A method for evaluating and optimizing the progressive collapse resistance of cable dome structures

Abstract

The present invention discloses a method for evaluating and optimizing the anti-progressive collapse performance of a cable dome structure. The evaluation method comprises the following steps: (1) obtaining, for each type of component, the displacement vector of the cable dome structure under load before and after the component is removed; (2) calculating its rate of change as an importance index of the component; (3) calculating the average importance index of all types of components as an evaluation index for the anti-progressive collapse performance of the cable dome structure; and (4) evaluating the anti-progressive collapse capability of the cable dome structure. The present invention introduces a component importance index to evaluate the importance of various types of components in the anti-progressive collapse of the structure, and uses its average value as a quantitative evaluation index for the anti-progressive collapse performance of the cable dome structure, which is reliable and effective. The evaluation method requires a small amount of calculation, does not require excessive external factor assumptions, and can be used in the optimization process of complex topological structures of cable domes.

Description

Technical Field

[0001] The present invention belongs to the field of architectural design, and more specifically, relates to a method for evaluating and optimizing the progressive collapse resistance of a cable dome structure. Background Art

[0002] The cable dome is a flexible structure based on Fuller's tensegrity concept, constructed from cables and struts and formed through tensioning. By leveraging the high tensile strength of the cables and applying prestress to control structural stiffness, the structure boasts numerous advantages, including light weight, excellent load-bearing capacity, and lightweight construction, leading to widespread practical engineering applications. With economic development and technological advancement, cable domes are poised to develop towards even larger spans, more complex forms, and innovative materials. However, they are also exposed to a variety of extreme and accidental loads, such as blasts and extreme weather conditions, which can lead to frequent progressive collapse events. Therefore, research on the progressive collapse resistance of flexible tensile structures, such as cable domes, is of great significance.

[0003] Current research on progressive structural collapse primarily focuses on frame structures, with relatively little research on long-span spatial structures. This is primarily due to the widespread belief that traditional long-span spatial structures, such as lattice shells, have high static indeterminacy, leading to the assumption that the failure of a single component is insufficient to significantly reduce the overall structural load-bearing capacity. However, cable domes differ from traditional long-span structures such as lattice shells in that they have low redundancy and are sensitive to unexpected disturbances such as construction errors, making them prone to collapse under overload or unexpected disturbances. Researchers such as Fan Feng, using techniques such as life-and-death units, instantaneous component removal, and transient loading to simulate cable breakage, have analyzed the internal force changes and node displacement responses of various cable dome structures after local failure and cable breakage. Researchers such as Jiang Xiaofeng, Cai Jianguo, and Zeng Bin have analyzed the dynamic response and collapse of various cable-string structures, including beam-string, cable-arch, and cable-string trusses, after local failure or cable breakage.

[0004] At present, the optimization design of cable dome structures generally focuses on four aspects: prestressing optimization, cross-section optimization, shape optimization and topology optimization. Among them, cross-section optimization, shape optimization and topology optimization are mainly carried out around the optimization goal of minimizing the weight of the structure. In fact, the weight of the cable dome structure itself is relatively light, and the steel consumption is generally less than 30kg / m 2, further quality optimization is of little significance. Therefore, design based on structural performance (such as progressive collapse resistance) is more valuable for theoretical research and engineering applications. However, the progressive collapse resistance of flexible tension structures such as cable domes is currently mostly evaluated from a qualitative and conceptual perspective, lacking a unified quantitative evaluation index. Existing evaluation methods, including robust indicators based on H∞ control theory, are not only theoretically demanding and computationally intensive, but also difficult to widely apply. Furthermore, the optimization design of progressive collapse resistance under extremely complex loading conditions has not yet been carried out. Summary of the Invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides a method for evaluating and optimizing the progressive collapse resistance of a cable dome structure. The method aims to evaluate the progressive collapse resistance of a cable dome topology by evaluating the rate of change of the structural displacement vector before and after removing specific types of components, and using the average value thereof. It has been verified that the index can be used to quantitatively evaluate the progressive collapse resistance of the dome structure, and the computational complexity is small. The method is applied to the optimization of the cable dome topology structure, simplifies the optimization problem, and brings the computational complexity of the topology optimization within an acceptable range. This solves the technical problem that the prior art lacks a reliable quantitative evaluation index to evaluate the progressive collapse resistance of the overall topology structure of the cable dome, and that when using evaluation indicators such as robustness for topology optimization, the computational complexity of the topology optimization is too large due to the excessive number of parameters that need to be assumed in advance.

