Flexible belt net folding modeling and unfolding dynamics simulation method

Abstract

The invention discloses a flexible belt net folding modeling and unfolding dynamics simulation method, which comprises the following steps of: firstly, constructing a geometric folding model, following a crease-strip alignment principle, ensuring that a crease strictly falls on an entity strip to ensure kinematics continuity, and calculating initial tensile strain and in-plane shear strain in a folding state; converting the pre-stress field into an initial pre-stress field to simulate an internal energy state of high-density folding; then, a membrane unit aerodynamic resistance model based on the instantaneous projection area is introduced into finite element simulation for dynamic solution; and finally, the expansion stability and the effective interception time window of the band network are quantitatively evaluated based on the node time history data, and the physical authenticity and the prediction precision of the flexible band network in expansion of dynamic simulation in the low-altitude protection scene are remarkably improved. According to the method, the problem of high-precision simulation of the whole process of the flexible belt net from folding storage to dynamic unfolding is effectively solved, and reliable method support is provided for parameter design and performance evaluation of the low-altitude interception net.

Description

Technical Field

[0001] This invention belongs to the field of low-altitude security defense and computational mechanics technology, and in particular, it is a method for flexible mesh folding modeling and unfolding dynamics simulation. Background Technology

[0002] Flexible interception net technology, with its significant advantages such as light weight, high folding and storage ratio, and large unfolded area, has become an important means of countering the threat of "low, slow, and small" targets in the field of low-altitude defense. In low-altitude defense scenarios, the interception net needs to be deployed and stably intercept targets within a very short time and limited space. Compared with rope nets woven from one-dimensional ropes, flexible strip nets have continuous two-dimensional planar structural characteristics. Their in-plane tensile and shear mechanical behavior is similar to that of a continuous medium film, thus possessing superior target containment performance and stress wave transmission dissipation mechanism, making them more suitable for low-altitude high-intensity defense missions.

[0003] However, for flexible strip nets used in low-altitude protection, there are still many technical bottlenecks in the existing technology for folding modeling and deployment dynamics simulation. First, there is a compatibility problem between discrete structures and continuous folding strategies. Flexible strip nets are composed of solid strips and discrete meshes, not ideal continuous films, and traditional folding modeling often ignores the geometric positional relationship between "creases" and "mesh openings." If creases cross the mesh openings during modeling, the folding mechanism will fail kinematically, failing to reflect the real physical constraints, and is prone to entanglement during rapid deployment at low altitudes, leading to protection failure. Second, the lack of an initial prestress field leads to simulation distortion. In conventional finite element simulations, flexible nets are often idealized to begin deployment in a stress-free state. However, in reality, to meet the miniaturization requirements of low-altitude protection devices, the strip net is in a high-density folded state, and its interior will generate significant initial tensile strain and in-plane shear strain due to forced bending and geometric compression. Ignoring these initial prestresses will lead to a serious deviation between the prediction of energy release and dynamic response in the early stage of deployment and reality. Finally, the existing aerodynamic drag models lack dimensionality. Existing dynamic modeling methods mostly follow the "lumped mass spring model" or "absolute nodal coordinate method" for rope nets, calculating aerodynamic drag based on one-dimensional rod and cable elements. This method cannot accurately describe the instantaneous projected area change and distributed drag characteristics of the flexible net as a two-dimensional panel in the flow field, resulting in insufficient prediction accuracy for low-altitude deployment speed, shape, and effective interception window.

[0004] Therefore, there is an urgent need for a folding modeling strategy that can take into account the discrete pore characteristics of the flexible mesh, and combine it with a finite element simulation method that considers the initial prestress and two-dimensional aerodynamic characteristics, so as to achieve accurate prediction of the unfolding behavior of the flexible mesh. Summary of the Invention

[0005] The purpose of this invention is to provide a method for modeling and simulating the unfolding dynamics of flexible strip meshes. By establishing a geometric mapping that aligns "creases" and "strips", the invention solves the problem of modeling the folding of discrete strip meshes. It also introduces a folding prestress field and a membrane unit aerodynamic model based on the instantaneous projected area to improve the accuracy of the unfolding dynamics simulation of flexible strip meshes in low-altitude protection scenarios.

