Seismic response analysis method of transmission tower based on Runge-Kutta method

Abstract

The present application discloses a method for analyzing the seismic response of a transmission tower based on the Runge-Kutta method. By obtaining the structural parameters of the transmission tower structure and spatially discretizing the structural parameters, the overall stiffness matrix and overall mass matrix of the transmission tower structure are obtained. This eliminates the need for commercial software to establish a finite element model of the transmission tower, thereby avoiding the problem of limited analysis accuracy due to the solution accuracy of commercial software. The method then uses preset motion control equations to determine the effective stiffness matrix and effective mass matrix of the transmission tower structure based on the overall stiffness matrix and the overall mass matrix. Furthermore, the Runge-Kutta method is used to analyze the response data of the transmission tower structure under external loads and seismic loads based on the effective stiffness matrix, the effective mass matrix, and the effective load vector. This method utilizes the fourth-order accuracy of the Runge-Kutta method to overcome the limitation of commercial software that can only achieve second-order accuracy, thereby improving the analysis accuracy of the seismic dynamic response analysis results of the transmission tower structure.

Description

Technical Field

[0001] The present application relates to the technical field of transmission tower structure safety, and in particular to a transmission tower seismic response analysis method based on the Runge-Kutta method. Background Art

[0002] Currently, the seismic dynamic response analysis of transmission tower structures primarily combines the finite element method with the time integration method. Finite element software (such as commercial structural analysis software like ANSYS and Abaqus) is used to spatially model and discretize the transmission tower structure, generating a finite element model. The seismic response is then solved and analyzed using the software's time integration method. However, the time integration methods currently used in these software include the Newmark method and the HHT-α method. These methods can only achieve second-order accuracy at best when unconditional stability is met. Consequently, the accuracy of the seismic dynamic response analysis of transmission tower structures is limited by the software's native time integration method, failing to meet the demand for higher analysis accuracy. Summary of the Invention

[0003] The present application provides a transmission tower seismic response analysis method based on the Runge-Kutta method to solve the technical problem that the current seismic dynamic response analysis method of transmission tower structures cannot meet the requirements of higher analysis accuracy.

[0004] In order to solve the above technical problems, in a first aspect, the present application provides a transmission tower seismic response analysis method based on the Runge-Kutta method, comprising:

[0005] Obtain the structural parameters of the transmission tower structure;

[0006] The structural parameters are spatially discretized to obtain the overall stiffness matrix and overall mass matrix of the transmission tower structure;

[0007] Using the preset motion control equations, the effective stiffness matrix and effective mass matrix of the transmission tower structure are determined according to the overall stiffness matrix and the overall mass matrix;

[0008] The Runge-Kutta method is used to analyze the response data of the transmission tower structure under external loads and seismic loads based on the effective stiffness matrix, effective mass matrix and effective load vector. The effective load vector is generated based on the external loads and seismic loads combined with a preset motion control method.

[0009] In some implementations, spatially discretizing the structural parameters to obtain the overall stiffness matrix and overall mass matrix of the transmission tower structure includes:

[0010] Based on the finite element method and structural parameters, the unit stiffness matrix and unit mass matrix of each rod unit in the transmission tower structure are established;

[0011] The unit stiffness matrix and unit mass matrix of multiple rod elements are combined to obtain the overall stiffness matrix and overall mass matrix.

[0012] In some implementations, determining the effective stiffness matrix and the effective mass matrix of the transmission tower structure based on the overall stiffness matrix and the overall mass matrix using the preset motion control equations includes:

[0013] Based on the preset linear parameters, the overall stiffness matrix and the overall mass matrix are linearly combined to obtain the damping matrix of the transmission tower structure;

[0014] According to the preset motion control equation, combined with the first preset control parameter and the damping matrix, the overall stiffness matrix and the overall mass matrix are time discretized to generate the effective stiffness matrix and the effective mass matrix.

[0015] In some implementations, the process of generating a payload vector includes:

[0016] Obtaining a seismic load vector and an external load vector, and superimposing the seismic load vector and the external load vector to form a target load vector;

[0017] According to the preset motion control equation and the second preset control parameter, the target load vector is time discretized to generate the effective load vector, which is:

[0018]

[0019] is the explicit form of the effective load vector, F T () is the transpose of the target load vector, t n is a discrete moment, Δt is a time step, and p3 and p4 are both second preset control parameters.

