A cross-shaped umbrella multi-dimensional numerical folding modeling method based on finite element simulation

Abstract

The application discloses a cross-shaped umbrella multi-dimension numerical folding modeling method based on finite element simulation, and the method can realize the establishment of an umbrella system simulation model close to a real initial folding state, lays a foundation for the next stage of relatively real simulation to reproduce the cross-shaped umbrella opening process and obtain the opening process data required by design, and ensures the realization of rapid iteration optimization in the cross-shaped umbrella research and development process.

Description

Technical Field

[0001] This invention belongs to the field of cross-shaped umbrella simulation technology, and particularly relates to a multi-dimensional numerical folding modeling method for cross-shaped umbrellas based on finite element simulation. Background Technology

[0002] The cruciform parachute is one of many parachute structural types, possessing advantages such as simple manufacturing, good stability, and low dynamic load during opening. It is commonly used as a deceleration tool to shorten the landing roll distance of aircraft, and in recent years has also been used as a stabilizing deceleration device for air-dropped naval weapons and low-speed descent high-altitude probe experiments. The opening process of a cruciform parachute includes three stages: straightening, inflation, and stabilization. The straightening and inflation stages are characterized by strong nonlinear time-varying fluid-structure interaction, and these periods are crucial for obtaining important characteristic parameters of the cruciform parachute, such as straightening force, canopy shape change, stress on the canopy, opening dynamic load, and inflation time. With the development of computer technology and the improvement of finite element simulation accuracy, it has become possible to obtain numerical solutions for the characteristic parameters of the cruciform parachute opening process. This overcomes the constraints of time and budget in experimental research and solves the current difficulties in obtaining some experimental parameters. Furthermore, the results can be displayed on a screen, allowing for a direct observation of canopy deformation and the loading process. Establishing a folding model of the cruciform parachute is the focus of simulation research on the cruciform parachute opening process.

[0003] In practical use, the components of a cross-shaped umbrella are connected according to a specific procedure, and then packaged into a canopy after warp and weft folds, following a defined packaging and folding process. This constitutes the true initial state of the cross-shaped umbrella during its opening process. Currently, scholars both domestically and internationally studying numerical simulations of cross-shaped umbrellas generally use a "☆"-shaped fold (which belongs to the warp fold of the canopy) to model the canopy inflation process. This approach relies on two assumptions: "the canopy model is an axisymmetric structure before inflation" and "the canopy has a certain air inlet size in its initial state." While simulation studies based on this model ensure the accuracy of the average opening load and canopy area obtained when the canopy is fully inflated, the deformation process during the coupling of the canopy and the flow field differs significantly from the dynamic load and the actual opening state. Furthermore, it is impossible to study the straightening process of the umbrella system. Some domestic scholars have also adopted the direct folding method and proposed a "Z"-shaped folding modeling method for parachutes based on initial matrix correction (which is a simple latitudinal folding method). Since it is necessary to avoid the penetration of adjacent layers of canopy at the bend, the folding density is relatively low. Compared with the dense warp and latitudinal folds during actual packaging, the initial stacking shape of the canopy is significantly different, which will inevitably affect the parachute deployment process. Summary of the Invention

[0004] Purpose of the invention

[0005] To overcome the current situation where the modeling of the cross-shaped umbrella's "☆" folding form differs significantly from the actual packaging state and cannot fully capture the characteristic parameters of the opening process, this invention provides a multi-dimensional numerical folding modeling method for cross-shaped umbrellas based on finite element simulation. This method enables the establishment of a simulation model of the umbrella system that closely approximates the actual initial folding state, laying the foundation for a more realistic simulation reproduction of the cross-shaped umbrella's opening process and the acquisition of the opening process data required for design in the next stage. This ensures rapid iterative optimization in the cross-shaped umbrella R&D process.

[0006] Invention Technology Solutions

[0007] A multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation includes the following steps:

[0008] Step 1, geometric modeling of the cross-shaped umbrella: Based on the size characteristics of the cross-shaped umbrella canopy, establish the geometric surface of a single canopy section and the geometric edge model of all the umbrella cords in the bundle form;

[0009] Step 2: Grid the umbrella canopy geometry and the parachute cord system geometry established in Step 1 to create a mesh model;

[0010] Step 3: Fold the individual umbrella canopy mesh model from Step 2 in the warp direction, and establish a complete umbrella canopy warp folded mesh model by copying, translating, selecting, and stitching nodes.

