A method, device and medium for optimizing temporary support points in spatial structure construction

By using the simulated plant growth algorithm (PGSA) to perform multivariate synchronous optimization of temporary support points for spatial structure construction, the problem of construction schemes relying on experience was solved, and efficient optimization of the location and number of support points was achieved, meeting construction requirements and reducing structural strain energy.

CN118364578BActive Publication Date: 2025-12-16SOUTH CHINA UNIV OF TECH
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Patent Information

Application Number
CN202410329062.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-03-21
Publication Date
2025-12-16
Estimated Expiration
2044-03-21

AI Technical Summary

Technical Problem

Existing technologies in spatial structure construction suffer from blindness due to reliance on experience in construction schemes. Optimization algorithms are complex and inefficient, failing to effectively solve the multivariable coupling problem of temporary support points in complex spatial structures.

Method used

The simulated plant growth algorithm (PGSA) is used to optimize the location and number of temporary support points. By establishing an objective function and constraints, multivariate synchronous optimization is performed, and the optimization results are verified by finite element analysis, thus avoiding the fragmentation of hierarchical optimization.

Benefits of technology

The simultaneous optimization of the location and number of temporary support points was achieved, reducing the impact of human factors, improving optimization efficiency, obtaining the global optimal solution, reducing structural strain energy, and meeting construction requirements.

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Abstract

The application discloses a kind of space structure construction temporary support point optimization method, equipment and medium.The method comprises: determining construction optimization variable and optimization target;Actual construction optimization problem is converted into mathematical optimization problem, growth search is carried out, and global optimal solution is output, that is, the optimal scheme of construction.The application avoids the limitations of past construction optimization over-reliance on the experience of engineering personnel, and realizes intelligent optimization arrangement of temporary support point by simulating plant growth algorithm.The actual engineering problem is converted into mathematical problem for algorithm optimization, and the position and quantity variables of temporary support point are placed in the same growth space, to realize the synchronous optimization of the quantity and position of construction temporary support point, avoid the fragmentation of the two by using hierarchical optimization, with high efficiency and ease of use.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of spatial structure construction optimization, in particular to a spatial structure construction temporary support point (such as support cradle point, hoisting point, lifting point, jacking point, etc.) optimization method based on a simulated plant growth algorithm, which is used to solve the problem of optimizing the number and position of temporary support points of a structure during construction. BACKGROUND

[0002] Spatial structures in China are developing towards larger spans and more complex structures. The stress system of the structure changes greatly during the construction process and is different from the stress system after the structure is formed, which puts forward higher requirements for the construction technology. The traditional construction optimization method is to use a multi-scheme comparison method or an exhaustive method, which has problems such as a large human factor influence and a large amount of analysis. The existing algorithm for construction optimization is still in its infancy, and the optimization examples are relatively simple and the optimization variables are relatively single. Therefore, in order to overcome the blindness of relying on experience to determine the construction scheme and reasonably select the construction scheme, a multi-parameter intelligent construction optimization method for complex spatial structure construction is needed.

[0003] On the other hand, new intelligent optimization algorithms represented by the simulated plant growth algorithm (PGSA) have been applied to the field of spatial structures to some extent, but are mostly limited to the field of structure design and have not been applied to the field of structure construction.

[0004] Wang Xin et al. proposed a large-span steel structure hoisting point hierarchical optimization method based on a particle swarm algorithm. This method uses a particle swarm algorithm for optimization and needs to set a penalty function, which has the problem of complex parameter setting. In addition, this method uses a hierarchical optimization approach, i.e., first optimizing the number of hoisting points in the outer layer and then optimizing the position of the hoisting points in the inner layer. This optimization approach cannot consider the coupling relationship between the two types of optimization variables, and if the number of hoisting points optimized in the previous rounds is not the optimal number, the results of the previous rounds of optimization are invalid, which has the problems of long optimization time and low efficiency.(Wang Xin, Chen Bowen, Lin Yuanshan, et al. Large-span steel structure hoisting point hierarchical optimization based on particle swarm algorithm[J]. Journal of Dalian University of Technology, 2012, 52(05):664-669.)

