Cable net dynamics analysis method and related device

Abstract

The invention discloses a cable net dynamics analysis method and a related device, the cable net dynamics analysis method adopts a cable unit of an absolute node coordinate method to obtain a mass matrix and generalized elastic force of a cable net system, under the condition that only the gravity of the cable net is considered, each node coordinate of the cable net under initial stress is obtained, and the cable net dynamics analysis method is obtained by combining the mass matrix and the generalized elastic force of the cable net. According to the method, a cable net kinetic equation after order reduction based on the static cohesion method is obtained, the impact condition of each node of the cable net when the wire falls is calculated, the kinetic analysis of the cable net is realized, and a basis is provided for the design and optimization of the cable net.

Description

Technical Field

[0001] The present invention relates to a method for analyzing the dynamics of a cable net and related devices, belonging to the field of dynamics analysis of flexible multi-body systems. Background Art

[0002] During the construction of power facilities, transmission conductors are installed on iron towers with the help of tension machines. Since extra-high voltage lines inevitably cross roads, railways or other existing infrastructures, when the conductor breaks or the tension machine fails, the conductor will cause serious impact damage to the facilities below. At present, a flexible protection system with a flexible protection cable net (such as a nylon rope net, hereinafter referred to as "cable net" for short) as the main load-bearing element is gradually replacing the traditional span design based on large steel structures due to its low cost and short installation period, and has become the main protection means in power construction. Accurate dynamic analysis of the cable net when the conductor falls into the cable net is the key to the design and optimization of the cable net, but there is no corresponding method at present. Summary of the Invention

[0003] The present application provides a method for analyzing the dynamics of a cable net and related devices, which solves the problems disclosed in the background art.

[0004] According to one aspect of the present application, a method for analyzing the dynamics of a cable net is provided, including:

[0005] Using a cable element of the absolute nodal coordinate method to obtain the mass matrix and the generalized elastic force of the cable net system; wherein, the cable net system includes a falling conductor and a cable net;

[0006] Determining the initial stress uniformly distributed on the cable net under the condition of only considering the self-gravity of the cable net, and using the iterative force density method to determine the coordinates of each node of the cable net under the initial stress; wherein, the node is the cable element node after finite element discretization of the cable net;

[0007] According to the coordinates of each node of the cable net under the initial stress, as well as the mass matrix and the generalized elastic force of the cable net, using the static condensation method to obtain the reduced-order dynamic equation of the cable net;

[0008] Calculating the impact conditions of each node of the cable net according to the reduced-order dynamic equation of the cable net, the mass matrix and the generalized elastic force of the cable net system.

[0009] Furthermore, the mass matrix and the generalized elastic force of the cable net system are as follows:

[0010] ;

[0011] Wherein, M is the mass matrix of the cable net system, V is the volume of the cable net system unit, ρ is the material density of the cable net system unit, S is the shape function of the cable net system unit, and T represents the transpose;

[0012] ;

[0013] Wherein, Q e is the generalized elastic force of the cable net system, and Q s is the generalized elastic force related to tension, and is the generalized elastic force related to bending.

[0014] Furthermore, in the iterative force density method, the force density coefficient of each cable segment is updated in each iteration;

[0015] The formula for updating the force density coefficient of the cable segment is:

[0016] ;

[0017] Wherein, are the force density coefficients of the j-th cable segment in the (p + 1)-th and p-th iterations respectively, and T d is the initial stress uniformly distributed on the cable segment, is the tension of the j-th cable segment in the p-th iteration;

[0018] The iteration convergence condition is:

[0019] ;

[0020] Wherein, tol T is the tension convergence error.

[0021] Furthermore, the reduced-order cable net dynamic equation is:

[0022] ;

[0023] Wherein, are the stiffness matrix after the condensation assembly of n subsystems, the Jacobian matrix of the constraint equation, the increment of the generalized coordinate, the increment of the Lagrange multiplier, the related force term, and the constraint equation respectively. The subsystem is a subsystem formed by dividing the cable net based on the static condensation method.