[0020] In some implementations, the preset motion control equation is:

[0021]

[0022] Among them, M is the overall mass matrix, C is the damping matrix, K is the overall stiffness matrix, Fg is the seismic load vector, Fe is the external load vector, is the acceleration vector, is the velocity vector and u is the displacement vector.

[0023] In some implementations, the response data includes displacement response data and velocity response data. The response data of the transmission tower under external loads and seismic loads is analyzed using the Runge-Kutta method based on the effective stiffness matrix, the effective mass matrix, and the effective load vector, including:

[0024] Using the Runge-Kutta method, define the vector variables of the displacement vector and the velocity vector, and define the intermediate process variable vector;

[0025] Based on vector variables and intermediate process variables, the matrix relationship constructed based on the effective stiffness matrix, effective mass matrix and effective load vector is solved to obtain the displacement response data and velocity response data of the transmission tower under external loads and seismic loads. The matrix relationship is:

[0026]

[0027] in, is the explicit form of the effective mass matrix, is the intermediate process variable vector, is the explicit form of the damping matrix, y n are the displacement vector and velocity vector at t n A vector variable at time, is the explicit representation of the payload vector.

[0028] In some implementations, the response data includes acceleration response data, and the method includes:

[0029] The acceleration response data of the transmission tower structure under external loads and seismic loads is solved by using the preset acceleration vector solution equation. The preset acceleration vector solution equation is:

[0030]

[0031] Among them, M is the overall mass matrix, C is the damping matrix, K is the overall stiffness matrix, is the acceleration response data, u n+1 is the displacement vector, F(t n+1 ) is the target load vector obtained by superimposing the earthquake load vector and the external load vector.

[0032] In a second aspect, the present application further provides a transmission tower seismic response analysis device based on the Runge-Kutta method, comprising:

[0033] An acquisition module, used to obtain structural parameters of the transmission tower structure;

[0034] Discrete module, used to spatially discretize the structural parameters and obtain the overall stiffness matrix and overall mass matrix of the transmission tower structure;

[0035] A determination module is used to determine an effective stiffness matrix and an effective mass matrix of the transmission tower structure according to an overall stiffness matrix and an overall mass matrix using a preset motion control equation;

[0036] The analysis module is used to analyze the response data of the transmission tower structure under external loads and seismic loads using the Runge-Kutta method based on the effective stiffness matrix, effective mass matrix and effective load vector. The effective load vector is generated based on the external loads and seismic loads combined with a preset motion control method.

[0037] In a third aspect, the present application further provides a computer device comprising a processor and a memory, wherein the memory is used to store a computer program, and when the computer program is executed by the processor, the transmission tower seismic response analysis method based on the Runge-Kutta method as in the first aspect is implemented.

[0038] In a fourth aspect, the present application further provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the transmission tower seismic response analysis method based on the Runge-Kutta method as in the first aspect.

[0039] Compared with the prior art, this application has at least the following beneficial effects:

[0040] By obtaining the structural parameters of the transmission tower structure and spatially discretizing the structural parameters, the overall stiffness matrix and overall mass matrix of the transmission tower structure are obtained, thereby eliminating the need to use commercial software to establish a finite element model of the transmission tower, avoiding the problem of limited analysis accuracy caused by the solution accuracy of commercial software; then, using the preset motion control equation, the effective stiffness matrix and effective mass matrix of the transmission tower structure are determined according to the overall stiffness matrix and the overall mass matrix, and using the Runge-Kutta method, the response data of the transmission tower structure under external loads and seismic loads are analyzed according to the effective stiffness matrix, effective mass matrix and effective load vector, so as to utilize the characteristic of the Runge-Kutta method that can achieve fourth-order accuracy to overcome the limitation that commercial software can only achieve second-order accuracy, and improve the analysis accuracy of the seismic dynamic response analysis results of the transmission tower structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flow chart of a method for analyzing the seismic response of a transmission tower based on the Runge-Kutta method according to an embodiment of the present application is shown;

[0042] Figure 2 This is a schematic diagram of the response result error of the system at time t=0.4 when different time steps are used in an embodiment of the present application;

