Numerical simulation method, device and equipment for conductor galloping based on central lumped mass three-node unit and storage medium

Abstract

The application discloses a wire galloping numerical simulation method and device based on a center concentrated mass three-node unit, equipment and a storage medium, relates to the technical field of numerical simulation, and comprises the following steps: discretizing a wire into a plurality of three-node units according to wire model information, wherein the three-node unit comprises a first end node, a second end node and a center node; determining the resultant external force of the center node of the three-node unit at the current time, and establishing a dynamics equation according to the resultant external force; predicting the coordinates of the center node of the unit at the next time according to the dynamics equation; and inversely solving the coordinates of the end nodes shared by adjacent three-node units at the next time by using geometric continuity constraints and end internal force balance conditions, so that the problem of low calculation efficiency caused by high global matrix calculation complexity of a traditional finite element method when the traditional finite element method is used to process non-uniform wire galloping simulation is solved.

Description

Technical Field

[0001] This application relates to the field of numerical simulation technology, and in particular to a method, apparatus, device and storage medium for numerical simulation of conductor galloping based on a centrally concentrated mass three-node element. Background Technology

[0002] Currently, the mainstream technique for numerical analysis of conductor galloping is the traditional finite element method (FEM). This method discretizes the conductor into a mesh, constructs a global stiffness and mass matrix, and uses implicit integration to solve a large set of equations to simulate the dynamic response. However, this technique has significant drawbacks: when simulating conductors with uneven mass distribution, such as those subjected to vibration dampers or non-uniform icing, the traditional nodal mass lumped method uses forced averaging for inertial property distribution at shared nodes, leading to distortion of local physical properties and severely reducing the accuracy of dynamic calculations under non-uniform structures. Furthermore, this method requires real-time updating, assembly, and solving of a massive global matrix, resulting in computational complexity that increases exponentially with the degrees of freedom, causing significant time consumption. More importantly, its strongly topologically coupled solution process has a strong data dependency, making it unable to effectively utilize modern GPUs and other multi-core parallel computing hardware, resulting in extremely low computational efficiency for long-distance conductor galloping simulations and failing to meet the needs of large-scale engineering applications.

[0003] In summary, the goal is to provide a numerical simulation method for conductor galloping that, while ensuring high simulation accuracy for non-uniform structures, avoids the time-consuming global matrix assembly and solution process of traditional methods, thereby significantly improving computational efficiency and adapting to modern parallel computing architectures to meet the needs of large-scale engineering simulations.

[0004] The above content is only used to help understand the technical solution of this application and does not represent an admission that the above content is prior art. Summary of the Invention

[0005] The main objective of this application is to provide a method, apparatus, device, and storage medium for numerical simulation of conductor galloping based on a centrally concentrated mass three-node element, aiming to solve the technical problem of how to improve the efficiency of large-scale engineering simulation calculations.

[0006] To achieve the above objectives, this application proposes a numerical simulation method for conductor galloping based on a centrally lumped mass three-node element. The method includes: Based on the conductor model information, the conductor is discretized into multiple three-node units, wherein the three-node unit includes a first end node, a second end node, and a center node; Determine the net external force at the center node of the three-node unit at the current moment, and establish the dynamic equation based on the net external force; Based on the dynamic equations, predict the coordinates of the central node of the three-node unit at the next moment; Based on the geometric relationship between the center nodes of adjacent three-node units, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node units at the next time step, the internal equilibrium equation is established and solved to obtain the coordinates of the end nodes shared by the adjacent three-node units at the next time step. The coordinates of the end nodes shared by the adjacent three-node units at the next moment are used as the output result of the conductor galloping simulation.

[0007] In one embodiment, determining the net external force at the central node of the three-node unit at the current moment includes: Based on the coordinates of the first end node, the second end node, and the center node of the three-node element in the world coordinate system, the internal force of the center node is obtained. The gravity is obtained based on the mass of the three-node unit; The aerodynamics are obtained based on the preset environmental parameters and the length of the three-node unit; The internal force of the central node, the gravity, and the aerodynamic force are taken as the resultant external force of the central node of the three-node unit at the current moment.

[0008] In one embodiment, obtaining the internal force at the central node based on the coordinates of the first end node, the second end node, and the central node in the world coordinate system of the three-node element includes: Obtain the local coordinate system corresponding to the three-node unit; Based on the coordinates of the first end node, the second end node, and the center node of the three-node element in the world coordinate system, the internal forces of the first end node and the second end node are obtained. Based on the internal forces of the first end node and the second end node, the expression for the internal force of the center node in the local coordinate system is obtained; The internal force expression of the center node in the local coordinate system is transformed by the rotation matrix between the local coordinate system and the world coordinate system to obtain the internal force expression of the center node in the world coordinate system. The internal forces of the central node are determined based on the expression of the internal forces of the central node in the world coordinate system.

[0009] In one embodiment, obtaining the internal forces of the first and second end nodes based on the coordinates of the first end node, the second end node, and the center node of the three-node element in the world coordinate system includes: Obtain the coordinates of the first end node, the second end node, the center node, the first elastic stiffness, the second elastic stiffness, the first initial distance, and the second initial distance of the three-node unit in the world coordinate system. The first elastic stiffness refers to the elastic stiffness of the conductor segment formed by the first end node and the center node, the second elastic stiffness refers to the elastic stiffness of the conductor segment formed by the second end node and the center node, the first initial distance refers to the initial distance between the first end node and the center node, and the second initial distance refers to the initial distance between the second end node and the center node. Based on the coordinates of the first end node, the coordinates of the center node, the first elastic stiffness, and the first initial distance, the internal force of the first end node is obtained; The internal force of the second end node is obtained based on the coordinates of the second end node, the coordinates of the center node, the second elastic stiffness, and the second initial distance.

[0010] In one embodiment, the preset environmental parameters include air density, relative wind speed, drag coefficient, lift coefficient, effective angle of attack, and conductor diameter; The aerodynamics obtained based on preset environmental parameters and the length of the three-node unit include: Aerodynamic drag is obtained based on the air density, relative wind speed, conductor diameter, drag coefficient, effective angle of attack, and length of the three-node unit. The aerodynamic lift is obtained based on the air density, relative wind speed, conductor diameter, lift coefficient, effective angle of attack, and length of the three-node unit. The aerodynamic drag and the aerodynamic lift are used as the aerodynamic forces of the three-node unit.

[0011] In one embodiment, predicting the coordinates of the center node of the three-node unit at the next moment based on the dynamic equation includes: Based on the aforementioned dynamic equations, the expression for the acceleration of the center of mass is obtained; Based on the centroid acceleration expression, the acceleration vector corresponding to the center node of the three-node unit at the next moment is obtained; By integrating the acceleration vector corresponding to the center node of the three-node unit over time, the coordinates of the center node of the three-node unit at the next time step are obtained.