[0024] According to another aspect of the present application, there is provided a cable net dynamic analysis device, which is characterized by including:

[0025] A mass matrix and generalized elastic force acquisition module, which uses cable elements of the absolute nodal coordinate method to acquire the mass matrix and generalized elastic force of the cable net system; wherein, the cable net system includes a falling wire and a cable net;

[0026] A cable net node coordinate determination module, which determines the initial stress uniformly distributed on the cable net under the condition of only considering the self-gravity of the cable net, and uses the iterative force density method to determine the coordinates of each node of the cable net under the initial stress; wherein, the node is the node of the cable element after the finite element discretization of the cable net;

[0027] The cable-net dynamic equation acquisition module obtains the reduced-order cable-net dynamic equation by using the static condensation method based on the coordinates of each node of the cable-net under the initial stress, as well as the mass matrix and the generalized elastic force of the cable-net;

[0028] The calculation module calculates the impact situation of each node of the cable-net according to the reduced-order cable-net dynamic equation, the mass matrix of the cable-net system, and the generalized elastic force.

[0029] Furthermore, in the mass matrix and generalized elastic force acquisition module, the mass matrix and the generalized elastic force of the cable-net system are given by the formula:

[0030] ;

[0031] In the formula, M is the mass matrix of the cable-net system, V is the volume of the cable-net system element, ρ is the material density of the cable-net system element, S is the shape function of the cable-net system element, and T represents the transpose;

[0032] ;

[0033] In the formula, Q e is the generalized elastic force of the cable-net system, Q s is the generalized elastic force related to tension, is the generalized elastic force related to bending.

[0034] Furthermore, in the iterative force density method of the cable-net node coordinate determination module, the force density coefficient of the cable segment is updated in each iteration;

[0035] The formula for updating the force density coefficient of the cable segment is:

[0036] ;

[0037] In the formula, are the force density coefficients of the j-th cable segment in the (p + 1)-th and p-th iterations respectively, T d is the initial stress uniformly distributed on the cable segment, is the tension of the j-th cable segment in the p-th iteration;

[0038] The iteration convergence condition is:

[0039] ;

[0040] In the formula, tol T is the tension convergence error.

[0041] Furthermore, in the cable-net dynamic equation acquisition module, the reduced-order cable-net dynamic equation is:

[0042] ;

[0043] In the formula, They are respectively the stiffness matrix after the lumped assembly of n subsystems, the Jacobian matrix of the constraint equations, the increment of the generalized coordinates, the increment of the Lagrange multipliers, the related force terms, and the constraint equations. The subsystems are the subsystems obtained by dividing the cable net based on the static condensation method.

[0044] According to another aspect of the present application, there is provided a computer-readable storage medium storing one or more programs, and the one or more programs include instructions that, when executed by a computing device, cause the computing device to execute the cable net dynamics analysis method.

[0045] According to another aspect of the present application, there is provided a computer device including one or more processors and one or more memories. The one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors. The one or more programs include instructions for executing the cable net dynamics analysis method.

[0046] The beneficial effects achieved by the present invention: The present invention uses cable elements based on the absolute nodal coordinate method to obtain the mass matrix and the generalized elastic force of the cable net system. Under the condition of only considering the self-gravity of the cable net, the coordinates of each node of the cable net under the initial stress are obtained. Combining the mass matrix and the generalized elastic force of the cable net, the cable net dynamics equation after reduction based on the static condensation method is obtained, and the impact conditions of each node of the cable net when the wire drops are calculated, realizing the dynamics analysis of the cable net and providing a basis for the design and optimization of the cable net. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flowchart of the cable net dynamics analysis method;

[0048] Figure 2 It is a partial view of the cable net;

[0049] Figure 3 It is a flowchart of the iterative force density method;

[0050] Figure 4 It is a cable net form-finding result diagram;

[0051] Figure 5 It is a schematic diagram of the static condensation algorithm;

[0052] Figure 6 It is a schematic diagram of the simulation model;

[0053] Figure 7 It is a comparison diagram of the vertical component of the free end velocity of a 19-meter wire;

[0054] Figure 8 It is a comparison diagram of the vertical component of the free end velocity of a 21-meter wire;

[0055] Figure 9Comparison of the stresses at the observation points of the 19-meter wire

[0056] Figure 10 Comparison of the stresses at the observation points of the 21-meter wire

[0057] Figure 11 Configuration of the simulation results of the 19m wire under an initial tension of 5KN

[0058] Figure 12 Configuration of the simulation results of the 21m wire under an initial tension of 15KN

[0059] Figure 13 Block diagram of the cable net dynamics analysis device Specific implementation manners

[0060] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and in no way limits the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0061] Unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions and values set forth in these embodiments do not limit the scope of the present application.