[0043] Figure 3 A schematic diagram of the displacement response results shown in an embodiment of the present application;

[0044] Figure 4 A schematic diagram showing displacement error results according to an embodiment of the present application;

[0045] Figure 5 A schematic diagram of a transmission tower structure model shown in an embodiment of the present application;

[0046] Figure 6 This is a schematic diagram showing the change in vertical displacement over time at a mass point on the right side of a transmission tower structure model shown in an embodiment of the present application;

[0047] Figure 7 This is a schematic diagram showing the change in vertical velocity over time at a mass point on the right side of a transmission tower structure model shown in an embodiment of the present application;

[0048] Figure 8 Schematic diagram of the vertical acceleration of the mass point on the right side of the transmission tower structure model shown in the embodiment of this application over time

[0049] Figure 9 This is a schematic diagram of the peak acceleration response moment results shown in an embodiment of the present application;

[0050] Figure 10 This is a schematic structural diagram of a transmission tower seismic response analysis device based on the Runge-Kutta method according to an embodiment of the present application;

[0051] Figure 11 This is a schematic diagram of the structure of a computer device shown in an embodiment of the present application. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0053] Please refer to Figure 1 , Figure 1 The flow chart of a transmission tower seismic response analysis method based on the Runge-Kutta method provided in the embodiment of the present application is provided. The transmission tower seismic response analysis method based on the Runge-Kutta method in the embodiment of the present application can be applied to computer devices, including but not limited to smart phones, laptops, tablet computers, desktop computers, physical servers, cloud servers and other devices. Figure 1 As shown, the transmission tower seismic response analysis method based on the Runge-Kutta method of this embodiment includes steps S101 to S104, which are described in detail as follows:

[0054] Step S101: Acquire structural parameters of a transmission tower structure.

[0055] In this step, a unified coordinate system is established for the transmission tower structure composed of multiple rod units, each rod and intersection node is numbered separately, and the structural parameters of the transmission tower are collected. The structural parameters include but are not limited to the intersection node position of each rod unit of the transmission tower, the cross-sectional dimensions of each rod unit, the material elastic modulus and material density, etc.

[0056] Step S102: spatially discretize the structural parameters to obtain an overall stiffness matrix and an overall mass matrix of the transmission tower structure.

[0057] In this step, spatial discretization is performed based on the finite element method to obtain the overall rigid body matrix and the overall mass matrix.

[0058] In some embodiments, step S102 includes:

[0059] Based on the finite element method and according to the structural parameters, a unit stiffness matrix and a unit mass matrix of each rod unit in the transmission tower structure are established;

[0060] The unit stiffness matrices and the unit mass matrices of the plurality of rod units are combined to obtain the overall stiffness matrix and the overall mass matrix.

[0061] In this embodiment, based on the finite element concept, the unit stiffness matrix and unit mass matrix of each rod element in the one-dimensional case are respectively expressed as:

[0062]

[0063] Among them, E e is the elastic modulus of the rod; A e is the cross-sectional area of ​​the rod, which is calculated based on the cross-sectional dimension data; l e is the length of the rod, which is calculated by the coordinate position of the intersection nodes at both ends; ρ e is the density of the rod.

[0064] For multi-dimensional cases, the degree of freedom of the rod element is transformed through the coordinate relationship of the node positions at both ends to obtain:

[0065] K e =G T K e G, M e =G T M e G,

[0066] Where n is the dimension of the transmission tower structure space, which is 2 for two-dimensional and 3 for three-dimensional; φ 1×n is the direction cosine vector determined by the position coordinates.

[0067] The element stiffness matrix Ke and the element mass matrix M e , assemble according to the node number relationship, and get:

[0068] Overall stiffness matrix: K = ∑K e ;

[0069] Overall mass matrix: M = ∑M e .

[0070] Step S103: using a preset motion control equation, according to the overall stiffness matrix and the overall mass matrix, determining the effective stiffness matrix and the effective mass matrix of the transmission tower structure.

[0071] In this step, optionally, the preset motion control equation is:

[0072]

[0073] Among them, M is the overall mass matrix, C is the damping matrix, K is the overall stiffness matrix, Fg is the seismic load vector, Fe is the external load vector, is the acceleration vector, is the velocity vector, u is the displacement vector, where under the initial conditions, u0=u(t0), t0 represents the initial time.

