CN105243185A - Monte Carlo method based tensegrity structure form-finding method - Google Patents
Monte Carlo method based tensegrity structure form-finding method Download PDFInfo
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Abstract
The present invention provides a Monte Carlo method based tensegrity structure form-finding method, and belongs to the field of tensegrity structure statics analysis. Aiming at the problems of lack of corresponding programs, a relatively low calculation speed, and lack of definitions for basic concepts and a processing method for particular cases, the steps adopted by the method of the present invention are as follows: step 1. setting an initial condition; step 2. randomly generating an initial configuration; step 3. randomly generating a new configuration and determining whether to accept the new configuration; step 4. checking whether a system is balanced; and step 5. obtaining a form-finding result. According to the Monte Carlo method based tensegrity structure form-finding method provided by the present invention, the particular case and technical problem in form-finding calculation of a tensegrity structure are solved, so that a speed of form-finding calculation is quickened; and a form-finding calculation process of the tensegrity structure by a Monte Carlo method is implemented by using MATLAB programming, so that a self-balanced configuration can be obtained rapidly and accurately, and the effects are significant.
Description
Technical field
The invention belongs to tension integral structure statics Analysis field, what relate 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 up of continuous stay cable and individual stamp, its concept is proposed by Fuller the earliest, owing to having graceful profile, and take full advantage of properties of materials, can weight reduction save material, to get the attention in recent years and developing rapidly, and achieving in many fields such as civil engineering work, aircraft deployable mechanism, biological cell engineering and materialogies and apply widely.
After the topological structure of a tension integral structure and element length are designated, need to determine its self-balance structure, be namely called and look for shape.Can shape be looked for be related to structure normally work, the research for tension integral structure be very important.Researchers, to the large quantifier elimination of having looked for shape method to carry out of tension integral structure, can use analytical method to carry out looking for shape for the simple tension integral structure with high symmetry.But for structure more generally, need to use numerical method.Force density method, Dynamic Relaxation, evolution algorithm, genetic algorithm etc. are all seen in report.However, still to lack more flexibly, more powerful, can be used for large-size or geometry is irregular and asymmetric tension integral structure form looks for the method for shape.For this reason, researchers propose Monte Carlo method introduced tension integral structure look for shape.
But these study the method not utilizing specific procedure to realize it, and being therefore difficult to is applied in engineering actual computation and guides the solution of technical matters.Meanwhile, method still has lower computing velocity, lacks the definition of basic concepts and the disposal route to special circumstances in computation process simultaneously.
Summary of the invention
For lacking corresponding program, lower and the problem lacked for the definition of key concept and the disposal route of special circumstances of computing velocity, the present invention proposes a kind of tension integral structure based on Monte Carlo method and look for shape method, look for shape to calculate to tension integral structure, thus obtain self-balance structure in engineering.
The object of the invention is to be achieved through the following technical solutions:
Tension integral structure based on Monte Carlo method looks for a shape method, comprises the steps:
Step one, setting starting condition:
In a program the geometric configuration of tension integral structure and material properties are set, the rigidity of unit is calculated, proposes the concept of connection matrix simultaneously and the unit order of connection is specified;
Step 2, stochastic generation initial configuration:
Utilize program stochastic generation initial configuration, obtain the coordinate vector matrix of each unit, then calculate the energy of configuration, and set node random file radius;
The new configuration of step 3, stochastic generation also judges whether to accept:
First node or last node are fixed, thus raises the efficiency and do not affect and look for shape result.Select a node at random again, with selected node for the centre of sphere, r is the reposition of interior random this node of setting of the ball of radius, thus generates new configuration.Constantly judge whether that drag-line occurs lax and deals with to it in the process, if without cable slack, carried out the calculating of new configuration energy, if there is cable slack, retightens node and carry out next round calculating.
Calculate the energy of new configuration, if be less than the energy of previous step configuration, accept new configuration, and replace original configuration with new configuration, if be greater than the energy of previous step, do not replace, carry out next round calculating.
