number is eb, drag-line number is es, wherein eb+es=m；
(2) material properties：The long L of original of the sectional area A of unit, the elastic modulus E of unit and unito；
(3) the rigidity S of computing unit；
(4) the connection matrix C of unit：For beginning and end according to from down to up, mode counterclockwise provides the connection of unit
Sequentially, starting point 1, terminal are -1；
Step 2: initial configuration is generated at random：
(1) initial configuration P is generated at random：P is the coordinates matrix of each node, and dimension is the coordinate vector square of n × 3, then each unit
Battle array g be：G=Cp；
(2) ENERGY E of configuration is calculated；
(3) setting node random file radius r；
Step 3: new configuration is generated at random and judges whether to receive：
(1) node is fixed；
(2) a certain node is selected at random, and using selected node as the centre of sphere, the node random file r set in step 2 is radius
Ball in set the new position of the node at random, so as to generate new configuration P '；
(3) it judges whether there is drag-line to relax, step 3 (1) is repeated if having, if carrying out step 3 without cable slack
(4)；
(4) ENERGY E of new configuration P ' is calculated ', if E '<E then receives new configuration, and original configuration, that is, P=is replaced with new configuration
P ', E=E '；Without replacing if E ' >=E, and repeat step 3 (1)；
(5) if iterations have reached 100 integral multiple, the ratio for receiving new configuration in this 100 step is calculated, if ratio is less than
50%, then it reduces radius and enables r=0.95r, if ratio is not less than 50%, radius is constant；
Step 4: whether check system balances：
Whether the balance of system balance to judge by node, and the internal force of each unit is fk=Sk(lk-lok), wherein, Sk,lk,lok
It represents k-th of element stiffness, length and original respectively to grow, then force density qkForIf meetThen system is put down
Equilibrium equation, C is rewritten as according to connection matrix C by weighing apparatusTDiag (q) CP=0；
One limits of error ε of setting obtains approximate equilibrium condition, uneven in the result of calculation of equilibrium equation equation left side by limiting
The maximum value F of torque battle arraymaxJudge whether system balances, if Fmax＜ ε then carry out step 5, if Fmax＞ ε then carry out step
Three；
Step 5: it obtains looking for shape result：
Each node coordinate is exported, tension integral structure self-balancing configuration is drawn according to coordinate, obtains final self-balancing configuration, and
Obtain the situation of change of other process variables in calculating process；
During the rigidity S of the computing unit, the rigidity of k-th of unit is according to formula Sk=Ek·Ak/lokIt calculates；
The ENERGY E is according to formulaIt calculates；
The displacement radius r is the half of longest unit in structure；
The limits of error ε is in the range of 10~100N.
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| CN106354906B (en) * | 2016-08-19 | 2019-08-02 | 西安电子科技大学 | A kind of netted deployable antenna based on triangle surface error looks for shape method |
| CN106934155B (en) * | 2017-03-13 | 2020-04-17 | 北京市建筑设计研究院有限公司 | Shape-finding method of cable truss structure |
| CN107194080B (en) * | 2017-05-25 | 2024-04-05 | 同济大学建筑设计研究院(集团)有限公司 | Structure determining method of spoke type tensioning system |
| CN108345729B (en) * | 2018-01-26 | 2021-07-27 | 东南大学 | Symmetrical cable-strut structure shape finding method based on group theory |
| CN108229054B (en) * | 2018-01-26 | 2021-07-27 | 东南大学 | Symmetrical tensioning integral structure shape finding method based on group theory |
| CN110792173B (en) * | 2019-10-28 | 2020-12-01 | 中冶建筑研究总院有限公司 | Tensioning integral triangular prism structure and shape finding method |
| US11413553B1 (en) | 2021-02-08 | 2022-08-16 | Marcio Sequeira De Oliveira | Structural parts kit for formation of architectural and structural didactic models |
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Inventor after: Zheng Zhiwei Inventor after: He Jingfeng Inventor after: Zhao Jianying Inventor after: Wang Yang Inventor before: Zheng Zhiwei Inventor before: Zhao Jianying Inventor before: Wang Yang |
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