[0011] Step 4: Perform latitudinal numerical folding modeling of the parachute canopy and parachute rope system on the mesh model of the parachute rope system in Step 2 and the warp folding mesh model of the parachute canopy in Step 3.

[0012] Step 5: Correct the mesh elements of the multi-dimensional numerical folding simulation model of the cross-shaped umbrella obtained in Step 4;

[0013] Step Six: Verify the opening of the cross-shaped umbrella multi-dimensional numerical folding simulation model obtained in Step Five. If the umbrella cannot be fully opened due to incorrect merging of mesh nodes, re-fold and model from Step Three.

[0014] Preferably, in step one, the geometric model of the canopy is a flat surface result, and the geometric model of the paracord is a geometric model of a "bundled" straight paracord system with a geometric edge structure.

[0015] Preferably, in step two, the quadrilateral shell element in the finite element preprocessing software is used to mesh the geometric surface representing the geometric features of the umbrella canopy established in step one; the seat belt element in the finite element preprocessing software is used to mesh the geometric edge structure representing the geometric features of the umbrella cord system established in step one.

[0016] Preferably, in step three, the mesh element copying function in the finite element preprocessing software is used to copy a single umbrella canopy twice in sequence. The copied umbrella canopy mesh is then translated, rotated, and stitched together to obtain a complete warp folded mesh model of the umbrella canopy.

[0017] Preferably, in step four, a rigid material plate structure is established, and a force or velocity is applied to it as the driving force for the latitudinal folding deformation of the canopy mesh model established in step three and the paracord mesh model established in step two; a constraint boundary is established based on the size of the parachute to limit the deformation range of the canopy and paracord; after the force or velocity is applied and the boundary is set, the finite element solver is submitted for simulation calculation.

[0018] Preferably, in step five, for the folded umbrella canopy mesh model, the spatial position of each mesh node before folding is calculated according to the umbrella canopy numerical values, and the reference geometric information of each corresponding node of the folded umbrella canopy is set for the restoration of the geometric dimensions of each unit of the umbrella canopy; for each mesh unit of the folded paracord system, the difference in length of the mesh unit before and after folding is calculated according to the paracord system numerical values, and the extension and retraction of each unit of the folded paracord system is set for the restoration of the length of the paracord system.

[0019] Preferably, after completing the longitudinal and latitudinal numerical folding simulation model of the cross-shaped umbrella, the ALE algorithm is used to verify whether the cross-shaped umbrella folding simulation model can open the umbrella correctly. If the mesh nodes are incorrectly stuck together during the inflation process, resulting in the umbrella not being fully inflated, the folding modeling is restarted from step three.

[0020] Preferred finite element preprocessing software includes HyperMesh and LS-PrePost.

[0021] Preferably, the finite element solver used is LS-DYNA.

[0022] Advantages of this invention: It proposes a multi-dimensional numerical folding simulation modeling method for cross-shaped umbrellas based on finite element simulation, establishes a simulation model of cross-shaped umbrellas that closely resembles the actual folding state of packaging, breaks through the limitations of the current "☆"-shaped folding modeling method in cross-shaped umbrella simulation, and realizes the establishment of a multi-dimensional folding simulation model of cross-shaped umbrellas that closely resembles the actual folding state. This lays the foundation for simulation research on the opening process of cross-shaped umbrellas and can provide more effective data support for designing systems to determine the design type of cross-shaped umbrellas and evaluate their performance. Attached Figure Description

[0023] Figure 1 It is a cross-shaped umbrella structure.

[0024] Figure 2 This is a geometric modeling diagram of a single cross-shaped umbrella canopy.

[0025] Figure 3This is a schematic diagram of the geometric model of the parachute cord system.

[0026] Figure 4 This is a schematic diagram of the grid division for a single umbrella canopy.

[0027] Figure 5 This is a schematic diagram of the grid division of the paracord system.

