Multi-target equivalent static wind load calculation method suitable for nonlinear structure

Abstract

The invention relates to a multi-target equivalent static wind load calculation method suitable for a nonlinear structure. The method comprises the following steps: firstly, carrying out a nonlinear structure wind tunnel test and establishing a corresponding finite element model; secondly, obtaining an average component of the equivalent static wind load through a wind tunnel test result, obtaining an equivalent static wind load not including the average component through time-history analysis of a finite element model, namely a pulsation component, and obtaining a multi-target linear equivalent static wind load through combined analysis of the pulsation component and the average component; and finally, on the basis of the multi-target linear equivalent quiet wind load, correcting the multi-target linear equivalent quiet wind load in combination with a nonlinear coefficient, calculating to obtain a multi-target nonlinear equivalent quiet wind load, and expressing the multi-target nonlinear equivalent quiet wind load as a wind pressure coefficient form. The simultaneous equivalence of multiple extreme responses of a nonlinear structure is realized, and a convenient and accurate equivalent static wind load is provided for engineering design.

Description

Technical Field

[0001] The invention belongs to the technical field of wind load calculation, and relates to a multi-objective equivalent static wind load calculation method suitable for nonlinear structures. Background Art

[0002] Equivalent static wind load is an important wind-resistant design method. It simplifies the wind-resistant design process of structures by converting complex wind load dynamic effects into equivalent static loads. This method can not only reflect the wind-induced vibration effects of the structure, but also facilitates combined calculations with other loads. Therefore, it is widely used in the wind-resistant design of wind-sensitive structures. The multi-objective equivalent static wind load calculation method can achieve a good match between the static response and the actual dynamic response of the structure at multiple locations under a single equivalent static wind load. Therefore, it has 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, which provides an effective technical means for the wind-resistant design of linear structures.

[0003] However, the existing multi-objective equivalent static wind load calculation method is mainly applicable to linear structures. When directly applied to nonlinear structures, it is impossible to achieve the equivalence of multiple extreme responses of the structure. This shows that the existing technology lacks a multi-objective equivalent static wind load calculation method specifically for nonlinear structures. At present, the wind-resistant design of nonlinear structures usually adopts a single-objective equivalent method based on the load wind vibration coefficient, but this method has obvious limitations. Under the action of the equivalent static wind load, it can only ensure that the response of a certain structural effect of the structure is equal to the dynamic extreme response, and it is impossible to achieve the equivalence of multiple extreme responses. For example, scholars such as Wu Lili usually adopt a single-objective equivalent method based on the load wind vibration coefficient for the 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 suitable for nonlinear structures to fill the gap in the existing technology and provide a more accurate and effective calculation method 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 above-mentioned existing multi-objective equivalent static wind load calculation method is only applicable to linear structures, the multi-objective equivalent static wind load of nonlinear structures cannot be accurately and effectively calculated, and cannot meet the requirements of structural wind resistance design, the present invention provides a multi-objective equivalent static wind load calculation method applicable to nonlinear structures, which realizes the simultaneous equivalence of multiple extreme responses of nonlinear structures, and provides a convenient and accurate equivalent static wind load for engineering design.

[0006] In order to achieve the above object, the present invention provides the following technical solutions: A multi-objective equivalent static wind load calculation method applicable to nonlinear structures includes the following steps: S1. Conduct nonlinear structural wind tunnel tests 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 maximum and minimum displacements and maximum and minimum stresses, for subsequent comparison of the equivalent effects of the equivalent load pulsating components.

[0007] S2. Obtain the average component of the equivalent static wind load through the wind tunnel test results of 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 of step S1, and obtain the multi-objective linear equivalent static wind load by combining the pulsating component and the average component; wherein the pulsating component is obtained by comprehensive calculation of basis vectors and combination coefficients, and the combination coefficients are obtained by comprehensive calculation of the structural response under the basis vectors and the structural response considering only the wind load; S3, based on the multi-objective linear equivalent static wind load in step S2, combined with the nonlinear coefficient By modifying 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; the nonlinear coefficient The modified multi-objective linear equivalent static wind load method is as follows: Calculation step S1: The extreme value response under the actual wind load time history in the wind tunnel test and the extreme value response under the modified equivalent static wind load , using the nonlinear coefficient Adjustment is made by comparing the difference between these two extreme responses with the extreme response under the actual wind load time history. to determine whether the preset error range is met; if not, the nonlinear coefficient needs to be readjusted. , until the conditions are met, thereby ensuring the safety and accuracy of the structural design under wind loads.