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] A method for modeling and simulating the unfolding dynamics of flexible mesh folding includes:

[0008] Step 1: Discretize the flexible mesh into multiple parallelogram mesh pieces, and arrange them periodically using the Miura-Ori origami configuration to obtain a geometric folding model based on the Miura-Ori configuration;

[0009] Step 2: Calculate the initial tensile strain and in-plane initial shear strain of the geometric folding model due to geometric deformation in the folded state, and convert the tensile strain and shear strain into the initial prestress field by combining the material constitutive relation.

[0010] Step 3: Import the geometric folding model generated in Step 1 into the finite element simulation software, assign it material physical properties, and discretize the mesh using four-node M3D4R membrane elements; set the initial prestress field and simulation boundary conditions, establish the connection relationship between the traction body and the flexible mesh, and set the output request for membrane element node coordinate data.

[0011] The deformation geometry nonlinearity of the membrane element is described by the Green-Lagrange strain tensor. The total strain is decomposed into the initial folding strain, linear strain and nonlinear strain. The initial prestress and air resistance load are introduced to establish the virtual work balance equation of the flexible mesh. The time step incremental method is used to transform the virtual work balance equation into the incremental equation of membrane element node dynamics for iterative solution to obtain the time history data of membrane element node position, velocity and acceleration during the entire mesh unfolding process.

[0012] Step 4: Based on the time history data of the membrane unit nodes, perform quantitative analysis on the low-altitude protection performance of the flexible strip net: Traverse each output time step, reconstruct the instantaneous geometric configuration of the strip net using the node coordinates of the membrane unit, calculate the instantaneous deployed projected area and instantaneous flight distance of the entire net, and obtain the area time history curve and distance time history curve; extract the maximum deployed projected area from the area time history curve and determine the flight distance to reach the maximum deployed projected area; according to the preset interception effectiveness threshold, search for continuous time periods that meet the area threshold conditions, and calculate the effective interception time window and the effective interception distance covered by the strip net within the continuous time period.

[0013] The significant advantages of this invention compared to existing technologies are:

[0014] (1) Solved the problem of folding modeling of discrete strip mesh: By using the geometric mapping method of "crease-strip" alignment, the physical feasibility of the Miura-Ori folding configuration on the strip mesh with pore features was ensured. High compression ratio storage and orderly unfolding were achieved by utilizing its single degree of freedom characteristics, effectively avoiding the risk of entanglement.

[0015] (2) Improved physical realism of the initial state: The initial tensile and shear prestress caused by folding were considered, which made up for the dynamic error caused by neglecting the initial strain in the traditional simulation, making the energy release and morphological evolution in the early stage of unfolding more consistent with the actual physical process.

[0016] (3) Improved accuracy of aerodynamic simulation: A membrane element aerodynamic drag model based on instantaneous projected area was proposed. Compared with the traditional one-dimensional line element model, it can more accurately characterize the distributed drag characteristics of two-dimensional mesh structure in the flow field and the influence of in-plane shear deformation on aerodynamic load. Attached Figure Description

[0017] Figure 1 This is a simulation flowchart of the flexible strip mesh of the present invention;

[0018] Figure 2 This is the overall configuration of the flexible mesh in the embodiments of the present invention;

[0019] Figure 3 This is a schematic diagram of the mesh discretization and geometric mapping of the present invention;

[0020] Figure 4 This is a schematic diagram of the complete flexible mesh Miura-Ori folding geometry constructed in an embodiment of the present invention;

[0021] Figure 5 This is a schematic diagram of the aerodynamic drag force analysis of the membrane unit based on the instantaneous projected area according to the present invention;

[0022] Figure 6 A schematic diagram illustrating the construction of a finite element simulation model based on membrane units in an embodiment of the present invention;

[0023] Figure 7 It is the time history evolution result of the dynamic simulation of the flexible strip net deployment in the embodiment of the invention. Detailed Implementation

[0024] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0025] The present invention provides a method for modeling and simulating the unfolding dynamics of a flexible mesh folding system, comprising the following steps:

[0026] Step 1: Construct a geometric folding model based on the Miura-Ori configuration and import it into the finite element simulation software as the initial geometric model. Discretize the flexible mesh into multiple parallelogram mesh pieces, and arrange them periodically using the Miura-Ori origami configuration. When establishing the periodic geometric mapping, follow the "crease-strip" alignment principle. By adjusting the geometric parameters of the mesh pieces, ensure that all peak and valley creases strictly fall on the solid fabric strips of the mesh, avoiding creases crossing the mesh area, thereby ensuring the kinematic continuity of the folding mechanism on the porous mesh. Figure 3 As shown in the figure. The constructed geometric folding model is then imported into the finite element simulation software as the initial model.

