A contact dynamics analysis method for flexible cable net systems based on incremental potential energy

Abstract

The application discloses a flexible rope net system contact dynamics analysis method based on incremental potential energy, relates to the technical field of nonlinear net structure analysis, solves the technical problem that dynamics analysis of flexible rope net system contact with a target is relatively complex, and the technical solution is as follows: total energy of the flexible rope net system is obtained according to elastic total potential energy and incremental total potential energy; new node positions in the contact process of the flexible rope net system and the target are updated according to the total energy, and the new node positions are continuously optimized to ensure that the total energy is minimum, and the total energy in each time step is obtained; the minimum value of the total energy in each time step is calculated to obtain the overall freedom degree vector of the flexible rope net system at the next moment; the node positions are obtained according to the overall freedom degree vector, and the contact dynamics analysis of the flexible rope net system is completed according to the node positions. The dynamics analysis difficulty of the flexible rope net system is reduced, and the grabbing efficiency of the flexible rope net system is improved.

Description

Technical Field

[0001] This application relates to the field of nonlinear network structure analysis technology, and in particular to a contact dynamics analysis method for flexible rope net systems based on incremental potential energy. Background Technology

[0002] With the increasing intensity and frequency of human space exploration, space debris (including defunct spacecraft, satellites, etc.) has become a serious factor affecting the safety of spacecraft. Currently, the most widely used method for debris removal is the flexible rope net system grasping method. However, because the contact dynamics between the flexible rope net system and the debris is a highly nonlinear contact dynamics problem, convergence using current analysis methods is difficult.

[0003] Therefore, in order to further advance the theoretical analysis and safe application of the grasping process of flexible rope net systems, this invention proposes a contact dynamics analysis method for flexible rope net systems based on incremental potential energy. Summary of the Invention

[0004] This application provides a contact dynamics analysis method for flexible rope net systems based on incremental potential energy. The technical purpose is to perform dynamic analysis on the contact process between the flexible rope net system and the target based on contact potential energy, thereby reducing the analysis difficulty and improving the grasping efficiency of the flexible rope net system.

[0005] The above-mentioned technical objective of this application is achieved through the following technical solution:

[0006] A contact dynamics analysis method for flexible rope-net systems based on incremental potential energy, comprising:

[0007] S1: Discretize the flexible rope net system according to the actual geometric shape and material parameters of the flexible rope net system, and calculate the total elastic potential energy of the discretized flexible rope net system.

[0008] S2: Calculate the incremental total potential energy of the flexible rope net system in contact with the target;

[0009] S3: Obtain the total energy of the flexible rope net system based on the total elastic potential energy and the incremental total potential energy;

[0010] S4: Update the new node positions of the flexible rope net system during the contact process with the target based on the total energy, and continuously optimize the new node positions to ensure that the total energy is minimized, thus obtaining the total energy within each time step;

[0011] S5: Calculate the minimum total energy within each time step to obtain the overall degree of freedom vector of the flexible rope net system at the next moment;

[0012] S6: Obtain the node positions based on the overall degree of freedom vector, and complete the contact dynamics analysis of the flexible rope net system based on the node positions.

[0013] The beneficial effects of this application are as follows: The contact dynamics analysis method for flexible rope net systems based on incremental potential energy described in this application discretizes the flexible rope net system according to the actual geometric shape and material parameters of the flexible rope net system, calculates the total elastic potential energy of the discretized flexible rope net system, calculates the incremental total potential energy of the flexible rope net system in contact with the target, obtains the total energy of the flexible rope net system based on the total elastic potential energy and the incremental total potential energy, updates the new node positions during the contact process between the flexible rope net system and the target based on the total energy, and continuously optimizes the new node positions to ensure that the total energy is minimized, obtaining the total energy within each time step, calculates the minimum value of the total energy within each time step to obtain the overall degree of freedom vector of the flexible rope net system at the next moment, obtains the node positions based on the overall degree of freedom vector, and completes the contact dynamics analysis of the flexible rope net system based on the node positions. This reduces the difficulty of dynamics analysis of flexible rope net systems and improves the grasping efficiency of flexible rope net systems. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of a flexible rope net system;

[0015] Figure 2 This is a schematic diagram showing the minimum distance between two units;

[0016] Figure 3 A schematic diagram showing the calculation parameters for elastic tensile potential energy and elastic bending potential energy;

[0017] Figure 4 This is a schematic diagram showing the calculation results of the node positions. Detailed Implementation

[0018] The technical solution of this application will be described in detail below with reference to the accompanying drawings.

[0019] The contact dynamics analysis method for a flexible rope net system based on incremental potential energy described in this application includes:

[0020] S1: Discretize the flexible rope net system based on the actual geometric shape and material parameters, and calculate the total elastic potential energy of the discretized flexible rope net system.