[0008] The beneficial effects of the present invention are: 1. The multi-objective equivalent static wind load calculation method for nonlinear structures disclosed in the present invention can be applied to nonlinear structures with good equivalent results compared to existing multi-objective equivalent static wind load calculation methods.

[0009] 2. The multi-objective equivalent static wind load calculation method disclosed in the present invention is suitable for nonlinear structures. Compared with the existing nonlinear structure design method that uses the load wind vibration coefficient to calculate the equivalent static wind load, this method ensures that the static response of multiple positions of the structure under the same equivalent static wind load is more consistent with the actual dynamic response.

[0010] 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

[0011] 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: Figure 1 This is a flow chart of the multi-objective equivalent static wind load calculation method applicable to nonlinear structures of the present invention; Figure 2 This is a wind tunnel test diagram of a photovoltaic array flexible bracket according to an embodiment of the present invention; Figure 3 This is a finite element model diagram of a photovoltaic array flexible bracket according to an embodiment of the present invention; Figure 4 This is a load distribution pattern diagram of an embodiment of the present invention; Figure 5 This is a diagram showing the equivalent situation of the minimum displacement value according to an embodiment of the present invention, wherein Figure 5 (a) is the line graph of the vertical displacement of each equivalent point at the minimum value, Figure 5 (b) is a scatter plot of the equivalent effects of each equivalent point at the minimum value; Figure 6 This is a diagram showing the equivalent situation of the maximum displacement of an embodiment of the present invention, where Figure 6 (a) is the vertical displacement line graph of each equivalent point with maximum value, Figure 6 (b) is a scatter plot of the equivalent effects of each equivalent point at the maximum value. DETAILED DESCRIPTION

[0012] 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.

[0013] like Figure 1 A multi-objective equivalent static wind load calculation method suitable for nonlinear structures is shown, which includes the following steps: S1. Conduct nonlinear structural wind tunnel tests 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 maximum and minimum displacements and maximum and minimum stresses, for subsequent comparison of the equivalent effects of the equivalent load pulsating components.

[0014] S2. Obtain the average component of the equivalent static wind load through the wind tunnel test results of 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 of step S1, and obtain the multi-objective linear equivalent static wind load by combining the pulsating component and the average component; wherein the pulsating component is obtained by comprehensive calculation of basis vectors and combination coefficients, and the combination coefficients are obtained by comprehensive calculation of the structural response under the basis vectors and the structural response considering only the wind load; The equivalent static wind load is expressed by the combination of average component, background component and resonance component, as shown in equations (1)-(2):

[0015] Where, is the average weight, and are the combination coefficients of background component and resonance component respectively, and are background component and resonance component respectively; is the equivalent static wind load excluding the average component, which is subsequently referred to as the pulsating component. is the eigenmode of wind load, It is Order vibration mode inertia force; is the combination coefficient, is the load basis vector matrix.

[0016] The combination coefficient of the eigenmode and structural modal inertia force in formula (2) is closely related to the equivalent extreme value response. For different equivalent targets, the combination coefficient is generally different. Therefore, in order to ensure that an equivalent static wind load can achieve the equivalence of multiple extreme value responses, the following conditions must be met:

[0017] Where, It is a control point The response influence line function, It is the control point when only the pulsating component is considered under the actual wind load. The extreme response of is the number of load basis vectors considered in the equivalence; the formula is expressed in a matrix as:

[0018] Where, is the influence line function matrix of the control point, is the response matrix of the load basis vectors.

[0019] S3, based on the multi-objective linear equivalent static wind load in step S2, combined with the nonlinear coefficient By modifying 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; the nonlinear coefficient The modified multi-objective linear equivalent static wind load method is as follows: Calculation step S1: The extreme value response under the actual wind load time history in the wind tunnel test and the extreme value response under the modified equivalent static wind load , using the nonlinear coefficient Adjustment is made by comparing the difference between these two extreme responses with the extreme response under the actual wind load time history. to determine whether the preset error range is met; if not, the nonlinear coefficient needs to be readjusted. , until the conditions are met, thereby ensuring the safety and accuracy of the structural design under wind loads.

[0020] For general nonlinear structures, due to the large number of structural members, the number of structural responses of concern is Usually greater than the number of load basis vectors considered in the equivalent , so formula (4) can only get the least squares solution, that is:

[0021] In the design stage, both the maximum and minimum responses of the structure are important, so the equivalent static wind load is expressed as:

[0022] In the formula represents the maximum response load of the structure, Represents the minimum response load of the structure.