[0005] Chinese patent CN109543226A discloses a "mixed intelligent optimization method for spatial structures", which is applied to the field of spatial structure design. It uses the global search ability of a particle swarm algorithm (PSO) with a high inertia weight to select a feasible solution near the global optimal solution, and uses a simulated plant growth algorithm (PGSA) to find the optimal solution. However, in this process, the type of optimization variable is single and the application scenario is limited. SUMMARY

[0006] To at least solve one of the problems existing in the prior art, the application proposes a space structure construction temporary support point optimization method based on a simulated plant growth algorithm (PGSA), which can perform multivariable synchronous optimization on temporary support points in the construction process of a complex space structure and obtain a global optimal solution.

[0007] To achieve the object of the application, the application provides a space structure temporary support point optimization method based on a simulated plant growth algorithm (PGSA), which introduces the simulated plant growth algorithm PGSA into the optimization of temporary support points in the construction process of a space structure, takes the positions and quantities of temporary support points in the construction process of the space structure as optimization variables, and takes the strain energy of the structure during construction as an optimization target, and the specific steps are as follows:

[0008] Step one, define the construction optimization variables and optimization target.

[0009] Step two, convert the actual construction optimization problem into a mathematical optimization problem. The positions of the temporary support points are converted into the feasible region of growth points through numbering, and the optimization variables are defined; the quantity of the temporary support points and the overall strain energy of the structure are comprehensively taken as the objective function (formula 1), and the optimization parameters such as the initial growth point, growth step and constraint condition are defined.

[0010]

[0011] In the formula, the design variables x and y are the position number and quantity of the lifting points respectively; s is the optimization target value; Q is the quantity of the lifting points, P is the external load vector of the structure, U is the node displacement vector of the structure, and k is a combination parameter which needs to be determined according to different examples. The structure strain energy is an index that can reflect the overall mechanical performance of the structure. When the structure is in an elastic small deformation working state, the energy loss in the loading and unloading process is ignored, and the overall strain energy of the structure can be calculated by the formula.

[0012] Set the constraint condition. In the construction process of the space structure, whether the structure deformation and stress meet the specification requirements needs to be considered, and the following constraint condition needs to be set:

[0013] (1) Maximum vertical displacement limit

[0014]

[0015] In the formula, δ is the maximum vertical displacement (m) of the lifted structure, L0 is the distance of the lifted structure support point, and 250 is the specification value.

[0016] (2) Allowable slenderness ratio

[0017]

[0018] The slenderness ratio λ of all components shall satisfy the above formula, [λ] = 150 for compression-bending components, [λ] = 300 for tension-bending components, and l0, i are the calculation length and the gyration radius, respectively.

[0019] (3) Strength

[0020] The strength of the component is checked according to the following formula:

[0021]

[0022] In the formula, N, M x , M y are the axial force of the bar, the bending moment around the x-axis (strong axis), and the bending moment around the y-axis (weak axis), respectively, and the remaining parameters are valued according to GB 50017-2017 "Steel Structure Design Standard".

[0023] (4) Stability

[0024] The stability of compression-bending components is checked according to the following formula. For solid compression-bending components with bending moment acting in the plane of symmetry, the stability in the plane of bending moment action shall be calculated according to formula (5), and the stability out of the plane of bending moment action shall be calculated according to formula (6). For biaxial symmetric solid I-shaped and box-shaped compression-bending components with bending moment acting in two principal planes, their stability shall be calculated according to formula (7) and formula (8), and the overall stability of biaxial compression-bending circular tubes shall be calculated according to formula (9):

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] In the formula, N, M, M x , M y are the axial force of the bar, the bending moment, the bending moment around the x-axis (strong axis), and the bending moment around the y-axis (weak axis), respectively, and the remaining parameters are valued according to GB 50017-2017 "Steel Structure Design Standard".

[0031] Step three, growth search is carried out. After each new set of growth points is generated, the value of the growth point is converted into a variable in actual construction, and the boundary conditions and loads of the spatial structure are modified accordingly, finite element analysis is carried out, and the objective function value of the growth point is obtained through calculation. Check whether the response (such as deformation and stress) of the structure meets the requirements, and based on the growth space optimization method of the objective function value, eliminate the growth points that do not meet the requirements, and continuously obtain the set of growth points, and calculate the morphogen concentration according to the set of growth points to determine the next growth point; when the optimal solution is searched by growth, or the maximum number of growth is reached, the algorithm is terminated, and the global optimal solution is output, that is, the optimal scheme of construction.

[0032] The application also provides a computer device, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to realize the steps of the foregoing method.

[0033] The application also provides a computer readable storage medium, which stores a computer program, wherein the computer program is executed by a processor to realize the steps of the foregoing method.

