CN105019348A - Layered optimization method based on immune particle swarm optimization-zigzag method of truss structure - Google Patents
Layered optimization method based on immune particle swarm optimization-zigzag method of truss structure Download PDFInfo
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Abstract
The invention discloses a layered optimization method based on an immune particle swarm optimization-zigzag method of a truss structure. The method is different from a general layered method in parallel and a general total space optimizing method, and adopts inner-outer nesting layered optimization, the size of an inner layer is optimized by a zigzag method, a one-to-one mapping relationship is formed between each kind of given shapes and the lightest mass of the inner layer, and a one-to-one mapping relationship is formed between each kind of the given shapes and the optimal section of the inner layer; the size of an outer layer is optimized by an immune particle swarm method, and a shape variable space is searched on the basis of the formed mapping relationships of the inner layer, so that a final optimized result is obtained. Through the adoption of the layered optimization method disclosed by the invention, a coupling relationship between two kinds of variables, such as a shape(a node coordinate) and the size, is favorably treated, the loss of a global optimal solution is avoided, besides a space range is effectively reduced, the searching efficiency is improved, and the layered optimization method has certain superiority. The layered optimization method disclosed by the invention can be applied for optimizing the shapes and the sizes of various truss structures.
Description
Technical Field
The invention belongs to the field of structure optimization, and relates to a method applied to optimization of the shape and size of a truss structure.
Background
The truss structure is a structure formed by hinging the rods, the stress of each rod is mainly axial tension and compression, the material performance can be fully utilized, the structural arrangement is flexible, and the application range is very wide. Truss structures are often used in large-span public buildings such as factory buildings, exhibition halls, gymnasiums and bridges.
Optimization of the shape and size of the truss structure is a classical problem, and safety, economy and the like of the structure can be improved through optimized design. The design variables are the section size of each rod piece and the coordinates of each node, and the two variables have different properties and are mutually coupled, so that the dimensionality and the complexity of the optimization problem are greatly increased, and the convergence difficulty and even the pathological phenomenon can occur.
The existing solutions of scholars at home and abroad can be generally divided into two types.
The first method is to divide the optimization of two types of variables into two layers of processing, and the two optimization methods of section size and node coordinate are parallel and are alternately carried out until convergence. The advantage of hierarchical optimization is that the scale of the problem can be reduced, the calculation amount is obviously reduced, but due to the nonlinearity of the problem and the coupling of two variables, the hierarchical optimization causes the reduction of the feasible domain of the solution space and the loss of the globally optimal solution, and the optimization result depends on the selection of the initial shape to a great extent.
The second method is to consider two kinds of variables simultaneously and optimize in the whole solution space. In recent years, intelligent algorithms are widely applied, such as Genetic Algorithm (GA), simulated annealing algorithm (SA), particle swarm algorithm (PSO), Ant Colony Optimization (ACO), differential evolution algorithm (DE), and the like, and corresponding improved intelligent algorithms, which combine two variables, namely cross section and coordinates, as variable sequences to directly search in a solution space, although the coupling relationship between the two variables can be conveniently processed, the loss of an optimal solution is avoided, and the method does not depend on the selection of an initial shape, but because the search space is rapidly expanded along with the increase of the number of variables, the iteration times and the calculated amount are usually huge, and the method is easy to fall into a local optimal solution.
The dentition method is a mature structure size optimization method. The mechanical criterion and mathematical programming are combined, and each time one step of optimization is carried out according to the mechanical criterion (full stress or full displacement criterion), the solution is pulled to a constraint boundary through a ray step, and the solution is carried out alternately until convergence is achieved. The Zhuberfang proposes and proves that for the structure optimization problem, the optimal solution is definitely located on the strictest constraint curved surface, and therefore the solution obtained by the tooth row method is the global optimal solution.
The immune particle swarm algorithm is an improved swarm intelligence algorithm. On the basis of a basic particle swarm algorithm, an immune mechanism based on survival probability adjustment is added, so that the probability of being trapped in local optimum is reduced, and the global search capability of the algorithm is improved.
