Method and system for quickly evaluating wind resistance limit load probability average value of structure

Abstract

The invention relates to a quick evaluation method and system for a wind resistance limit load probability average value of a structure, and the method comprises the following steps: S1, carrying out a wind tunnel test on the structure or obtaining a wind load time history of each point on the surface of the structure by adopting a wind tunnel test result in a database, building a finite element model through finite element numerical analysis software, and carrying out the elastic time history calculation, determining each key position of the structure and a corresponding response time history; s2, extracting the most unfavorable response of each key position, and respectively solving the most unfavorable wind load mode corresponding to each most unfavorable response by adopting an LRC method; s3, based on a stability increment elastic-plastic analysis theory, judging the stability of the structure by adopting an energy method, and solving a wind-resistant ultimate bearing capacity average value of the structure; the problems that the speed of solving the wind-resistant ultimate bearing capacity of the structure through a traditional structure elastic-plastic calculation method is low, and the accuracy of solving the wind-resistant ultimate bearing capacity of the structure is affected due to the fact that a traditional static stability method cannot reflect incomplete correlation and randomness of a real wind load on the structure are solved are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of building structure safety design, and relates to a method and system for quickly evaluating the probabilistic average value of a structure's wind resistance ultimate load, and in particular to a method and system for quickly evaluating the probabilistic average value of a structure's wind resistance ultimate load that takes into account the incomplete correlation and randomness of wind loads. Background Art

[0002] In recent years, under the influence of rare strong winds, structures have been found to enter an elastic-plastic state or even collapse, requiring significant economic costs for structural repair or reconstruction. Current research and structural specifications, both domestically and internationally, focus on the structural effects and corresponding design methods under commonly encountered wind loads with short average return periods. In recent years, performance-based wind-resistant design methods have become a hot topic in wind engineering research and are poised to become the next generation of structural wind-resistant design methods. A key component of this design approach is determining the ultimate wind-resistant bearing capacity and probability of occurrence of structures under rare strong winds.

[0003] Currently, research on methods for calculating the ultimate bearing capacity of structures under earthquakes is largely mature, such as the incremental dynamic analysis method (IDA). Some scholars at home and abroad have attempted to apply these methods to the field of structural wind engineering. However, wind loads exhibit time-varying randomness and long-lasting characteristics, which differ significantly from earthquake loads. The number of wind pressure time-history samples generated using Monte Carlo simulations, as well as the load duration of each sample, are far greater than those for earthquake samples. The use of multi-sample IDA methods incurs significant computational and time costs, making them difficult to widely use for probabilistic analysis of the ultimate wind bearing capacity of structures.

[0004] The static shakedown method is another approach for determining the ultimate bearing capacity of structures under complex loads. Because it ignores the elastic-plastic development of the structure and focuses solely on the characteristics of the structure's limit state, it offers the potential for improving the efficiency of calculating the ultimate wind bearing capacity of structures. However, wind loads act on structures as multi-point excitations, with distributions characterized by incomplete correlation and randomness. Current static shakedown methods, both domestically and internationally, treat external loads as one-dimensional, mutually independent, or fully correlated multidimensional loads. These methods do not directly consider the spatial correlation and randomness of wind loads on the building surface. Consequently, existing methods struggle to accurately determine the probabilistic statistical value of a structure's ultimate wind bearing capacity.

[0005] Therefore, it is necessary to consider the incomplete correlation and randomness of wind loads at various points on the structure, and combine the shakedown theorem to conduct a probabilistic analysis of the ultimate bearing capacity of the structure under wind loads to facilitate structural design. Summary of the Invention

[0006] In view of this, the present invention provides a method and system for quickly evaluating the probabilistic average value of the structural wind resistance ultimate bearing capacity in order to solve the problems that the traditional structural elastic-plastic calculation method is slow in solving the structural wind resistance ultimate bearing capacity and the traditional static stability method is unable to reflect the incomplete correlation and randomness of the actual wind load on the structure, which affects the accuracy of the solved structural wind resistance ultimate bearing capacity and makes it difficult to obtain the statistical average value of the ultimate bearing capacity, which is inconvenient for structural design.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A rapid evaluation method for the probabilistic average value of a structure's wind resistance ultimate load comprises the following steps:

[0009] S1. Conduct a wind tunnel test on the structure or use the wind tunnel test results in the database to obtain the wind load time history at each point on the structure surface. Simultaneously, establish a finite element model using finite element numerical analysis software, perform elastic time history calculations on the structure under wind load, and determine each key position of the structure and the corresponding response time history.