[0006] To achieve the above object, according to one aspect of the present invention, a method for evaluating the progressive collapse resistance of a cable dome topology structure is provided, which comprises the following steps:

[0007] (1) For each type of component in the cable dome structure to be optimized, a dynamic response analysis is performed to obtain the displacement vector of the cable dome structure under load before and after the component is removed;

[0008] (2) according to the displacement vectors of the cable dome structure under load before and after the removal of each type of component obtained in step (1), calculating the rate of change of the displacement response of the cable dome structure under load as the importance index of the component;

[0009] (3) For the cable dome structure to be optimized, the average importance index of all categories of components is calculated as an evaluation index of the anti-progressive collapse performance of the cable dome structure;

[0010] (4) According to the principle that the greater the progressive collapse resistance index of the cable dome structure, the worse the progressive collapse resistance of the cable dome structure, the anti-progressive collapse capability of the cable dome structure is evaluated.

[0011] Preferably, in the method for evaluating the progressive collapse resistance of a cable dome topological structure, the dynamic response analysis in step (1) is performed using a full dynamic equivalent load instantaneous unloading method, namely:

[0012] The component is replaced by an equivalent force, and then the equivalent force is unloaded. The displacement response when the equivalent force begins to be unloaded and when it reaches the final state under damping is recorded, and the displacement vector of the cable dome structure under load before and after the component is removed is obtained.

[0013] Preferably, in the method for evaluating the progressive collapse resistance of a cable dome topological structure, the importance index of the component in step (2) is calculated as ρ i Calculate as follows:

[0014]

[0015] Where ‖‖ represents the Euclidean norm, s0, s 1i are the displacement vectors of the structure under load before and after component i is removed. i The smaller it is, the smaller the displacement response of the structure after removing a certain component i is, and the less important the component is, otherwise it is more important.

[0016] Preferably, in the method for evaluating the progressive collapse resistance of a cable dome topological structure, the progressive collapse resistance index of the cable dome structure in step (3) is calculated according to the following method:

[0017]

[0018] in, is the progressive collapse resistance index of the cable dome structure, and n is the total number of component categories of the cable dome structure.

[0019] According to another aspect of the present invention, a method for optimizing a cable dome topology based on progressive collapse resistance is provided, comprising the following steps:

[0020] S1. Obtaining preset constraints of the optimization solution, determining the topology optimization variables and the search range of the optimization variables according to the constraints, and obtaining the topology optimization space;

[0021] S2. Determine the value of the optimization variable in the topological structure optimization space determined in step S1 to obtain the cable dome structure to be evaluated;

[0022] S3. Using the method for evaluating the progressive collapse resistance of a cable dome topological structure provided by the present invention, quantitatively evaluate the progressive collapse resistance of the cable dome structure to be evaluated obtained in step S2;

[0023] S4. Repeat steps S2 and S3 until the progressive collapse resistance of the cable dome structure to be evaluated reaches a preset optimization condition, and then output the cable dome structure as a topology structure optimization result.

[0024] Preferably, in the cable dome topology structure optimization method based on progressive collapse resistance, the preset constraint conditions in step S1 include the range of the number of cable trusses, the range of structural topology shape redundancy, etc.

[0025] Preferably, in the cable dome topology structure optimization method based on progressive collapse resistance, the preset optimization conditions in step S4 include:

[0026] Progressive collapse resistance index of cable dome structure smallest;

[0027] Progressive collapse resistance index of cable dome structure The degree of reduction exceeds a preset threshold;

[0028] The progressive collapse resistance index of the cable dome structure to be evaluated in the last two times The difference is less than the preset threshold.

[0029] According to another aspect of the present invention, a method for optimizing the progressive collapse resistance of a cable dome topology structure is provided, comprising the following steps:

[0030] A. For a cable dome structure to be optimized, the cable dome topology structure is optimized according to the cable dome topology structure optimization method based on progressive collapse resistance according to any one of claims 5 to 7 to obtain an optimized structural topology shape of the cable dome structure;

[0031] B. For the structural topology shape of the optimized cable dome structure obtained in step A, extract its single-frame model for local shape optimization.

[0032] Preferably, in the method for optimizing the progressive collapse resistance of the cable dome topology structure, the specific steps of performing local optimization of the shape of the single element in step B are as follows:

[0033] B1. For the optimized cable dome structure, obtain the component importance index ρ of each type of component i Normalize to obtain the component importance coefficient β of each type of component j ; Calculate according to the following method:

[0034]

[0035] Where n is the total number of component categories, j = 1, 2,…, n.

[0036] B2. Extract the single-frame model of the structural topology of the cable dome structure to reduce the maximum value of the member importance coefficient β of the components in the single-frame model max As the optimization goal, the shape characteristics of a single frame model are used as optimization variables and the optimization algorithm is used for optimization.