Disclosure of Invention
The technical problem is as follows:the invention provides a truss structure hierarchical optimization method based on an immune particle swarm optimization-odontoid method, which is nested and layered, has high search efficiency and obtains a global optimal solution with high probability.
The technical scheme is as follows:the invention relates to a truss structure layering optimization method based on an immune particle swarm optimization-odontology method, which comprises the following steps of:
1) determining a truss structure optimization target, design variables and constraint conditions:
the optimization objective is structural qualityWThe lightest weight;
the optimized design variables of the truss structure comprise the section size of the rod piece needing optimized designA=[A 1 , A 2 ,…, A m ]And node coordinatesX=[X 1 , X 2 ,…, X n ] ；
The constraint condition comprises stress constraint of the rod pieceσ i ≤σ i a ,i=1~mNode displacement constraintsu i ≤ u i lim ,i=1~pInstability of pressure barConstrainingσ i ≤σ i cr ，i=1~mAnd upper and lower constraints of section and coordinateA i min ≤ A i ≤ A i max ，i=1~m ，X i min ≤ X i ≤ X i max ，i=1~nWhereinσ i a Is as followsiThe allowable stress of the material of the root bar,u i lim is as followsiThe limit value of the coordinates of the individual nodes,σ i cr is as followsiThe critical stress of the root bar member for instability,A i min andA i max respectively a lower and an upper boundary of the cross-sectional dimension,X i min andX i max respectively a lower bound and an upper bound of coordinates,mthe number of the rod members is the same as the number of the rod members,nin order to design the number of coordinates of the node,pthe number of node coordinates for controlling displacement;
2) carrying out parametric modeling on the optimized truss structure to obtain a structural model, wherein the modeled design parameters comprise the section size to be optimizedAAnd node coordinatesX；
3) Aiming at the structural model established in the step 2), adopting an immune particle swarm algorithm and using node coordinatesXFor particles, the optimum cross-section of the inner layer in a given shapeA in The lightest weight of the corresponding inner layerW in As the fitness of the particles, the particles are updated through a particle group velocity formula, the particles are screened according to the survival probability, and finally the searched global lightest weight is outputW best And corresponding globally optimal shapeX best Global optimum cross sectionA best 。
Further, the inner layer in the step 3) has the lightest weightW in Is obtained by calculation through a tooth row law subfunction, specifically, a given node coordinateXSetting the initial sectionA (0) As input, the iterative computation is performed in the following manner:
each iteration firstly solves the internal force and displacement of the structure of the structural model in the step 2) by a finite element method or a matrix displacement method, extracts and outputs the rod stress required by the iterationσ=[σ 1 ,σ 2 ,…, σ m ]And node displacementu=[u 1 ,u 2 ,…,u p ]Then, the section is scaled in a ray step to enable the strictest constraint to reach a limit value, then whether the structural quality is converged is judged, if so, the iterative computation is ended, and the optimal section of the inner layer is outputA in And the lightest weight of the inner layerW in ；
When the structure mass is not converged, if the structure mass is reduced compared with the previous round, the passive rod piece executes a full stress step, the active rod piece takes the larger value of the full displacement step and the full stress step corresponding to the maximum displacement ratio, then the next round of iteration is carried out, and if the structure mass is increased compared with the previous round, the structure mass is increased according to the following stepsA (j) = A (j-2) To cross section variationA (j) Updating and relaxing the coefficientη (j) Updated as (1/2~1/3)η (j-1) And then entering the next iteration.