[0021] Specifically, the geometry of the flexible rope net system includes the side length of the flexible net, the length of the discrete unit of the flexible net, and the number of discrete nodes. The material parameters of the flexible rope net system include the elastic modulus, density, and cross-sectional area of ​​the rope.

[0022] As a specific embodiment, the flexible rope net system in this application is composed of a hexagonal net structure.

[0023] To simulate the deformation behavior of a flexible net structure under mechanical loads, the flexible rope net system is discretized, and the total elastic potential energy of the discretized flexible rope net system is calculated, including:

[0024] Discretize each side of the flexible rope net system into N nodes, then the vector representation of the i-th node is x. i =(x i ,y i ,z i );

[0025] like Figure 1 As shown, the two nodes {x i ,x j The relative deformation between}, i.e., the elastic tensile potential energy, is expressed as:

[0026]

[0027] Where EA represents tensile stiffness; e ij =x j -x i This represents the edge vector between the j-th node and the i-th node;

[0028] The relative deformation between the two sides, i.e., the elastic bending potential energy, can be expressed as:

[0029]

[0030] Where EI represents bending stiffness; Let represent the positive vector of the ij-th edge. Let $\mathbf{jk}$ represent the positive vector of the $jk$-th edge. This represents the average length of two adjacent edges ij and jk; relevant calculation parameters are as follows: Figure 3 As shown.

[0031] Therefore, the total elastic potential energy of the flexible rope net system is N. s One elastic tension unit and N b The sum of the elastic bending elements is expressed as:

[0032]

[0033] S2: Calculate the incremental total potential energy of the flexible rope net system in contact with the target.

[0034] Specifically, the distance between two edges is defined as a constrained optimization problem, expressed as:

[0035]

[0036] The distance from a node to a triangular cell is defined as a constrained optimization problem, expressed as:

[0037]

[0038] When both constraint optimization problems described by equations (4) and (5) are applied, the minimum distance between elements is the relationship between points, such as... Figure 2 As shown in (a), the minimum distance is defined as:

[0039] d PP =|x i -x j |;(6)

[0040] When only one constraint optimization problem is applied in equations (4) and (5), the minimum distance between elements is the relationship between points and edges, such as... Figure 2 As shown in (b), the minimum distance is defined as:

[0041]

[0042] When no constraints are applied, the minimum distance between elements is the relationship between faces, such as... Figure 2 As shown in (c) and (d), the minimum distance is defined as:

[0043]

[0044] In summary, equation (5) can be simplified to:

[0045]

[0046] The minimum distance between the aforementioned units includes the minimum distance between points, between points and lines, between points and surfaces, between lines, between lines and surfaces, and between surfaces.

[0047] When two edges are parallel, equation (8) will have a denominator of 0. In this case, this application simplifies the relationship between edges to the relationship between points and edges. The non-penetrating condition of the k-th element in the flexible rope net system is then expressed by incremental potential energy as follows:

[0048]

[0049] Among them, C k (d k ) represents the contact potential energy between the k-th unit and the target when they approach each other; d k The k-th element represents the minimum Euclidean distance between the k-th element and the target; K represents the potential stiffness. Indicates the distance of the trap.

[0050] Therefore, the flexible rope net system and the target's N c The total potential energy of the non-penetrating increment of a contact unit can be expressed as:

[0051]

[0052] The aforementioned incremental potential energy is the contact potential energy between the flexible rope net system and the target, which increases as the contact distance decreases.

[0053] S3: The total energy of the flexible rope net system is obtained based on the total elastic potential energy and the incremental total potential energy.

[0054] Specifically, the total energy of the flexible rope net system S Represented as:

[0055]

[0056] Where q represents the overall degree of freedom vector of the flexible rope net system; Let S denote the diagonal mass matrix; T denotes the extremum of S on an acceptable set of trajectories for a flexible rope net system considering contact; t denotes time.

[0057] S4: Update the new node positions of the flexible rope net system during the contact process with the target based on the total energy, and continuously optimize the new node positions to ensure that the total energy is minimized, thus obtaining the total energy within each time step.

[0058] Specifically, to minimize the total energy, this application updates the time step of the new node position using the Eulerian method. The total energy within each time step is then expressed as:

[0059]

[0060] Where h represents the time step; q represents the global degree of freedom vector of the flexible rope net system at the next moment, which needs to be solved. t This represents the overall degree of freedom vector of the flexible rope net system at time t. This represents the velocity of the flexible rope net system at time t.

[0061] S5: Calculate the minimum total energy within each time step to obtain the overall degree of freedom vector of the flexible rope net system at the next moment.