[0037] Preferably, the optimization algorithm of the method for optimizing the progressive collapse resistance of the cable dome topology structure is preferably a global optimization algorithm.

[0038] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0039] This paper introduces a component importance index to evaluate the importance of various components in the structure's progressive collapse resistance, and uses its average value as a quantitative indicator for the cable dome's progressive collapse resistance. This index reliably and effectively provides a quantitative assessment of the cable dome's progressive collapse resistance. Furthermore, the dynamic response and collapse mode resulting from local component failure in a typical cable dome case study were analyzed using the ANSYS / LS-DYNA platform. This evaluation method requires minimal computational effort and eliminates the need for excessive external factor assumptions. It can be applied to the optimization of complex cable dome topologies, maintaining an acceptable computational burden.

[0040] Finally, the present invention proposes a step-by-step optimization design scheme based on the combination of overall optimization and local optimization to improve the overall progressive collapse resistance of the cable dome structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a schematic diagram of the roof structure of the Yiqi National Fitness Sports Center in Inner Mongolia, which is the optimization object of the embodiment of the present invention; Figure 1 (a) is the structural model, Figure 1 (b) is the structural plan; Figure 1 (b) is a cross-sectional view of the structure;

[0042] Figure 2 This is a schematic diagram of the entire process of equivalent force action according to an embodiment of the present invention;

[0043] Figure 3 is the displacement response analysis result of the embodiment of the present invention, wherein Figure 3 (a) is the vertical displacement response when the equivalent force begins to unload; Figure 3 (b) is the vertical displacement response when reaching the final state under damping;

[0044] Figure 4 is an energy response time history diagram of an embodiment of the present invention;

[0045] Figure 5 is a time history diagram of internal force response according to an embodiment of the present invention;

[0046] Figure 6 Schematic diagram of the topological structure model with different numbers of frames in the embodiment of the present invention, wherein Figure 6 (a) is a schematic diagram of the 16-frame topological structure model; Figure 6 (b) is a schematic diagram of the 12-frame topological structure model;

[0047] Figure 7 Schematic diagram of different topological structure models according to the embodiment of the present invention, wherein Figure 7 (a) is a schematic diagram of the structure of Dome #1. Figure 7 (b) is a schematic diagram of the structure of Dome #2. Figure 7 (c) is a schematic diagram of the dome #3 structure. Figure 7 (d) is a schematic diagram of the structure of dome #4;

[0048] Figure 8 The statistical results of importance coefficients after normalization of 13 types of rods in Example 1 of the present invention are as follows;

[0049] Figure 9 It is a schematic diagram of the local optimization result of an embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0051] The method for evaluating the progressive collapse resistance of a cable dome topological structure provided by the present invention comprises the following steps:

[0052] (1) For each type of component in the cable dome structure to be optimized, a dynamic response analysis is performed to obtain the displacement vector of the cable dome structure under load before and after the component is removed;

[0053] The dynamic response analysis is preferably performed using the full dynamic equivalent load instantaneous unloading method, namely:

[0054] Substituting the component for the component with an equivalent force, then unloading the equivalent force, recording the displacement response when the equivalent force begins to be unloaded and reaches the final state under damping, and obtaining the displacement vector of the cable dome structure under load before and after the component is removed;

[0055] (2) according to the displacement vectors of the cable dome structure under load before and after the removal of each type of component obtained in step (1), calculating the rate of change of the displacement response of the cable dome structure under load as the importance index of the component;

[0056] The importance index of the component is expressed as ρ i Calculate as follows:

[0057]

[0058] Where ‖‖ represents the Euclidean norm, s0, s 1i are the displacement vectors of the structure under load before and after component i is removed. i The smaller it is, the smaller the displacement response of the structure after removing a certain component i is, and the less important the component is, otherwise it is more important.

[0059] (3) For the cable dome structure to be optimized, the average importance index of all categories of components is calculated as the anti-progressive collapse performance evaluation index of the cable dome structure; the anti-progressive collapse performance index of the cable dome structure is calculated according to the following method:

[0060]

[0061] in, is the progressive collapse resistance index of the cable dome structure, and n is the total number of component categories of the cable dome structure.

[0062] (4) According to the principle that the greater the progressive collapse resistance index of the cable dome structure, the worse the progressive collapse resistance of the cable dome structure, the anti-progressive collapse capability of the cable dome structure is evaluated.