[0062] Meanwhile, it should be understood that, for the sake of description, the dimensions of the various parts shown in the accompanying drawings are not drawn in actual proportional relationship.

[0063] Technologies, methods and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods and devices should be regarded as part of the specification.

[0064] In all the examples shown and discussed here, any specific value should be construed as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values.

[0065] It should be noted that: like reference signs and letters denote like items in the following drawings, and thus, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0066] The Absolute Nodal Coordinate Formulation (ANCF) is an advanced finite element method mainly used for simulating complex mechanical systems, especially excelling in dealing with nonlinear dynamics problems. In ANCF, the shape, position, and motion state of an object are directly described by the absolute coordinates of each node, rather than being indirectly represented through shape functions. This method provides a more flexible framework that can handle large deformations, large displacements, and non-rigid body behaviors, such as the simulation of rubber, biological materials, etc. The core of ANCF lies in its coordinate system, which not only includes position coordinates but may also contain higher-order coordinates such as velocity and acceleration. This representation allows the elements to deform freely without any geometric constraints, thus better simulating physical phenomena in the real world.

[0067] The force density method is a numerical calculation method for obtaining the initial configuration of a flexible cable net. The algorithm sets the force density coefficient as the key core index and updates the spatial coordinates of the cable net nodes to achieve a uniform distribution of stress in the cable net. The iterative force density method is improved based on the force density method, and it updates the force density coefficient once in each iterative step, while the force density coefficient of the force density method is a constant value under the initial definition.

[0068] ‌ ‌ is a method for reducing the degrees of freedom in structural dynamic analysis, mainly used to simplify calculations and improve computational efficiency. Its basic principle is to divide the degrees of freedom of the structure into two groups: the primary degrees of freedom and the secondary degrees of freedom. The primary degrees of freedom are the parts with more prominent responses, such as the horizontal displacements of the floors of a frame structure; the secondary degrees of freedom are the parts with smaller responses, such as the vertical displacements and rotations at the ends of beams. Through matrix operations, the influence of the secondary degrees of freedom can be condensed onto the primary degrees of freedom, thus reducing the computational workload. The static condensation method condenses the secondary degrees of freedom in the dynamic equation of the structure through matrix operations and only retains the primary degree of freedom vector, thereby simplifying the calculation. The specific steps include: dividing the degrees of freedom of the structure into primary degrees of freedom and secondary degrees of freedom; assuming that the response part caused by the inertial forces on the secondary degrees of freedom can be ignored and its entire response is only determined by the structural stiffness; converting the primary and secondary degrees of freedom through the stiffness matrix so that the dynamic equation only contains the primary degree of freedom vector.

[0069] The embodiments of this application are based on the absolute nodal coordinate method, the iterative force density method, and A cable net dynamics analysis method is provided, aiming to perform cable net dynamics analysis during wire dropping, and providing a basis for cable net design and optimization. This cable net dynamics analysis method can be executed by an analysis device, which can be a terminal device or a server. Among them, the terminal device can include, but is not limited to, mobile phones, computers, smart wearable devices, smart vehicle-mounted devices, etc., and the embodiments of the present application do not make limitations; the server can be an independent physical server, or a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, big data, and artificial intelligence platforms, etc., and the embodiments of the present application do not make limitations. Optionally, this cable net dynamics analysis method can also be executed collaboratively by multiple electronic devices with computing power. For the convenience of description, subsequent embodiments will be described with the analysis device executing.

[0070] Please refer to Figure 1 , Figure 1 which is a flowchart of a cable net dynamics analysis method provided by an embodiment of the present application. This method can be executed by an analysis device, and this cable net dynamics analysis method can at least include the following steps:

[0071] Step 1, using cable elements of the absolute nodal coordinate method, obtain the mass matrix and generalized elastic force of the cable net system; where the cable net system includes the dropped wire and the cable net.

