A Multi-Objective Equivalent Static Wind Load Calculation Method Applicable to Nonlinear Structures

Abstract

This invention relates to a method for calculating multi-objective equivalent static wind loads applicable to nonlinear structures. First, wind tunnel tests are conducted on the nonlinear structure, and a corresponding finite element model is established. Second, the average component of the equivalent static wind load is obtained from the wind tunnel test results. Time history analysis of the finite element model yields the equivalent static wind load excluding the average component, i.e., the fluctuating component. The fluctuating and average components are combined for analysis to obtain the multi-objective linear equivalent static wind load. Finally, based on the multi-objective linear equivalent static wind load, a nonlinear coefficient is incorporated to correct the multi-objective linear equivalent static wind load, resulting in the calculation of the multi-objective nonlinear equivalent static wind load, which is expressed as a wind pressure coefficient. This method achieves simultaneous equivalence of multiple extreme responses of the nonlinear structure, providing a convenient and accurate equivalent static wind load for engineering design.

Description

Technical Field

[0001] This invention belongs to the field of wind load calculation technology, and relates to a multi-objective equivalent static wind load calculation method applicable to nonlinear structures. Background Technology

[0002] Equivalent static wind load is an important wind-resistant design method. It simplifies the wind-resistant design process by transforming the complex dynamic effects of wind loads into equivalent static loads. This method can reflect the wind-induced vibration effects of structures and is easy to combine with other loads for calculation, thus it is widely used in the wind-resistant design of wind-sensitive structures. Multi-objective equivalent static wind load calculation methods can achieve good agreement between the static response and the actual dynamic response of a structure at multiple locations under a single equivalent static wind load, and therefore have been widely used in wind-resistant design. For example, scholars such as Chen Bo proposed a multi-objective equivalent static wind load analysis method for large-span spatial structures, providing an effective technical means for the wind-resistant design of linear structures.

[0003] However, existing multi-objective equivalent static wind load calculation methods are mainly applicable to linear structures. When directly applied to nonlinear structures, they cannot achieve equivalence of multiple extreme responses. This indicates a lack of a dedicated multi-objective equivalent static wind load calculation method for nonlinear structures. Currently, wind-resistant design of nonlinear structures typically employs a single-objective equivalent method based on load-wind vibration coefficients. However, this method has significant limitations. Under the obtained equivalent static wind load, it can only guarantee that the response of a single structural effect is equal to the dynamic extreme response, but it cannot achieve equivalence of multiple extreme responses. For example, scholars such as Wu Lili often use a single-objective equivalent method based on load-wind vibration coefficients for wind-resistant design of nonlinear structures.

[0004] In view of the above problems, there is an urgent need to invent a multi-objective equivalent static wind load calculation method applicable to nonlinear structures, so as to fill the gap in the existing technology and provide a more accurate and effective calculation means for the wind-resistant design of nonlinear structures. Summary of the Invention

[0005] In view of this, in order to solve the problem that the existing multi-objective equivalent static wind load calculation methods are only applicable to linear structures, and cannot accurately and effectively calculate the multi-objective equivalent static wind load of nonlinear structures, thus failing to meet the wind resistance design requirements of structures, this invention provides a multi-objective equivalent static wind load calculation method applicable to nonlinear structures, realizing the simultaneous equivalence of multiple extreme responses of nonlinear structures, and providing convenient and accurate equivalent static wind loads for engineering design.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A multi-objective equivalent static wind load calculation method applicable to nonlinear structures includes the following steps:

[0008] S1. Conduct wind tunnel tests on nonlinear structures and establish corresponding finite element models; based on the wind pressure coefficient time history obtained from the wind tunnel tests, conduct dynamic response analysis to obtain the extreme values ​​of various structural responses, including displacement maxima and minima, and stress maxima and minima, for subsequent comparison of the equivalent effects of equivalent load pulsation components.