[0027] Step 2: Calculate the initial prestress field in the folded state. Based on the folded geometric parameters, calculate the initial tensile strain and in-plane initial shear strain generated by geometric deformation in the folded state of the geometric folded model. Combined with the material constitutive relation, the tensile strain and shear strain are transformed into the initial prestress field, which is used as the initial condition for the finite element simulation model.

[0028] Step 3: Construct a finite element simulation model incorporating aerodynamic drag and perform dynamic solutions. Import the geometric folding model generated in Step 1 into the finite element simulation software, assign it material physical properties, and discretize the mesh using four-node M3D4R membrane elements. Set the initial prestress field and simulation boundary conditions (mass of the traction body, initial velocity, and launch angle) from Step 2; establish the connection relationship between the traction body and the flexible mesh, and set the output request for membrane element node coordinate data.

[0029] In the dynamic solution stage, the Green-Lagrange strain tensor is used to describe the large deformation geometric nonlinearity of the M3D4R membrane element, decomposing the total strain into initial folding strain, linear strain, and nonlinear strain. In the time-step iteration of the dynamic solution, an aerodynamic drag model based on the instantaneous projected area is introduced: the angle between the normal vector of each membrane element and the relative air velocity vector is calculated in real time, thus obtaining the instantaneous projected area and the corresponding air drag. The drag is then mapped to the membrane element nodes according to the principle of uniform mass distribution. Finally, a virtual work balance equation is established, including elastic deformation energy, initial prestress potential energy, external aerodynamic load work, and inertial force. The time-step incremental method is used to transform the virtual work equation into an incremental finite element nodal dynamic equation for iterative solution, obtaining the time-history evolution data of membrane element nodal positions, velocities, and accelerations throughout the entire mesh unfolding process.

[0030] Step 4: Post-processing of simulation results and performance evaluation. Based on the time history data of the membrane unit nodes obtained in Step 3, the low-altitude protection performance of the flexible belt net is quantitatively analyzed. First, traversing each output time step, the instantaneous geometric configuration of the belt net is reconstructed using the node coordinates of the membrane units. The current shape of each membrane unit is redrawn in three-dimensional space, and all the deformed membrane units are spliced ​​together to form the complete instantaneous geometric configuration of the flexible belt net at that moment. The instantaneous deployed area S(t) and instantaneous flight distance D(t) of the entire net are calculated based on the area of ​​the instantaneous geometric configuration and the coordinates of the net center, obtaining the area-time curve and the distance-time curve. Second, the maximum deployed area S is extracted from the area-time curve. max And determine the flight distance D when the unfolded area is at its maximum at the moment that area is reached. max Finally, based on the preset interception effectiveness threshold coefficient, a continuous time period that meets the area threshold condition is searched, and the effective interception time window ∆t and the effective interception distance ∆d covered by the flexible strip net within that time period are calculated to quantitatively evaluate the deployment stability and interception effectiveness of the flexible strip net.

[0031] In step one, the geometry of the mesh is defined by its length a, width b, acute interior angle β, and dihedral angle θ between adjacent meshes, as follows: Figure 3 As shown. Based on these parameters, a series of derived dimensional parameters (ω, l, v, h) and angular parameters (γ, δ) reflecting the mesh connection relationship can be further derived. These parameters are the core basis for establishing the precise alignment relationship of the "crease-strip", and their calculation formulas are as follows:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] In the formula: a is the length of the mesh; b is the width of the mesh; β is the acute interior angle of the mesh; θ is the dihedral angle between adjacent meshes; γ is the projection angle of the width direction of adjacent meshes on the macroscopic unfolding plane; δ is the projection angle of the length direction of adjacent meshes on the macroscopic unfolding plane; ω is the macroscopic projection length in the width direction of adjacent meshes; l is the macroscopic projection length in the length direction of adjacent meshes; v is the projection component of the mesh side length on the width axis; h is the overall thickness of the folding model; projection refers to the vertical projection along the overall thickness direction of the folding model onto the macroscopic unfolding plane with mesh.

[0039] The single-degree-of-freedom motion process of the flexible mesh from a fully folded state to a fully unfolded state is described by controlling the change of the dihedral angle θ.