[0034] Compared with the prior art, the application has at least the following advantages and effects:

[0035] Firstly, the actual engineering construction problem is converted into a mathematical problem that can be optimized by an algorithm, the intelligent algorithm is used for optimization by establishing an objective function, the problem of judging according to engineering experience in the traditional engineering is avoided, the influence of human factors is reduced, and the obtained optimization result is often better.

[0036] Secondly, the multiple variables are placed in the same growth space for synchronous optimization, the position feasible region of the temporary support point is numbered, and the life and death parameters of the temporary support point are introduced, so that the position and number of the temporary support point are optimized synchronously, the coupling of the two is considered, the two are not separated in layered optimization, the optimization target is more clear, and the optimization efficiency is higher.

[0037] Thirdly, the optimization algorithm is applied to the construction optimization field of the spatial structure, and the coupling relationship of different types of optimization variables, including the position and number of the temporary support point, is solved, so that the multiple variables can be optimized synchronously.

[0038] Fourthly, the PGSA does not need to set complex parameters such as penalty function and crossover rate when optimizing, only needs to set initial growth points and growth step parameters, and has good usability. When the PGSA optimizes, the next growth point is selected based on the morphogen concentration of the random probability, complex ill-conditioned problems can be better handled, and the optimization result is more accurate. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1A schematic diagram of a temporary support point optimization process of a spatial structure in an embodiment of the present application.

[0040] Figure 2 A schematic diagram of an analysis model of an embodiment of the present application.

[0041] Figure 3 A schematic diagram of a change curve of a target function value of a structure optimization process of an embodiment of the present application.

[0042] Figure 4 A schematic diagram of a change curve of a strain energy of a structure optimization process of an embodiment of the present application.

[0043] Figure 5 A schematic diagram of a lifting point position before optimization in an embodiment of the present application.

[0044] Figure 6 A schematic diagram of a lifting point position after optimization in an embodiment of the present application.

[0045] Figure 7 A vertical displacement nephogram (unit: mm) before optimization in an embodiment of the present application.

[0046] Figure 8 A vertical displacement nephogram (unit: mm) after optimization in an embodiment of the present application. DETAILED DESCRIPTION

[0047] To make the objectives, technical solutions and advantages of embodiments of the present application clearer, the following will be combined with the accompanying drawings of the embodiments of the present application to make a clear and complete description of the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative work are within the protection scope of the present application.

[0048] Referring to Figure 1 The present application provides a temporary support point optimization method for a spatial structure based on a simulated plant growth algorithm (PGSA), which comprises the following steps:

[0049] Step one: the construction optimization variables are the positions and numbers of the temporary support points, and the optimization target is the lowest structure strain energy under the condition of the least number of temporary support points and the optimal position of the temporary support points.

[0050] Step two: the actual construction optimization problem is converted into a mathematical optimization problem. The positions of the temporary support points are converted into feasible regions of growth points through numbering, and the optimization variables are defined; the number of temporary support points and the overall strain energy of the structure are comprehensively considered as a target function (Formula 1), and the initial growth point x0, the growth step step and the constraint condition are defined.

[0051] The target function is used to realize that the structural strain energy is as small as possible on the basis of the least number of support points, and the target function is

[0052]

[0053] In the formula, s is an optimization target value, design variables x and y are respectively lifting point position number and quantity, Q is the number of lifting points, k is a combination parameter, P is a structure external load vector, U is a node displacement vector of the structure, a superscript T is a mathematical transpose operator symbol, is a structural strain energy, and the structural overall strain energy is an index capable of reflecting the overall mechanical performance of the structure. When the structure is in an elastic small deformation working state, the overall strain energy thereof can be calculated by using the formula.

[0054] Constraint conditions are set. In the construction process of the space structure, whether the structural deformation and stress meet the specification requirements needs to be considered, and the following constraint conditions need to be set:

[0055] (1) Maximum vertical displacement limit value

[0056]

[0057] In the formula, δ is the maximum vertical displacement (m) of the lifted structure, and L0 is the support point distance of the lifted structure.

[0058] (2) Allowable slenderness ratio

[0059]

[0060] The slenderness ratio λ of all members should meet the formula, and in some embodiments of the present application, for a compression-bending member, [λ] = 150, and for a tension-bending member, [λ] = 300. In formula (3), l0 and i are respectively the calculation length and the rotation radius of the member.