[0009] S2. Obtain the average component of the equivalent static wind load through the wind tunnel test results in step S1. Obtain the equivalent static wind load excluding the average component, i.e., the fluctuating component, through the time history analysis of the finite element model in step S1. Obtain the multi-objective linear equivalent static wind load by combining the fluctuating component and the average component. The fluctuating component is obtained by comprehensively calculating the basis vector and the combination coefficient. The combination coefficient is obtained by comprehensively calculating the structural response under the basis vector and the structural response considering only the wind load.

[0010] S3. Based on the multi-objective linear equivalent static wind load in step S2, and combined with nonlinear coefficients... By correcting the multi-objective linear equivalent static wind load, the multi-objective nonlinear equivalent static wind load is calculated and expressed as a wind pressure coefficient; where the nonlinear coefficient The modified multi-objective linear equivalent static wind load method is as follows: Calculate the extreme response under the actual wind load time history in the wind tunnel test in step S1. Extreme response under modified equivalent static wind load Using nonlinear coefficients Adjustments were made by comparing the difference between these two extreme responses with the extreme response under the actual wind load time history. The ratio is used to determine whether the preset error range is met; if not, the nonlinear coefficient needs to be readjusted. This continues until the conditions are met, thereby ensuring the safety and accuracy of the structural design under wind loads.

[0011] The beneficial effects of this invention are as follows:

[0012] 1. The multi-objective equivalent static wind load calculation method for nonlinear structures disclosed in this invention, compared with the existing multi-objective equivalent static wind load calculation methods, enables the multi-objective equivalent static wind load calculation method to be applied to nonlinear structures, and the equivalent results are good.

[0013] 2. The multi-objective equivalent static wind load calculation method for nonlinear structures disclosed in this invention, compared with the existing nonlinear structure design method which uses the load wind vibration coefficient to calculate the equivalent static wind load, makes the static response at multiple locations of the structure under the same equivalent static wind load match the actual dynamic response better.

[0014] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0015] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0016] Figure 1 This is a flowchart of the multi-objective equivalent static wind load calculation method applicable to nonlinear structures according to the present invention;

[0017] Figure 2 This is a wind tunnel test diagram of a flexible photovoltaic array support according to an embodiment of the present invention;

[0018] Figure 3 This is a finite element model diagram of a flexible photovoltaic array support according to an embodiment of the present invention;

[0019] Figure 4 This is a load distribution pattern diagram of an embodiment of the present invention;

[0020] Figure 5 This is an equivalent diagram of the displacement minimum value in an embodiment of the present invention, wherein... Figure 5 (a) is a line graph showing the vertical displacement of each equivalent point at the minimum value. Figure 5 (b) is a scatter plot of the equivalent effects at each equivalent point of the minimum value;

[0021] Figure 6 This is an equivalent diagram of the maximum displacement value in an embodiment of the present invention, wherein... Figure 6 (a) is a line graph showing the vertical displacement of the equivalent points at the maximum value. Figure 6 (b) is a scatter plot of the equivalent effects at each equivalent point of the maximum value. Detailed Implementation

[0022] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0023] like Figure 1 The method for calculating multi-objective equivalent static wind loads applicable to nonlinear structures, as shown, includes the following steps:

[0024] S1. Conduct wind tunnel tests on nonlinear structures and establish corresponding finite element models; specifically: based on the wind pressure coefficient time history obtained from the wind tunnel test, conduct dynamic response analysis to obtain the extreme values ​​of various structural responses, including displacement maxima and minima, and stress maxima and minima, for subsequent comparison of the equivalent effects of equivalent load pulsation components.

[0025] S2. Obtain the average component of the equivalent static wind load through the wind tunnel test results in step S1. Obtain the equivalent static wind load excluding the average component, i.e., the fluctuating component, through the time history analysis of the finite element model in step S1. Obtain the multi-objective linear equivalent static wind load by combining the fluctuating component and the average component. The fluctuating component is obtained by comprehensively calculating the basis vector and the combination coefficient. The combination coefficient is obtained by comprehensively calculating the structural response under the basis vector and the structural response considering only the wind load.