[0012] In one embodiment, the step of establishing and solving the internal equilibrium equation based on the geometric relationship between the center nodes of adjacent three-node elements, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node elements at the next time step, to obtain the coordinates of the shared end nodes of the adjacent three-node elements at the next time step, includes: Based on the geometric relationship between the center nodes of adjacent three-node units, the first three-node unit and the second three-node unit are determined, wherein the first three-node unit and the second three-node unit are adjacent, and the second end node of the first three-node unit is the first end node of the second three-node unit; The centroid distance between adjacent units is obtained based on the coordinates of the center node of the first three-node unit at the next time step and the coordinates of the center node of the second three-node unit at the next time step. Based on the distance between the centroids of adjacent units, the second elastic stiffness and the second initial distance corresponding to the first three-node unit, and the first elastic stiffness and the first initial distance corresponding to the second three-node unit, an internal equilibrium equation is established in conjunction with the internal force equilibrium condition. Solve the internal equilibrium equation to obtain the coordinates of the second end node of the first three-node unit at the next time step; The coordinates of the second end node of the first three-node unit at the next time step are used as the coordinates of the end node shared by the adjacent three-node units at the next time step.

[0013] In addition, to achieve the above objectives, this application also proposes a numerical simulation device for conductor galloping based on a centrally lumped mass three-node unit. The numerical simulation device for conductor galloping based on a centrally lumped mass three-node unit includes: a partitioning module, used to discretize the conductor into multiple three-node units according to the conductor model information, wherein the three-node unit includes a first end node, a second end node, and a central node. A module is established to determine the net external force at the center node of the three-node unit at the current moment, and to establish a dynamic equation based on the net external force. The prediction module is used to predict the coordinates of the center node of the three-node unit at the next moment based on the dynamic equation. The solution module is used to establish and solve the internal equilibrium equation based on the geometric relationship between the center nodes of adjacent three-node elements, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node elements at the next time step, so as to obtain the coordinates of the end nodes shared by the adjacent three-node elements at the next time step. The output module is used to output the coordinates of the end nodes shared by the adjacent three-node units at the next moment as the output result of the conductor galloping simulation.

[0014] Furthermore, to achieve the above objectives, this application also proposes a numerical simulation device for conductor galloping based on a centrally lumped mass three-node element. The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor. The computer program is configured to implement the steps of the numerical simulation method for conductor galloping based on a centrally lumped mass three-node element as described above.

[0015] In addition, to achieve the above objectives, this application also proposes a storage medium, which is a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element as described above.

[0016] In addition, to achieve the above objectives, this application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element as described above.

[0017] This application discretizes the conductor into multiple three-node elements based on the conductor model information. Each three-node element includes a first end node, a second end node, and a center node. The net external force on the center node of each three-node element at the current moment is determined, and a dynamic equation is established based on this net external force. The coordinates of the center node of each three-node element at the next moment are predicted based on the dynamic equations. An internal equilibrium equation is established and solved based on the geometric relationship between the center nodes of adjacent three-node elements, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node elements at the next moment, yielding the coordinates of the shared end nodes of adjacent three-node elements at the next moment. The coordinates of the shared end nodes of each adjacent three-node element at the next moment are used as the output result of the conductor galloping simulation. By employing a discretization method using three-node elements with a centrally concentrated mass, mass and inertial properties are concentrated at the geometric center of each element. By utilizing the balance of internal and external forces within the element, a system of multibody dynamic equations is established with the element center as the independent solution object. Because the element dynamics equations are decoupled, the calculation process does not rely on the assembly and inversion of the global matrix, thus solving the problem of low computational efficiency caused by the high computational complexity and difficulty in parallelization of the global matrix in the traditional finite element method when simulating the galloping of non-uniform conductors. Compared with existing technologies, this method significantly improves the computational speed while ensuring the simulation accuracy of non-uniform mass distribution structures. It is easily adapted to modern GPU parallel computing architectures, enabling efficient time-domain simulation of galloping of large-scale, long-distance transmission lines. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating an embodiment of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element in this application. Figure 2 This is a diagram of a three-node dynamic element provided in Embodiment 1 of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element in this application; Figure 3 This is a flowchart illustrating Embodiment 2 of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element in this application. Figure 4 This is the element connection diagram provided in Embodiment 2 of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element in this application; Figure 5 This is a schematic diagram of the module structure of the numerical simulation device for conductor galloping based on a centrally concentrated mass three-node unit, as described in this application embodiment. Figure 6 This is a schematic diagram of the equipment structure of the hardware operating environment involved in the numerical simulation method of conductor galloping based on a centrally concentrated mass three-node unit in the embodiments of this application.

[0021] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0022] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0023] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0024] The main solution of this application embodiment is as follows: The conductor is discretized into multiple three-node units based on the conductor model information, wherein each three-node unit includes a first end node, a second end node, and a center node; the net external force of the center node of each three-node unit at the current moment is determined, and a dynamic equation is established based on the net external force; the coordinates of the center node of each three-node unit at the next moment are predicted based on the dynamic equation; an internal equilibrium equation is established and solved based on the geometric relationship between the center nodes of adjacent three-node units, the internal force equilibrium condition, and the coordinates of the center nodes of each three-node unit at the next moment, to obtain the coordinates of the shared end nodes of adjacent three-node units at the next moment; the coordinates of the shared end nodes of each adjacent three-node unit at the next moment are used as the output result of the conductor galloping simulation.

[0025] In this embodiment, for ease of description, the following description uses a conductor galloping numerical simulation system based on a centrally concentrated mass three-node unit as the execution subject.

[0026] The mainstream technique for numerical analysis of conductor galloping is the traditional finite element method (FEM). This method discretizes the conductor into a mesh, constructs a global stiffness and mass matrix, and uses implicit integration to solve a large set of equations to simulate the dynamic response. However, this technique has significant drawbacks: First, when simulating conductors with uneven mass distribution, such as those subjected to vibration dampers or non-uniform icing, the traditional nodal mass lumped method uses forced averaging for inertial property distribution at shared nodes, leading to distortion of local physical properties and severely reducing the accuracy of dynamic calculations under non-uniform structures. Second, because this method requires real-time updating, assembly, and solving of the massive global matrix, the computational complexity increases exponentially with the degrees of freedom, resulting in significant time consumption. More importantly, its strongly topologically coupled solution process has a strong data dependency, making it impossible to effectively utilize modern GPUs and other multi-core parallel computing hardware, resulting in extremely low computational efficiency for long-distance conductor galloping simulations and failing to meet the needs of large-scale engineering applications.

[0027] This application provides a solution that employs a discretization method using three-node elements with a centrally concentrated mass. This concentrates mass and inertial properties at the geometric center of each element and utilizes the balance of internal and external forces within the element to establish a system of multibody dynamic equations with the element center as the independent solution object. Because the element dynamic equations are decoupled, the computation process does not depend on the assembly and inversion of the global matrix, thus solving the problem of low computational efficiency caused by the high computational complexity and difficulty in parallelization of the global matrix in traditional finite element methods for simulating non-uniform conductor galloping. Compared with existing technologies, this method significantly improves computational speed while maintaining the simulation accuracy for non-uniform mass distribution structures. It is easily adapted to modern GPU parallel computing architectures, enabling efficient time-domain simulation of large-scale, long-distance transmission line galloping.

[0028] It should be noted that the executing entity in this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or an electronic device capable of performing the above functions, such as a conductor galloping numerical simulation system based on a centrally lumped mass three-node element. The following description uses a conductor galloping numerical simulation system based on a centrally lumped mass three-node element as an example to illustrate this embodiment and the subsequent embodiments.