Further, the specific process of the immune particle swarm algorithm in the step 3) is as follows:
a) in node coordinatesXFor particles, the optimum cross-section of the inner layer in a given shapeA in The lightest weight of the corresponding inner layerW in Setting parameters including inertial weight for fitness of particlesω、Acceleration factorc 1 、c 2 Population sizeNNumber of added particlesMNumber of iterationsT max Weighting coefficientaRandomly generating the first generation within the constraint range of the upper and lower bounds of the nodeNIndividual particle position and velocity, size of said populationNNamely the number of the node coordinates;
b) first, the previous generation is updated by the formula of particle group velocityNParticle, updateGbest k And its corresponding particle positionXtemp k And cross sectionAtemp k WhereinGbest k indicates that all particles in the population are inkThe optimal lightest mass of the obtained population in the process of the secondary iteration is randomly generated to be newMEach particle, calculating the survival probability of each particleP(X)According to the survival probabilityP(X)To this endM+NArranging the particles in descending order, taking beforeNThe particles are a new generation of particle group, whereinkThe current iteration number is;
c) if the set iteration number is reachedT max If so, the iteration is ended and the global lightest weight is outputW best =Gbest Tmax Global optimum shapeX best =Xtemp Tmax Globally optimal cross sectionA best =Atemp Tmax Otherwise, returning to the step b).
Further, in the step 3), the survival probability of each particle is calculated according to the following formulaP (X i )：
(1)
(2)
(3)
Wherein,P(X i )is as followsiThe probability of survival of the individual particles,PF(X i )is as followsiThe probability of selection of an individual particle based on affinity,PD(X i )is as followsiThe probability of selection of an individual particle based on concentration,ain order to be the weighting coefficients,W(X i )is as followsiMass corresponding to each particle.
According to the method, inner and outer nested hierarchical optimization is adopted, the inner layer is subjected to size optimization by adopting a tooth row method, each given shape and the lightest mass and the optimal section of the given shape form a one-to-one mapping relation, the outer layer is subjected to searching on the basis of the mapping relation formed by the inner layer by using an immune particle swarm method to obtain a final optimization result, the nested hierarchical optimization well processes the coupling relation of two types of variables, the loss of the global optimal solution is avoided, and meanwhile, compared with the method of directly searching in the whole solution space, the range of the understanding space is effectively reduced, the searching efficiency is improved, and the iteration times and the calculated amount are reduced.
Has the advantages that:compared with the prior art, the invention has the following advantages:
compared with a common parallel layering method, the nested layering optimization method adopted in the method forms a one-to-one mapping relation between each shape and the optimal section by an inner-layer zigzag method, and the outer-layer immune particle swarm optimization directly carries out global search on a shape variable space based on the inner-layer mapping relation, so that the method is independent of selection of an initial solution, better processes the coupling relation of two types of variables, and avoids the possibility of losing the global optimal solution due to the fact that the solution space is split;
compared with the method of searching in the whole solution space by using a uniform variable method or directly using an intelligent algorithm, such as a genetic algorithm, an ant colony algorithm and the like, the method effectively reduces the dimensionality of the search space, reduces the iteration times and the calculated amount and improves the search efficiency through hierarchical optimization.
An immune regulation mechanism is added to the outer layer basic particle swarm method to form the immune particle swarm method, so that the advantages of the swarm intelligence method are retained, premature convergence and over concentration of particles are avoided, the probability that the method falls into local optimum is reduced, and the global search capability of the method is improved.
Drawings
FIG. 1 is a flow chart of the method master function of the present invention.
FIG. 2 is a flow chart of the tooth row method subfunction of the present invention.
FIG. 3 is a schematic diagram of the convergence path of the tooth row method.
Fig. 4a is a diagram of the initial shape of a 25-bar space truss.
Fig. 4b is a diagram of the optimal shape of the 25-bar space truss.