[0063] The cable dome topology optimization method based on progressive collapse resistance performance includes the following steps:

[0064] S1. Obtaining preset constraints of the optimization solution, determining the topology optimization variables and the search range of the optimization variables according to the constraints, and obtaining the topology optimization space;

[0065] The preset constraints, such as the range of the number of cable trusses, the range of the redundancy of the structural topology, etc.;

[0066] S2. Determine the value of the optimization variable in the topological structure optimization space determined in step S1 to obtain the cable dome structure to be evaluated;

[0067] S3. Using the method for evaluating the progressive collapse resistance of a cable dome topological structure provided by the present invention, quantitatively evaluate the progressive collapse resistance of the cable dome structure to be evaluated obtained in step S2;

[0068] S4. Repeat steps S2 and S3 until the progressive collapse resistance of the cable dome structure to be evaluated reaches a preset optimization condition, and then output the cable dome structure as a topology structure optimization result.

[0069] The preset optimization conditions include but are not limited to:

[0070] Progressive collapse resistance index of cable dome structure smallest;

[0071] Progressive collapse resistance index of cable dome structure The degree of reduction exceeds a preset threshold;

[0072] The progressive collapse resistance index of the cable dome structure to be evaluated in the last two times The difference is less than the preset threshold.

[0073] The method for optimizing the progressive collapse resistance of a cable dome topology structure provided by the present invention comprises the following steps:

[0074] A. For a cable dome structure to be optimized, the cable dome topology structure is optimized according to the cable dome topology structure optimization method based on the progressive collapse resistance performance provided by the present invention to obtain the optimized structural topology shape of the cable dome structure;

[0075] B. For the structural topology of the optimized cable dome structure obtained in step A, extract its single-frame model for local shape optimization. The specific steps for local optimization of the single-frame shape are as follows:

[0076] B1. For the optimized cable dome structure, obtain the component importance index ρ of each type of component i Normalize to obtain the component importance coefficient β of each type of component j ; Calculate according to the following method:

[0077]

[0078] Where n is the total number of component categories, j = 1, 2,…, n.

[0079] B2. Extract the single-frame model of the structural topology of the cable dome structure to reduce the maximum value of the member importance coefficient β of the components in the single-frame model max As the optimization target, the shape characteristics of the single frame model are used as optimization variables and an optimization algorithm is used for optimization; the optimization algorithm is preferably a global optimization algorithm, such as a genetic algorithm.

[0080] The following are examples:

[0081] Taking the Geiger cable dome structure as an example, the roof of the National Fitness Center in Yiqi, Inner Mongolia, Figure 1As shown in the figure, the span is 71.2 meters, the rise is 5.5 meters, the truss is divided into 20 equal parts in the circumference, and is arranged symmetrically along the center. Each cable truss includes 13 types of members, including outer inclined cables (DC1), middle inclined cables (DC2), inner inclined cables (DC3), outer ridge cables (RC1), middle ridge cables (RC2), inner ridge cables (RC3), outer support rods (OS), middle support rods (MS), inner support rods (IS), outer hoop cables (OHC), inner hoop cables (IHC), inner tension ring upper chords (IUS) and inner tension ring lower chords (ILS), with a design load of 0.4KN / m 2 The structure is fixed and hinged on the surrounding compression ring beam. The structural plan and section of the structural model are as follows: Figure 1 The cross-sectional parameters and initial prestress of each component are shown in Table 1, where the elastic moduli of the cables and compression rods are 160 GPa and 206 GPa, respectively.

[0082] Table 1 Structural component parameters and initial prestress values

[0083]

[0084] The method for evaluating the progressive collapse resistance of a cable dome topological structure provided by the present invention comprises the following steps:

[0085] (1) For each type of component in the cable dome structure to be optimized, a dynamic response analysis is performed to obtain the displacement vector of the cable dome structure under load before and after the component is removed;

[0086] The dynamic response analysis is performed using the full dynamic equivalent load instantaneous unloading method, namely:

[0087] Substituting the component for the component with an equivalent force, then unloading the equivalent force, recording the displacement response when the equivalent force begins to be unloaded and reaches the final state under damping, and obtaining the displacement vector of the cable dome structure under load before and after the component is removed;

[0088] The specific steps are as follows:

[0089] Cable-strut element and equivalent force model establishment:

[0090] When analyzing with Ansys / Ls-dyna software, LINK167 and LINK160 are selected to simulate cable and rod elements respectively, and prestress is applied by defining the offset. The formula is as follows:

[0091] F=K×max{ΔL,0.0}

[0092] K=EA / (L0-offset)

[0093] Where ΔL and L0 are the length change and initial length of the member, respectively; E and A are the elastic modulus and cross-sectional area, respectively; and offset is the offset. For the LINK160 rod element, a bilinear dynamic material model is used, and the failure strain is defined as 0.01. This means that during the analysis, if the rod element strain exceeds 0.01, it is removed from the structure.