[0010] S2, extracting the most unfavorable response in the response time history of each key position in step S1, and using the LRC method to solve the most unfavorable wind load mode corresponding to each most unfavorable response;

[0011] S3. Based on the theory of shakedown incremental elastoplastic analysis, the energy method is used to determine the stability of the structure and obtain the average value of the structure's ultimate wind bearing capacity. The loading method in the shakedown incremental elastoplastic analysis is as follows: construct a load domain according to the most unfavorable load distribution patterns solved in step S2, then expand the load domain by linearly increasing the static load step by step, and use the variable amplitude loading method to solve the model's ultimate wind load to ensure calculation speed and accuracy.

[0012] Furthermore, the key positions of the structure selected for analysis in step S1 are generally positions where plastic hinges are likely to be generated in the structure, such as the beam-column junction, the beam end position, the column foot position, the beam mid-span position or the concentrated load position.

[0013] Furthermore, step S2 obtains the response time history corresponding to a key position i of the structure by elastic time history analysis. , the most unfavorable wind load at point k when the most unfavorable response occurs at structure i is obtained by the LRC method , the expression formula is shown in formula (1) and formula (2):

[0014] (1)

[0015] (2)

[0016] in, is the average wind pressure at point k, is the peak factor, is the standard deviation of the wind load time history at point k, is the correlation coefficient between the response time history at point i and the pulsating wind pressure time history at point k, is the time history of the pulsating wind load at point k, is the standard deviation of the response time at point i.

[0017] Furthermore, the LRC method in step S2 can obtain the most unfavorable wind load combination for all loading points of the structure. This combination is the most unfavorable load distribution form with the highest probability when the most unfavorable response occurs at a certain key position i of the structure. The most unfavorable load distribution forms corresponding to multiple key positions can be combined to form a load domain. The ultimate wind bearing capacity of the structure determined according to the load domain is regarded as the average value of the ultimate wind bearing capacity of the structure.

[0018] Further, step S3 is specifically as follows:

[0019] S31. Based on the theorem that a structure will remain stable under any cyclic load path within the convex stable domain, determine the loading scheme along the load domain boundary or corner points;

[0020] S32. The increment of plastic strain during a load cycle within one cycle of cyclic loading. and plastic strain energy They are:

[0021] (3)

[0022] (4)

[0023] Among them, V is the volume of the model structure. When the plastic strain increment inside the structure and plastic strain rate When both are 0, no plastic strain is generated inside the structure during the cyclic loading process, and the work done by the plastic stress is zero, that is, , indicating that a stable residual stress field was generated during this load cycle, indicating that the structure has reached a stable state. Under cyclic loading, the plastic strain energy of the structure is used as the criterion for determining whether the structure has reached a stable limit state, i.e., an energy-based judgment. This method is based on the following: when the structure is in a stable state, the external load amplitude and the plastic energy dissipation of the structure are linearly related; when the structure is in an incremental failure state, the external load amplitude and the plastic energy dissipation of the structure are nonlinearly related.

[0024] Furthermore, in step S32, after the model undergoes plastic deformation, the residual stress field inside the model continues to develop with each cyclic loading, gradually reaching a stable state. Then, the next round of cyclic loading is performed, and the above steps are repeated until the structure reaches the ultimate stability state. In this way, the range of the structural stability domain can be quickly obtained. This method is called stable incremental elastoplastic analysis.

[0025] Furthermore, the specific steps of applying the energy method to determine the ultimate bearing capacity of the structure in step S32 are as follows:

[0026] S321, from 0 to Then to Three loading steps constitute one cycle. The load at each point in a most unfavorable load distribution mode determined by the LRC method is multiplied by the load multiplier. , the structure is repeated several times from 0 to Then to Cyclic loading, the plastic strain energy at each unloading is calculated by formula (4). After multiple cycles, if the plastic strain energy does not increase, it means that the structure has not generated new plastic strain, a stable residual stress field has been formed, and a stable state has been reached;

[0027] S322, continue to select the most unfavorable load distribution mode corresponding to the remaining key positions, repeat the above step S321 until the load distribution mode corresponding to all n key positions of the structure is loaded, that is, the loading point is reached ,form The corresponding load domain records the load multiplier corresponding to the structure that has reached the stable state at this moment ;

[0028] S323, continue to select the next loading point , and repeat steps S321 and S322 to continue cyclic loading; if the load multiplier If there is a nonlinear relationship with the plastic energy increment of the structure, the maximum load multiplier for the structure to maintain a stable state is determined. , the load multiplier that keeps the structure in a stable state for the last time Multiplying by the initial basic wind pressure gives the average value of the structure's ultimate wind bearing capacity.