[0072] It should be noted that calculating the mass matrix and elastic force of the cable net system is essentially a process of constructing a cable net system model based on cable elements of the absolute nodal coordinate method. The cable element of the absolute nodal coordinate method is a unit type in the absolute nodal coordinate method unit library. Since the Euler-Bernoulli beam assumption is adopted, that is, it is assumed that the cross-section is rigid and always perpendicular to the central axis, the cable element does not need to consider cross-section deformation and only retains the gradient vector along the central axis direction. Therefore, it is a reduced beam element type.

[0073] The absolute nodal coordinate method is a theoretical and method system for describing flexible bodies, which is a combination of continuum mechanics and finite element theory. Traditional finite elements use displacement and rotation as nodal coordinates and default to contain small deformation assumptions. When describing the large deformation and large displacement coupled motion of flexible bodies, a follower coordinate system must be introduced to distinguish displacement from deformation, which will lead to a highly nonlinear system equation and difficult to solve. The absolute nodal coordinate method uses the spatial position and gradient vector defined in the global coordinate system as nodal coordinates, without the need to introduce a follower coordinate system. The derived system equation has a simple form, and the mass matrix is constant, that is, the definition of the mass matrix does not contain time variables, and there are no Coriolis forces and centrifugal forces, solving the dynamic stiffening problem in the dynamics of flexible multi-body systems and making the results more accurate.

[0074] The wire element of the absolute nodal coordinate method uses the global position vectors at the head and tail nodes and the gradient vector along the central axis as the nodal coordinates to describe the nonlinear dynamic behavior of the wire, which has the advantage of describing complex deformations with fewer elements. The absolute nodal coordinate method is used to characterize the dynamic behavior of the wire after fracture. This theory is applicable to the modeling and solution of large flexibility bodies and can more accurately and conveniently describe the geometric nonlinear dynamic behavior of the wire.

[0075] Assume that the degree of freedom of the cable element is 12, and the shape function is a 3×12 matrix S, as follows:

[0076] S = [S1I 3×3 , S2I 3×3 , S3I 3×3 , S4I 3×3 ;

[0077] In the formula, I 3×3 is a 3×3 identity matrix, and S1~S4 are the 4 shape functions of the cable element;

[0078] ;

[0079] In the formula, is a dimensionless parameter, l is the length of the cable element in the undeformed configuration, and x is the material coordinate on the central axis of the cable element.

[0080] Both the wire and the cable net can be modeled by the finite element method based on the absolute nodal coordinate method, and the solution methods for both are the same. Therefore, the mass matrix and the generalized elastic force of the fallen wire and cable net can be uniformly expressed as the mass matrix and the generalized elastic force of the cable net system.

[0081] The mass matrix of the cable net system can be expressed as:

[0082] ;

[0083] In the formula, M is the mass matrix of the cable net system, V is the volume of the cable net system element, dV represents the volume element, indicating that a volume integral is performed here, ρ is the material density of the cable net system element, S is the shape function of the cable net system element, and T represents the transpose.

[0084] The strain energy of the cable element of the absolute nodal coordinate method can be divided into two parts, one related to the axial tension or compression of the center line, and the other related to bending. Therefore, the deformation energy of the cable element can be expressed as:

[0085] ;

[0086] In the formula, U is the deformation energy of the cable element, E is the Young's modulus of the material, A is the cross-sectional area of the cable element, I is the polar moment of inertia of the cable element cross-section, is the tensile strain of the cable element axis, is the bending of the cable unit axis, are the first-order and second-order gradient vectors along the axis direction at the current integration point, respectively.

[0087] The generalized elastic force of the cable-net system can be expressed as:

[0088] ;

[0089] Where Q e is the generalized elastic force of the cable-net system, Q s is the generalized elastic force associated with stretching, is the generalized elastic force related to bending, and e is the node coordinate of the cable element.

[0090] Step 2: Determine the uniformly distributed initial stress on the cable net considering only the gravity of the cable net itself, and use the iterative force density method to determine the coordinates of each node of the cable net under the initial stress; the nodes are the cable unit nodes after the cable net is discretized by the finite element.