[0094] The full dynamic equivalent load instantaneous unloading method is used for analysis: the replacement time, duration and unloading time of the equivalent force are respectively 2 times, 20 times and 1 / 10 times of the residual structure natural vibration period (2s in this embodiment). The whole process time of the equivalent force in this embodiment is as follows: Figure 2 shown.

[0095] Analysis of the displacement response of the structure after removing the outer ring cable:

[0096] Figure 3 Figures (a) and (b) show the vertical displacement responses at the beginning of the equivalent force unloading (t = 44 s) and at the final state under damping (t = 200 s), respectively. It can be seen that: 1) after the equivalent force replaces the member and reaches equilibrium, the node displacement is consistent with the initial structure. 2) After the external ring cable is removed, the connected nodes 2 and 9 rapidly move to either side of the ring, causing the other external ring cable units and all the members connected to the external ring cable to experience varying degrees of horizontal displacement. 3) Due to the failure of the external ring cable and the resulting weakening of its support for the external compression member, all the upper and lower nodes of the external compression member experienced significant vertical displacement. Nodes 3 and 2, directly connected to the failed member, experienced vertical displacements of 5.03 m and 2.49 m, respectively. The displacement changes of the external compression member nodes of other cable-truss trusses are negatively correlated with the distance from the failed member.

[0097] In addition, internal force and energy response and collapse mode analysis are carried out as follows:

[0098] Energy response analysis: Figure 4 The figure shows the change of kinetic energy of the structure within t=200s. It can be found that: 1) After the equivalent force replaced the failed member, the structure showed a certain kinetic energy response, and the structure was in a non-equilibrium state. After that, the kinetic energy gradually decreased under the action of damping, and the kinetic energy in the structure became 0 44 seconds ago. 2) Unloading began at t=44s, and the structure changed from an equilibrium state to an unequilibrium state again. The internal force began to redistribute, and a large kinetic energy appeared. After that, the kinetic energy gradually decreased under the action of damping, and tended to an equilibrium state again around 75s, and the kinetic energy became 0.

[0099] Internal force response analysis: Figure 5This graph shows the time-course evolution of the internal forces in the cable-truss members adjacent to the failed outer hoop cable. It reveals the following: 1) After the outer hoop cable was removed, the internal forces in the outer ridge cable, outer hoop cable, and outer compression member directly connected to node 2 all reached zero. Afterward, the structure redistributed internal forces, allowing these members to continue functioning. However, the outer hoop cable experienced the greatest loss of prestress, decreasing by 90%. 2) The internal forces in the other members decreased to varying degrees, with the outer oblique cable experiencing the most significant reduction, a 90% decrease.

[0100] Collapse mode analysis: After removing the external cables, the structure experienced a significant dynamic response; nearly all components experienced displacements exceeding 1 / 50 of their span. By the time the structure reached final equilibrium, the prestress had been virtually completely lost, resulting in 100% collapse. The maximum vertical displacement occurred at node 17 (the upper node of the external compression rod), producing a 5.58m vertical displacement.

[0101] (2) according to the displacement vectors of the cable dome structure under load before and after the removal of each type of component obtained in step (1), calculating the rate of change of the displacement response of the cable dome structure under load as the importance index of the component;

[0102] The importance index of the component is expressed as ρ i Calculate as follows:

[0103]

[0104] Where ‖‖ represents the Euclidean norm, s0, s 1i are the displacement vectors of the structure under load before and after component i is removed. i The smaller it is, the smaller the displacement response of the structure after removing a certain component i is, and the less important the component is, otherwise it is more important.

[0105] The dynamic response and collapse mode of the structure after removing all the members in sequence are analyzed. The results are shown in Table 2. It can be found that removing different members will produce different dynamic responses and collapse modes. Among them, removing the inner and outer ring cables will produce a large collapse area and a large vertical displacement; removing the upper chord of the tension ring is the second most severe; removing the outer oblique cable, middle oblique cable, inner oblique cable, outer ridge cable, middle ridge cable, inner ridge cable, outer pressure rod, middle pressure rod, inner pressure rod and the lower chord of the tension ring is the least severe, indicating that different members have different importance for the continuous collapse of the structure.