[0040] In step two, it is assumed that the Miura-Ori folding deformation is concentrated at the crease, and the initial strain tensor generated by the mesh... From initial tensile strain In-plane initial shear strain Composition. Among them, the initial tensile strain The calculation formula is:

[0041]

[0042] In the formula: a is the original physical length of the mesh; a0 is the geometric projection length of the folded model in the macroscopic unfolding plane. θ is the dihedral angle between adjacent mesh panels.

[0043] In-plane initial shear strain It is generated by coupling the half-tangent of the dihedral angle with the sine of the acute interior angle of the mesh:

[0044]

[0045] In the formula: β is the acute interior angle of the mesh.

[0046] Based on the generalized Hooke's law, the initial strain tensor is transformed into the initial stress field σ0 through the material constitutive matrix D:

[0047]

[0048]

[0049]

[0050] In the formula: E is the elastic modulus of the flexible mesh, and ν is the Poisson's ratio of the flexible mesh.

[0051] In step three, based on the vector relationship between the membrane unit's motion velocity and the airflow velocity, the aerodynamic load on each membrane unit is calculated. Using the principle of uniform mass distribution, the aerodynamic load on the membrane unit is mapped to the four corner nodes, such as... Figure 5 As shown. During the motion of each membrane unit, the direction of air resistance is always parallel to the direction of the relative velocity vector. Air resistance... The following formula is used to derive:

[0052]

[0053] In the formula: ρ is the air density, C D Here, A is the dimensionless drag coefficient (determined by wind tunnel testing), U is the area of ​​the membrane unit, and U is the relative velocity vector between the air and the membrane unit. The unit vector of air velocity in the direction of drag. .

[0054] At time t during the motion, the instantaneous projected area A of the i-th membrane unit is... 0i (t) is:

[0055]

[0056] In the formula: air speed With the membrane unit normal vector The angle between them.

[0057] In step three, the large deformation geometric nonlinearity of the membrane element is described based on the Green-Lagrange strain tensor, and the total strain of the membrane element is... Decomposed into folded initial strain Linear strain and nonlinear strain :

[0058]

[0059] In the formula: For the initial strain tensor of folding, For linear strain tensor, It is a nonlinear strain tensor.

[0060] By introducing initial prestress and air resistance loads, a virtual work equilibrium equation for the flexible mesh is established:

[0061]

[0062]

[0063] In the formula: This refers to the virtual work done inside the flexible mesh (including elastic deformation energy and initial prestress potential energy). For the virtual work done on the flexible belt network (including work done by air resistance), M is the total number of nodes, and F is the virtual work done on the network. d,i air resistance of the membrane unit The air resistance vector assigned to the i-th node. Let i be the virtual displacement vector of the i-th node. This represents the virtual work done by the inertial force of the flexible belt net.

[0064] The virtual work equation is transformed into an incremental equation of membrane unit nodal dynamics using the time-step incremental method for iterative solution:

[0065]

[0066] In the formula: M is the mesh mass matrix, C is the mesh damping matrix, ∆R is the residual force load vector, K T The total tangent stiffness matrix is ​​derived from the linear stiffness matrix K. L Nonlinear stiffness matrix K N and the prestress stiffness matrix K 𝜎0 composition, .

[0067] By solving the equation in finite element software, the displacement increment ∆x, velocity increment ∆v, and acceleration increment ∆a of all membrane element nodes in the mesh at the current time step can be obtained.

[0068] In step four, the specific calculation method for the key performance indicators is as follows:

[0069] (1) Instantaneous unfolded projected area S(t) and maximum unfolded projected area S max To characterize the actual interception capability of the interception net against the target, the projected area of ​​the net is used as the evaluation index. Assume there are N membrane elements in the finite element model, and at time t, the actual projected area of ​​the i-th membrane element is A. 0i (t), the simulation stopping time is denoted as T. end Then the instantaneously unfolded projected area S(t) of the mesh is the sum of the projected areas of all membrane units:

[0070]

[0071] Maximum unfolded projected area S max The peak value of the area-time curve is:

[0072]

[0073] (2) Instantaneous flight distance D(t) and distance D when the unfolded area is at its maximum max Define the geometric centroid of the netted structure as the reference point. Let the centroid coordinates of the launch point at t=0 be P0, and the instantaneous centroid coordinates at time t be P(t). The instantaneous flight distance D(t) is the displacement modulus of the centroid relative to the launch point.