[0029] The rapid evaluation system for the probability average value of the structural wind resistance ultimate load includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the rapid evaluation method for the probability average value of the structural wind resistance ultimate load is implemented.

[0030] The rapid assessment system of the probabilistic average value of the structural wind resistance ultimate load is used to carry out structural elastic-plastic response assessment under rare strong winds considering the incomplete correlation and randomness of wind loads.

[0031] The rapid assessment system of the probability average value of the structural wind resistance ultimate load is suitable for structures with insignificant structural amplification effect, that is, structures with a background response significantly greater than a resonance response, that is, structures with greater stiffness.

[0032] The beneficial effects of the present invention are:

[0033] Wind loads are characterized by strong randomness, long duration, and incomplete correlation between loads at each point. Using the traditional incremental dynamic method (IDA) to analyze the ultimate wind load capacity of a structure for each wind load sample and perform statistical analysis results in a significant computational burden and time cost. The present invention combines static shakedown theory with a load response correlation coefficient method to rapidly estimate the probabilistic mean value of the ultimate wind load capacity of a structure, taking into account the incomplete correlation and randomness of wind loads. Compared to the results of the traditional IDA method, the calculation results of this invention have higher accuracy and significantly improved computational efficiency.

[0034] This rapid assessment method, based on the probabilistic average of a structure's ultimate wind load, yields results for the ultimate wind load capacity of rigid structures that closely approximate those obtained using the multi-sample IDA method. Furthermore, only a limited number of elastic-plastic cyclic loading cycles are required to obtain the results, significantly improving computational efficiency. The entire process is simple, efficient, and convenient for engineering designers.

[0035] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0037] Figure 1 This is a flow chart of the method for quickly evaluating the probabilistic average value of the structural wind resistance ultimate load of the present invention;

[0038] Figure 2 This is a loading scheme diagram for determining structural stability along the load domain boundary and corner points of the present invention, where Figure 2 (a) is the loading diagram for determining the structural stability along the load domain boundary. Figure 2 (b) Loading diagram for determining structural stability along the loading corners;

[0039] Figure 3 (a) is a load multiplier path diagram for determining the ultimate bearing capacity of a structure using the energy method of the present invention. Figure 3(b) Cyclic loading diagram for determining the ultimate bearing capacity of the structure using the energy method;

[0040] Figure 4 This is a diagram showing the definition of test model parameters and wind direction angles for the embodiment;

[0041] Figure 5 This is a diagram showing the location and numbering of the portal frame of the test model of the embodiment;

[0042] Figure 6 This is a diagram of a single-span portal steel frame model of an embodiment test model, wherein Figure 6 (a) is the elevation drawing of the portal frame. Figure 6 (b) is the finite element model diagram of the portal frame;

[0043] Figure 7 The in-plane bending moment time history at the base of the windward column of the test model of the embodiment;

[0044] Figure 8 The most unfavorable load distribution diagram with the highest probability obtained based on the LRC method for the test model of the embodiment;

[0045] Figure 9 Figure 2 is a load magnification factor diagram of the test model of the embodiment, where Figure 9 (a) is the load magnification factor changing with the loading step, Figure 9 (b) Loading path diagram for the first 21 steps of loading;

[0046] Figure 10 is a diagram of the structural plastic strain energy increment of each cycle of the test model of the embodiment, wherein Figure 10 (a) is the graph showing the change of plastic strain energy with load magnification. Figure 10 (b) Figure 10 (a) A partial enlarged view; Figure 10 (c) is the logarithmic graph of plastic strain energy versus load magnification factor;

[0047] Figure 11 This is a graph showing the maximum horizontal displacement IDA of the roof ridge of the test model in the embodiment;

[0048] Figure 12 Figure 2 is a probability statistical diagram of the load multiplier for 100 time history samples of the test model of the embodiment. DETAILED DESCRIPTION

[0049] The following describes the embodiments of the present invention through specific examples. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention.