[0061] (3) Strength

[0062] The strength of the member is checked according to the following formula:

[0063]

[0064] In the formula, N, M x , and M y are respectively the axial force, the bending moment around the x-axis (strong axis), and the bending moment around the y-axis (weak axis), A n is the net cross-sectional area of the member, γ x and γ y are respectively the plastic development coefficients of the cross section around the x-axis and the y-axis, W nx and W ny are respectively the net cross-sectional modulus of the cross section around the x-axis and the y-axis, and f is the steel strength design value.

[0065] (4) Stability

[0066] The stability of the compression-bending member is checked by the following formula. For the solid compression-bending member with bending moment acting in the plane of symmetry, the stability in the plane of bending moment is calculated by formula (5) and the stability out of the plane of bending moment is calculated by formula (6). For the biaxial compression-bending member with bending moment acting in two principal planes, the stability is calculated by formula (7) and (8) for the solid I-shaped and box-shaped sections, and the overall stability of the biaxial compression-bending circular tube is calculated by formula (9):

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] In the formula, N, M x , and M y are the axial force, the bending moment around the x-axis (strong axis), and the bending moment around the y-axis (weak axis), respectively, A is the sectional area of the member, is the stability coefficient of the axial compression member, is the stability coefficient of the axial compression member in the plane of bending moment, is the stability coefficient of the axial compression member out of the plane of bending moment, and are the overall stability coefficients of the bending member, and β is the equivalent bending moment coefficient, β my and β my are the equivalent bending moment coefficients in the plane of bending moment, β tx and β ty are the equivalent bending moment coefficients out of the plane of bending moment, W is the gross sectional modulus, W 1x is the gross sectional modulus of the compression-maximum fiber in the plane of bending moment, W x and W y are the gross sectional moduli for the strong axis and the weak axis, respectively, γ m , γ x , and γ y are the sectional plastic development coefficients, N′ Ex and N′ ExEuler critical forces around x and y axis, the calculation formula is (10) and (11), λ 0x and λ 0y is the conversion slenderness ratio, and the section influence coefficient is 0.7 for the closed section in some embodiments of the present application, and 1.0 for the other.

[0075] Step three, growth search is performed. After each new set of growth points is generated, the value of the growth point is converted into a variable in actual construction, and the boundary conditions and loads of the spatial structure are modified accordingly, finite element analysis is performed, and the objective function value of the current growth point is obtained through calculation. Whether the response (such as deformation and stress) of the structure meets the requirements preset in step two is checked, and the growth points that do not meet the requirements are removed, and the set of growth points is obtained. The function values of each growth point in the set of growth points are sorted in size, and the morphogen concentration is calculated according to the set of growth points, so as to determine the next growth point. min Step three, growth search is performed. After each new set of growth points is generated, the value of the growth point is converted into a variable in actual construction, and the boundary conditions and loads of the spatial structure are modified accordingly, finite element analysis is performed, and the objective function value of the current growth point is obtained through calculation. Whether the response (such as deformation and stress) of the structure meets the requirements preset in step two is checked, and the growth points that do not meet the requirements are removed, and the set of growth points is obtained. The function values of each growth point in the set of growth points are sorted in size, and the morphogen concentration is calculated according to the set of growth points, so as to determine the next growth point.

[0076] In some embodiments of the present application, the growth points that do not meet the requirements include: the newly added growth points whose temporary support point number and position coordinate number exceed the feasible region, and the repeated newly added growth points.

[0077] Step four, the optimal value f min and the growth point x min of the current growth are found, and whether it is the global optimal value is judged. If yes, the global optimal value F min and the corresponding growth point X min are updated, otherwise the growth is continued. When the optimal solution is searched by the growth, the set of growth points is empty set, or the maximum number of growth is reached, the algorithm is terminated, and the global optimal solution is output, that is, the optimal scheme of construction.

[0078] In some embodiments of the present application, in order to study the applicability of the spatial structure construction temporary support point optimization method based on intelligent algorithm, a regular four-pyramid bolt-sphere flat plate grid structure is selected as the optimization object, a mixed algorithm running file is written by using MATLAB and ANSYS APDL language, and optimization is realized through data interaction.