[0023] For nonlinear structures, Equation (4) is no longer valid. Under the action of equivalent static wind load, there is still a large deviation between the equivalent extreme value response of the structure and the true extreme value response. Therefore, the nonlinear coefficient is introduced. To correct the equivalent static wind load; since the nonlinear structure is sensitive to the direction of the load, the nonlinear coefficient needs to be calculated separately for the maximum and minimum response values and , as shown in formula (8) and formula (9):

[0024] Where, represents the modified equivalent static wind load, represents the maximum response load of the modified structure, ; Will Substituting the initial value into equations (8) and (9) to obtain the linear equivalent static wind load, the equivalent extreme value response is calculated by applying it to the finite element model. Compared with the true extreme value response, if equation (10) is satisfied, the nonlinear coefficient is output. and the multi-objective equivalent static wind load of the nonlinear structure; 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.

[0025]

[0026] Where, represents the maximum node response under the modified equivalent wind load, represents the maximum extreme value response under the real wind load time history, represents the equivalent error; In order to facilitate practical application, the equivalent static wind load is expressed as a wind pressure coefficient according to formula (11):

[0027] Where, is the air density, is the wind speed at the reference height.

[0028] Example

[0029] Taking a photovoltaic array flexible support with wind-resistant cables as an example, the flexible support is a quasi-nonlinear structure. The basic wind speed is set to 30m / s. The structural parameters include an inclination angle of 0 degrees, a span of 30m, and a spacing of 4m. The multi-objective equivalent static wind load calculated by the present invention can achieve good equivalent results. The specific scheme is as follows: 1) Wind tunnel test and average component of equivalent load Carry out wind tunnel pressure test on photovoltaic array flexible support, such as Figure 2 As shown in Figure 2, the wind pressure coefficient time history is calculated based on the test results and used as the added load for the subsequent wind-induced vibration response analysis. At the same time, the average wind pressure coefficient can be obtained as the average component of the subsequent equivalent load.

[0030] 2) Finite element analysis

[0031] Establish a finite element model of the photovoltaic array flexible bracket, such as Figure 3 Based on the local basic wind pressure and the wind pressure coefficient time history obtained from the wind tunnel test, a dynamic response analysis was carried out to obtain the extreme values ​​of the structural response, including the maximum and minimum displacements and the maximum and minimum stresses, which were used for subsequent comparison of the equivalent effects of the equivalent load pulsation components.

[0032] 3) Equivalent load pulsation component

[0033] First, the structure was divided into six zones. Since the photovoltaic array has six rows, each zone contains one row of flexible supports. Sinusoidal loads of the same sign were applied as an equivalent pulsating load and analyzed. Figure 4 shows the load distribution pattern at each node on a cable.

[0034] After determining the load pattern, the next step is to construct the load basis vectors. Based on the partitioning, a total of six basis vectors are constructed. The specific construction method is: each region corresponds to a basis vector. For nodes within that region, the node normal force is 1, and for nodes in other locations, the node normal force is 0.

[0035] After constructing the basis vectors, the combination coefficient can be calculated according to Equation (4). The combination coefficients {C} for the minimum and maximum displacements 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. This coefficient reflects the ratio of the equivalent load pulsation components between each region.

[0036] 4) Equivalent static wind load

[0037] After obtaining the equivalent load pulsation component, it is combined with the average value to obtain the linear equivalent static wind load. Finally, due to the nonlinearity of the structure, the nonlinear coefficient needs to be adjusted based on the equivalent result and the actual structural response to optimize the equivalent result. The final iteration results in the minimum and maximum nonlinear coefficients of 1.44 and 1.56, respectively.

[0038] The final equivalent result is Figure 5 and Figure 6 As shown, Figure 5 (a) is the line graph of the vertical displacement of each equivalent point at the minimum value, Figure 5 (b) is a scatter plot of the equivalent effects of each equivalent point at the minimum value; Figure 6 (a) is the vertical displacement line graph of each equivalent point with maximum value, Figure 6 (b) is a scatter plot of the equivalent effects of each equivalent point at the maximum value. The results show that for the equivalent effect of the minimum value, the maximum value in each row agrees well, while the mid-span area in each row agrees less well, causing the equivalent points to deviate further from the reference line y=x (Figure 5(b)). Compared to the equivalent effect of the maximum value, the equivalent points of the maximum value are more concentrated on both sides of the reference line y=x (Figure 6(b)). The equivalent results show that the present invention can achieve a good equivalent effect.