[0050] When calculating the ultimate wind load capacity of actual engineering structures, traditional structural elastoplastic and static shakedown methods require statistical analysis of a large number of samples to determine the ultimate load capacity under different probabilities, taking into account the random nature of wind loads. This results in a complex calculation process. However, the average value is an important representative value of random variables and can be directly used to evaluate the wind resistance of a structure. Therefore, calculating the average value of the ultimate load capacity of a structure avoids the need to calculate multiple sets of load histories, greatly simplifying the calculation process.

[0051] At the same time, when solving the ultimate wind bearing capacity of the structure, the traditional static stability method needs to consider the correlation of the loads at each point while considering multiple loading points. If the loads are considered to be completely independent, the calculation needs to be divided into multiple load ranges according to the number of external loads to envelop the correlation characteristics between all points. This leads to the need to iterate continuously during the calculation process to find external loads that meet the correlation, which seriously affects the calculation efficiency. If the loads are considered to be completely correlated, the multi-dimensional loads can be regarded as a single one-dimensional load. The calculation efficiency is high but it cannot reflect the characteristics of incomplete spatial correlation of wind loads. The most unfavorable load distribution pattern related to the structural response can reflect the actual wind load distribution. Taking into account the correlation problem of wind loads, a one-dimensional static stability analysis can be directly performed according to this distribution pattern.

[0052] In summary, the load distribution pattern selection method based on the load response correlation coefficient (LRC) method is a commonly used method for calculating equivalent static wind loads in structural wind resistance calculations. Its basic principle is to use the correlation coefficient between load and response as a weighting factor for the wind load at any point, thereby determining the wind load distribution at key locations where the response reaches a maximum value. This resulting load distribution pattern represents the most likely and realistically unfavorable wind load distribution.

[0053] like Figure 1 A rapid evaluation method for the probabilistic average value of a structure's wind resistance ultimate load is shown, comprising the following steps:

[0054] S1. Conduct a wind tunnel test on the structure or use the wind tunnel test results in the database to obtain the wind load time history at each point on the structure surface. Simultaneously, establish a finite element model using finite element numerical analysis software, perform elastic time history calculations on the structure under wind load, and determine each key position of the structure and the corresponding response time history.

[0055] S2, extracting the most unfavorable response in the response time history of each key position in step S1, and using the LRC method to solve the most unfavorable wind load mode corresponding to each most unfavorable response;

[0056] The response time history corresponding to a key position i of the structure is obtained by elastic time history analysis. The most unfavorable wind load at point k when the most unfavorable response occurs at position i of the structure is obtained by the LRC method. The expression formulas are shown in Equation (1) and Equation (2):

[0057] (1)

[0058] (2)

[0059] in, is the average wind pressure at point k, is the peak factor, is the standard deviation of the wind load time history at point k, is the correlation coefficient between the response time history at point i and the pulsating wind pressure time history at point k, is the time history of the pulsating wind load at point k, is the standard deviation of the response time history at point i. The LRC method can be used to determine the most unfavorable wind load combination for all loading points of the structure. This combination is the most unfavorable load distribution form with the highest probability of the most unfavorable response occurring at a key position i of the structure. The most unfavorable load distribution forms corresponding to multiple key positions can be combined to form a load domain. The ultimate wind bearing capacity of the structure determined according to this load domain is regarded as the average value of the ultimate wind bearing capacity of the structure.

[0060] S3. Based on the theory of shakedown incremental elastoplastic analysis, the energy method is used to determine the stability of the structure and obtain the average value of the structure's ultimate wind bearing capacity. The loading method in the shakedown incremental elastoplastic analysis is as follows: construct a load domain according to the most unfavorable load distribution patterns solved in step S2, then expand the load domain by linearly increasing the static load step by step, and use the variable amplitude loading method to solve the model's ultimate wind load to ensure calculation speed and accuracy.

[0061] The key issue in determining the ultimate bearing capacity of a structure is how to use the most unfavorable load distribution pattern extracted above to perform an elastic-plastic analysis according to a simplified process, so that the calculated results are basically consistent with those of traditional structural elastic-plastic solution methods such as the multi-sample IDA method. Therefore, this paper proposes a cyclic loading method and uses an energy method to determine the limit state of the structure.

[0062] The concept of the static shakedown theorem states that for a structure made of perfectly elastic-plastic material, if a time-independent, self-equilibrating residual stress field can be found when the load varies within a given range, and if, when added to the internal stress field generated under the assumption that the structure is perfectly elastic, the yield condition is not violated at any point, the structure is considered stable. In other words, the shakedown limit state of a structure is defined as the state in which the maximum self-equilibrium stress field exists within the structure, and the load at this point is the shakedown limit load.