[0074]

[0075] When S(t) reaches its peak value S max The time is denoted as t peak The flight distance at this point is D. max :

[0076]

[0077] (3) Effective Spatiotemporal Window. The effective spatiotemporal window is used to evaluate the ability of the interceptor network to maintain a high deployment rate. The effective interception threshold coefficient is set as η, S theory This represents the theoretical maximum projected area when the netting is fully tiled. Search for conditions that meet the criteria. The continuous time interval Δt and the flight distance range Δd.

[0078] Example

[0079] In this embodiment, the physical parameters of the flexible mesh are set as follows: the mesh has an overall square shape, such as... Figure 2 As shown, the material consists of a uniformly distributed square grid with planar dimensions of 2000mm × 2000mm and mesh sizes of 25mm × 25mm. The grid thickness is 0.5mm, and the material density is 1.44g / cm³. 3 The elastic modulus E = 10.08 GPa and the Poisson's ratio ν = 0.03.

[0080] The specific implementation steps of this method are as follows: Figure 1 As shown:

[0081] Step 1: Construct a geometric folding model based on the Miura-Ori configuration and import it into the finite element simulation software as the initial geometric model. Discretize the flexible mesh into multiple parallelogram mesh pieces, and arrange them periodically using the Miura-Ori origami configuration. When establishing the periodic geometric mapping, follow the "crease-strip" alignment principle. By adjusting the geometric parameters of the mesh pieces, ensure that all peak and valley creases strictly fall on the solid fabric strips of the mesh, avoiding creases crossing the mesh area, thereby ensuring the kinematic continuity of the folding mechanism on the porous mesh. Figure 2As shown. Based on the physical dimensions and discrete requirements of the mesh, the geometric parameters of a single parallelogram mesh are set as follows: mesh length a = 200 mm, mesh width b = 200.39 mm, and acute interior angle β = 86.42°. The dihedral angle θ between adjacent meshes is set as the folding control variable; in this embodiment, the dihedral angle in the initial folded state is set to θ = 26°. Based on the above parameters, a complete flexible mesh Miura-Ori folding geometric model is constructed, as shown. Figure 4 As shown in the image. The constructed geometric folding model is then imported into the Abaqus software as the initial model.

[0082] Step 2: Calculate the initial prestress field in the folded state.

[0083] In the initialization phase of the finite element simulation, the internal prestress caused by high-density folding is considered. It is assumed that the Miura-Ori fold deformation is concentrated at the creases, the mesh body is a rigid panel, and the initial strain is generated by the coupling of the dihedral angle and the mesh geometric parameters. The initial strain tensor of the geometric folding model is... From initial tensile strain In-plane initial shear strain Composition. Among them, the initial tensile strain The calculation formula is:

[0084]

[0085] In the formula: a is the original physical length of the mesh; a0 is the geometric projection length of the folded model in the macroscopic unfolding plane. θ is the dihedral angle between adjacent mesh panels.

[0086] In-plane initial shear strain It is generated by coupling the half-tangent of the dihedral angle with the sine of the acute interior angle of the mesh:

[0087]

[0088] In the formula: β is the acute interior angle of the mesh.

[0089] Based on the generalized Hooke's law, the initial strain tensor is transformed into the initial stress field σ0 through the material constitutive matrix D:

[0090]

[0091]

[0092]

[0093] In the formula: E is the elastic modulus of the flexible mesh, and ν is the Poisson's ratio of the flexible mesh.

[0094] In Abaqus software, the calculated initial stress σ0 is assigned as a field variable to the corresponding membrane unit through the Initial Conditions function and the Stress option in Predefined Field, simulating the prestress state caused by folding storage.

[0095] Step 3: Construct a finite element simulation model that includes aerodynamic drag and perform dynamic solutions.

[0096] The Abaqus / Explicit explicit dynamics solver was used. The geometric folding model generated in step one was imported into the software, and elastic material physical properties were assigned to it. The section type was selected as "Membrane," and the physical thickness was specified. M3D4R membrane elements were used for mesh discretization. The initial prestress field and simulation boundary conditions (mass, initial velocity, and launch angle of the traction body) from step two were set, and a gravity field was defined for the entire system. Component models of the traction body (rigid body) and the traction belt (flexible body) were established separately. The physical connection between the two was simulated using "Tie" constraints to ensure the continuity of kinetic energy transfer. Figure 6 As shown, create a "Dynamic, Explicit" analysis step, and appropriately set the time length, incremental step control parameters, and output request for element node coordinate data.