When iterations reaches the integral multiple of 100, then calculate the ratio accepting new configuration in this 100 step, if ratio is lower, then reduced radius.
Whether step 4, check system balance:
Whether the balance of system is balanced by node and judges, if the internal force meeting each unit is 0, and system balancing.In fact want to reach complete equipilibrium due to error and just need more iterations, and reduce gradually along with the increase nodal displacement radius of iterations, more iterations does not just have too large practical significance.Therefore can limit according to error specification error, setting approximate equilibrium condition.
Step 5, obtain looking for shape result:
Shape result is looked in output, i.e. each node coordinate, and draws tension integral structure self-equilibrating configuration according to coordinate.
The present invention has the following advantages:
1, the look for special circumstances in shape calculating and technical matters for tension integral structure solve, thus accelerate the speed of looking for shape to calculate;
2, utilize MATLAB programming realization Monte Carlo method to look for shape computation process to tension integral structure, quick and precisely can obtain its self-equilibrating configuration, Be very effective.
Accompanying drawing explanation
Fig. 1 is the process flow diagram that Monte Carlo method looks for shape to calculate;
Fig. 2 is that shape computation process energy curves figure looked for by T prism;
Fig. 3 is that the initial configuration generated in shape computation process looked for by T prism;
Fig. 4 is that the configuration obtained after 10000 steps calculate in shape computation process looked for by T prism;
Fig. 5 is that the configuration obtained after 30000 steps calculate in shape computation process looked for by T prism;
Fig. 6 is the final configuration meeting the setting of approximate equilibrium condition that T prism looks for shape to calculate.
Embodiment
Below in conjunction with accompanying drawing, technical scheme of the present invention is further described; but be not limited thereto; everyly technical solution of the present invention modified or equivalent to replace, and not departing from the spirit and scope of technical solution of the present invention, all should be encompassed in protection scope of the present invention.
Embodiment one: present embodiments provide for parameter definition and establishing method that a kind of tension integral structure based on Monte Carlo method looks for shape method, as shown in Figure 1, specifically comprise the steps:
Step one, setting starting condition, can be divided into the following steps to carry out:
1.1, remember that unit adds up to m, nodes is n, and depression bar number is e
b, drag-line number is e
s, wherein e
b+ e
s=m.
1.2, material properties: (depression bar and drag-line are designated as A respectively to need the material properties of setting to comprise the sectional area A of unit
b, A
s) and the elastic modulus E (E of unit
b, E
s, the material of general homogeneous unit is all identical) and the former long L of unit
o(L
ob, L
osif the length of unit is different, respectively the former long matrix L of row input cell
o).
1.3, the rigidity S of computing unit: the rigidity of a kth unit is according to formula S
k=E
ka
k/ L
okcalculate.
1.4, the connection matrix C of unit: can according to from down to up for starting point and terminal, counterclockwise mode specifies the order of connection of unit, and starting point is 1, and terminal is-1.
Step 2, stochastic generation initial configuration, can be divided into the following steps to carry out:
2.1, stochastic generation initial configuration P:p is the coordinates matrix of a node, and dimension is n × 3, and the coordinate vector matrix g of so each unit is g=Cp.
2.2, the ENERGY E of configuration is calculated: gross energy is according to formula
calculate, wherein, S
k, l
k, l
okrepresent a kth element stiffness respectively, length and former length.
2.3, node random file radius r is set: the half being chosen to be the longest unit in structure.
The new configuration of step 3, stochastic generation also judges whether to accept, and the following steps can be divided into carry out:
3.1, fix a node (as first node or last node) and look for shape result to improve counting yield and not affect.
3.2, random selected a certain node, with selected node for the centre of sphere, r is the reposition of interior random this node of setting of the ball of radius, thus generates new configuration P '.
3.3, judged whether that drag-line occurs lax, if having, repeated step 3.1, if without cable slack, carry out 3.4.