[0063] S31, such as Figure 2As shown, in order to solve the corresponding ultimate load when the structure reaches the stable state, the theorem that the structure will maintain the stable state under any cyclic load path in the convex stable domain is quoted. According to the structural requirements, the following is selected: Figure 2 (a) along the load domain boundary or as Figure 2 (b) Loading scheme for determining structural stability by corner loading.

[0064] After the model structure produces plastic deformation, the residual stress field inside the model structure continues to develop with each cyclic loading and gradually reaches a stable state. Then the next round of cyclic loading is carried out, and the above steps are repeated until the structure reaches the ultimate stable state. In this way, the range of the structural stability domain can be quickly obtained. This method is called stable incremental elastoplastic analysis.

[0065] S32. In order to determine the stability of the model structure in the plasticity increment method, the energy criterion-based determination method is used. The increment of plastic strain in a load cycle within a cycle under cyclic loading is and plastic strain energy for:

[0066] (3)

[0067] (4)

[0068] Among them, V is the volume of the model structure. When the plastic strain increment inside the structure and plastic strain rate When both are 0, no plastic strain is generated inside the structure during the cyclic loading process, and the work done by the plastic stress is zero, that is, This indicates that a stable residual stress field is generated during this load cycle, indicating that the structure has reached a stable state. Therefore, under cyclic loading, the plastic strain energy of the structure can be used as a criterion for determining whether the structure has reached a stable limit state.

[0069] The basis for determining the structural stability limit state using this method is that when the structure is in a stable state, the external load amplitude and the structural plastic energy dissipation have a linear relationship; when the structure is in an incremental failure state, the external load amplitude and the structural plastic energy dissipation have a nonlinear relationship. Based on this theory, the present invention uses the energy method as the basis for determining structural stability.

[0070] The specific steps for determining the ultimate bearing capacity of a structure using the energy method are as follows:

[0071] S321, Figure 3 (a) is the load multiplier path diagram for determining the ultimate bearing capacity of the structure using the energy method, from 0 to Then to Three loading steps constitute one cycle. The load at each point in a most unfavorable load distribution mode determined by the LRC method is multiplied by the load multiplier. , the structure is repeated several times from 0 to Then to Cyclic loading, the plastic strain energy at each unloading is calculated by formula (4). After multiple cycles, if the plastic strain energy does not increase, it means that the structure has not generated new plastic strain, a stable residual stress field has been formed, and a stable state has been reached;

[0072] S322, continue to select the most unfavorable load distribution mode corresponding to the remaining key positions, repeat the above step S321 until the load distribution mode corresponding to all n key positions of the structure is loaded, that is, the loading point is reached ,form The corresponding load domain records the load multiplier corresponding to the structure that has reached the stable state at this moment ;

[0073] S323, continue to select the next loading point , and repeat steps S321 and S322 to continue cyclic loading; if the load multiplier If there is a nonlinear relationship with the plastic energy increment of the structure, the maximum load multiplier for the structure to maintain a stable state is determined. , Figure 3 (b) Cyclic loading diagram for determining the ultimate bearing capacity of a structure using the energy method, and the load multiplier for the last time that the structure remains in a stable state Multiplying by the initial basic wind pressure gives the average value of the structure's ultimate wind bearing capacity.

[0074] Combining the shakedown-plastic increment method and the LRC method, the present invention proposes a structural ultimate bearing capacity assessment method that combines the shakedown theory and the LRC method, which can be used to carry out structural elastic-plastic response assessment under rare strong winds considering the incomplete correlation and randomness of wind loads.

[0075] Example

[0076] 1. Data preparation

[0077] The wind load data is derived from wind tunnel test data. The low-rise building size selected is a model with a span of B = 16m, a depth of D = 40m, a cornice height of H0 = 8m, and a roof slope of β = 4.8°. The test model size parameters and wind direction angle are defined as follows: Figure 4As shown. Based on the building's surrounding environment, the average wind velocity profile index of the atmospheric boundary layer flow field was determined to be 0.20, and the turbulence intensity at a height of 10m was 0.25. The wind tunnel test wind field scale ratio and the model geometry scale ratio were both 1:100. The test wind direction angle ranged from 0 to 90 degrees, measured at 15-degree intervals, for a total of seven angles. By comparing the response results across all wind directions, this case will use the time history data at a wind direction angle of 75 degrees.