[0106] Table 2 Dynamic responses and collapse modes caused by removing different members

[0107]

[0108]

[0109] (3) For the cable dome structure to be optimized, the average importance index of all categories of components is calculated as the anti-progressive collapse performance evaluation index of the cable dome structure; the anti-progressive collapse performance index of the cable dome structure is calculated according to the following method:

[0110]

[0111] in, is the progressive collapse resistance index of the cable dome structure, and n is the total number of component categories of the cable dome structure.

[0112] The anti-progressive collapse performance index of the Yiqi National Fitness Center in Inner Mongolia was calculated. The results are:

[0113] (4) According to the principle that the greater the progressive collapse resistance index of the cable dome structure, the worse the progressive collapse resistance of the cable dome structure, the anti-progressive collapse capability of the cable dome structure is evaluated.

[0114] To verify the reliability of the average importance index provided by this invention as an evaluation metric for progressive collapse resistance, the present invention altered the progressive collapse resistance of a cable dome structure by adjusting the number of topological bays. With other conditions remaining unchanged, a greater number of topological bays in a cable dome structure resulted in better progressive collapse resistance.

[0115] The number of cable trusses in the original structure is adjusted from 20 to 16 and 12, such as Figure 6 As shown in Figure 2, the calculated progressive collapse resistance performance indicators are: It can be seen that as the number of structural cable trusses gradually decreases, the anti-progressive collapse performance index gradually increases, and the overall anti-progressive collapse performance gradually weakens. This index can reflect the anti-progressive collapse performance of the overall topological structure and is suitable for quantitatively evaluating the anti-progressive collapse ability of the cable dome structure.

[0116] The cable dome topology optimization method based on progressive collapse resistance provided in this embodiment includes the following steps:

[0117] S1. Obtaining preset constraints of the optimization solution, determining the topology optimization variables and the search range of the optimization variables according to the constraints, and obtaining the topology optimization space;

[0118] The preset constraints are as follows: in terms of structural topology, the Geiger and Levy cable rod arrangements, which are currently the most common and most widely used in engineering projects, are mainly adopted; in terms of the number of cable trusses, the more the number, the better the resistance to progressive collapse, but this increases the cost and construction price, and the angles between adjacent cable trusses are too small, which increases the difficulty of node construction. Therefore, the number of cable trusses in this article is controlled to no more than 20.

[0119] S2. Determine the value of the optimization variable in the topological structure optimization space determined in step S1 to obtain the cable dome structure to be evaluated;

[0120] This embodiment takes the change of structural topology and enhancement of structural redundancy as an example. Based on the original topological structure model Dome #1, the topological relationship of the original structure's outer ring cable rod components is adjusted from Geiger type to Levy type to obtain Dome #2. Based on Dome #2, the topological relationship of the structure's middle ring cable rod components is adjusted from Geiger type to Levy type to obtain Dome #3. Based on Dome #3, the topological relationship of the structure's inner ring cable rod components is further adjusted from Geiger type to Levy type to obtain Dome #4. Figure 7 shown.

[0121] S3. Using the method for evaluating the progressive collapse resistance of a cable dome topological structure provided by the present invention, quantitatively evaluate the progressive collapse resistance of the cable dome structure to be evaluated obtained in step S2;

[0122] S4. Repeat steps S2 and S3 until the progressive collapse resistance of the cable dome structure to be evaluated reaches a preset optimization condition, and then output the cable dome structure as a topology structure optimization result.

[0123] The preset optimization conditions for the selection amount in this embodiment are:

[0124] The progressive collapse resistance index of the dome structure smallest;

[0125] The study shows that as the topological relationship of the members gradually adjusts from the Geiger type to the Levy type from the outer circle to the inner circle, the overall performance index of the structure gradually decreases, and the overall anti-progressive collapse performance gradually increases: the anti-progressive collapse performance index of the dome #1 element model is The progressive collapse resistance index of Dome #2 is The progressive collapse resistance index of Dome #3 is The progressive collapse resistance index of Dome #4 is

[0126] After overall optimization, the importance coefficient of the outer ring cable members decreased from 0.5355 in Dome #1 to 0.5083 in Dome #4, a decrease of 5.08%. This indicates that both changing the structural topology and increasing structural redundancy can effectively improve the overall progressive collapse resistance of the structure.

[0127] The method for optimizing the progressive collapse resistance of a cable dome topology structure provided in this embodiment includes the following steps:

[0128] A. For a cable dome structure to be optimized, the cable dome topology structure is optimized according to the cable dome topology structure optimization method based on the progressive collapse resistance performance provided by the present invention to obtain the optimized structural topology shape of the cable dome structure;

[0129] Dome #4 designed in this embodiment, i.e., the Levy-type cable dome structure, was further locally optimized.