Fig. 5 is a graph of the convergence of the mass of a 25-bar space truss.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
1) Determining a truss structure optimization target, design variables and constraint conditions:
the optimization objective is structural qualityWThe lightest weight;
the optimized design variables of the truss structure comprise the section size of the rod piece needing optimized designA=[A 1 , A 2 ,…, A m ]And node coordinatesX=[X 1 , X 2 ,…, X n ] ；
The constraint condition comprises stress constraint of the rod pieceσ i ≤σ i a ,i=1~mNode displacement constraintsu i ≤ u i lim ,i=1~pBuckling restraint of compression barσ i ≤σ i cr ,i=1~mAnd upper and lower constraints of section and coordinateA i min ≤ A i ≤ A i max ,i=1~m ，X i min ≤ X i ≤ X i max ,i=1~nWhereinσ i a Is as followsiThe allowable stress of the material of the root bar,u i lim is as followsiThe limit value of the coordinates of the individual nodes,σ i cr is as followsiThe critical stress of the root bar member for instability,A i min andA i max respectively a lower and an upper boundary of the cross-sectional dimension,X i min andX i max respectively a lower bound and an upper bound of the coordinate;
2) parameterised modelling of the optimized truss structure, the design parameters including the cross-sectional dimensions to be optimizedAAnd node coordinatesXSetting other conditions such as load working conditions, rod piece topological relation, determined node coordinates and the like;
3) aiming at the structural model established in the step 2), adopting an immune particle swarm algorithm and using node coordinatesXFor particles, the optimum cross-section of the inner layer in a given shapeA in The lightest weight of the corresponding inner layerW in As the fitness of the particles, updating the particles through a particle group velocity formula and screening the particles according to the survival probability, and finallyPost-outputting the searched global lightest weightW best And corresponding globally optimal shapeX best Global optimum cross sectionA best 。
Wherein the inner layer in the step 3) has the lightest weightW in Is obtained by calculation through a tooth row law subfunction, specifically, a given node coordinateXSetting the initial sectionA (0) As input, rod stress constraint, node displacement constraint, compression bar instability constraint and section upper and lower limit constraint are considered, the section of the rod is optimized, and the corresponding inner layer optimal section is obtained and outputA in And the lightest weight of the inner layerW in 。
The tooth row method is an optimization method combining mechanical criteria with mathematical programming, and the basic idea is that according to the mechanical criteria (full stress or full displacement criteria), every optimization step is carried out, the solution is scaled to a constraint boundary through ray steps, and the optimization steps are carried out alternately until convergence is achieved. The convergence process is as shown in fig. 3, and continuously travels between the strictest boundary and the infeasible domain, the search path is zigzag, and when exceeding the optimal point, the search path moves back to two steps and advances in smaller steps until the optimal point is searched. The tooth row method flow chart is shown in fig. 2, and the specific steps are explained as follows:
given the initial design size variableA (0)Coefficient of relaxationη (0) =0.6-1.8Initial mass of structureW (0)(any large number, e.g. of10 10 ）；
Solving the internal force and displacement of the structure of the structural model in the step 2) by a finite element method or a matrix displacement method, and extracting and outputting the rod piece stress required by the wheelσ=[σ 1 ,σ 2 ,…, σ m ]And node displacementu=[u 1 ,u 2 ,…,u p ]；
(iii) working at each workerMaximum stress ratio under the conditionr max And maximum displacement ratioμ max Then executing the ray step, using the maximum response ratioξScaling the solution to the boundary of the feasible domain:
(1)
(2)
calculating structural massW k)；
Fourthly, judging whether the convergence is generated, if soEnding the iteration and outputtingA (k) AndW (k) otherwise, continuing;
wu ifW (k) < W (k-1) Dividing the rod into a passive rod and an active rod according to the positive and negative influences of the increase of the area of the rod on the displacement;
the passive rod member executes a full stress step:
(3)
(4)
the driving rod is a larger value of a full displacement step and a full stress step corresponding to the maximum displacement ratio, wherein the full displacement step is as follows:
(5)
(6)
(7)
to obtainA (k+1)Turning to 2) continuing iterative computation;
sixthly, ifW (k) > W (k-1) And reducing the relaxation coefficient to 1/3-1/2, returning the section variable to two steps, and turning to 2) to carry out repeated iteration calculation.
(8)
(9)
The immune particle swarm method adopted in the step 3) is an improved intelligent method formed by adding an immune selection mechanism on the basis of a basic particle swarm method, and the defects of over-concentration and premature convergence of particles are avoided while the advantages of the swarm intelligent method are kept, so that the method has better global search capability.