[0029] Based on this, embodiments of this application provide a numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element of this application.

[0030] In this embodiment, the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element includes steps S10 to S50: Step S10: Discretize the conductor into multiple three-node units according to the conductor model information, wherein the three-node unit includes a first end node, a second end node, and a center node; It should be noted that the conductor model information refers to the initial data set used to characterize the physical and geometric properties of the transmission conductor, specifically including but not limited to: the total length of the conductor, the number of segments, the physical properties, gravitational properties, aerodynamic properties of each segment, and related initial conditions. A three-node element refers to the basic computational unit formed after the conductor is discretized; each three-node element participates in the calculation as an independent dynamic entity. The first end node and the second end node refer to the two boundary connection points of the same three-node element along the conductor axis, used to realize the geometric connection and internal force transfer between adjacent three-node elements. The first end node is located to the left of the center node, and the second end node is located to the left of the center node. The center node is the node defined at the geometric center of the three-node element, used to centrally characterize all the mass and inertial properties of the element, and serves as the main body for solving the element's dynamic equations.

[0031] Specifically, based on the input total length of the conductor and the segmentation requirements, the system automatically divides the continuous conductor model into multiple sequentially connected units in space, with each line segment constituting a three-node unit. For example... Figure 2As shown, each unit consists of node 1 (first end node), node 3 (second end node) at both ends, and node 2 (center node) located at the geometric center. Physical connections between units are achieved by sharing end nodes. Simultaneously, the system generates a center node at the midpoint of each three-node unit segment and assigns all inertial parameters corresponding to that unit, such as mass and moment of inertia, to this center node. Thus, the conductor is transformed from a continuous physical entity into a computational model composed of multiple discrete dynamic units with "mass concentrated at the center and ends only responsible for connection."

[0032] Understandably, because this method innovatively concentrates the mass and inertial properties of the element entirely at the geometric center node, rather than distributing them to multiple end nodes as in the traditional finite element method, each element becomes a rigid body system that can be solved independently in terms of dynamics. Therefore, executing step S10 can avoid the problem of local inertial description distortion of non-uniform structures (such as those with vibration dampers or abrupt changes in ice thickness) caused by the average distribution of node mass in the traditional method. This lays the foundation for subsequent high-precision, parallelizable dynamic calculations at the discretization stage, significantly improving the model fidelity and computational reliability of non-uniform conductor galloping simulation.

[0033] Step S20: Determine the net external force at the center node of the three-node unit at the current moment, and establish the dynamic equation based on the net external force; It should be noted that the net external force on a three-node element at the current moment refers to the vector sum of all forces acting on the center of mass (i.e., the central node) of the three-node element, including internal forces generated by element deformation and externally applied loads. The dynamic equations refer to the differential equations describing the motion state of the central node.

[0034] Specifically, the system calculates the internal elastic restoring force (internal force) of the three-node element based on its geometric configuration at the current moment, and simultaneously calculates external loads such as gravity and aerodynamics based on the given environmental conditions and element properties. Based on the resultant external forces (gravity, aerodynamics, and internal forces at the central node), the motion equation, i.e., the dynamic equation, of the central node can be directly established.

[0035] At each time t, after determining the net external forces (including gravity, aerodynamic forces, and internal forces at the central nodes) acting on all element center nodes (node ​​2), the dynamic equations are established as follows:

[0036] in, Let be the acceleration vector of the central node. Where C is the total mass of the unit, and C is the structural damping coefficient. For the internal forces at the central node in the world coordinate system, For gravity load, It is an aerodynamic load.

[0037] Understandably, since this method concentrates the element mass and directly establishes the dynamic equations at the center of mass, step S20 can avoid the complex process of indirectly deriving the system motion equations by assembling the global mass matrix and stiffness matrix in the traditional finite element method, thus significantly simplifying the equation establishment process and improving the efficiency and transparency of the calculation setup.

[0038] In one feasible implementation, step S20 may include: obtaining the internal force of the center node based on the coordinates of the first end node, the second end node, and the center node of the three-node unit in the world coordinate system; obtaining the gravity based on the mass of the three-node unit; obtaining the aerodynamic force based on preset environmental parameters and the length of the three-node unit; and using the internal force of the center node, the gravity, and the aerodynamic force as the resultant external force of the center node of the three-node unit at the current moment.

[0039] It should be noted that the world coordinate system refers to a fixed global reference system used to describe the spatial position of the entire traverse system. The coordinates of the first end node, the second end node, and the center node are the position vectors of the three nodes of this three-node element in the world coordinate system. The mass of the three-node element refers to the total mass of the traverse segment it represents, concentrated at its center node. The internal force at the center node refers to the elastic restoring force acting on the center node due to element deformation. The preset environmental parameters refer to the physical constants and state parameters required for calculating aerodynamics. The length of the three-node element refers to the initial or current length of the traverse segment it represents. Aerodynamics refers to the aerodynamic load generated by wind acting on the traverse segment of this element.

[0040] Specifically, the system reads the node coordinate vector stored at the current moment, calculates the internal forces based on these coordinates and the element's material properties (such as elastic modulus and cross-sectional area); simultaneously, it calculates the gravity vector based on the element's mass and gravitational acceleration; and based on environmental and geometric parameters such as current wind speed, air density, and conductor diameter, it uses aerodynamic formulas to calculate the aerodynamic lift and drag acting on the element. The calculated internal forces, gravity, and aerodynamic forces are then used as the resultant external force.

[0041] Further, obtaining the internal force of the center node based on the coordinates of the first end node, the second end node, and the center node in the world coordinate system of the three-node unit includes: obtaining the local coordinate system corresponding to the three-node unit; obtaining the internal forces of the first end node and the second end node based on the coordinates of the first end node, the second end node, and the center node in the world coordinate system of the three-node unit; obtaining the internal force expression of the center node in the local coordinate system based on the internal forces of the first end node and the second end node; transforming the internal force expression of the center node in the local coordinate system according to the rotation matrix between the local coordinate system and the world coordinate system to obtain the internal force expression of the center node in the world coordinate system; and determining the internal force of the center node based on the internal force expression of the center node in the world coordinate system.

[0042] It should be noted that the local coordinate system refers to a reference system defined by the geometric characteristics of the three-node element itself, which moves with the element, and its origin is usually located at the element's center of mass (center node). The internal forces at the first and second end nodes are elastic forces generated by the relative displacement between the end node and the center node, respectively. The expression for the internal force of the center node in the local coordinate system refers to the internal force vector acting on the center node obtained by transforming the internal forces of the two end nodes to the local coordinate system, based on the principle of force balance. The rotation matrix between the local and world coordinate systems is a transformation matrix used to describe the orientation of each axis of the local coordinate system relative to the world coordinate system. The expression for the internal force of the center node in the world coordinate system refers to the expression after transforming the internal force vector from the local coordinate system back to the world coordinate system using the rotation matrix.

[0043] Specifically, such as Figure 2 As shown in the figure Represents the global coordinate system, nodes The position in the global coordinate system is represented as . This represents a local coordinate system. The local coordinate system is defined as follows: the origin of the local coordinate system is located at the center node of the element (the centroid of the element). The direction of the axis is: , shaft and Vertical, and Coplanar with nodes 1, 2, and 3 The direction of the axis is determined according to the right-hand screw rule.