[0097] In the dynamic solution stage, the Green-Lagrange strain tensor is used to describe the large deformation geometric nonlinearity of the M3D4R membrane element, and the total strain is expressed as... It is decomposed into folded initial strain, linear strain, and nonlinear strain.

[0098]

[0099] In the formula: For the initial strain tensor of folding, For linear strain tensor, It is a nonlinear strain tensor.

[0100] In the time-step loop of the dynamic solution, an aerodynamic drag model based on the instantaneous projected area is introduced: the angle between the normal vector of each membrane element and the relative air velocity vector is calculated in real time, thereby obtaining the instantaneous projected area and the corresponding air drag. The drag is then mapped to the membrane element nodes according to the principle of uniform mass distribution, such as... Figure 5 As shown. During the motion of each membrane unit, the direction of air resistance is always parallel to the direction of the relative velocity vector. Air resistance... The following formula is used to derive:

[0101]

[0102] In the formula: ρ is the air density, C D Here, is the dimensionless drag coefficient (obtained from wind tunnel tests), A is the area of ​​the membrane unit, and U is the relative velocity vector between the air and the membrane unit. The unit vector of air velocity in the direction of drag. .

[0103] The instantaneous projected area A0 of the membrane unit is:

[0104]

[0105] In the formula: air speed With the membrane unit normal vector The angle between them.

[0106] By introducing initial prestress and air resistance loads, a virtual work equilibrium equation for the flexible mesh is established:

[0107]

[0108]

[0109] In the formula: This refers to the virtual work done inside the flexible mesh (including elastic deformation energy and initial prestress potential energy). For the virtual work done on the flexible belt network (including work done by air resistance), M is the total number of nodes, and F is the virtual work done on the network. d,i air resistance of the membrane unit The air resistance vector assigned to the i-th node. Let i be the virtual displacement vector of the i-th node. This represents the virtual work done by the inertial force of the flexible belt net.

[0110] The virtual work equation is transformed into an incremental equation of finite element nodal dynamics using the time-step incremental method for iterative solution.

[0111]

[0112] In the formula: M is the mesh mass matrix, C is the mesh damping matrix, ∆R is the residual force load vector, K T The total tangent stiffness matrix is ​​derived from the linear stiffness matrix K. L Nonlinear stiffness matrix K N and the prestress stiffness matrix K 𝜎0 composition, .

[0113] By solving the equation in finite element software, the displacement increment ∆x, velocity increment ∆v, and acceleration increment ∆a of all membrane element nodes in the mesh at the current time step can be obtained.

[0114] Step 4: Post-processing of simulation results and performance evaluation

[0115] After the solution is completed, the morphological evolution sequence of the flexible strip mesh during the unfolding process is extracted in the Visualization module, such as... Figure 7 As shown. By traversing each output time step, the instantaneous geometry of the mesh is reconstructed using the node coordinates of the membrane elements. The instantaneous unfolded area S(t) and instantaneous flight distance D(t) of the entire mesh are calculated, yielding area-time and distance-time curves. The maximum unfolded area S is extracted from the time history curves. max And determine the flight distance D when the unfolded area is at its maximum at the moment that area is reached. max Based on the preset interception effectiveness threshold, a continuous time period that meets the area threshold condition is searched, and the effective interception time window ∆t and the effective interception distance ∆d covered by the flexible strip net within that time period are calculated to quantitatively evaluate the deployment stability and interception effectiveness of the flexible strip net.

[0116] Through the above implementation in the Abaqus environment, the entire process of flexible strip mesh from folded storage to dynamic deployment can be simulated efficiently and accurately, providing a reliable simulation platform for the parameter design, performance prediction and optimization of interception systems.