[0074] In some embodiments, step S103 includes:

[0075] Based on preset linear parameters, linearly combining the overall stiffness matrix and the overall mass matrix to obtain a damping matrix of the transmission tower structure;

[0076] According to the preset motion control equation, combined with the first preset control parameter and the damping matrix, the overall stiffness matrix and the overall mass matrix are time discretized to generate the effective stiffness matrix and the effective mass matrix.

[0077] In this embodiment, optionally, the damping matrix is ​​Rayleigh damping, specifically:

[0078] C=αM+βK;

[0079] Among them, α and β are constants that do not depend on the structural frequency, that is, the above-mentioned preset linear parameters.

[0080] Based on the left side of the above preset motion control equation, combined with the first preset control parameter and the damping matrix, the overall stiffness matrix and the overall mass matrix are time discretized to generate the explicit effective stiffness matrix: and the explicit form of the effective mass matrix

[0081]

[0082]

[0083] Where Δt is the time step; p1 and p2 are control parameters, and I is the identity matrix.

[0084] Optionally,

[0085] It should be noted that the effective mass matrix and the effective stiffness matrix of this embodiment are both in explicit expression forms, which can effectively avoid the iterative solution process and reduce the difficulty of solution.

[0086] In some embodiments, the process of generating the payload vector includes:

[0087] Acquire a seismic load vector and an external load vector, and superimpose the seismic load vector and the external load vector to form a target load vector;

[0088] According to the preset motion control equation and in combination with the second preset control parameter, the target load vector is time discretized to generate the effective load vector, which is:

[0089]

[0090] is the explicit form of the effective load vector, F T () is the transpose of the target load vector, t n is a discrete moment, Δt is a time step, and p3 and p4 are both second preset control parameters.

[0091] In this embodiment, the external load vector can be derived by superimposing loads on the transmission tower, such as the load imposed by snow on the pole element. The seismic load is calculated based on the earthquake ground acceleration: Fg = -M1A(t), where 1 is a column vector of all 1 elements; t is time; and A(t) is the ground acceleration at the time of the earthquake. The acceleration can be scaled as needed.

[0092] The earthquake load and external load are uniformly expressed as the target load: F(t) = Fg + Fe;

[0093] Based on the right side of the motion control equation, construct an explicit effective load vector:

[0094]

[0095] in, is the explicit form of the effective load vector, F T () is the transpose of the target load vector, t nis a discrete moment, Δt is a time step, and p3 and p4 are both second preset control parameters.

[0096] Optionally,

[0097] It should be noted that the values ​​of the control parameters p1, p2, p3, and p4 are consistent with the second-order fourth-order Gauss implicit Runge-Kutta time discretization, and the solved variables have fourth-order accuracy.

[0098] Step S104: Analyze the response data of the transmission tower structure under the external load and the seismic load using the Runge-Kutta method based on the effective stiffness matrix, the effective mass matrix, and the effective load vector, wherein the effective load vector is generated based on the external load and the seismic load in combination with the preset motion control method.

[0099] In this embodiment, the response data includes but is not limited to displacement response data, velocity response data, and acceleration response data.

[0100] In some embodiments, step S104 includes:

[0101] Using the Runge-Kutta method, defining vector variables of a displacement vector and a velocity vector, and defining an intermediate process variable vector;

[0102] Based on the vector variables and the intermediate process variables, a matrix relationship constructed based on the effective stiffness matrix, the effective mass matrix, and the effective load vector is solved to obtain the displacement response data and the velocity response data of the transmission tower under the external load and the seismic load.

[0103] In this embodiment, a vector variable is defined as follows: y=[u T ,v T ] T ; Where v is the velocity vector, theoretically In t n There is always

[0104] Define the intermediate process variable vector:

[0105] Solve the matrix relationship: in, is the explicit form of the effective mass matrix, is the intermediate process variable vector, is the explicit form of the damping matrix, y n are the displacement vector and velocity vector at t n A vector variable at time, is the explicit representation of the payload vector.