[0078] The finite element model is established based on the model parameters, in which the portal frame layout of the factory building is as follows: Figure 5 As shown, the column spacing is 8m, with a total of six columns. A finite element model of a single-span portal frame with a span of 16m, a height of 8m, and a roof slope of 4.8° was established. The frame columns were made of variable-section I-shaped steel with cross-sectional dimensions of H450~750×200×8×10, and the frame beams were made of uniform-section I-shaped steel with cross-sectional dimensions of H460×200×8×10. The portal frame beams and columns, as well as the columns and foundation, are all rigidly connected. The model has sufficient out-of-plane support and local stability, as shown in the figure. Figure 6 (a) shown. Figure 6 (b) The finite element model of this rigid frame is established using Shell elements. The material constitutive relationship is ideal elastic-plastic, the elastic modulus is 210 GPa, the yield strength is 235 MPa, and it obeys the Von Mises yield criterion.

[0079] 2. Elastic-Plastic Time History Analysis

[0080] First, determine the key positions of the portal frame: the bottom of the windward column, the junction of the windward beam and column, the mid-span of the beam, the junction of the leeward beam and column, and the bottom of the windward column. Through the elastic time history analysis of the portal frame, the bending moment response time history of each key position of the structure is obtained, and the time when the extreme bending moment response occurs at this point is determined. Figure 7 The time history of the in-plane bending moment response of the section at the bottom of the windward column is shown. This point has an extreme value response at the 7240th loading step, and the in-plane extreme bending moment at this time is 2.388×10 5 N·m.

[0081] 3. LRC method to solve the most unfavorable load distribution mode

[0082] The above elastic-plastic time history analysis is used to obtain the in-plane bending moment response time history of each position, and the most unfavorable load distribution with the highest probability is obtained using formula (1), where g = 3.5. Figure 8 It represents the load distribution pattern of the section at the bottom of the windward column determined by the LRC method, where the red line is the most unfavorable load distribution with the highest probability, and the blue line is the average wind load distribution.

[0083] 4. Determine the ultimate wind resistance capacity of the portal frame based on the shakedown incremental elastoplastic analysis and the most unfavorable load distribution mode

[0084] This load distribution pattern is subjected to linear step-by-step static loading calculation, and variable amplitude loading is adopted to ensure calculation speed and accuracy. Triangular cyclic loading is selected, and the number of cycles for each load amplitude is 10. The loading path is as follows: Figure 9 shown. Figure 9 In (a), the load multiplier is first increased by 0.1. When the load multiplier reaches 1.35, it is then increased by 0.05. Finally, when the load multiplier reaches 1.6, it is increased by 0.01. Figure 9 (b) shows the loading path for the first 21 steps.

[0085] The load value corresponding to each position is loaded and unloaded cyclically, which is counted as one cycle, and the structural plastic strain energy increment of the cycle is used as a statistic. Figure 10 The trends of the plastic strain energy increments for each cycle as the load magnification factor increases are shown. Figures (a) and (b) show that the first loading cycle generates the highest plastic strain energy. When the corresponding load magnification factor is 1.93, the plastic strain energy increment for the second loading cycle at this location is 1.87 J. Thereafter, the plastic strain energy increment gradually decreases with increasing cycles, reaching 1.697 J for the tenth loading cycle. When the corresponding load magnification factor is 1.94, the plastic strain energy increment exhibits a trend of first decreasing, then increasing, and then decreasing again with increasing cycles. The increment for the ninth loading cycle is 3.211 J, second only to the increment for the second loading cycle. The figures show that for load magnification factors up to and including 1.93, the plastic strain energy increment decreases with the number of cycles, and the total plastic strain energy of the structure gradually converges to an equilibrium state and no longer increases, indicating the formation of a stable residual stress field within the structure. Since the ultimate load of the shakedown is the same as the ultimate load of the structure, the ultimate load that the structure can withstand is 1.93 times the basic wind pressure, which is 1.54 kN / m 2 . As the load increases further, the residual stress field is no longer stable, the plastic strain energy increment does not converge, and the total plastic energy of the structure increases further until the structure is destroyed. Figure (c) shows the logarithmic processing of Figures (a) and (b). It can be observed that there is a clear boundary between the stable and unstable states. Before the amplification factor is 1.93, the load increase and the plastic strain energy increment are approximately linear (due to the error in the finite element calculation, the plastic energy increment fluctuates, but the overall relationship is still linear); after the amplification factor is 1.93, the relationship is nonlinear, and the plastic strain energy increment in each cycle is almost the same, which further verifies the above results.