[0044] The step of obtaining the internal forces of the first and second end nodes based on the coordinates of the first end node, the second end node, and the center node of the three-node unit in the world coordinate system includes: acquiring the coordinates of the first end node, the second end node, and the center node of the three-node unit in the world coordinate system, a first elastic stiffness, a second elastic stiffness, a first initial distance, and a second initial distance, wherein the first elastic stiffness refers to the elastic stiffness corresponding to the conductor segment formed by the first end node and the center node, the second elastic stiffness refers to the elastic stiffness corresponding to the conductor segment formed by the second end node and the center node, the first initial distance refers to the initial distance between the first end node and the center node, and the second initial distance refers to the initial distance between the second end node and the center node; obtaining the internal forces of the first end node based on the first end node coordinates, the center node coordinates, the first elastic stiffness, and the first initial distance; and obtaining the internal forces of the second end node based on the second end node coordinates, the center node coordinates, the second elastic stiffness, and the second initial distance.

[0045] It should be noted that the first elastic stiffness and the second elastic stiffness are axial tensile / compressive stiffness parameters describing the two "semi-units" from the center node to the two end nodes, respectively, and are usually determined by the elastic modulus, cross-sectional area, and half-unit length of the conductor material. The first initial distance and the second initial distance are the spatial distances between the first end node and the center node, and between the second end node and the center node, respectively, in their undeformed (initial) states.

[0046] Specifically, the calculation process for the internal elastic force of the three-node element at each time t is as follows: like Figure 2 As shown, the coordinates of the known element nodes in the world coordinate system are... and the elastic stiffness within the unit Solve for the elastic forces inside the element.

[0047] The internal forces at nodes 1 and 3 are expressed in world coordinates as follows:

[0048] in: It is the first initial distance between nodes 1 and 2. It is the second initial distance between nodes 3 and 2. This represents the first elastic stiffness between nodes 1 and 2. This represents the second elastic stiffness between nodes 3 and 2, and is the internal force at the first end node. For the internal forces at the second end node, To represent the coordinates of the first end node, Represents the coordinates of the central node. This represents the coordinates of the second end node.

[0049] According to the internal force equilibrium equation, the internal force at node 2 in the local coordinate system can be expressed as follows:

[0050] in, For the internal forces at the central nodes in the local coordinate system, For the internal forces at the central node in the local coordinate system The magnitude of the component of force along the axial direction, For the internal forces at the central node in the local coordinate system The magnitude of the component of force along the axial direction, For the internal forces at the central node in the local coordinate system The magnitude of the component of force along the axial direction, Let be the angle between the first end node vector and the center node vector. The angle between the vectors of the second end nodes and the vector of the center node is denoted as . .

[0051] According to the definition of a local coordinate system, the rotation matrix R between the local coordinate system and the global coordinate system can be written in the following form:

[0052] in, To represent the coordinates of the first end node, Represents the coordinates of the central node. This represents the coordinates of the second end node.

[0053] Therefore, the internal forces of node 2 (the central node) in the global (world) coordinate system are expressed as follows:

[0054] Where R is the rotation matrix between the local coordinate system and the global coordinate system. For the internal forces at the central nodes in the local coordinate system, The internal forces at the center node in the world coordinate system.

[0055] Further, the preset environmental parameters include air density, relative wind speed, drag coefficient, lift coefficient, effective angle of attack, and conductor diameter; obtaining aerodynamics based on the preset environmental parameters and the length of the three-node unit includes: obtaining aerodynamic drag based on the air density, relative wind speed, conductor diameter, drag coefficient, effective angle of attack, and the length of the three-node unit; obtaining aerodynamic lift based on the air density, relative wind speed, conductor diameter, lift coefficient, effective angle of attack, and the length of the three-node unit; and using the aerodynamic drag and aerodynamic lift as the aerodynamics of the three-node unit.

[0056] It should be noted that air density is the mass of air per unit volume. The relative wind speed is the vector difference between the incoming wind speed and the velocity of the conductor element at that point. The drag coefficient and lift coefficient are dimensionless parameters used to describe the aerodynamic characteristics of the conductor cross-section at a specific angle of attack. The effective angle of attack is the angle between the relative wind speed direction and the plane normal to the conductor axis. The conductor diameter refers to the equivalent outer diameter of the conductor (including potential icing). Aerodynamic drag is the aerodynamic component acting along the relative wind speed direction. Aerodynamic lift is the aerodynamic component acting perpendicular to the relative wind speed direction (within the plane determined by the wind speed and the conductor axis).

[0057] Specifically, when performing conductor galloping analysis, the external loads on the conductor include gravitational loads and aerodynamic loads. Gravity load Determined by the mass of the three-node element, the direction is along the negative Z-axis of the global coordinate system:

[0058] Where m is the concentrated mass of the unit, and g is the gravitational acceleration (usually taken as 9.8 m / s²).

[0059] Since the element model in this embodiment mainly focuses on the translational galloping characteristics of the conductor and does not include torsional degrees of freedom, the aerodynamic loads only calculate aerodynamic lift and drag. Based on the quasi-steady assumption, drag... and lift The calculation formula is as follows:

[0060] in: air density; Relative wind speed; The diameter of the wire; The total length of the unit; and These are the drag coefficient and lift coefficient, respectively. For an effective angle of attack.

[0061] In this embodiment, the complex resultant external force is decomposed into three independent and parallel computable components: internal force, gravity, and aerodynamic force. These components are then solved one by one based on clear physical laws (Hooke's law, Newton's laws, and quasi-steady aerodynamic theory). This modularizes and makes the force calculation process explicit, solving the complexity of the traditional implicit finite element method where force and displacement are coupled and iterative solutions are required. This lays the foundation for subsequent efficient explicit time integration and parallel computing.

[0062] The above are merely feasible implementations of step S20 provided in this embodiment. This embodiment does not specifically limit the specific implementation of step S20.

[0063] Step S30: Based on the dynamic equation, predict the coordinates of the center node of the three-node unit at the next moment; It should be noted that the coordinates of the center node at the next moment refer to the estimated position of the geometric center (i.e., the center node) of the three-node unit in the global world coordinate system after the current simulation time step ends, and are represented by a position vector.

[0064] Specifically, based on the dynamic equations established in step S20 (i.e., the relationship between net external force and acceleration), the system solves for the acceleration vector of the center node at the current moment. Using a numerical integration method, the velocity and position of the center node at the previous moment (or the current moment) are used as initial conditions, combined with the currently calculated acceleration, to advance one time step, thereby calculating the velocity and position coordinates of the center node at the next moment. This process transforms force information (through acceleration) into motion information (position and velocity).

[0065] It is understandable that, since the dynamic equations of each node in this application are independent and do not depend on the solution of the global matrix, step S30 can avoid the huge computational overhead and iterative instability caused by solving large nonlinear equations in the traditional implicit integration method, thereby achieving explicit updates of motion state with higher computational efficiency and better numerical robustness, and improving the speed and reliability of single-step calculation.

[0066] In one feasible implementation, step S30 may include: obtaining the expression for the center of mass acceleration according to the dynamic equation; obtaining the acceleration vector corresponding to the center node of the three-node unit at the next moment based on the expression for the center of mass acceleration; and integrating the acceleration vector corresponding to the center node of the three-node unit over time to obtain the coordinates of the center node of the three-node unit at the next moment.