[0130] It is particularly important to note here that the topological structure optimization is aimed at the optimization of the overall structure of the cable dome. Therefore, it is necessary to adopt absolute data indicators, that is, the progressive collapse resistance index as the optimization target. For local optimization, it is necessary to focus on the overall performance. Therefore, the data needs to be normalized to reflect the relative data changes within the structure. The maximum value of the component importance coefficient needs to be used as the optimization target.

[0131] B. For the structural topology of the optimized cable dome structure obtained in step A, extract its single-frame model for local shape optimization. The specific steps for local optimization of the single-frame shape are as follows:

[0132] B1. For the optimized cable dome structure, obtain the component importance index ρ of each type of component i Normalize to obtain the component importance coefficient β of each type of component j ; Calculate according to the following method:

[0133]

[0134] Wherein, n is the total number of component categories, j=1, 2, ..., n, and in this embodiment, n=13.

[0135] This example calculates 13 types of rods, specifically as follows:

[0136]

[0137] Figure 8 The importance coefficients of the 13 types of members in this case show that: (1) Each type of member has a different importance coefficient, among which the member importance coefficient of the outer ring cable is the largest, followed by the inner ring cable. The structural dynamic response after the member is removed is large, and it is a key member. (2) The importance coefficient of the tension ring chord is second, and the impact on the structure after removal is large, and it is an important member. (3) The importance coefficients of the other types of members are small, and no (local) continuous collapse will occur after removal, and they are ordinary members. (4) In general, the order of the importance coefficients of the various types of members is: ring cable > ridge cable > oblique cable > compression member.

[0138] B2. Extract the single-frame model of the structural topology of the cable dome structure to reduce the maximum value of the member importance coefficient β of the components in the single-frame model maxAs the optimization target, the shape characteristics of the single frame model are used as optimization variables and an optimization algorithm is used for optimization; the optimization algorithm is preferably a global optimization algorithm, such as a genetic algorithm.

[0139] From the above analysis of the importance coefficient of the rod, it can be seen that the larger the importance coefficient of the rod, the greater the dynamic response after removal, and the more likely it is to cause the progressive collapse of the structure. Therefore, we further explore the optimization model that makes the maximum value of the importance coefficient of the rod as small as possible, that is, explore β max For the model in this paper, the importance coefficient of the outer ring cable (member 10) is the largest, so the optimization objective is minβ 10 .

[0140]

[0141] Where, X i is the optimization variable. Studies have shown that shape parameters have a significant impact on the structural resistance to progressive collapse compared to parameters such as component cross-section size and prestress size. Therefore, this paper takes three groups of shape parameter variables for optimization design: (1) the height difference S1 between the upper node of the outer pressure rod (node 3) and the support node (node 1), and the height difference S2 between the upper node of the middle pressure rod (node 5) and the support node (node 1); (2) the length H1 of the outer pressure rod and the length H2 of the middle pressure rod; (3) the radius R1 of the outer ring cable and the radius R2 of the inner ring cable; Figure 9 As shown. X i,max and X i,min To optimize the upper and lower limits of the variables, 120% and 80% of the initial values of each variable are taken respectively, as shown in Table 3.

[0142] Table 3 Control range of each optimization variable

[0143]

[0144] A genetic algorithm was used, and the optimization design was performed using the interactive algorithm of MATLAB and ANSYS / LS-DYNA. The specific process is as follows: (1) Based on the accuracy of the solution and the number of variables, individuals of appropriate length were generated in MATLAB and formed into an initial population. The population size was set to 20 in this paper. (2) MATLAB input the basic information of each individual in the initial population into ANSYS / LS-DYNA, established a basic structural model, and calculated the prestress of each member through an iterative method. (3) ANSYS / LS-DYNA calculated the fitness value based on the optimization index, then saved all the result information and input it back to MATLAB for recording. (4) The calculation results of each individual were summarized and analyzed, and the best individual was selected, and its individual code and individual solution were recorded. (5) The best individual code was generated through crossover mutation to generate a new code. The crossover probability was set to 0.8 and the mutation probability was set to 0.2 in this paper. (6) Based on the number of iterations (set to 200 in this paper), it was decided whether to continue the optimization. If not, the process would return to the first step. If yes, the final optimal solution would be output.

[0145] Through the iterative optimization process of the outer loop importance coefficient, it can be found that (1) as the number of iterations increases, the structural optimization index β 10 Continuously decreasing, after 82 times, the optimization index tends to be stable; (2) During the optimization process, β 10 It dropped from 0.5083 to 0.2020, with an optimization rate of 60.26%. At this time, S1=2.7118, S2=4.7452, H1=8.0957, H2=6.8778, R1=29.0796, R2=13.5751; (3) The study also found that the three groups of variables have different optimization efficiencies when they are optimized separately, among which the optimization efficiency of the ring cable radius is the highest, reaching 53.73%; the compression rod length is second, at 10.35%; and the node elevation on the compression rod is the worst, at only 1.01%.