3.4, the ENERGY E of new configuration P ' is calculated ', if E ' < E, accept new configuration, and replace original configuration and P=P ', E=E with new configuration '; If E ' >=E, does not replace, and repeat step 3.1.
If 3.5 iterationses reach the integral multiple of 100, then calculate the ratio accepting new configuration in this 100 step, if ratio is lower than 50%, then reduced radius makes r=0.95r, if ratio is not less than 50%, then radius is constant.
Whether step 4, check system balance.
Whether the balance of system is balanced by node and judges, the internal force of each unit is f
k=S
k(l
k-l
ok), then force density q
kfor
if meet
then system balancing.Balance equation can be rewritten as C according to connection matrix C
tdiag (q) CP=0.
Within the scope of 10 ~ 100N, set that one is less according to scantling and character and numerical value is suitable limits of error ε obtains approximate equilibrium condition, can by limiting the maximal value F of out-of-balance force matrix in result of calculation on the left of balance equation equation
maxjudge whether system balances, if F
max< ε then carries out step 5, if F
max> ε then carries out step 3.
Step 5, obtain looking for shape result.
Export each node coordinate, draw tension integral structure self-equilibrating configuration according to coordinate, obtain final self-equilibrating configuration, and obtain the situation of change of other process variable in computation process.
Embodiment two: present embodiments provide for the MATLAB programming realization that a kind of T prism tension integral structure based on Monte Carlo method looks for shape method, comprise the steps:
Step one, setting starting condition, can be divided into the following steps to carry out:
1.1, T prism geometric parameter setting, only provides unit number setting parameter statement.
m＝12。
1.2, material properties: set respectively the material properties of depression bar and drag-line, only provides the material properties setting program section of depression bar.
Ab＝200；
Eb＝2.06e+5；
Lob＝2.7806e+3。
1.3, the rigidity S of computing unit, only provides depression bar element stiffness component (matrix the first row).
Sb=Eb*Ab/Lob; The element stiffness of % depression bar
Sr1=[Sb; Sb; Sb]; % depression bar stiffness matrix
1.4, the connection matrix C (the capable n row of m) of unit, front eb=3 behavior depression bar, rear es=9 behavior drag-line (only providing the first row depression bar L1 connection matrix):
Cr1=[1,0,0,0,0 ,-1]; % depression bar L1, node 1 is starting point 6 is terminal
Step 2, stochastic generation initial configuration, can be divided into the following steps to carry out:
2.1, stochastic generation initial configuration P.
P=randi ([-2000,2000], n, 3); % [imin, imax] uniform random number group
g＝C*P：
2.2, the ENERGY E of configuration is calculated.
E=1/2*sum (S.* (L '-Lo) .^2); The gross energy of % system initial configuration
2.3, node random file radius r is set.
R=max (L)/2; % is set as the half of the longest unit
The new configuration of step 3, stochastic generation also judges whether to accept, and the following steps can be divided into carry out:
3.1, a node is fixed.
J=randi ([1, n-1]); % is selected node 1 ~ (n-1) at random, and node n fixes
3.2, random selected a certain node, with selected node for the centre of sphere, r is the reposition of interior random this node of setting of the ball of radius, thus generates new configuration T, only provides the statement of setting X-coordinate.
T (j, 1)=2*r* (rand (1,1)-0.5)+P (j, 1); % sets X-coordinate at random
3.3, judged whether that drag-line occurs lax.
ifmin(L(eb+1：m)′-Lo(eb+1：m))＜0
3.4, the ENERGY E of new configuration P ' is calculated ', and determine whether accept new configuration, provide the program segment accepting new configuration.
W＝1/2*sum(S.*(L′-Lo).^2)；
ifW＜E
E＝W；
P＝T；
3.5, calculate the ratio accepting new configuration in 100 steps, according to the ratio of acceptance judge whether change radius, only provide the ratio of acceptance lower than 50% program segment.
ifk/100＜0.5
r＝0.95*r；
end
Whether step 4, check system balance.
Step 5, obtain looking for shape result, and draw configuration with line order.