[0067] It should be noted that the expression for the center-of-mass acceleration is a mathematical expression derived directly from Newton's second law, describing the relationship between the acceleration of the central node and the net external force acting on it. Its typical form is: acceleration equals net external force divided by mass. The acceleration vector refers to the vector composed of the acceleration components of the central node along each coordinate axis in the world coordinate system at a given moment. Time integration is a numerical calculation method used to recursively calculate the motion state at the next moment based on the current motion state (position, velocity, acceleration) and the laws of motion (dynamic equations).

[0068] Specifically, the expression for the acceleration of the center of mass can be obtained from the dynamic equations as follows:

[0069] in, Let be the acceleration vector of the central node. Where C is the total mass of the unit, and C is the structural damping coefficient. For the internal forces at the central node in the world coordinate system, For gravity load, It is an aerodynamic load.

[0070] After obtaining the acceleration vector of the element, the explicit Euler method is used for time integration to obtain the velocity and position at time t+1.

[0071] In this embodiment, by adopting a fully decoupled unit-level motion update strategy based on explicit integration, the prediction of the state of each three-node unit at the next moment depends only on its own physical quantity at the current moment, without waiting for or solving for information from other units. This solves the problem of strong data dependence and low parallel efficiency caused by global coupling in the traditional implicit finite element method, and provides a core computational framework for realizing large-scale, high-efficiency parallelized conductor galloping simulation.

[0072] The above are merely feasible implementations of step S30 provided in this embodiment. This embodiment does not specifically limit the specific implementation of step S30.

[0073] Step S40: Based on the geometric relationship between the center nodes of adjacent three-node units, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node units at the next moment, establish the internal equilibrium equation and solve it to obtain the coordinates of the end nodes shared by the adjacent three-node units at the next moment. It should be noted that geometric relationships refer to the spatial constraints satisfied between adjacent three-node elements, determined by physical connections. Specifically, this means that the second end node of the i-th element coincides with the first end node of the (i+1)-th element. The internal force equilibrium condition states that at the shared end node, the internal forces from the left element and the internal forces from the right element are equal in magnitude and opposite in direction, i.e., their vector sum is zero. The internal equilibrium equations are a set of equations established by combining geometric relationships and internal force equilibrium conditions to solve for the unknown location of the shared end node. The shared end node of adjacent three-node elements refers to the node that physically connects two adjacent three-node elements; it is the spatial coincidence point between the second end node of the left element and the first end node of the right element.

[0074] Specifically, after obtaining the predicted coordinates of the center nodes of all three-node elements at the next time step, the system processes each pair of adjacent elements. Based on the new coordinates of the center nodes of these two elements, a spatial straight line (geometric relationship) can be determined. The new position of the shared end node falls on this straight line, which is a geometric constraint. Simultaneously, based on the element internal force calculation formula (Hooke's Law), the node is subjected to elastic forces from the left and right elements. The magnitudes of these two forces depend on the difference between the distance from the node to the left and right center nodes and their initial distances, as well as their respective elastic stiffness. In equilibrium, these two forces should be equal in magnitude and opposite in direction along the straight line (internal force equilibrium condition). Combining these two conditions, a univariate equation (internal equilibrium equation) can be established regarding the distance from the shared node to the left (or right) center node. Solving this equation determines the precise position of the shared end node on the line segment, thus obtaining its world coordinates.

[0075] Understandably, since the motion of each central node in step S30 is predicted independently, if the constraint solution in step S40 is not performed, the discrete elements will physically break or overlap. Performing step S40 can prevent the model from losing structural continuity due to independent updates, thereby ensuring that the entire conductor remains a coherent physical entity after deformation, improving the physical realism and geometric consistency of the simulation.

[0076] Step S50: The coordinates of the end nodes shared by the adjacent three-node units at the next moment are used as the output result of the conductor galloping simulation.

[0077] It should be noted that conductor galloping simulation refers to the process of simulating the spatial morphology and motion of transmission lines under loads such as wind and ice over time using numerical calculation methods. The output results refer to the quantifiable and analyzable data generated by the simulation calculation, which is usually a sequence of spatial coordinates of all nodes of the conductor at each simulation moment. These coordinates completely define the geometric shape of the conductor at that moment.

[0078] Specifically, after steps S30 and S40, the system has obtained the coordinates of all center nodes and all shared end nodes at the next time step. For the two non-shared end nodes (boundary nodes) at the beginning and end of the model, their coordinates are usually directly given by the boundary conditions (such as fixed suspension points). At this point, the simulation system possesses the coordinate set of all nodes of the conductor at the next time step. These coordinate data, along with timestamps, are recorded as the output of the current time step. These results can be used for real-time visualization of the conductor's undulating form, or stored for subsequent dynamic analyses such as amplitude, frequency, and trajectory.

[0079] Understandably, since the final output of this method is the precise coordinates of all nodes of the conductor at every moment, rather than just the coordinates of the center node or intermediate physical quantities, step S50 can avoid the problem in traditional methods where additional post-processing interpolation is required to obtain the complete conductor shape due to incomplete output information. This directly provides complete spatiotemporal motion data that can be used for engineering analysis (such as spacing verification and fatigue assessment), improving the direct usability of simulation results and analysis efficiency.

[0080] This embodiment provides a numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element. The conductor is discretized into multiple three-node elements based on the conductor model information. Each three-node element includes a first end node, a second end node, and a center node. The net external force on the center node of each three-node element at the current moment is determined, and a dynamic equation is established based on this net external force. The coordinates of the center node of each three-node element at the next moment are predicted based on the dynamic equation. An internal equilibrium equation is established and solved based on the geometric relationship between the center nodes of adjacent three-node elements, the internal force equilibrium conditions, and the coordinates of the center nodes of each three-node element at the next moment, yielding the coordinates of the shared end nodes of adjacent three-node elements at the next moment. The coordinates of the shared end nodes of all adjacent three-node elements at the next moment are used as the output of the conductor galloping simulation. By employing the discretization method of the centrally concentrated mass three-node element, mass and inertial properties are concentrated at the geometric center of each element. By utilizing the balance of internal and external forces within the element, a system of multibody dynamic equations is established with the element center as the independent solution object. Because the element dynamics equations are decoupled, the calculation process does not rely on the assembly and inversion of the global matrix, thus solving the problem of low computational efficiency caused by the high computational complexity and difficulty in parallelization of the global matrix in the traditional finite element method when simulating the galloping of non-uniform conductors. Compared with existing technologies, this method significantly improves the computational speed while ensuring the simulation accuracy of non-uniform mass distribution structures. It is easily adapted to modern GPU parallel computing architectures, enabling efficient time-domain simulation of galloping of large-scale, long-distance transmission lines.

[0081] Based on the first embodiment of this application, in the second embodiment of this application, the content that is the same as or similar to that in Embodiment 1 above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 3 The numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element further includes steps S44 to S44: Step S41: Based on the geometric relationship between the center nodes of adjacent three-node units, determine the first three-node unit and the second three-node unit, wherein the first three-node unit and the second three-node unit are adjacent, and the second end node of the first three-node unit is the first end node of the second three-node unit. Specifically, the system traverses all three-node elements in a discrete order along the conductor axis. For any i-th three-node element (defined as the first three-node element), its downstream adjacent (i+1)-th three-node element is defined as the second three-node element. These two elements are physically connected end-to-end; therefore, the second end node of the first three-node element and the first end node of the second three-node element are the same point in space, i.e., they share an end node.