In the present problem, the node coordinates are usedXIs a particle, consisting ofNThe particles form a population with an optimal cross section of the inner layer under a given shapeA in The lightest weight of the corresponding inner layerW in As the fitness of the particles, updating the particles through a particle group velocity formula in each iteration, and according to the survival probabilityP(X)Screening, and obtaining next generation particles by comprehensively considering particle concentration (particle concentration degree) and affinity (corresponding mass) of the particles and the antigen according to survival probability until reaching set iteration timesT max Outputting the searched global lightest weightW best And corresponding globally optimal shapeX best Global optimum cross sectionA best 。
The flow chart of the immune particle swarm major function is shown in FIG. 1, and the specific steps are explained as follows:
setting parameters of algorithm, including inertial weightω、Acceleration factorc 1 、c 2 Population sizeNNumber of added particlesMNumber of iterationsT max Weighting coefficienta。
Secondly, initializing the particle swarm. Random generationNIndividual particles and their velocities, care being taken to constrain the range to be feasible.
(10)
(11)
And updating to generate the next generation group according to the following standard particle swarm velocity formula.
(12)
(13)
Wherein,Pbest k (i)indicating the lightest mass (individual optima) obtained by the ith particle in the iterative process,Gbest k indicating the lightest mass obtained for the population in the iterative process (population optimal). RecordingGbest k Corresponding particle positionXtemp k And cross sectionAtemp k 。
Fourthly, random generationMThe method is the same as that of particle.
Fifthly, toM+NAccording to survival probability of each particleP（X i ）Descending order, before takingNAnd the second generation group.
(14)
(15)
(16)
Wherein,afor weighting coefficients, for adjusting affinity selection probabilityPF(X i )And concentration selection probabilityPD(X i )The influence factor of (c).
Sixthly, judging whether the maximum iteration number is reachedT max If yes, the calculation is finished and the global lightest weight is outputW best =Gbest Tmax Global optimum shapeX best =Xtemp Tmax Globally optimal cross sectionA best =Atemp Tmax Otherwise, turning to the third step.
The effectiveness of the method is verified by a 25-rod space truss classical example.
The initial shape of the 25-bar space truss is shown in fig. 4a, and the nodal coordinates and dimensional variables are shown in table 1 a. The initial coordinate series is [ X4, Y4, Z4, X8, Y8]=[0.9525,0.9525,2.54,2.54,2.54]. The node loads for the two conditions are shown in table 1 b. The displacement constraint is that the displacements of the nodes 1 and 2 in the directions of x, y and z are not more than +/-0.889 cm, and the lower limit of the size is 0.0645cm2. Modulus of elasticity of materialE=68.95GPa, density ρ =2678kg/m3The allowable stress of the rod is +/-275.8 MPa, and the local stable critical stress is-39.27EA i /L i 2 。
TABLE 1a
TABLE 1b
TABLE 2
For this problem, the population size is setN=20, number of additional particlesM=5, maximum number of iterations T max = 120. The structure was randomly optimized 10 times using this method. The optimal shape of the structure is shown in fig. 4b, which is obviously different from the initial shape. The final optimization result and comparison are shown in table 2, and fig. 5 is a structural quality convergence curve in the sub-optimization process of 5, so that the method has a good convergence trend, and the obtained optimization result is better than the results obtained by other methods. Compared with the method of directly searching in the shape and size combined space, the displacement constraint of the text is stricter, the obtained optimal mass is lighter, the efficiency of the internal and external hierarchical search algorithm of the text is higher, and the optimization effect is better.
The above examples are only preferred embodiments of the present invention, it should be noted that: it will be apparent to those skilled in the art that various modifications and equivalents can be made without departing from the spirit of the invention, and it is intended that all such modifications and equivalents fall within the scope of the invention as defined in the claims.