[0106] Calculate the intermediate process variable vector After that, calculate the displacement response data u n+1 and speed response data v n+1 :

[0107]

[0108] Among them, satisfy

[0109] In some embodiments, the response data includes acceleration response data, and the method further comprises:

[0110] The acceleration response data of the transmission tower structure under the external load and seismic load is solved by using a preset acceleration vector to solve the equation. The preset acceleration vector solution equation is:

[0111]

[0112] Among them, M is the overall mass matrix, C is the damping matrix, K is the overall stiffness matrix, is the acceleration response data, u n+1 is the displacement vector, F(t n+1 ) is the target load vector obtained by superimposing the earthquake load vector and the external load vector.

[0113] In this embodiment, let Represents the acceleration error. Since both displacement and velocity have fourth-order accuracy,

[0114]

[0115] t n+1 Substitute the motion control equation at time into the above formula to obtain: It can be seen that the acceleration can also achieve fourth-order accuracy.

[0116] Furthermore, the safety of the transmission tower structure is analyzed based on the displacement response data, velocity response data and acceleration response data of the transmission tower structure.

[0117] As an example and not a limitation, the above technical solution provided by this application is compared with the Newmark-β method (parameters when taking the highest accuracy, i.e., second-order accuracy) used in commercial software such as ANSYS and Abaqus, and the technical effects that can be achieved by this application are specifically described.

[0118] For example, this embodiment analyzes a typical single-degree-of-freedom system to verify the high accuracy and effectiveness of the present method in solving the structural motion equations for displacement, velocity, and acceleration. The single-degree-of-freedom system equation is: Where ξ is the physical damping, ω is the frequency, and f is the load.

[0119] Free vibration: ξ=0.2,ω=2π,f=0, and initial conditions are u0=1.0 and Figure 2 The error in the system response at t = 0.4 is shown for different time steps. Since the slope of the logarithmic plot represents the accuracy of convergence, it can be seen that this method can achieve fourth-order accuracy for displacement, velocity, and acceleration simultaneously. This achieves higher convergence accuracy than traditional second-order analysis methods.

[0120] Forced vibration: take ξ=0.1, ω 2 =4000, f=10sin100πt, initial static, displacement unit is mm. The system response can be divided into the transient response dominated by the natural frequency in the initial stage and the steady-state response dominated by the external excitation frequency after the transient response decays. Figure 3 and Figure 4 The system displacement response and displacement error results are shown, respectively. The exact solution is the solution for the damping system under cyclic loading. When the time step is the same, the error of the solution obtained by this method (i.e., the newly invented method) is three orders of magnitude smaller than that of the Newmark-β method. Even with a four-fold time step, it still provides more accurate results. During the steady-state response phase, this method only solves for three time points within a cycle, and the error remains very small.

[0121] For example, this example verifies the stability and accuracy of this method. Figure 5 The transmission tower structure model shown is a two-dimensional truss structure model, in which the connecting rod has two cross-sectional sizes. Figure 5 The cross-sectional area of ​​the rod of the winning bid s is 600mm 2 , the cross-sectional area of ​​the remaining rods is 3000mm 2 , the length parameters of each rod are as follows Figure 5 As shown. The material properties of each rod are: density 7850kg / m 3 , Young's modulus 2 × 105 MPa, and a 150 kg mass at each hinge point at each end of the transmission tower. Spatial discretization was performed using rod elements, ignoring the influence of the rod's own weight. Rayleigh damping was used with a damping coefficient of 2% for the first two modes, and the system was initially stationary. Because an exact solution for the system is difficult to obtain, the Newmark-β method solution with a time step of Δt = 0.0001 s was used as a reference solution.

[0122] Working condition (1): The loads acting on the left and right mass points of the transmission tower structure model are 120000sin(0.5πt)N and 120000cos(0.5πt)N respectively. Figure 6 、 Figure 7 、 Figure 8The results of the vertical displacement, velocity and acceleration of the right mass point changing with time are shown respectively. It can be seen that when the time step is the same, this method can give more accurate results for the displacement, velocity and acceleration responses than the Newmark-β method, and even when the time step is 4 times longer, it still gives more accurate results.

[0123] Working condition (2): The seismic wave load uses the El Centro seismic wave, which acts on the ground constraint with the right direction as positive. The response results and peak response time of the mass point on the right side under this seismic load are as follows: Figure 9 The figure shows a comparison of the peak acceleration response moments. It can be seen that, for the same time step, this method provides more accurate results for the peak response than the Newmark-β method. This is especially true when using a time step of 4 or more times at discrete time points. However, since excessively large time steps will miss the peak response moments, they should be kept within a reasonable range in practical applications.