[0082] Understandably, since this method explicitly defines the connection topology and node roles between elements, performing step S41 can avoid the force transmission path being disordered or the geometric constraint being applied incorrectly due to unclear connection relationships during the calculation process. This ensures that the subsequent internal force equilibrium equations can be correctly and uniquely established, improving the logical rigor of the calculation process and the repeatability of the results.

[0083] Step S42: Based on the coordinates of the center node of the first three-node unit at the next time step and the coordinates of the center node of the second three-node unit at the next time step, obtain the centroid distance between adjacent units. It should be noted that the centroid distance between adjacent elements refers to the straight-line distance between the center nodes of the first three-node element and the center nodes of the second three-node element at the next predicted moment.

[0084] Specifically, such as Figure 4 As shown, at time t+1, the distance between the centroid ① of element 1 (the first three-node element) and the centroid ② of element 2 (the second three-node element) is... :

[0085] in, It is the coordinate of the center node of the first three-node element at the next moment. The coordinates of the center node of the second and third node units at the next time step.

[0086] Understandably, since this method directly uses the independently predicted coordinates of the center node to calculate the distance, step S42 can avoid the problem in traditional methods that require complex deformation gradients or iterative solutions to determine the relative positions of elements. Thus, it can quickly obtain key geometric parameters with the simplest vector operations, providing direct input for establishing explicit internal force equilibrium equations and improving computational efficiency.

[0087] Step S43: Based on the distance between the centroids of the adjacent units, the second elastic stiffness and the second initial distance corresponding to the first three-node unit, and the first elastic stiffness and the first initial distance corresponding to the second three-node unit, an internal equilibrium equation is established in conjunction with the internal force equilibrium condition. Specifically, such as Figure 4 As shown, assume that the distance between nodes 1 and 3 and the centroid node of element 1 is... Based on the equilibrium of internal forces, we can obtain:

[0088] in, This represents the second elastic stiffness between node 2 and node 3 of element 1. This represents the first elastic stiffness between node 1 and node 2 of element 2. This represents the second initial distance between node 2 and node 3 in element 1. This represents the first initial distance between node 1 and node 2 in unit 2.

[0089] Understandably, because this method cleverly transforms the solution of complex spatial node positions into a scalar equation with a single distance variable through geometric collinearity constraints, step S43 can avoid the problem of traditional finite element methods requiring the establishment and solution of complex equations with multiple degrees of freedom coupling to satisfy the coordination conditions. This greatly simplifies the handling of connection conditions and improves the solution efficiency and numerical stability.

[0090] Step S44: Solve the internal equilibrium equation to obtain the coordinates of the second end node of the first three-node unit at the next time step.

[0091] Specifically, such as Figure 4 As shown, solving the internal equilibrium equation yields the position of nodes 1,3 (or 2,1) in the global coordinate system at time t+1. :

[0092] in, This represents the coordinates of the first end node of the c-th element node. The coordinates of the second end node of the c-th unit node.

[0093] Understandably, since the internal equilibrium equation is a simple linear scalar equation, performing step S44 can avoid the problems of iterative divergence, slow convergence, or the need to select initial values ​​that may occur when solving nonlinear equation systems. This ensures that the position of the shared end node can be determined quickly, accurately, and uniquely each time, improving the robustness of the calculation process and the determinism of the results.

[0094] Step S45: The coordinates of the second end node of the first three-node unit at the next time moment are used as the coordinates of the end node shared by the adjacent three-node units at the next time moment.

[0095] Specifically, numerical simulation of conductor galloping based on centrally concentrated mass three-node elements (the explanation is how the data is transformed, obtained, and the correlation between them).

[0096] Understandably, since this method determines the connection point coordinates of two units and performs data association in one calculation, step S45 can avoid the minor inconsistencies (numerical errors) that may be caused by calculating and storing the two coordinates separately, as well as the additional data synchronization overhead. This ensures the consistency of the model geometry, simplifies data management, and improves the efficiency and coordination of the overall simulation process.

[0097] This embodiment provides a numerical simulation method for conductor galloping based on three-node elements with a central concentrated mass. Based on the geometric relationship between the central nodes of adjacent three-node elements, a first three-node element and a second three-node element are determined, wherein the first and second three-node elements are adjacent, and the second end node of the first three-node element is the first end node of the second three-node element. The distance between the centroids of adjacent elements is obtained based on the coordinates of the central nodes of the first and second three-node elements at the next time step. An internal equilibrium equation is established based on the distance between the centroids of adjacent elements, the second elastic stiffness and second initial distance corresponding to the first three-node element, and the first elastic stiffness and first initial distance corresponding to the second three-node element, combined with internal force equilibrium conditions. The internal equilibrium equation is solved to obtain the coordinates of the second end node of the first three-node element at the next time step. The coordinates of the second end node of the first three-node element at the next time step are used as the coordinates of the shared end node of the adjacent three-node elements at the next time step. This paper solves the key problem of broken physical connections or geometric inconsistencies between adjacent units caused by the independent motion update of each unit in the simulation of conductor galloping based on centrally concentrated mass discretization. It enables the rapid and accurate determination of the spatial location of the connection point between adjacent discrete units without relying on global iteration and large matrix solutions, using only simple geometric relationships and local force balance conditions. This improves the ability of the simulation model to maintain structural continuity during dynamic deformation, the local decoupling of the calculation process, and the overall solution efficiency.

[0098] It should be noted that the above examples are only for understanding this application and do not constitute a limitation on the numerical simulation method of conductor galloping based on the centrally concentrated mass three-node element of this application. Any simple transformations based on this technical concept are within the protection scope of this application.

[0099] This application also provides a numerical simulation device for conductor galloping based on a centrally lumped mass three-node element. Please refer to [reference needed]. Figure 5 The numerical simulation device for conductor galloping based on a centrally concentrated mass three-node unit includes: The partitioning module 10 is used to discretize the conductor into multiple three-node units according to the conductor model information, wherein the three-node unit includes a first end node, a second end node, and a center node; Module 20 is established to determine the net external force at the center node of the three-node unit at the current moment, and to establish a dynamic equation based on the net external force. The prediction module 30 is used to predict the coordinates of the center node of the three-node unit at the next moment based on the dynamic equation. The solution module 40 is used to establish and solve the internal equilibrium equation based on the geometric relationship between the center nodes of adjacent three-node units, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node units at the next time step, so as to obtain the coordinates of the end nodes shared by the adjacent three-node units at the next time step. The output module 50 is used to output the coordinates of the end nodes shared by the adjacent three-node units at the next moment as the output result of the conductor galloping simulation.