[0062] If the node positions can be obtained by calculating the minimum value, then the overall degree of freedom vector of the flexible rope net system at the next moment can be expressed as:

[0063]

[0064] According to q t+1 To obtain the node positions, q ≡ [x0, x1, ..., x i ,...,x N-1 ]T ,i∈[0,N-1].

[0065] S6: Obtain the node positions based on the overall degree of freedom vector, and complete the contact dynamics analysis of the flexible rope net system based on the node positions.

[0066] Specifically, by using Newton's optimization algorithm to solve the above problem, the node position information of the flexible rope net system during the grasping process can be obtained, and the calculation results are as follows: Figure 4 As shown.

[0067] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations of these embodiments within the scope of the principles and technical concept of the present invention still fall within the protection scope of the present invention.

Claims

1. A contact dynamics analysis method for a flexible rope-net system based on incremental potential energy, characterized in that, include: S1: Discretize the flexible rope net system based on its geometry and material parameters, and calculate the total elastic potential energy of the discretized flexible rope net system; wherein, each side of the flexible rope net system is discretized into... The nth node, then the nth The vector representation of the nodes is as follows ; S2: Calculate the incremental total potential energy of the flexible rope net system in contact with the target, including: Define the distance between two edges as a constrained optimization problem, expressed as: ，（4）； The distance from a node to a triangular cell is defined as a constrained optimization problem, expressed as: ，（5）； When both constraint optimization problems described by equations (4) and (5) are applied, the minimum distance between elements is the relationship between points, defined as: ，（6）； When only one constraint optimization problem is applied in equations (4) and (5), the minimum distance between elements is the relationship between points and edges, defined as: ，（7）； When no constraints are applied, the minimum distance between elements is the relationship between faces, defined as: （8）； In summary, equation (5) can be simplified to: ，（9）； The first flexible rope net system The non-penetration condition of each unit is expressed by incremental potential energy as follows: ，（10）； in, Indicates the first The incremental potential energy between units when they approach the target; Indicates the first The minimum Euclidean distance between each unit and the target; Indicates potential energy stiffness; Indicates the distance of the trap; Therefore, the flexible rope net system and the target The total potential energy of the non-penetrating increment of a contact unit can be expressed as: ，（11）； S3: Obtain the total energy of the flexible rope net system based on the total elastic potential energy and the incremental total potential energy; S4: Update the new node positions of the flexible rope net system during the contact process with the target based on the total energy, and continuously optimize the new node positions to ensure that the total energy is minimized, thus obtaining the total energy within each time step; S5: Calculate the minimum total energy within each time step to obtain the overall degree of freedom vector of the flexible rope net system at the next moment; S6: Obtain the node positions based on the overall degree of freedom vector, and complete the contact dynamics analysis of the flexible rope net system based on the node positions.

2. The method as described in claim 1, characterized in that, In step S1, the geometry of the flexible rope net system includes the side length of the flexible net, the length of the discrete unit of the flexible net, and the number of discrete nodes. The material parameters of the flexible rope net system include the elastic modulus, density, and cross-sectional area of ​​the rope.

3. The method as described in claim 1, characterized in that, In step S1, the flexible rope net system is discretized, and the total elastic potential energy of the discretized flexible rope net system is calculated, including: The relative deformation between two nodes, i.e., the elastic tensile potential energy, is expressed as: ；（1） in, Indicates tensile stiffness; Indicates the first The node and the first Edge vectors between nodes; The relative deformation between the two sides, i.e., the elastic bending potential energy, can be expressed as: （2） in, Indicates bending stiffness; Indicates the first The positive vector of the edge, Indicates the first The positive vector of the edge; Indicates two adjacent edges , The average length; The total elastic potential energy of the flexible rope net system can be expressed as: ，（3）。 4. The method as described in claim 3, characterized in that, When two sides are parallel, the relationship between sides in equation (8) is simplified to the relationship between points and sides.

5. The method as described in claim 4, characterized in that, In step S3, the total energy of the flexible rope net system Represented as: ，（12）； in, This represents the overall degree of freedom vector of the flexible rope net system; Represents the diagonal mass matrix; The flexible rope net system that takes into account contact makes Extreme values ​​on an acceptable set of trajectories; Indicates time.

6. The method as described in claim 5, characterized in that, Step S4 includes: By updating the time step of the new node position using the Euler method, the total energy within each time step is expressed as: ，（13）； in, Indicates the time step; ; Indicates the current The overall degree of freedom vector of the flexible rope net system at time t. Indicates the current The speed of the flexible rope net system at any given moment.

7. The method as described in claim 6, characterized in that, In step S5, the overall degree of freedom vector of the flexible rope net system at the next moment is expressed as: ，（14）； according to Get the node position. .

Images