[0079] A regular four-pyramid bolt-sphere flat plate grid structure is shown in Figure 2 , which is 43.9m long, 12.4m wide, and has a total building area of about 590m 2 . The grid members adopt steel pipes with diameters of 48*3.5 and 60*3.5, and the steel material is Q235. The elastic modulus of the steel material is 2.06*105 N / mm 2 , Poisson's ratio is 0.3, density 7850kg / m 3 .

[0080] The optimization variables, objective function, constraint conditions and other indexes in the calculation are defined as follows:

[0081] Optimization variables:

[0082] The position and number of the net rack lifting points are taken as the optimization variables. Specifically, 8 lifting point position variables are set in the optimization program, the different numbers represent different positions by numbering the lifting point feasible region alternative positions, and the number of the lifting point is taken as the optimization variable. 8 life and death variables are set to control the change of the number of the lifting point. Therefore, the total number of design variables N = 16.

[0083] Objective function:

[0084] The optimization objective of the present example is to obtain the smallest number of structure lifting points under the premise of meeting the structure response, and the minimum structure strain energy under the condition of the same number of lifting points, that is The combination parameter k of the present example is 1 x 10 -8 .

[0085] Constraint conditions:

[0086] Including maximum vertical displacement limit, allowable slenderness ratio, strength and stability.

[0087] Calculation results:

[0088] In the lifting optimization process, the optimization process of the PGSA algorithm is tracked and analyzed, and the results are shown in Figure 3 and Figure 4 .

[0089] The variable conditions before and after optimization are shown in Table 1, combined with Figure 3 and Figure 4 It can be seen that after optimization, the number of lifting points is reduced from 8 to 5, which has obvious optimization effect. After 33 growth by using the foregoing method of the present application, the number of lifting points is reduced to 5, and the structure strain energy is 1187.93J. After 76 growth, the optimal value of the objective function reaches 5.00067635, and the structure strain energy is reduced to the lowest value under the number of lifting points, which is 676.35J, which is reduced by 43.06% compared with the initial value of 5 lifting point optimization. After 276 growth, the growth space no longer produces new growth points and gradually becomes an empty set, and the program reaches the termination condition, and the optimization is completed.

[0090] Table 1 Comparison of optimization variables before and after optimization

[0091] Initial growth point [8 23 38 55 76 91 106 124 1 1 1 1 1 1 1 1] Optimal solution [9 25 40 59 71 87 94 114 1 0 0 1 1 0 1 1]

[0092] The lifting point positions of the structure before and after optimization are shown in Figs. Figure 5 and Figure 6 The displacement cloud maps are shown in Figs. Figure 7 and Figure 8 The maximum vertical displacement of the structure before optimization is 14.49 mm, the initial value of the maximum vertical displacement of the structure after entering the 5 lifting point optimization is 100.28 mm, and the final value of the maximum vertical displacement of the structure after optimization is 23.82 mm. The maximum stress of the structure before optimization is -49.89 MPa, the initial value of the maximum stress of the structure after entering the 5 lifting point optimization is -100.47 MPa, and the final value of the maximum stress of the structure after optimization is -70.12 MPa.

[0093] It can be seen that after the method is optimized, the lifting points are reduced and the structure response is correspondingly increased, but the structure response is still within the limit range. The method can be used for construction lifting point optimization, can find the optimal position of the lifting point on the basis of optimizing the number of lifting points, reduce the displacement and stress response of the structure, and has the significance of guiding the actual construction.

[0094] In some embodiments of the present application, a computer device is provided, comprising a memory and a processor, the memory stores a computer program, and the processor implements the steps of the method in the above-mentioned embodiments when executing the computer program.

[0095] In some embodiments of the present application, a computer readable storage medium is provided, which stores a computer program, and the computer program is executed by a processor to implement the steps of the method in the above-mentioned embodiments.

[0096] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by a computer program instructing related hardware, and the computer program can be stored in a non-volatile computer readable storage medium, and when executed, can include the processes of the above-mentioned embodiments.

[0097] In summary, the PGSA-based spatial structure construction temporary support point optimization method has good optimization effect in solving the optimization problem in the spatial structure construction process, can realize the synchronous optimization of the position and number of temporary support points, has the advantages of fast optimization speed and easy operation, and can be well applied to the guidance of the actual construction process of the spatial structure.

[0098] As described above, the present application can be well implemented.

[0099] The embodiments of the present application are not limited by the above-mentioned embodiments, and any changes, modifications, substitutions, combinations and simplifications made without departing from the spirit and principles of the present application shall be equivalent replacement methods and shall be included in the protection scope of the present application.