[0086] 5. Verification of calculation result accuracy and efficiency

[0087] In order to further verify the accuracy of the method proposed in the present invention, it should be compared with the average value of the ultimate wind bearing capacity of the structure obtained under the action of multiple groups of wind load samples. Based on the wind load time history of the wind tunnel test, the present invention uses the harmonic superposition method to generate 100 groups of random wind load time histories with the same spectral characteristics and statistical characteristics as the wind tunnel test data. Since the use of the IDA method to analyze the average value of the ultimate wind bearing capacity of the structure requires amplitude modulation calculation of all load time history samples, it will consume a lot of time. In order to save time, the present invention first finds the load distribution pattern at the moment when the most unfavorable response of the structure occurs under the action of a single load time history sample, and then obtains the ultimate wind bearing capacity according to the flowchart steps of the present invention, and compares it with the ultimate wind bearing capacity obtained by the IDA method under the load time history sample to verify its accuracy. After ensuring the accuracy of the single sample result, the ultimate wind bearing capacity of the structure under all wind load time history samples is obtained according to the flowchart steps of the present invention, and the average value of the ultimate bearing capacity is obtained by statistics, and then compared with the average value directly obtained by the LRC method, thereby verifying the accuracy of the method for quickly solving the average value of the ultimate wind bearing capacity of the structure proposed in the present invention.

[0088] The ultimate wind resistance of the structure obtained under a single load time history sample is 1.54kN / m 2 Using this load history to perform IDA analysis, the IDA curve of the roof ridge horizontal displacement amplification factor change is as follows: Figure 11 As shown in the figure, the horizontal displacement of the roof suddenly increases when the load multiple is 2.08. At this time, the structure reaches the limit state. Therefore, the ultimate bearing capacity of the structure is determined to be 1.98 times the basic wind pressure, and the corresponding load size is 1.584kN / m 2 , which is 2.7% different from the result obtained by the method of the present invention. The difference is small, indicating that the result of the shakedown incremental elastoplastic analysis based on the load distribution at the moment when the most unfavorable response of the structure occurs has higher accuracy.

[0089] The most unfavorable load distribution of 100 groups of samples was subjected to shakedown incremental elastoplastic analysis. Figure 12 The probability statistics of the load multipliers corresponding to the ultimate wind bearing capacity for 100 sets of the most unfavorable load distribution patterns are given. The overall load multipliers vary in the range of [1.60, 2.23], with a mean of 1.956 and a standard deviation of 0.1331. Therefore, the average ultimate wind bearing capacity is 1.56 kN / m 2 , compared with the average wind resistance ultimate bearing capacity of the structure obtained by the present invention of 1.54kN / m 2 The difference is less than 2%, demonstrating the high accuracy of the proposed method. It is worth noting that, using the same computer configuration, obtaining a single IDA curve using the IDA method takes four days, while obtaining the average wind resistance of the structure using the proposed method takes approximately four hours. This significantly improves the efficiency of the proposed method compared to the IDA method.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A rapid evaluation method for the probabilistic average value of a structure's wind load resistance, characterized in that: The following steps are involved: S1. Conduct a wind tunnel test on the structure or use the wind tunnel test results in the database to obtain the wind load time history at each point on the structure surface. Simultaneously, establish a finite element model using finite element numerical analysis software, perform elastic time history calculations on the structure under wind load, and determine each key position of the structure and the corresponding response time history. S2, extracting the most unfavorable response in the response time history of each key position in step S1, and using the LRC method to solve the most unfavorable wind load mode corresponding to each most unfavorable response; S3. Based on the theory of shakedown incremental elastoplastic analysis, the energy method is used to determine the stability of the structure and obtain the average value of the structure's ultimate wind bearing capacity. The loading method in the shakedown incremental elastoplastic analysis is as follows: construct a load domain according to the most unfavorable load distribution patterns solved in step S2, then expand the load domain by linearly increasing the static load step by step, and use the variable amplitude loading method to solve the model's ultimate wind load to ensure calculation speed and accuracy.

2. The rapid assessment method according to claim 1, wherein: The key positions of the structure selected by the analysis in step S1 are positions where plastic hinges are likely to be generated in the structure, such as the beam-column junction, the beam end position, the column foot position, the beam mid-span position or the concentrated load position.