Embodiment three: present embodiment for example with T prism, gives process and result that the tension integral structure based on Monte Carlo method looks for shape to calculate, comprises the steps:
Step one, setting starting condition.
T prism geometric parameter sets: unit number is m=12, e
b=3 depression bars, e
s=9 drag-lines, nodes n=6.The material properties setting of pull bar and depression bar.
Step 2, stochastic generation initial configuration.
Stochastic generation initial configuration P, as shown in Figure 3, and calculates the ENERGY E of configuration.Often to walk in iterative computation all calculate obtain the energy of configuration to understand its variation tendency, as Fig. 2.
The new configuration of step 3, stochastic generation also judges whether to accept.
Calculate the ENERGY E of new configuration P ' ', and determine whether accept new configuration.T prism looks for the configuration that obtains after 10000 steps and 30000 steps calculate in shape computation process as illustrated in figures 4-5.Calculate the ratio accepting new configuration in every 100 steps, judge whether to change radius.
Whether step 4, check system balance.
Step 5, obtain looking for shape result.What T prism looked for shape to calculate meets the final configuration of approximate equilibrium condition setting as shown in Figure 6.
Claims (5)
1. the tension integral structure based on Monte Carlo method looks for a shape method, it is characterized in that described method step is as follows:
Step one, setting starting condition:
(1) remember that unit adds up to m, nodes is n, and depression bar number is e
b, drag-line number is e
s, wherein e
b+ e
s=m;
(2) material properties: the former long L of the sectional area A of unit, the elastic modulus E of unit and unit
o;
(3) the rigidity S of computing unit;
(4) the connection matrix C of unit: for starting point and terminal according to from down to up, counterclockwise mode specifies the order of connection of unit, and starting point is 1, and terminal is-1;
Step 2, stochastic generation initial configuration:
(1) stochastic generation initial configuration P:p is the coordinates matrix of each node, and dimension is n × 3, then the coordinate vector matrix g of each unit is: g=Cp;
(2) ENERGY E of configuration is calculated;
(3) node random file radius r is set;
The new configuration of step 3, stochastic generation also judges whether to accept:
(1) node is fixed;
(2) random selected a certain node, with selected node for the centre of sphere, the node random file r set in step 2 is the reposition of interior random this node of setting of the ball of radius, thus generates new configuration P ';
(3) judged whether that drag-line occurs lax, if having, repeated step (1), if without cable slack, carry out (4);
(4) ENERGY E of new configuration P ' is calculated ', if E ' <E, accept new configuration, and replace original configuration and P=P ', E=E with new configuration '; If E ' >=E, does not replace, and repeat step (1);
(5) if iterations reaches the integral multiple of 100, then calculate the ratio accepting new configuration in this 100 step, if ratio is lower than 50%, then reduced radius makes r=0.95r, if ratio is not less than 50%, then radius is constant;
Whether step 4, check system balance:
Whether the balance of system is balanced by node and judges, the internal force of each unit is f
k=S
k(l
k-l
ok), wherein, S
k, l
k, l
okrepresent a kth element stiffness, length and former length, then force density q respectively
kfor
if meet
then system balancing, is rewritten as C according to connection matrix C balance equation
tdiag (q) CP=0;
Set a limits of error ε and obtain approximate equilibrium condition, by limiting the maximal value F of out-of-balance force matrix in result of calculation on the left of balance equation equation
maxjudge whether system balances, if F
max< ε then carries out step 5, if F
max> ε then carries out step 3;
Step 5, obtain looking for shape result:
Export each node coordinate, draw tension integral structure self-equilibrating configuration according to coordinate, obtain final self-equilibrating configuration, and obtain the situation of change of other process variable in computation process.
2. the tension integral structure based on Monte Carlo method according to claim 1 looks for shape method, and when it is characterized in that the rigidity S of described computing unit, the rigidity of a kth unit is according to formula S
k=E
ka
k/ L
okcalculate.