[0026] The equivalent static wind load is represented by a combination of the mean component, the background component, and the resonance component, as shown in equations (1)-(2):

[0027]

[0028] In the formula, For average components, and These are the combination coefficients for the background component and the resonance component, respectively. and These are the background component and the resonance component, respectively; The equivalent static wind load, excluding the mean component, will be referred to hereafter as the pulsating component. For the eigenmodes of wind load, It is the first Mode-of-motion inertial force; For combination coefficients, Let be the load basis vector matrix.

[0029] In equation (2), the combination coefficients of intrinsic modes and structural modal inertial forces are closely related to the equivalent extreme response. For different equivalent targets, the combination coefficients are generally different. Therefore, in order to ensure that an equivalent static wind load achieves the equivalence of multiple extreme responses, the following conditions need to be met:

[0030]

[0031] In the formula, Control point The response influence line function, The control point is the one that only considers the pulsating component under actual wind load. The extreme response, This is the number of load basis vectors considered in the equivalent case; the formula can be expressed in matrix form as follows:

[0032]

[0033] In the formula, It is the influence line function matrix of the control points. It is the response matrix of the load basis vectors.

[0034] S3. Based on the multi-objective linear equivalent static wind load in step S2, and combined with nonlinear coefficients... By correcting the multi-objective linear equivalent static wind load, the multi-objective nonlinear equivalent static wind load is calculated and expressed as a wind pressure coefficient; where the nonlinear coefficient The modified multi-objective linear equivalent static wind load method is as follows: Calculate the extreme response under the actual wind load time history in the wind tunnel test in step S1. Extreme response under modified equivalent static wind load Using nonlinear coefficients Adjustments were made by comparing the difference between these two extreme responses with the extreme response under the actual wind load time history. The ratio is used to determine whether the preset error range is met; if not, the nonlinear coefficient needs to be readjusted. This continues until the conditions are met, thereby ensuring the safety and accuracy of the structural design under wind loads.

[0035] For general nonlinear structures, due to the large number of structural members, the number of structural responses of interest is... This number is typically greater than the number of load basis vectors considered in the equivalent case. Therefore, equation (4) can only yield a least-squares solution, i.e.:

[0036]

[0037] During the design phase, both the maximum and minimum responses of the structure are important; therefore, the equivalent static wind load is expressed as:

[0038]

[0039] In the formula This represents the maximum response load of the structure. This represents the minimum response load of the structure.

[0040] For nonlinear structures, equation (4) no longer holds. Under the calculated equivalent static wind load, the equivalent extreme response of the structure still deviates significantly from the actual extreme response. Therefore, a nonlinear coefficient is introduced. To correct for the equivalent static wind load; since nonlinear structures are sensitive to the direction of load application, the nonlinear coefficients need to be calculated separately for the maxima and minima of the response. and As shown in equations (8) and (9):

[0041]

[0042] In the formula, This indicates a correction to the equivalent static wind load. This represents the maximum response load of the modified structure. ;

[0043] Will Substituting the initial values ​​into equations (8) and (9) yields the linear equivalent static wind load. Applying this load to the finite element model, the equivalent extreme response is calculated. Comparing this with the actual extreme response, if equation (10) is satisfied, the nonlinear coefficient is output. And the nonlinear structure multi-objective equivalent static wind load; if equation (10) is not satisfied, the nonlinear coefficient is increased or decreased according to the difference between the two and iterated until equation (10) is satisfied.

[0044]

[0045] In the formula, This represents the maximum nodal response under the modified equivalent wind load. This represents the maximum extreme response under the actual wind load time history. Indicates equivalent error;

[0046] For ease of practical application, the obtained equivalent static wind load is expressed as the wind pressure coefficient according to equation (11):

[0047]

[0048] In the formula, air density, Wind speed at reference altitude.

[0049] Example

[0050] Taking a flexible support structure for a photovoltaic array with wind-resistant cables as an example, this flexible support structure is a quasi-nonlinear structure with a basic wind speed of 30 m / s. The structural parameters include an inclination angle of 0 degrees, a span of 30 m, and a spacing of 4 m. The multi-objective equivalent static wind load calculated by this invention can achieve good equivalent results. The specific scheme is as follows:

[0051] 1) Wind tunnel test and average component of equivalent load

[0052] Wind tunnel pressure tests were conducted on the flexible support structure of the photovoltaic array, such as... Figure 2 As shown, the wind pressure coefficient time history is calculated based on the test results and used as the load for subsequent wind vibration response analysis. At the same time, the average wind pressure coefficient can be obtained as the average component of the subsequent equivalent load.