[0091] See also Figure 2 , assuming that there are s cable segments connected at node i, the force density coefficient of the jth cable segment can be expressed as:

[0092] ;

[0093] Where q j is the force density coefficient of the j-th cable segment, T j and l j are the tension and length of the j-th cable segment respectively.

[0094] In the coordinate system (X, Y, Z), the coordinate of node i is marked as (x i ,y i ,z i ), according to the force density method, the linear equilibrium equation of the force density at node i can be expressed as:

[0095] ;

[0096] Where x z and y z are the X- and Y-axis coordinates of node z, respectively. Nodes i and z are the two end nodes of the jth cable segment. Similarly, the linear equilibrium equations for all cable segment nodes can be obtained. By solving these simultaneous linear equilibrium equations, all nodes and coordinates can be obtained.

[0097] For the traditional force density method, it is assumed that the force density coefficient of each cable segment is constant, so the tension of the cable segment can be expressed as:

[0098] ;

[0099] In the formula, is the new length of the j-th cable segment, which can be solved from the obtained spatial coordinates of the nodes. When the length of the cable cross-section changes, the tension of the cable cross-section also changes. Therefore, the traditional force density method will make the tension of the cable cross-section non-uniform.

[0100] Therefore, the iterative force density method is adopted here. The idea is to update the force density coefficient in each iterative step so that the tension of each cable segment in the final form-finding result is equal to the uniform tension (i.e., the initial stress T uniformly distributed on the cable segment d ).

[0101] See Figure 3 , the process of the iterative force density method can be as follows:

[0102] 1) Define the initial tension, read the initial node coordinates, and calculate the initial force density coefficient;

[0103] 2) Calculate the X and Y axis coordinates of the internal nodes;

[0104] 3) Calculate the vertical tension of the nodes, and obtain the cable segment length and tension;

[0105] 4) If the force density coefficients of all cable segments are 1, the algorithm ends; otherwise, update the force density coefficient and the node coordinates, and go to 2).

[0106] In the above method, the formula for updating the cable segment force density coefficient in each iterative step can be expressed as:

[0107] ;

[0108] In the formula, are the force density coefficients of the j-th cable segment in the (p + 1)-th and p-th iterations respectively, is the tension of the j-th cable segment in the p-th iteration.

[0109] The iterative convergence condition is:

[0110] ;

[0111] In the formula, tol T is the tension convergence error, which can generally be set to 10 -3 .

[0112] With the iterative update of the force density coefficient, the tension value of the cable cross-section will be closer to the preset uniform tension value of the cable cross-section. Therefore, after form-finding using the iterative force density method, the maximum tension ratio of the pre-tensions of each cable segment in the cable net is almost equal to 1, meeting the requirement of the uniformity of the cable segment tension. The form-finding result is as Figure 4 shown.

[0113] Step 3: Based on the coordinates of each node of the cable net under the initial stress, as well as the mass matrix and generalized elastic force of the cable net, the dynamic equation of the cable net after reduction is obtained using the static condensation method.

[0114] Based on the reduction theory of the static condensation method, the cable net is divided into n parts, and each part is called a subsystem. The degrees of freedom of each subsystem are divided into internal degrees of freedom and boundary degrees of freedom. Lagrange multipliers connecting adjacent subsystems are defined to ensure the continuity of the displacement field between subsystems. After solving the interface equation, the degrees of freedom of each subsystem are solved by back substitution. The condensation processes of the internal degrees of freedom and Lagrange multipliers of each subsystem are as Figure 5 shown.

[0115] Taking the k-th subsystem as an example, the following linear algebraic equations need to be solved during the Newton-Raphson iteration process:

[0116] ;

[0117] In the formula, the variable , the variable , the variable , are respectively the mass matrix, the Jacobian matrix of the elastic force vector, the elastic force vector, the Jacobian matrix of the constraint equation, the gravity vector, the contact force vector, and the constraint equation of the k-th subsystem, are respectively the increment of the generalized coordinates and the Lagrange increment of the k-th subsystem, are respectively the solution parameters in the generalized α method used to solve the equation, the generalized coordinate acceleration, and the Lagrange multiplier.