[0100] The conductor galloping numerical simulation device based on a centrally lumped mass three-node element provided in this application, employing the conductor galloping numerical simulation method based on a centrally lumped mass three-node element in the above embodiments, can solve the technical problem of how to improve the efficiency of large-scale engineering simulation calculations. Compared with the prior art, the beneficial effects of the conductor galloping numerical simulation device based on a centrally lumped mass three-node element provided in this application are the same as the beneficial effects of the conductor galloping numerical simulation method based on a centrally lumped mass three-node element provided in the above embodiments, and other technical features in the conductor galloping numerical simulation device based on a centrally lumped mass three-node element are the same as the features disclosed in the methods of the above embodiments, and will not be repeated here.

[0101] The establishment module 20 is further configured to obtain the internal force of the center node based on the coordinates of the first end node, the second end node, and the center node in the world coordinate system of the three-node unit; obtain the gravity based on the mass of the three-node unit; obtain the aerodynamic force based on the preset environmental parameters and the length of the three-node unit; and use the internal force of the center node, the gravity, and the aerodynamic force as the resultant external force of the center node of the three-node unit at the current moment.

[0102] The establishment module 20 is further configured to obtain the local coordinate system corresponding to the three-node unit; obtain the internal forces of the first end node and the second end node based on the coordinates of the first end node, the second end node, and the center node in the world coordinate system; obtain the internal force expression of the center node in the local coordinate system based on the internal forces of the first end node and the second end node; transform the internal force expression of the center node in the local coordinate system based on the rotation matrix between the local coordinate system and the world coordinate system to obtain the internal force expression of the center node in the world coordinate system; and determine the internal force of the center node based on the internal force expression of the center node in the world coordinate system.

[0103] The establishment module 20 is further configured to obtain the coordinates of the first end node, the coordinates of the second end node, the coordinates of the center node, the first elastic stiffness, the second elastic stiffness, the first initial distance, and the second initial distance of the three-node unit in the world coordinate system. The first elastic stiffness refers to the elastic stiffness corresponding to the conductor segment formed by the first end node and the center node; the second elastic stiffness refers to the elastic stiffness corresponding to the conductor segment formed by the second end node and the center node; the first initial distance refers to the initial distance between the first end node and the center node; and the second initial distance refers to the initial distance between the second end node and the center node. Based on the first end node coordinates, the center node coordinates, the first elastic stiffness, and the first initial distance, the internal force of the first end node is obtained. Based on the second end node coordinates, the center node coordinates, the second elastic stiffness, and the second initial distance, the internal force of the second end node is obtained.

[0104] The establishment module 20 is further configured to obtain aerodynamic drag based on the air density, relative wind speed, conductor diameter, drag coefficient, effective angle of attack, and length of the three-node unit; obtain aerodynamic lift based on the air density, relative wind speed, conductor diameter, lift coefficient, effective angle of attack, and length of the three-node unit; and use the aerodynamic drag and aerodynamic lift as the aerodynamic force of the three-node unit.

[0105] The prediction module 30 is further configured to obtain the expression for the center of mass acceleration based on the dynamic equation; obtain the acceleration vector corresponding to the center node of the three-node unit at the next moment based on the expression for the center of mass acceleration; and integrate the acceleration vector corresponding to the center node of the three-node unit over time to obtain the coordinates of the center node of the three-node unit at the next moment.

[0106] The solution module 40 is further configured to: obtain the centroid distance between adjacent units based on the coordinates of the center node of the first three-node unit and the center node of the second three-node unit at the next time step; establish an internal equilibrium equation based on the centroid distance between adjacent units, the second elastic stiffness and the second initial distance corresponding to the first three-node unit, and the first elastic stiffness and the first initial distance corresponding to the second three-node unit, combined with the internal force equilibrium condition; solve the internal equilibrium equation to obtain the coordinates of the second end node of the first three-node unit at the next time step; and use the coordinates of the second end node of the first three-node unit at the next time step as the coordinates of the end node shared by the adjacent three-node units at the next time step.

[0107] This application provides a conductor galloping numerical simulation device based on a centrally lumped mass three-node unit. The conductor galloping numerical simulation device based on a centrally lumped mass three-node unit includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the conductor galloping numerical simulation method based on a centrally lumped mass three-node unit in the above embodiment 1.

[0108] The following is for reference. Figure 6 This document illustrates a structural schematic diagram of a conductor galloping numerical simulation device based on a centrally lumped mass three-node unit, suitable for implementing embodiments of this application. The conductor galloping numerical simulation device based on a centrally lumped mass three-node unit in this application embodiment may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Descriptions), PMPs (Portable Media Players), and in-vehicle terminals (e.g., in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 6 The numerical simulation device for conductor galloping based on a centrally concentrated mass three-node element shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0109] like Figure 6 As shown, a conductor galloping numerical simulation device based on a centrally concentrated mass three-node unit may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in ROM (Read Only Memory) 1002 or a program loaded from storage device 1003 into random access memory (RRAM) 1004. The RAM 1004 also stores various programs and data required for the operation of the conductor galloping numerical simulation device based on the centrally concentrated mass three-node unit. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to I / O interface 1006: input devices 1007 including, for example, touchscreens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. Communication device 1009 allows the wire galloping numerical simulation equipment based on a centrally lumped mass three-node unit to exchange data wirelessly or via wire. Although the figure shows a wire galloping numerical simulation equipment based on a centrally lumped mass three-node unit with various systems, it should be understood that it is not required to implement or possess all the systems shown. More or fewer systems can be implemented alternatively.

[0110] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from ROM 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0111] The conductor galloping numerical simulation device based on a centrally lumped mass three-node element provided in this application, employing the conductor galloping numerical simulation method based on a centrally lumped mass three-node element in the above embodiments, can solve the technical problem of how to improve the efficiency of large-scale engineering simulation calculations. Compared with the prior art, the beneficial effects of the conductor galloping numerical simulation device based on a centrally lumped mass three-node element provided in this application are the same as the beneficial effects of the conductor galloping numerical simulation method based on a centrally lumped mass three-node element provided in the above embodiments, and other technical features in this conductor galloping numerical simulation device based on a centrally lumped mass three-node element are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0112] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0113] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0114] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, which are used to execute the wire galloping numerical simulation method based on a centrally concentrated mass three-node unit in the above embodiments.

[0115] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0116] The aforementioned computer-readable storage medium may be included in a numerical simulation apparatus for conductor galloping based on a centrally lumped mass three-node element; or it may exist independently and not assembled into a numerical simulation apparatus for conductor galloping based on a centrally lumped mass three-node element.

[0117] The aforementioned computer-readable storage medium carries one or more programs, which, when executed by the aforementioned one or more programs, cause the conductor galloping numerical simulation device based on the centrally lumped mass three-node element to perform the conductor galloping numerical simulation based on the centrally lumped mass three-node element.

[0118] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0119] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0120] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0121] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described numerical simulation method for conductor galloping based on a centrally lumped mass three-node element. This addresses the technical problem of improving the efficiency of large-scale engineering simulation calculations. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the numerical simulation method for conductor galloping based on a centrally lumped mass three-node element provided in the above embodiments, and will not be elaborated upon here.

[0122] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element.

[0123] The computer program product provided in this application can solve the technical problem of how to improve the computational efficiency of large-scale engineering simulation. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the conductor galloping numerical simulation method based on a centrally concentrated mass three-node element provided in the above embodiments, and will not be repeated here.