[0146] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for evaluating the progressive collapse resistance of a cable dome topology structure, characterized in that: The following steps are involved: (1) For each type of component in the cable dome structure to be optimized, a dynamic response analysis is performed to obtain the displacement vector of the cable dome structure under load before and after the component is removed; (2) Based on the displacement vectors of the cable dome structure under load before and after the removal of each type of component obtained in step (1), the rate of change of the displacement response of the cable dome structure under load is calculated as the importance index of the component; the importance index of the component is calculated as follows: Calculate as follows: ； in represents the Euclidean norm, 、 Components Displacement vectors of the structure under load before and after removal; The smaller it is, the more components are removed. The smaller the displacement response of the post-structure, the less important the component is, and vice versa; (3) For the cable dome structure to be optimized, the average importance index of all categories of components is calculated as the anti-progressive collapse performance evaluation index of the cable dome structure; the anti-progressive collapse performance index of the cable dome structure is calculated according to the following method: ； in, is the progressive collapse resistance index of the cable dome structure. is the total number of component categories of the cable dome structure; (4) According to the principle that the greater the progressive collapse resistance index of the cable dome structure, the worse the progressive collapse resistance of the cable dome structure, the anti-progressive collapse capability of the cable dome structure is evaluated.

2. The method for evaluating the progressive collapse resistance of a cable dome topological structure according to claim 1, wherein: The dynamic response analysis in step (1) is performed using the full dynamic equivalent load instantaneous unloading method, namely: The component is replaced by an equivalent force, and then the equivalent force is unloaded. The displacement response when the equivalent force begins to be unloaded and reaches the final state under damping is recorded to obtain the displacement vector of the cable dome structure under load before and after the component is removed.

3. A method for optimizing cable dome topology based on progressive collapse resistance, characterized in that: The following steps are involved: S1. Obtaining preset constraints of the optimization solution, determining the topology optimization variables and the search range of the optimization variables according to the constraints, and obtaining the topology optimization space; S2. Determine the value of the optimization variable in the topological structure optimization space determined in step S1 to obtain the cable dome structure to be evaluated; S3. quantitatively evaluating the progressive collapse resistance of the cable dome structure obtained in step S2 using the progressive collapse resistance evaluation method for a cable dome topological structure according to any one of claims 1 to 2; S4. Repeat steps S2 and S3 until the progressive collapse resistance of the cable dome structure to be evaluated reaches a preset optimization condition, and then output the cable dome structure as a topology structure optimization result.

4. The cable dome topology optimization method based on progressive collapse resistance according to claim 3, characterized in that: The preset constraint conditions in step S1 include the range of the number of cable trusses and the range of redundancy of the structural topology shape.

5. The cable dome topology optimization method based on progressive collapse resistance according to claim 3, characterized in that: The preset optimization conditions in step S4 include: Progressive collapse resistance index of cable dome structure smallest; Progressive collapse resistance index of cable dome structure The degree of reduction exceeds a preset threshold; The progressive collapse resistance index of the cable dome structure to be evaluated in the last two times The difference is less than the preset threshold.

6. A method for optimizing the progressive collapse resistance of a cable dome topology, characterized in that: The following steps are involved: A. For a cable dome structure to be optimized, optimizing the cable dome topology structure according to the cable dome topology structure optimization method based on progressive collapse resistance according to any one of claims 3 to 5 to obtain an optimized structural topology shape of the cable dome structure; B. For the structural topology shape of the optimized cable dome structure obtained in step A, extract its single-frame model for local shape optimization.

7. The method for optimizing the progressive collapse resistance of a cable dome topology structure according to claim 6, wherein: The specific steps for local optimization of the shape of the single product in step B are as follows: B1. For the optimized cable dome structure, obtain the component importance index of each type of component Normalize to obtain the component importance coefficient of each type of component ; Calculate according to the following method: ； in, is the total number of component categories, ; B2. Extract the single-frame model of the cable dome structure's topological shape to reduce the maximum value of the member importance coefficient in the single-frame model. As the optimization goal, the shape characteristics of a single frame model are used as optimization variables and the optimization algorithm is used for optimization.

8. The method for optimizing the progressive collapse resistance of a cable dome topology structure according to claim 7, wherein: The optimization algorithm is preferably a global optimization algorithm.

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