[0118] After organizing the linear algebraic equations, we can get:

[0119] ;

[0120] In the formula, the parameter , the parameter , the parameter , the parameter , the parameter , the parameter , the parameter , the parameter , are all submatrices of represents the submatrix related only to the internal degrees of freedom, represents the submatrix related only to the boundary degrees of freedom, both represent the submatrices related to the boundary and internal degrees of freedom, respectively represent the related to the internal degrees of freedom and the boundary degrees of freedom, Represents the degrees of freedom related to the interior and the degrees of freedom related to the boundary, respectively , Represents the degrees of freedom related to the interior and the degrees of freedom related to the boundary, respectively , are related to the internal degrees of freedom and , are related to the internal degrees of freedom and .

[0121] The increment of the internal variable of the kth subsystem can be expressed as:

[0122] ;

[0123] In the formula, the parameters ,parameter ,parameter ,parameter , To constitute The four sub-matrices of the inverse, represents the submatrix related only to the internal variables, represents the submatrix related only to the boundary variables, Both represent submatrices related to internal variables and boundary variables. Internal variables are variables retained for internal degrees of freedom, and boundary variables are variables retained for the corresponding degrees of freedom of the boundary coordination constraint equations.

[0124] Finally, the equilibrium equations of each subsystem are assembled to obtain the equilibrium equations of the interface problem, that is, the reduced-order cable net dynamics equations:

[0125] ;

[0126] Where, They are the stiffness matrix after condensed assembly of n subsystems, the Jacobian matrix of the constraint equation, the increment of generalized coordinates, the increment of Lagrange multipliers, the related force terms and the constraint equation.

[0127] Step 4: Calculate the impact of each node in the cable net based on the reduced-order cable net dynamics equation, the mass matrix of the cable net system, and the generalized elastic force. Specifically, the mass matrix and generalized elastic force of the cable net system are input into the reduced-order cable net dynamics equation to calculate the impact of each node in the cable net.

[0128] The above method uses the cable element of the absolute nodal coordinate method to obtain the mass matrix and generalized elastic force of the cable net system. When only considering the gravity of the cable net itself, the coordinates of each node of the cable net under the initial stress are obtained. Combined with the mass matrix and generalized elastic force of the cable net, the dynamic equation of the cable net after reduction based on the static condensation method is obtained. The impact of each node of the cable net when the wire falls is calculated, realizing the dynamic analysis of the cable net and providing a basis for the design and optimization of the cable net.

[0129] To further illustrate the above method, the following simulation was performed:

[0130] Established Figure 6 In the cable net system model shown, one end of the wire is fixed with a ball joint and the other end is freely released. The initial tension is 5KN, 10KN and 15KN respectively, and the wire length is selected as 19 meters and 21 meters.

[0131] The cable net has 644 units and 7608 degrees of freedom. After static condensation, the degrees of freedom are reduced to 1167. The wires are divided into units every 0.5 meters. The cable net is suspended by four ball joints. The mesh size is 0.4m×0.4m. Other parameters are shown in Table 1.

[0132] Table 1 Parameters of conductors and cable nets

[0133]

[0134] The program corresponding to the method was written and run in a C++ environment, and the visualization of the results was implemented in an open source data visualization software called Paraview. Figure 7 and Figure 8 is the comparison result of the vertical velocity of the free tip under different wire lengths, Figure 9 and Figure 10 is the comparison structure of the stress at the measuring point under different wire lengths, Figure 11 and Figure 10 The configuration diagrams of 19-meter and 21-meter conductors impacting the cable net at different times under an initial tension of 10 kN obtained by simulation calculation are colored based on the numerical components of the velocity.

[0135] The simulation results show that the above method is correct and effective. The results can help engineers find the weak links in the protective structure and strengthen them, that is, optimize the cable net.

[0136] The above method can greatly shorten the design and development cycle of the cable net system, save development costs, and provide theoretical and technical support for the safe construction of the power system.

[0137] See Figure 13 , Figure 13 This is a block diagram of a cable net dynamics analysis device provided in an embodiment of the present application. Figure 13An embodiment of the present invention is a virtual device that can be loaded and executed by a computer device, which may include the above analysis device. Figure 13 The device may include a mass matrix and a generalized elastic force acquisition module, a cable net node coordinate determination module, a cable net dynamics equation acquisition module, and an analysis module. When used to execute the above cable net dynamics analysis method, it can:

[0138] The mass matrix and generalized elastic force acquisition module uses cable elements based on the absolute nodal coordinate method to obtain the mass matrix and generalized elastic force of the cable net system. Among them, the cable net system includes a fallen conductor and a cable net.