[0117] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for modeling and simulating the unfolding dynamics of a flexible mesh folding system, characterized in that, include: Step 1: Discretize the flexible mesh into multiple parallelogram mesh pieces, and arrange them periodically using the Miura-Ori origami configuration to obtain a geometric folding model based on the Miura-Ori configuration; Step 2: Calculate the initial tensile strain and in-plane initial shear strain of the geometric folding model due to geometric deformation in the folded state, and convert the tensile strain and shear strain into the initial prestress field by combining the material constitutive relation. Step 3: Import the geometric folding model generated in Step 1 into the finite element simulation software, assign it material physical properties, and discretize the mesh using four-node M3D4R membrane elements; set the initial prestress field and simulation boundary conditions, establish the connection relationship between the traction body and the flexible mesh, and set the output request for membrane element node coordinate data. Based on the Green-Lagrange strain tensor to describe the deformation geometric nonlinearity of the membrane unit, the total strain is decomposed into folding initial strain, linear strain and nonlinear strain. The initial prestress and air resistance load are introduced to establish the virtual work balance equation of the flexible belt mesh. The virtual work balance equation is transformed into an incremental equation of membrane element node dynamics by using the time step incremental method, and the time history data of membrane element node position, velocity and acceleration are obtained throughout the entire process of mesh unfolding. Step 4: Based on the time history data of the membrane unit nodes, perform quantitative analysis on the low-altitude protection performance of the flexible strip net: Traverse each output time step, reconstruct the instantaneous geometric configuration of the strip net using the node coordinates of the membrane unit, calculate the instantaneous deployed projected area and instantaneous flight distance of the entire net, and obtain the area time history curve and distance time history curve; extract the maximum deployed projected area from the area time history curve and determine the flight distance to reach the maximum deployed projected area; according to the preset interception effectiveness threshold, search for continuous time periods that meet the area threshold conditions, and calculate the effective interception time window and the effective interception distance covered by the strip net within the continuous time period.

2. The flexible strip mesh folding modeling and unfolding dynamics simulation method according to claim 1, characterized in that, When arranging the mesh periodically, the "crease-strip" alignment principle is followed. By adjusting the geometric parameters of the mesh, it is ensured that all peak and valley creases fall precisely on the solid fabric strips with the mesh, avoiding creases from crossing the mesh area.

3. The flexible strip mesh folding modeling and unfolding dynamics simulation method according to claim 1, characterized in that, The initial prestress field is: ； In the formula , ; ， ； Where D is the material constitutive matrix. The initial tensile strain. ν is the initial in-plane shear strain, E is the elastic modulus of the flexible mesh, ν is the Poisson's ratio of the flexible mesh, a is the mesh length, a0 is the geometric projection length of the folded model in the macroscopic unfolding plane, θ is the dihedral angle between adjacent meshes, and β is the acute interior angle of the mesh.

4. The flexible strip mesh folding modeling and unfolding dynamics simulation method according to claim 1, characterized in that, Initial prestress includes folding initial strain Linear strain and nonlinear strain : For initial prestress; The air resistance load is: In the formula: ρ is the air density, C D Let A be the dimensionless drag coefficient, A be the area of ​​the membrane unit, and U be the relative velocity vector between the air and the membrane unit. The unit vector of air velocity in the direction of drag; The virtual work balance equation for the flexible belt mesh is: This represents the virtual work done inside the flexible mesh. For the external virtual work of the flexible strip network, M is the total number of nodes, and F is the virtual work. d,i Assign the air resistance vector of the membrane unit to the i-th node. Let i be the virtual displacement vector of the i-th node. The virtual work done by the inertial force of the flexible belt net; The incremental equation for the nodal dynamics of the membrane unit is: In the formula: M is the mesh mass matrix, C is the mesh damping matrix, ∆R is the residual force load vector, K T This is the total tangent stiffness matrix.

5. The flexible strip mesh folding modeling and unfolding dynamics simulation method according to claim 1, characterized in that, instantaneously The unfolded projected area is the sum of the projected areas of all membrane units: Where N is the membrane element format in the finite element model. The actual projected area of ​​the i-th membrane unit; The maximum unfolded projected area is the peak value of the area time history curve: Where T end This is the simulation stopping time; The flight distance to reach the maximum deployed projected area is S(t), and the peak value is S. max The instantaneous flight distance D(t) is the displacement modulus of the center of mass relative to the launch point. P0 is the centroid coordinate of the launch point at time t=0, and P(t) is the instantaneous centroid coordinate at time t.

6. The flexible strip mesh folding modeling and unfolding dynamics simulation method according to claim 5, characterized in that, The effective interception time window and the effective interception distance with network coverage within that continuous time period are calculated by searching for conditions. The continuous time interval Δt and flight distance range Δd are obtained; where S theory η is the theoretical maximum projected area when the net is fully laid flat, and η is the set effective interception threshold coefficient.

Images