[0124] In order to implement the transmission tower seismic response analysis method based on the Runge-Kutta method corresponding to the above method embodiment, to achieve the corresponding functions and technical effects. Figure 10 , Figure 10 The following is a block diagram of a transmission tower seismic response analysis device based on the Runge-Kutta method provided in an embodiment of the present application. For ease of illustration, only the parts relevant to this embodiment are shown. The transmission tower seismic response analysis device based on the Runge-Kutta method provided in an embodiment of the present application includes:

[0125] An acquisition module 1001 is used to acquire structural parameters of a transmission tower structure;

[0126] A discretization module 1002 is configured to spatially discretize the structural parameters to obtain an overall stiffness matrix and an overall mass matrix of the transmission tower structure;

[0127] A determination module 1003 is configured to determine an effective stiffness matrix and an effective mass matrix of the transmission tower structure according to the overall stiffness matrix and the overall mass matrix using a preset motion control equation;

[0128] An analysis module 1004 is configured to analyze response data of the transmission tower structure under external loads and seismic loads using the Runge-Kutta method based on the effective stiffness matrix, the effective mass matrix, and an effective load vector, wherein the effective load vector is generated based on the external loads and seismic loads in combination with the preset motion control method.

[0129] In some embodiments, the discrete module 1002 is configured to:

[0130] Based on the finite element method and according to the structural parameters, a unit stiffness matrix and a unit mass matrix of each rod unit in the transmission tower structure are established;

[0131] The unit stiffness matrices and the unit mass matrices of the plurality of rod units are combined to obtain the overall stiffness matrix and the overall mass matrix.

[0132] In some embodiments, the determining module 1003 is configured to:

[0133] Based on preset linear parameters, linearly combining the overall stiffness matrix and the overall mass matrix to obtain a damping matrix of the transmission tower structure;

[0134] According to the preset motion control equation, combined with the first preset control parameter and the damping matrix, the overall stiffness matrix and the overall mass matrix are time discretized to generate the effective stiffness matrix and the effective mass matrix.

[0135] In some embodiments, the apparatus further comprises a generating module configured to:

[0136] Acquire a seismic load vector and an external load vector, and superimpose the seismic load vector and the external load vector to form a target load vector;

[0137] According to the preset motion control equation and in combination with the second preset control parameter, the target load vector is time discretized to generate the effective load vector, which is:

[0138]

[0139] is the explicit form of the payload vector, F T () is the transpose of the target load vector, t n is a discrete moment, Δt is a time step, and p3 and p4 are both second preset control parameters.

[0140] In some embodiments, the preset motion control equation is:

[0141]

[0142] Among them, M is the overall mass matrix, C is the damping matrix, K is the overall stiffness matrix, Fg is the seismic load vector, Fe is the external load vector, is the acceleration vector, is the velocity vector and u is the displacement vector.

[0143] In some embodiments, the response data includes displacement response data and velocity response data, and the determination module 1003 is configured to:

[0144] Using the Runge-Kutta method, defining vector variables of a displacement vector and a velocity vector, and defining an intermediate process variable vector;

[0145] Based on the vector variables and the intermediate process variables, a matrix relationship constructed based on the effective stiffness matrix, the effective mass matrix, and the effective load vector is solved to obtain the displacement response data and the velocity response data of the transmission tower under the external load and the seismic load. The matrix relationship is:

[0146]

[0147] in, is the explicit form of the effective mass matrix, is the intermediate process variable vector, is the explicit form of the damping matrix, y n are the displacement vector and velocity vector at t n A vector variable at time, is the explicit representation of the payload vector.

[0148] In some embodiments, the response data includes acceleration response data, and the apparatus further includes a solution module configured to:

[0149] The acceleration response data of the transmission tower structure under the external load and seismic load is solved by using a preset acceleration vector to solve the equation. The preset acceleration vector solution equation is:

[0150]

[0151] Among them, M is the overall mass matrix, C is the damping matrix, K is the overall stiffness matrix, is the acceleration response data, u n+1 is the displacement vector, F(t n+1 ) is the target load vector obtained by superimposing the earthquake load vector and the external load vector.