Claims (4)
1. A truss structure layered optimization method based on an immune particle swarm optimization-odontoid method is characterized by comprising the following steps:
1) determining a truss structure optimization target, design variables and constraint conditions:
the optimization objective is structural qualityWThe lightest weight;
the optimized design variables of the truss structure comprise the section size of the rod piece needing optimized designA=[A 1 , A 2 ,…, A m ]And node coordinatesX=[X 1 , X 2 ,…, X n ] ；
The constraint condition comprises stress constraint of the rod pieceσ i ≤σ i a ,i=1~mNode displacement constraintsu i ≤ u i lim ,i=1~pBuckling restraint of compression barσ i ≤σ i cr ，i=1~mAnd upper and lower constraints of section and coordinateA i min ≤ A i ≤ A i max ，i=1~m ，X i min ≤ X i ≤ X i max ，i=1~nWhereinσ i a Is as followsiThe allowable stress of the material of the root bar,u i lim is as followsiThe limit value of the coordinates of the individual nodes,σ i cr is as followsiThe critical stress of the root bar member for instability,A i min andA i max respectively a lower and an upper boundary of the cross-sectional dimension,X i min andX i max respectively a lower bound and an upper bound of coordinates,mthe number of the rod members is the same as the number of the rod members,nin order to design the number of coordinates of the node,pthe number of node coordinates for controlling displacement;
2) carrying out parametric modeling on the optimized truss structure to obtain a structural model, wherein the modeled design parameters comprise the section size to be optimizedAAnd node coordinatesX；
3) Aiming at the structural model established in the step 2), adopting an immune particle swarm algorithm and using node coordinatesXFor particles, the optimum cross-section of the inner layer in a given shapeA in The lightest weight of the corresponding inner layerW in As the fitness of the particle, updating the particle by the particle group velocity formulaScreening particles according to survival probability, and finally outputting the searched global lightest weightW best And corresponding globally optimal shapeX best Global optimum cross sectionA best 。
2. The method for optimizing the truss structure by layering based on the immunoparticles swarm optimization-odontoid method according to claim 1, wherein the inner layer in step 3) is the lightest in weightW in Is obtained by calculation through a tooth row law subfunction, specifically, a given node coordinateXSetting the initial sectionA (0) As input, the iterative computation is performed in the following manner:
each iteration firstly solves the internal force and displacement of the structure of the structural model in the step 2) by a finite element method or a matrix displacement method, extracts and outputs the rod stress required by the iterationσ=[σ 1 ,σ 2 ,…, σ m ]And node displacementu=[u 1 ,u 2 ,…,u p ]Then, the section is scaled in a ray step to enable the strictest constraint to reach a limit value, then whether the structural quality is converged is judged, if so, the iterative computation is ended, and the optimal section of the inner layer is outputA in And the lightest weight of the inner layerW in ；
When the structure mass is not converged, if the structure mass is reduced compared with the previous round, the passive rod piece executes a full stress step, the active rod piece takes the larger value of the full displacement step and the full stress step corresponding to the maximum displacement ratio, then the next round of iteration is carried out, and if the structure mass is increased compared with the previous round, the structure mass is increased according to the following stepsA (j) = A (j-2) To cross section variationA (j) Updating and relaxing the coefficientη (j) Updated as (1/2~1/3)η (j-1) And then entering the next iteration.
3. The method for the hierarchical optimization of the truss structure based on the immune particle swarm optimization-odontoid method according to claim 1 or 2, wherein the specific process of the immune particle swarm optimization in the step 3) is as follows:
a) in node coordinatesXFor particles, the optimum cross-section of the inner layer in a given shapeA in The lightest weight of the corresponding inner layerW in Setting parameters including inertial weight for fitness of particlesω、Acceleration factorc 1 、c 2 Population sizeNNumber of added particlesMNumber of iterationsT max Weighting coefficientaRandomly generating the first generation within the constraint range of the upper and lower bounds of the nodeNIndividual particle position and velocity, size of said populationNNamely the number of the node coordinates;
b) first, the previous generation is updated by the formula of particle group velocityNParticle, updateGbest k And its corresponding particle positionXtemp k And cross sectionAtemp k WhereinGbest k indicates that all particles in the population are inkThe optimal lightest mass of the obtained population in the process of the secondary iteration is randomly generated to be newMEach particle, calculating the survival probability of each particleP(X)According to the survival probabilityP(X)To this endM+NArranging the particles in descending order, taking beforeNThe particles are a new generation of particle group, whereinkThe current iteration number is;
c) if the set iteration number is reachedT max If so, the iteration is ended and the global lightest weight is outputW best =Gbest Tmax Global optimum shapeX best =Xtemp Tmax Globally optimal cross sectionA best =Atemp Tmax Otherwise, returning to the step b).