3. The rapid assessment method according to claim 2, wherein: Step S2 obtains the response time history corresponding to a key position i of the structure by elastic time history analysis , the most unfavorable wind load at point k when the most unfavorable response occurs at structure i is obtained by the LRC method , the expression formula is shown in formula (1) and formula (2): （1） （2） in, is the average wind pressure at point k, is the peak factor, is the standard deviation of the wind load time history at point k, is the correlation coefficient between the response time history at point i and the pulsating wind pressure time history at point k, is the time history of the pulsating wind load at point k, is the standard deviation of the response time at point i.

4. The rapid assessment method according to claim 3, wherein: The most unfavorable wind load combination of all loading points of the structure obtained by the LRC method in step S2 is the most unfavorable load distribution form with the highest probability when the most unfavorable response occurs at a key position i of the structure. The most unfavorable load distribution forms corresponding to multiple key positions can be combined to form a load domain. The ultimate wind bearing capacity of the structure determined according to the load domain is regarded as the average value of the ultimate wind bearing capacity of the structure.

5. The rapid assessment method according to claim 4, wherein: Step S3 is specifically as follows: S31. Based on the theorem that a structure will remain stable under any cyclic load path within the convex stable domain, determine the loading scheme along the load domain boundary or corner points; S32. The increment of plastic strain during a load cycle within one cycle of cyclic loading. and plastic strain energy They are: （3） （4） Among them, V is the volume of the model structure. When the plastic strain increment inside the structure and plastic strain rate When both are 0, no plastic strain is generated inside the structure during the cyclic loading process, and the work done by the plastic stress is zero, that is, , indicating that a stable residual stress field is generated in this load cycle, and it can be judged that the structure has reached a stable state; under the action of cyclic load, the plastic strain energy of the structure is used as the judgment criterion for the structure to reach a stable state, that is, the judgment is based on the energy criterion; the basis for judging the stability limit state of the structure by this method is: when the structure is in a stable state, the external load amplitude and the structural plastic energy dissipation are linearly related; if the structure is in an incremental damage state, the external load amplitude and the structural plastic energy dissipation are nonlinearly related.

6. The rapid assessment method according to claim 5, wherein: In step S32, after the model undergoes plastic deformation, the residual stress field inside the model continues to develop with each cyclic loading, gradually reaching a stable state. The next round of cyclic loading is then performed, and the above steps are repeated until the structure reaches the ultimate stability state. In this way, the range of the structural stability domain can be quickly obtained. This method is called stable incremental elastoplastic analysis.

7. The rapid assessment method according to claim 6, wherein: The specific steps of applying the energy method to determine the ultimate bearing capacity of the structure in step S32 are as follows: S321, from 0 to Then to Three loading steps constitute one cycle. The load at each point in a most unfavorable load distribution mode determined by the LRC method is multiplied by the load multiplier. , the structure is repeated several times from 0 to Then to Cyclic loading, the plastic strain energy at each unloading is calculated by formula (4). After multiple cycles, if the plastic strain energy does not increase, it means that the structure has not generated new plastic strain, a stable residual stress field has been formed, and a stable state has been reached; S322, continue to select the most unfavorable load distribution mode corresponding to the remaining key positions, repeat the above step S321 until the load distribution mode corresponding to all n key positions of the structure is loaded, that is, the loading point is reached ,form The corresponding load domain records the load multiplier corresponding to the structure that has reached the stable state at this moment ; S323, continue to select the next loading point , and repeat steps S321 and S322 to continue cyclic loading; if the load multiplier If there is a nonlinear relationship with the plastic energy increment of the structure, the maximum load multiplier for the structure to maintain a stable state is determined. , the load multiplier that keeps the structure in a stable state for the last time Multiplying by the initial basic wind pressure gives the average value of the structure's ultimate wind bearing capacity.

8. A rapid assessment system for the probabilistic average value of a structure's wind load limit, characterized by: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method for rapidly evaluating the probabilistic average value of the structural wind resistance ultimate load according to any one of claims 1 to 7 is implemented.

9. The rapid assessment system for the probabilistic average value of structural wind load limit according to claim 8, characterized in that: Used to evaluate the elastic-plastic response of structures under rare strong winds, taking into account the incomplete correlation and randomness of wind loads.

10. The rapid assessment system according to claim 9, wherein: It is suitable for structures with insignificant amplification effects, that is, structures with a larger stiffness, where the background response is significantly greater than the resonance response.

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