[0139] It should be noted that in the mass matrix and generalized elastic force acquisition module, the mass matrix and generalized elastic force of the cable net system are calculated by the following formulas:

[0140] ;

[0141] In the formula, M is the mass matrix of the cable net system, V is the volume of the cable net system element, ρ is the material density of the cable net system element, S is the shape function of the cable net system element, and T represents the transpose.

[0142] ;

[0143] In the formula, Q e is the generalized elastic force of the cable net system, Q s is the generalized elastic force related to tension, is the generalized elastic force related to bending.

[0144] The cable net node coordinate determination module determines the initial stress uniformly distributed on the cable net considering only the self-gravity of the cable net, and uses the iterative force density method to determine the coordinates of each node of the cable net under the initial stress. Among them, the node is the node of the cable element after the finite element discretization of the cable net.

[0145] It should be noted that in the iterative force density method of the cable net node coordinate determination module, the force density coefficient of the cable segment is updated each time.

[0146] The formula for updating the force density coefficient of the cable segment is:

[0147] ;

[0148] In the formula, are the force density coefficients of the j-th cable segment in the (p + 1)-th and p-th iterations respectively, T d is the initial stress uniformly distributed on the cable segment, is the tension of the j-th cable segment in the p-th iteration;

[0149] The iteration convergence condition is:

[0150] ;

[0151] where tol T is the tension convergence error.

[0152] The cable-net dynamic equation acquisition module obtains the reduced-order cable-net dynamic equation by using the static condensation method based on the coordinates of each node of the cable-net under the initial stress, as well as the mass matrix and the generalized elastic force of the cable-net.

[0153] It should be noted that in the cable-net dynamic equation acquisition module, the reduced-order cable-net dynamic equation is:

[0154] ;

[0155] where are respectively the stiffness matrix after the condensation assembly of n subsystems, the Jacobian matrix of the constraint equation, the increment of the generalized coordinates, the increment of the Lagrange multiplier, the relevant force term, and the constraint equation. The subsystem is a subsystem formed by dividing the cable-net based on the static condensation method.

[0156] The analysis module calculates the impact conditions of each node of the cable-net according to the reduced-order cable-net dynamic equation, the mass matrix of the cable-net system, and the generalized elastic force.

[0157] The above device uses cable elements based on the absolute nodal coordinate method to obtain the mass matrix and the generalized elastic force of the cable-net system. Under the condition of only considering the self-gravity of the cable-net, the coordinates of each node of the cable-net under the initial stress are obtained. Combining the mass matrix and the generalized elastic force of the cable-net, the reduced-order cable-net dynamic equation based on the static condensation method is obtained, and the impact conditions of each node of the cable-net when the wire drops are calculated, realizing the dynamic analysis of the cable-net and providing a basis for the design and optimization of the cable-net.

[0158] This application also relates to a computer-readable storage medium that stores one or more programs. The one or more programs include instructions that, when executed by a computing device, cause the computing device to execute the cable-net dynamic analysis method.

[0159] This application also relates to a computer device that includes one or more processors and one or more memories. The one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors. The one or more programs include instructions for executing the cable-net dynamic analysis method.

[0160] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0161] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0162] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0163] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0164] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are included in the scope of the claims of the present invention to be approved.

Claims

1. A method for analyzing the dynamics of a cable net, characterized in that, Including: Cable elements using the absolute nodal coordinate method to obtain the mass matrix and generalized elastic force of the cable net system; wherein, the cable net system includes a fallen conductor and a cable net; Determine the initial stress uniformly distributed on the cable net considering only the self-gravity of the cable net, and use the iterative force density method to determine the coordinates of each node of the cable net under the initial stress; wherein, the node is the node of the cable element after finite element discretization of the cable net; According to the coordinates of each node of the cable net under the initial stress, as well as the mass matrix and generalized elastic force of the cable net, use the static condensation method to obtain the reduced-order dynamic equation of the cable net; Calculate the impact situation of each node of the cable net according to the reduced-order dynamic equation of the cable net, the mass matrix and generalized elastic force of the cable net system.