[0124] The above description is only a part of the embodiments of this application and does not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. A numerical simulation method of conductor galloping based on a central lumped mass three-node element, characterized by, The method includes: Based on the conductor model information, the conductor is discretized into multiple three-node units, wherein the three-node unit includes a first end node, a second end node, and a center node; Determine the net external force at the center node of the three-node unit at the current moment, and establish the dynamic equation based on the net external force; Based on the dynamic equations, predict the coordinates of the central node of the three-node unit at the next moment; Based on the geometric relationship between the center nodes of adjacent three-node units, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node units at the next time step, the internal equilibrium equation is established and solved to obtain the coordinates of the end nodes shared by the adjacent three-node units at the next time step. The coordinates of the end nodes shared by each of the adjacent three-node units at the next moment are used as the output result of the conductor galloping simulation. The process of establishing and solving the internal equilibrium equations based on the geometric relationship between the center nodes of adjacent three-node units, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node units at the next time step, to obtain the coordinates of the shared end nodes of the adjacent three-node units at the next time step, includes: Based on the geometric relationship between the center nodes of adjacent three-node units, the first three-node unit and the second three-node unit are determined, wherein the first three-node unit and the second three-node unit are adjacent, and the second end node of the first three-node unit is the first end node of the second three-node unit; The centroid distance between adjacent units is obtained based on the coordinates of the center node of the first three-node unit at the next time step and the coordinates of the center node of the second three-node unit at the next time step. Based on the distance between the centroids of adjacent units, the second elastic stiffness and the second initial distance corresponding to the first three-node unit, and the first elastic stiffness and the first initial distance corresponding to the second three-node unit, an internal equilibrium equation is established in conjunction with the internal force equilibrium condition. Solve the internal equilibrium equation to obtain the coordinates of the second end node of the first three-node unit at the next time step; The coordinates of the second end node of the first three-node unit at the next time step are used as the coordinates of the end node shared by the adjacent three-node units at the next time step.

2. The method as described in claim 1, characterized in that, Determining the net external force at the central node of the three-node unit at the current moment includes: Based on the coordinates of the first end node, the second end node, and the center node of the three-node element in the world coordinate system, the internal force of the center node is obtained. The gravity is obtained based on the mass of the three-node unit; The aerodynamics are obtained based on the preset environmental parameters and the length of the three-node unit; The internal force of the central node, the gravity, and the aerodynamic force are taken as the resultant external force of the central node of the three-node unit at the current moment.

3. The method as described in claim 2, characterized in that, The process of obtaining the internal force at the central node based on the coordinates of the first end node, the second end node, and the central node of the three-node element in the world coordinate system includes: Obtain the local coordinate system corresponding to the three-node unit; Based on the coordinates of the first end node, the second end node, and the center node of the three-node element in the world coordinate system, the internal forces of the first end node and the second end node are obtained. Based on the internal forces of the first end node and the second end node, the expression for the internal force of the center node in the local coordinate system is obtained; The internal force expression of the center node in the local coordinate system is transformed by the rotation matrix between the local coordinate system and the world coordinate system to obtain the internal force expression of the center node in the world coordinate system. The internal forces of the central node are determined based on the expression of the internal forces of the central node in the world coordinate system.

4. The method as described in claim 3, characterized in that, The process of obtaining the internal forces at the first and second end nodes based on the coordinates of the first end node, the second end node, and the center node of the three-node element in the world coordinate system includes: Obtain the coordinates of the first end node, the second end node, the center node, the first elastic stiffness, the second elastic stiffness, the first initial distance, and the second initial distance of the three-node unit in the world coordinate system. The first elastic stiffness refers to the elastic stiffness of the conductor segment formed by the first end node and the center node, the second elastic stiffness refers to the elastic stiffness of the conductor segment formed by the second end node and the center node, the first initial distance refers to the initial distance between the first end node and the center node, and the second initial distance refers to the initial distance between the second end node and the center node. Based on the coordinates of the first end node, the coordinates of the center node, the first elastic stiffness, and the first initial distance, the internal force of the first end node is obtained; The internal force of the second end node is obtained based on the coordinates of the second end node, the coordinates of the center node, the second elastic stiffness, and the second initial distance.

5. The method as described in claim 2, characterized in that, The preset environmental parameters include air density, relative wind speed, drag coefficient, lift coefficient, effective angle of attack, and conductor diameter; The aerodynamics obtained based on preset environmental parameters and the length of the three-node unit include: Aerodynamic drag is obtained based on the air density, relative wind speed, conductor diameter, drag coefficient, effective angle of attack, and length of the three-node unit. The aerodynamic lift is obtained based on the air density, relative wind speed, conductor diameter, lift coefficient, effective angle of attack, and length of the three-node unit. The aerodynamic drag and the aerodynamic lift are used as the aerodynamic forces of the three-node unit.

6. The method as described in claim 1, characterized in that, The step of predicting the coordinates of the center node of the three-node unit at the next moment based on the dynamic equation includes: Based on the aforementioned dynamic equations, the expression for the acceleration of the center of mass is obtained; Based on the centroid acceleration expression, the acceleration vector corresponding to the center node of the three-node unit at the next moment is obtained; By integrating the acceleration vector corresponding to the center node of the three-node unit over time, the coordinates of the center node of the three-node unit at the next time step can be obtained.

7. A numerical simulation device for conductor galloping based on a centrally lumped mass three-node element, characterized in that, The device includes: The partitioning module is used to discretize the conductor into multiple three-node units based on the conductor model information, wherein the three-node unit includes a first end node, a second end node, and a center node; A module is established to determine the net external force at the center node of the three-node unit at the current moment, and to establish a dynamic equation based on the net external force. The prediction module is used to predict the coordinates of the center node of the three-node unit at the next moment based on the dynamic equation. The solution module is used to establish and solve the internal equilibrium equation based on the geometric relationship between the center nodes of adjacent three-node elements, the internal force equilibrium conditions, and the coordinates of the center nodes of the three-node elements at the next time step, so as to obtain the coordinates of the end nodes shared by the adjacent three-node elements at the next time step. The output module is used to output the coordinates of the end nodes shared by the adjacent three-node units at the next moment as the output result of the conductor galloping simulation. The solution module is further configured to determine the first three-node unit and the second three-node unit based on the geometric relationship between the center nodes of adjacent three-node units, wherein the first three-node unit and the second three-node unit are adjacent, and the second end node of the first three-node unit is the first end node of the second three-node unit; obtain the centroid distance between adjacent units based on the coordinates of the center nodes of the first three-node unit and the second three-node unit at the next time step; establish an internal equilibrium equation based on the centroid distance between adjacent units, the second elastic stiffness and the second initial distance corresponding to the first three-node unit, and the first elastic stiffness and the first initial distance corresponding to the second three-node unit, combined with the internal force equilibrium condition; solve the internal equilibrium equation to obtain the coordinates of the second end node of the first three-node unit at the next time step; and use the coordinates of the second end node of the first three-node unit at the next time step as the coordinates of the end node shared by the adjacent three-node units at the next time step.

8. A numerical simulation device for conductor galloping based on a centrally lumped mass three-node element, characterized in that, The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element as described in any one of claims 1 to 6.

9. A storage medium, characterized in that, The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, it implements the steps of the numerical simulation method for conductor galloping based on a centrally concentrated mass three-node element as described in any one of claims 1 to 6.

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