[0053] 2) Finite element analysis

[0054] Establish a finite element model of the flexible support for the photovoltaic array, such as Figure 3 As shown. Based on the local basic wind pressure and the wind pressure coefficient time history obtained from wind tunnel tests, dynamic response analysis was carried out to obtain the extreme values ​​of various structural responses, including displacement maxima and minima, and stress maxima and minima, which are used for subsequent comparison of the equivalent effects of equivalent load pulsation components.

[0055] 3) Equivalent load pulsation component

[0056] First, the structure is divided into zones. Since the photovoltaic array has 6 rows, it is divided into 6 regions, each containing 1 row of flexible supports. The load distribution pattern of the equivalent pulsating load is analyzed by applying sinusoidal loads of the same sign. Figure 4 shows the load distribution pattern of each node on a single cable.

[0057] After determining the load pattern, the next step is to construct the load basis vectors. Based on the partitioning, a total of 6 basis vectors are constructed. The specific construction method is as follows: each region corresponds to one basis vector. For nodes belonging to that region, the node normal force is 1, and the node normal force at other locations is 0.

[0058] After constructing the basis vectors, the combination coefficients can be calculated according to equation (4). The combination coefficients {C} for the displacement minimum and maximum are [2.11, 1.45, 1.62, 1.62, 1.82, 2.54] and [2.06, 1.06, 0.73, 0.73, 0.94, 1.31], respectively. These coefficients reflect the ratio of the magnitudes of the equivalent load fluctuation components between each region.

[0059] 4) Equivalent static wind load

[0060] After obtaining the equivalent load fluctuation component, it can be combined with the average load to obtain the linear equivalent static wind load. Finally, due to the structural nonlinearity, the nonlinear coefficients need to be adjusted according to the equivalent results and the actual structural response to optimize the equivalent results. The final iteration yields nonlinear coefficients of 1.44 and 1.56 for the minimum and maximum values, respectively.

[0061] The final equivalent result is as follows Figure 5 and Figure 6 As shown, Figure 5 (a) is a line graph showing the vertical displacement of each equivalent point at the minimum value. Figure 5 (b) is a scatter plot of the equivalent effects at each equivalent point of the minimum value; Figure 6 (a) is a line graph showing the vertical displacement of the equivalent points at the maximum value. Figure 6(b) is a scatter plot showing the equivalent effects of each equivalent point for the maximum value. The results show that for the equivalence of the minimum value, the maximum values ​​in each row match well, while the matching in the middle region of each row is less good, causing the equivalent points to deviate further from the reference line y=x (Figure 5(b)). Compared to the equivalence of the maximum value, the equivalent points for the maximum value are more concentrated on both sides of the reference line y=x (Figure 6(b)). The equivalence results demonstrate that this invention can achieve a good equivalence effect.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating multi-objective equivalent static wind loads applicable to nonlinear structures, characterized in that, Includes the following steps: S1. Conduct wind tunnel tests on nonlinear structures and establish corresponding finite element models; S2. Obtain the average component of the equivalent static wind load through the wind tunnel test results in step S1. Obtain the equivalent static wind load excluding the average component, i.e., the pulsating component, through the time history analysis of the finite element model in step S1. Obtain the multi-objective linear equivalent static wind load by combining the analysis of the pulsating component and the average component. The pulsating component is obtained by the comprehensive calculation of the basis vector and the combination coefficient. The combination coefficient is obtained by the comprehensive calculation of the structural response under the basis vector and the structural response considering only the wind load. S3. Based on the multi-objective linear equivalent static wind load in step S2, and combined with nonlinear coefficients... By correcting the multi-objective linear equivalent static wind load, the multi-objective nonlinear equivalent static wind load is calculated and expressed as a wind pressure coefficient; where the nonlinear coefficient The modified multi-objective linear equivalent static wind load method is as follows: Calculate the extreme response under the actual wind load time history in the wind tunnel test in step S1. Extreme response under modified equivalent static wind load Using nonlinear coefficients Adjustments were made by comparing the difference between these two extreme responses with the extreme response under the actual wind load time history. The ratio is used to determine whether the preset error range is met; if not, the nonlinear coefficient needs to be readjusted. This continues until the conditions are met, thereby ensuring the safety and accuracy of the structural design under wind loads.