Claims

1. A method for optimizing temporary support points during spatial structure construction, characterized in that, Includes the following steps: Determine the construction optimization variables and optimization objectives; The actual construction optimization problem is transformed into a mathematical optimization problem. The locations of temporary support points are converted into feasible regions of growth points by numbering, and optimization variables are defined. The overall strain energy of the structure is taken as the objective function, and the initial growth point, growth step size, and constraints are defined. Among them, the location and number of temporary support points are determined as optimization variables of construction. The optimization objectives are to minimize the structural strain energy and optimize the location of temporary support points when the number of temporary support points is minimized. By numbering the candidate locations of the feasible regions of temporary support points and introducing the birth and death variables of temporary support points, the simultaneous optimization of location and number is achieved. The algorithm performs a growth search. After generating a new set of growable points, the values ​​of the grow points are transformed into variables in actual construction. The boundary conditions and loads of the spatial structure are modified accordingly. Finite element analysis is performed to calculate the objective function value of the grow points. The structural response is verified to meet the requirements. Based on the growth space optimization method of the objective function's merits, unqualified grow points are eliminated. The algorithm continuously obtains a set of growable points and calculates the morpheme concentration based on the set of grow points to determine the next grow point. When the growth search finds the optimal solution or reaches the maximum number of growth iterations, the algorithm terminates and outputs the global optimal solution, which is the optimal construction plan.

2. The method for optimizing temporary support points in spatial structure construction according to claim 1, characterized in that, The objective function is: In the formula: To optimize the target value, variables x and y are designed as the lift point location number and quantity, respectively. Q To increase the number of points, k is a combination parameter. P The external load vector of the structure. U Let be the nodal displacement vector of the structure. This refers to the structural strain energy.

3. The method for optimizing temporary support points in spatial structure construction according to claim 1, characterized in that, The constraints include the maximum vertical displacement limit, the allowable slenderness ratio of the component, strength, and stability constraints.

4. The method for optimizing temporary support points in spatial structure construction according to claim 3, characterized in that, The constraints include: Maximum vertical displacement limit ; The allowable aspect ratio must meet the following requirements. ; The formula for verifying the strength of a component is as follows: ; For a solid-web compression-bending member with bending moment acting in the plane of symmetry, the formula for calculating stability in the plane of bending moment is as follows: The formula for calculating out-of-plane stability under bending moment is: The formula for calculating the stability of biaxially symmetric solid-web I-beam and box-section compression-bending members with bending moments acting in two principal planes is as follows: , The formula for calculating the stability of a circular tube member subjected to bending moment under biaxial compression and bending is as follows: ; In the formula, The distance between the support points of the lifted structure. , These are the calculated length and radius of gyration of the component, respectively. Let be the net cross-sectional area of ​​the component. and These are the net section modulus of the cross section with respect to the x-axis and y-axis, respectively. This is the design strength value for steel. , , , These are the axial force, bending moment, bending moment about the x-axis, and bending moment about the y-axis of the member, respectively. The cross-sectional area of ​​the component. For a member under axial compression, the stability coefficient is... This is the stability coefficient of an axially compressed member in the plane of bending moment. This is the stability coefficient of an axially compressed member outside the plane of bending moment. , and The overall stability coefficient of the bending member. This is the equivalent bending moment coefficient. and This is the equivalent bending moment coefficient in the plane of action of the bending moment. and The out-of-plane equivalent bending moment coefficient is the bending moment coefficient. For gross section modulus, This is the gross section modulus of the fiber under maximum compression in the plane of bending moment. and These are the gross section moduli about the strong axis and the weak axis, respectively. , and The coefficient for plastic development of the cross section. and These are the Euler critical forces about the x-axis and y-axis, respectively. and To convert the slenderness ratio, This is the cross-sectional influence coefficient.

5. The method for optimizing temporary support points in spatial structure construction according to claim 1, characterized in that, The growth points that do not meet the conditions include: new growth points whose number of temporary support points and location coordinates exceed the feasible domain, and duplicate new growth points.

6. The method for optimizing temporary support points in spatial structure construction according to any one of claims 1-5, characterized in that, During the growth search, the objective function value of the initial growth point is obtained through structural analysis. f (x0) and use it as the global optimum. F min The initial value is determined, and then a parallel search is performed with multiple different growth lengths to generate new growth points for the current growth cycle.

7. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

Citation Information

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