3. the tension integral structure based on Monte Carlo method according to claim 1 looks for shape method, it is characterized in that described ENERGY E is according to formula
calculate.
4. the tension integral structure based on Monte Carlo method according to claim 1 looks for shape method, it is characterized in that described displacement radius r is the half of the longest unit in structure.
5. the tension integral structure based on Monte Carlo method according to claim 1 looks for shape method, it is characterized in that described limits of error ε is within the scope of 10 ~ 100N.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106354906A (en) * | 2016-08-19 | 2017-01-25 | 西安电子科技大学 | Mesh-shaped extendible antenna shape-finding method based on triangular patch errors |
| CN106934155A (en) * | 2017-03-13 | 2017-07-07 | 北京市建筑设计研究院有限公司 | A kind of cable-truss structure looks for shape method |
| CN107194080A (en) * | 2017-05-25 | 2017-09-22 | 同济大学建筑设计研究院(集团)有限公司 | A kind of structure determination methodology of radial tensioning system |
| CN108229054A (en) * | 2018-01-26 | 2018-06-29 | 东南大学 | A kind of symmetrical tension integral structure based on the group theory looks for shape method |
| CN108345729A (en) * | 2018-01-26 | 2018-07-31 | 东南大学 | A kind of symmetrical cable-rod structure based on the group theory looks for shape method |
| CN110792173A (en) * | 2019-10-28 | 2020-02-14 | 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 |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101582095A (en) * | 2009-06-19 | 2009-11-18 | 东南大学 | Non-linear dynamic finite element method for determining cable-strut system static balancing state |
| CN102622485A (en) * | 2012-03-16 | 2012-08-01 | 东南大学 | Morphological analysis inverse iteration method for determining space structural lofting states of cable-strut-beam system |
| CN104765925A (en) * | 2015-04-14 | 2015-07-08 | 温州大学 | Cable-strut pretension structure stretch forming optimal selection method based on error sensitivity analysis |
-
2015
- 2015-09-10 CN CN201510573837.XA patent/CN105243185B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101582095A (en) * | 2009-06-19 | 2009-11-18 | 东南大学 | Non-linear dynamic finite element method for determining cable-strut system static balancing state |
| CN102622485A (en) * | 2012-03-16 | 2012-08-01 | 东南大学 | Morphological analysis inverse iteration method for determining space structural lofting states of cable-strut-beam system |
| CN104765925A (en) * | 2015-04-14 | 2015-07-08 | 温州大学 | Cable-strut pretension structure stretch forming optimal selection method based on error sensitivity analysis |
Non-Patent Citations (1)
| Title |
|---|
| 李悦 等: "张拉整体结构的蒙特卡罗找形方法", 《损伤、断裂与微纳米力学学术研讨会》 * |
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| CN106354906A (en) * | 2016-08-19 | 2017-01-25 | 西安电子科技大学 | Mesh-shaped extendible antenna shape-finding method based on triangular patch errors |
| 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 |
| CN106934155A (en) * | 2017-03-13 | 2017-07-07 | 北京市建筑设计研究院有限公司 | A kind of cable-truss structure 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 |
| CN107194080A (en) * | 2017-05-25 | 2017-09-22 | 同济大学建筑设计研究院(集团)有限公司 | A kind of structure determination methodology of radial tensioning system |
| 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 |
| CN108229054A (en) * | 2018-01-26 | 2018-06-29 | 东南大学 | A kind of symmetrical tension integral structure based on the group theory looks for shape method |
| CN108345729A (en) * | 2018-01-26 | 2018-07-31 | 东南大学 | A kind of symmetrical cable-rod structure based on the group theory looks for shape method |
| CN108345729B (en) * | 2018-01-26 | 2021-07-27 | 东南大学 | Symmetrical cable-strut structure shape finding method based on group theory |
| CN110792173A (en) * | 2019-10-28 | 2020-02-14 | 中冶建筑研究总院有限公司 | Tensioning integral triangular prism structure and shape finding method |
| 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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