2. The multi-objective equivalent static wind load calculation method as described in claim 1, characterized in that, In step S1, dynamic response analysis is carried out based on the wind pressure coefficient time history obtained from the wind tunnel test to obtain the extreme values ​​of various structural responses, including displacement maximum and minimum values ​​and stress maximum and minimum values, which are used to compare the equivalent effect of the equivalent load pulsation component in subsequent tests.

3. The multi-objective equivalent static wind load calculation method as described in claim 1, characterized in that, In step S2, the equivalent static wind load is represented by a combination of the mean component, background component, and resonance component: In the formula, For average components, and These are the combination coefficients for the background component and the resonance component, respectively. and These are the background component and the resonance component, respectively; The equivalent static wind load, excluding the mean component, will be referred to hereafter as the pulsating component. For the eigenmodes of wind load, It is the first Mode-of-motion inertial force; For combination coefficients, Let be the load basis vector matrix.

4. The multi-objective equivalent static wind load calculation method as described in claim 3, characterized in that, In step S2, the combination coefficients of intrinsic modes and structural modal inertial forces are closely related to the equivalent extreme response. For different equivalent targets, the combination coefficients are generally different. Therefore, in order to ensure that an equivalent static wind load achieves the equivalence of multiple extreme responses, the following conditions need to be met: In the formula, Control point The response influence line function, The control point is the one that only considers the pulsating component under actual wind load. The extreme response, This is the number of load basis vectors considered in the equivalent case; the formula can be expressed in matrix form as follows: In the formula, It is the influence line function matrix of the control points. It is the response matrix of the load basis vectors.

5. The multi-objective equivalent static wind load calculation method as described in claim 4, characterized in that, In step S3, for general nonlinear structures, due to the large number of structural members, the number of structural responses is... This number is typically greater than the number of load basis vectors considered in the equivalent case. Therefore, equation (4) can only yield a least-squares solution, i.e.: During the design phase, both the maximum and minimum responses of the structure are important. The equivalent static wind load is expressed as: In the formula This represents the maximum response load of the structure. This represents the minimum response load of the structure.

6. The multi-objective equivalent static wind load calculation method as described in claim 4, characterized in that, In step S3, for nonlinear structures, equation (4) no longer holds. At this point, the equivalent extreme response of the structure under the calculated equivalent static wind load still deviates significantly from the actual extreme response. Therefore, a nonlinear coefficient is introduced. To correct for the equivalent static wind load; since nonlinear structures are sensitive to the direction of load application, the nonlinear coefficients need to be calculated separately for the maxima and minima of the response. and As shown in equations (8) and (9): In the formula, This indicates a correction to the equivalent static wind load. This represents the maximum response load of the modified structure. ; Will Substituting the initial values ​​into equations (8) and (9) yields the linear equivalent static wind load. Applying this load to the finite element model, the equivalent extreme response is calculated. Comparing this with the actual extreme response, if equation (10) is satisfied, the nonlinear coefficient is output. And nonlinear structure multi-objective equivalent static wind load; if equation (10) is not satisfied, the nonlinear coefficient is increased or decreased according to the difference between the two and iterated until equation (10) is satisfied; In the formula, This represents the maximum nodal response under the modified equivalent wind load. This represents the maximum extreme response under the actual wind load time history. Indicates equivalent error; For ease of practical application, the obtained equivalent static wind load is expressed as the wind pressure coefficient according to equation (11): In the formula, air density, Wind speed at reference altitude.

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