[0152] The aforementioned Runge-Kutta method-based transmission tower seismic response analysis device can implement the Runge-Kutta method-based transmission tower seismic response analysis method described in the aforementioned method embodiment. The optional options in the aforementioned method embodiment also apply to this embodiment and are not described in detail here. The remaining details of the present application embodiment can be referenced to the aforementioned method embodiment and are not further described in this embodiment.

[0153] Figure 11 This is a schematic diagram of the structure of a computer device provided in one embodiment of the present application. Figure 11 As shown, the computer device 11 of this embodiment includes: at least one processor 110 ( Figure 11Only one is shown in the figure) a processor, a memory 111, and a computer program 112 stored in the memory 111 and executable on the at least one processor 110, wherein the processor 110 implements the steps of any of the above method embodiments when executing the computer program 112.

[0154] The computer device 11 may be a computing device such as a smart phone, a tablet computer, a desktop computer, a cloud server, etc. The computer device may include but is not limited to a processor 110 and a memory 111. It will be understood by those skilled in the art that Figure 11 This is merely an example of the computer device 11 and does not constitute a limitation on the computer device 11 . The computer device 11 may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device 11 may also include input and output devices, network access devices, etc.

[0155] The processor 110 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. A general-purpose processor may be a microprocessor or any conventional processor.

[0156] In some embodiments, the memory 111 may be an internal storage unit of the computer device 11, such as a hard disk or memory of the computer device 11. In other embodiments, the memory 111 may also be an external storage device of the computer device 11, such as a plug-in hard disk, a SmartMedia Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. equipped on the computer device 11. Furthermore, the memory 111 may also include both an internal storage unit of the computer device 11 and an external storage device. The memory 111 is used to store an operating system, application programs, a boot loader, data, and other programs, such as the program code of the computer program. The memory 111 may also be used to temporarily store data that has been output or is about to be output.

[0157] In addition, an embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in any of the above method embodiments are implemented.

[0158] An embodiment of the present application provides a computer program product. When the computer program product is run on a computer device, the computer device implements the steps in the above-mentioned various method embodiments when executing the computer program product.

[0159] In several embodiments provided in the present application, it is understood that each box in the flow chart or block diagram can represent a part of a module, program segment or code, and the part of the module, program segment or code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, which depends on the functions involved.

[0160] If the functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device to execute all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage media include: various media that can store program codes, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks or optical disks.

[0161] The specific embodiments described above further illustrate the objectives, technical solutions, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of this application by those skilled in the art should be included within the scope of protection of this application.

Claims

1. A transmission tower seismic response analysis method based on the Runge-Kutta method, characterized in that: include: Obtain the structural parameters of the transmission tower structure; spatially discretizing the structural parameters to obtain an overall stiffness matrix and an overall mass matrix of the transmission tower structure; Determining an effective stiffness matrix and an effective mass matrix of the transmission tower structure according to the overall stiffness matrix and the overall mass matrix using a preset motion control equation; Analyzing response data of the transmission tower structure under external loads and seismic loads using the Runge-Kutta method based on the effective stiffness matrix, the effective mass matrix, and an effective load vector, wherein the effective load vector is generated based on the external loads and seismic loads in combination with the preset motion control equations; The response data includes displacement response data and velocity response data. The Runge-Kutta method is used to analyze the response data of the transmission tower under external loads and seismic loads based on the effective stiffness matrix, the effective mass matrix, and the effective load vector, including: Using the Runge-Kutta method, defining vector variables of a displacement vector and a velocity vector, and defining an intermediate process variable vector; Based on the vector variables and the intermediate process variables, a matrix relationship constructed based on the effective stiffness matrix, the effective mass matrix, and the effective load vector is solved to obtain the displacement response data and the velocity response data of the transmission tower under the external load and the seismic load. The matrix relationship is: in, is the explicit form of the effective mass matrix, is the intermediate process variable vector, is the explicit form of the damping matrix, y n are the displacement vector and velocity vector at t n A vector variable at time, is the explicit representation of the payload vector.