[0039] 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 multi-objective equivalent static wind load calculation method suitable for nonlinear structures, characterized in that: The following steps are involved: S1. Conduct nonlinear structural wind tunnel tests and establish corresponding finite element models; S2. Obtain an average component of the equivalent static wind load through the wind tunnel test results of step S1, obtain an equivalent static wind load excluding the average component, i.e., a pulsating component, through a time history analysis of the finite element model of step S1, and obtain a multi-objective linear equivalent static wind load by combining the pulsating component and the average component; The pulsation component is obtained by comprehensive calculation of basis vectors and combination coefficients, and the combination coefficient is obtained by comprehensive calculation of the structural response under basis vectors and the structural response considering only wind loads. S3, based on the multi-objective linear equivalent static wind load in step S2, combined with the nonlinear coefficient By modifying 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; the nonlinear coefficient The modified multi-objective linear equivalent static wind load method is as follows: Calculation step S1: The extreme value response under the actual wind load time history in the wind tunnel test and the extreme value response under the modified equivalent static wind load , using the nonlinear coefficient Adjustment is made by comparing the difference between these two extreme responses with the extreme response under the actual wind load time history. to determine whether the preset error range is met; if not, the nonlinear coefficient needs to be readjusted. , 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 according to claim 1, characterized in that: In step S1, a dynamic response analysis is performed based on the wind pressure coefficient time history obtained from the wind tunnel test to obtain the extreme values ​​of various structural responses, including the maximum and minimum displacements and the maximum and minimum stresses, which are used for subsequent comparison of the equivalent effects of the equivalent load pulsation components.

3. The multi-objective equivalent static wind load calculation method according to claim 1, characterized in that: The equivalent static wind load in step S2 is expressed by a combination of average component, background component and resonance component: Where, is the average weight, and are the combination coefficients of background component and resonance component respectively, and are background component and resonance component respectively; is the equivalent static wind load excluding the average component, which is subsequently referred to as the pulsating component. is the eigenmode of wind load, It is Order vibration mode inertia force; is the combination coefficient, is the load basis vector matrix.

4. The multi-objective equivalent static wind load calculation method according to claim 3, characterized in that: The combination coefficient of the eigenmode and structural modal inertia force in step S2 (2) is closely related to the equivalent extreme response. For different equivalent targets, the combination coefficient is generally different. Therefore, in order to ensure that an equivalent static wind load can achieve the equivalence of multiple extreme responses, the following conditions need to be met: Where, It is a control point The response influence line function, It is the control point when only the pulsating component is considered under the actual wind load. The extreme response of is the number of load basis vectors considered in the equivalence; the formula is expressed in a matrix as: Where, is the influence line function matrix of the control point, is the response matrix of the load basis vectors.

5. The multi-objective equivalent static wind load calculation method according to claim 4, characterized in that: In step S3, for a general nonlinear structure, due to the large number of structural members, the number of structural responses is Usually greater than the number of load basis vectors considered in the equivalent , so formula (4) can only get the least squares solution, that is: 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 represents the maximum response load of the structure, Represents the minimum response load of the structure.

6. The multi-objective equivalent static wind load calculation method according to claim 4, characterized in that: In step S3, for nonlinear structures, formula (4) no longer holds true. Under the action of the equivalent static wind load, there is still a large deviation between the equivalent extreme value response of the structure and the true extreme value response. Therefore, the nonlinear coefficient is introduced. To correct the equivalent static wind load; since the nonlinear structure is sensitive to the direction of the load, the nonlinear coefficient needs to be calculated separately for the maximum and minimum response values and , as shown in formula (8) and formula (9): Where, represents the modified equivalent static wind load, represents the maximum response load of the modified structure, ; Will Substituting the initial value into equations (8) and (9) to obtain the linear equivalent static wind load, the equivalent extreme value response is calculated by applying it to the finite element model. Compared with the true extreme value response, if equation (10) is satisfied, the nonlinear coefficient is output. and the multi-objective equivalent static wind load of the nonlinear structure; if the formula (10) is not satisfied, the nonlinear coefficient is increased or decreased according to the difference between the two and iterated until the formula (10) is satisfied; Where, represents the maximum node response under the modified equivalent wind load, represents the maximum extreme value response under the real wind load time history, represents the equivalent error; In order to facilitate practical application, the equivalent static wind load is expressed as a wind pressure coefficient according to formula (11): Where, is the air density, is the wind speed at the reference height.

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