4. The method for the hierarchical optimization of the truss structure based on the immune particle swarm optimization-odontoid method according to claim 3, wherein in the step 3), the survival probability of each particle is calculated according to the following formulaP (X i )：
(1)
(2)
(3)
Wherein,P(X i )is as followsiThe probability of survival of the individual particles,PF(X i )is as followsiThe probability of selection of an individual particle based on affinity,PD(X i )is as followsiThe probability of selection of an individual particle based on concentration,ain order to be the weighting coefficients,W(X i )is as followsiMass corresponding to each particle.
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| CN110545552A (en) * | 2019-09-02 | 2019-12-06 | 重庆三峡学院 | Multipath transmission routing method based on immune particle swarm |
| CN113221415A (en) * | 2021-05-13 | 2021-08-06 | 广东省科学院智能制造研究所 | Truss girder structure optimization method and device based on ABAQUS |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008001348A2 (en) * | 2006-06-26 | 2008-01-03 | Ben-Gurion University Of The Negev Research And Development Authority | Method for estimating the strength of bodies and structures |
| CN101859104A (en) * | 2010-06-09 | 2010-10-13 | 桂林电子科技大学 | Relative sensitivity method for optimizing shapes of discrete truss structure and continuum structure |
| CN102140823A (en) * | 2010-01-29 | 2011-08-03 | 上海卫星工程研究所 | Design method for truss structure |
| CN102867101A (en) * | 2012-09-29 | 2013-01-09 | 北京航空航天大学 | Method for determining truss structure parameters |
| CN104484537A (en) * | 2014-12-30 | 2015-04-01 | 西安电子科技大学 | Electromechanical integrated optimization method for sectional dimensions of ribs of metal truss type antenna housing |
-
2015
- 2015-07-20 CN CN201510427385.4A patent/CN105019348B/en not_active Expired - Fee Related
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008001348A2 (en) * | 2006-06-26 | 2008-01-03 | Ben-Gurion University Of The Negev Research And Development Authority | Method for estimating the strength of bodies and structures |
| CN102140823A (en) * | 2010-01-29 | 2011-08-03 | 上海卫星工程研究所 | Design method for truss structure |
| CN101859104A (en) * | 2010-06-09 | 2010-10-13 | 桂林电子科技大学 | Relative sensitivity method for optimizing shapes of discrete truss structure and continuum structure |
| CN102867101A (en) * | 2012-09-29 | 2013-01-09 | 北京航空航天大学 | Method for determining truss structure parameters |
| CN104484537A (en) * | 2014-12-30 | 2015-04-01 | 西安电子科技大学 | Electromechanical integrated optimization method for sectional dimensions of ribs of metal truss type antenna housing |
Non-Patent Citations (2)
| Title |
|---|
| 杨生意: "具有可靠度约束的桁架结构组合优化设计", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
| 沈圣等: "钢桁架桥的设计分析与优化综述", 《山西建筑》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108924755A (en) * | 2018-06-29 | 2018-11-30 | 合肥工业大学 | DV-HOP indoor orientation method based on immunity particle cluster optimization |
| CN108924755B (en) * | 2018-06-29 | 2020-05-22 | 合肥工业大学 | DV-HOP indoor positioning method based on immune particle swarm optimization |
| CN109451012A (en) * | 2018-11-01 | 2019-03-08 | 宜通世纪物联网研究院(广州)有限公司 | End cloud collaborative load balancing scheduling method, system and storage medium |
| CN110545552A (en) * | 2019-09-02 | 2019-12-06 | 重庆三峡学院 | Multipath transmission routing method based on immune particle swarm |
| CN110545552B (en) * | 2019-09-02 | 2023-04-14 | 重庆三峡学院 | Multipath transmission routing method based on immune particle swarm |
| CN113221415A (en) * | 2021-05-13 | 2021-08-06 | 广东省科学院智能制造研究所 | Truss girder structure optimization method and device based on ABAQUS |
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