2. The method according to claim 1, characterized in that The mass matrix and generalized elastic force of the cable net system, the formula is: ； In the formula, M is the mass matrix of the cable net system, V is the volume of the cable net system element, ρ is the material density of the cable net system element, S is the shape function of the cable net system element, and T represents the transpose; ； In the formula, Q e is the generalized elastic force of the cable net system, and Q s is the generalized elastic force related to tension, and is the generalized elastic force related to bending.

3. The method according to claim 1, wherein In the iterative force density method, the force density coefficient of the cable segment is updated each time; The formula for updating the force density coefficient of the cable segment is: ； In the formula, are the force density coefficients of the j-th cable segment in the (p + 1)-th and p-th iterations respectively, and T d is the initial stress uniformly distributed on the cable segment, is the tension of the j-th cable segment in the p-th iteration; The iterative convergence condition is: ； where, tol T is the tension convergence error.

4. The method according to claim 1, wherein The reduced-order dynamic equation of the cable net is: ； In the formula, They are respectively the stiffness matrix after the condensed assembly of n subsystems, the Jacobian matrix of the constraint equations, the increment of the generalized coordinates, the increment of the Lagrange multipliers, the relevant force terms, and the constraint equations. The subsystems are the subsystems obtained by dividing the cable net based on the static condensation method.

5. A cable net dynamics analysis device, characterized in that, Including: A mass matrix and generalized elastic force acquisition module, which uses cable elements with the absolute nodal coordinate method to obtain the mass matrix and generalized elastic force of the cable net system; wherein, the cable net system includes a fallen conductor and a cable net; A module for determining the coordinates of each node of the cable net, which determines the initial stress uniformly distributed on the cable net considering only the self-gravity of the cable net, and uses the iterative force density method to determine the coordinates of each node of the cable net under the initial stress; wherein, the node is the node of the cable element after finite element discretization of the cable net; A cable net dynamic equation acquisition module, which obtains the reduced-order dynamic equation of the cable net by using the static condensation method according to the coordinates of each node of the cable net under the initial stress, as well as the mass matrix and generalized elastic force of the cable net; A calculation module, which calculates the impact situation of each node of the cable net according to the reduced-order dynamic equation of the cable net, the mass matrix and generalized elastic force of the cable net system.

6. The device according to claim 5, characterized in that, In the mass matrix and generalized elastic force acquisition module, the mass matrix and generalized elastic force of the cable net system, the formula is: ； In the formula, M is the mass matrix of the cable net system, V is the volume of the cable net system element, ρ is the material density of the cable net system element, S is the shape function of the cable net system element, and T represents the transpose; ； where Q e is the generalized elastic force of the cable net system, and Q s is the generalized elastic force related to stretching, and is the generalized elastic force related to bending.

7. The device according to claim 5, characterized in that, In the iterative force density method of the module for determining the coordinates of each node of the cable net, the force density coefficient of the cable segment is updated each time; The formula for updating the force density coefficient of the cable segment is: ； In the formula, are the force density coefficients of the j-th cable segment in the (p + 1)-th and p-th iterations respectively, and T d is the initial stress uniformly distributed on the cable segment, is the tension of the j-th cable segment in the p-th iteration; The iterative convergence condition is: ； where, tol T is the tension convergence error.

8. The device according to claim 5, characterized in that, In the cable net dynamic equation acquisition module, the reduced-order dynamic equation of the cable net is: ； In the formula, are respectively the stiffness matrix after the condensed assembly of n subsystems, the Jacobian matrix of the constraint equations, the increment of the generalized coordinates, the increment of the Lagrange multipliers, the relevant force terms, and the constraint equations. The subsystems are the subsystems formed by dividing the cable net based on the static condensation method.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores one or more programs, and the one or more programs include instructions that, when executed by a computing device, cause the computing device to execute the method according to any one of claims 1 to 4.

10. A computer device, characterized in that, Including: One or more processors, and one or more memories, the one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors, and the one or more programs include instructions for executing the method according to any one of claims 1 to 4.

Images