2. The transmission tower seismic response analysis method based on the Runge-Kutta method according to claim 1, characterized in that: The spatial discretization of the structural parameters to obtain the overall stiffness matrix and overall mass matrix of the transmission tower structure includes: Based on the finite element method and according to the structural parameters, a unit stiffness matrix and a unit mass matrix of each rod unit in the transmission tower structure are established; The unit stiffness matrices and the unit mass matrices of the plurality of rod units are combined to obtain the overall stiffness matrix and the overall mass matrix.

3. The transmission tower seismic response analysis method based on the Runge-Kutta method according to claim 1, characterized in that: The method of determining the effective stiffness matrix and the effective mass matrix of the transmission tower structure according to the overall stiffness matrix and the overall mass matrix by using the preset motion control equations includes: Based on preset linear parameters, linearly combining the overall stiffness matrix and the overall mass matrix to obtain a damping matrix of the transmission tower structure; According to the preset motion control equation, combined with the first preset control parameter and the damping matrix, the overall stiffness matrix and the overall mass matrix are time discretized to generate the effective stiffness matrix and the effective mass matrix.

4. The transmission tower seismic response analysis method based on the Runge-Kutta method according to claim 1, characterized in that: The generation process of the payload vector includes: Acquire a seismic load vector and an external load vector, and superimpose the seismic load vector and the external load vector to form a target load vector; According to the preset motion control equation and in combination with the second preset control parameter, the target load vector is time discretized to generate the effective load vector, which is: is the explicit form of the payload vector, F T () is the transpose of the target load vector, t n is a discrete moment, Δt is a time step, and p3 and p4 are both second preset control parameters.

5. The transmission tower seismic response analysis method based on the Runge-Kutta method according to any one of claims 1 to 4, characterized in that: The preset motion control equation is: Among them, M is the overall mass matrix, C is the damping matrix, K is the overall stiffness matrix, Fg is the seismic load vector, Fe is the external load vector, is the acceleration vector, is the velocity vector and u is the displacement vector.

6. The transmission tower seismic response analysis method based on the Runge-Kutta method according to claim 1, characterized in that: The response data includes acceleration response data, and the method includes: The acceleration response data of the transmission tower structure under the external load and seismic load is solved by using a preset acceleration vector to solve the equation. The preset acceleration vector solution equation is: Among them, M is the overall mass matrix, C is the damping matrix, K is the overall stiffness matrix, is the acceleration response data, v n+1 is the speed response data, u n+1 is the displacement vector, F(t n+1 ) is the target load vector obtained by superimposing the earthquake load vector and the external load vector.

7. A transmission tower seismic response analysis device based on the Runge-Kutta method, characterized in that: include: An acquisition module, used to obtain structural parameters of the transmission tower structure; A discretization module is used to spatially discretize the structural parameters to obtain an overall stiffness matrix and an overall mass matrix of the transmission tower structure; a determination module, configured to determine an effective stiffness matrix and an effective mass matrix of the transmission tower structure according to the overall stiffness matrix and the overall mass matrix using a preset motion control equation; an analysis module for analyzing response data of the transmission tower structure under external loads and seismic loads using the Runge-Kutta method based on the effective stiffness matrix, the effective mass matrix, and an effective load vector, wherein the effective load vector is generated based on the external loads and seismic loads in combination with the preset motion control equation; The response data includes displacement response data and velocity response data, and the determination module is configured to: Using the Runge-Kutta method, defining vector variables of a displacement vector and a velocity vector, and defining an intermediate process variable vector; Based on the vector variables and the intermediate process variables, a matrix relationship constructed based on the effective stiffness matrix, the effective mass matrix, and the effective load vector is solved to obtain the displacement response data and the velocity response data of the transmission tower under the external load and the seismic load. The matrix relationship is: in, is the explicit form of the effective mass matrix, is the intermediate process variable vector, is the explicit form of the damping matrix, y n are the displacement vector and velocity vector at t n A vector variable at time, is the explicit representation of the payload vector.

8. A computer device, characterized in that: The method comprises a processor and a memory, wherein the memory is used to store a computer program, and when the computer program is executed by the processor, the method for analyzing the seismic response of a transmission tower based on the Runge-Kutta method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium, characterized in that It stores a computer program, which, when executed by a processor, implements the transmission tower seismic response analysis method based on the Runge-Kutta method as claimed in any one of claims 1 to 6.

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