[0028] Figure 6 This is a schematic diagram of the warp folding model of the umbrella canopy.

[0029] Figure 7 This is a schematic diagram of the umbrella canopy folding model in the latitudinal direction.

[0030] Figure 8 This is a schematic diagram of the latitudinal folding model of the paracord system.

[0031] Figure 9 This is a schematic diagram of the overall assembly model of the umbrella system simulation model.

[0032] Figure 10 This is a diagram illustrating the canopy extension phase.

[0033] Figure 11 This is a schematic diagram of the paracord system pull-out stage.

[0034] Figure 12 This is a schematic diagram of an umbrella system fully inflated. Detailed Implementation

[0035] The present invention is achieved through the following technical solution.

[0036] A multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation includes the following steps:

[0037] Step 1: Geometric Modeling of the Cross-Shaped Umbrella

[0038] According to the design drawings of the cross-shaped umbrella structure, the cross-shaped umbrella consists of a canopy (including reinforcing strips) and a rope system (including ropes, fork straps, connecting straps, etc.).

[0039] The umbrella canopy consists of two identical rectangular fabric panels that intersect at approximately right angles, forming a flat surface with four identical rectangular panels. This means the complete geometry of the umbrella canopy can be obtained by sewing together these four identical panels. Considering the structural symmetry of the canopy panels, the geometry of a single panel can be created in CAD software according to the dimensional characteristics of a cross-shaped umbrella. Subsequently, during the umbrella simulation model creation stage, the complete umbrella canopy model is obtained by copying the mesh of a single panel, avoiding repetitive operations in the geometric modeling stage.

[0040] The paracords are connected to the outer edges of the four canopy flaps. Paracords connected to the same canopy flap form a group, and at the intersection of these groups, they are connected to a fork tape, forming a total of four fork tapes. At the intersection of these four fork tapes, they are connected to a connecting tape. A geometric model of the conical "bundled" type straightened paracord system is created in CAD software, which is in the form of a geometric edge structure.

[0041] Step 2: Mesh Generation of Individual Umbrella Canopy and Cord System

[0042] Import the cross-shaped umbrella geometric model established in step one into the finite element preprocessing software. Use quadrilateral shell elements to mesh the geometric surfaces that characterize the geometric features of the umbrella canopy established in step one. Use seat belt elements (this element type allows setting the length variation of each component element) to mesh the geometric edge structure that characterizes the geometric features of the umbrella cord system established in step one.

[0043] Step 3: Create a warp-folded mesh model of the complete umbrella canopy.

[0044] In the finite element preprocessing software, the single umbrella canopy mesh model established in step two is folded in the warp direction. Then, the mesh element copying function in the software is used to copy the single umbrella canopy mesh model twice in sequence. After translation, rotation and node merging, the copied umbrella canopy mesh is translated to obtain the complete umbrella canopy warp folding mesh model, realizing the umbrella canopy folding type in the "umbrella canopy warp flat folding" step in the cross-shaped umbrella packaging process.

[0045] Step 4: Weft-wise numerical folding modeling of the canopy and parachute lines

[0046] The shell and seatbelt elements will shift and deform under external loads. The latitudinal folding deformation is achieved by applying force or velocity to the rigid material plate structure, which serves as the driving force for the canopy mesh model established in step three and the paracord mesh model established in step two. Simultaneously, to ensure that the latitudinal and longitudinal dimensions of the canopy and paracord after numerical calculation are comparable to the actual packaging dimensions, constraint boundaries should be established based on the umbrella pack dimensions to limit the deformation range of the canopy and paracord. After loading and boundary settings are completed, the simulation calculation is submitted to the finite element solver. After the calculation is completed, the specific folding process can be viewed in post-processing through animation.

[0047] This step realizes the latitudinal numerical folding modeling of the cross-shaped umbrella based on finite element simulation, and establishes a simulation model of the umbrella system packaged into the umbrella bag in the actual packaging process of the cross-shaped umbrella using the "Z" folding method.

[0048] Step 5: Correct the mesh elements of the cross-shaped umbrella folding simulation model.

[0049] After numerical calculation, the dimensions of the canopy and lines of the folded cross-shaped umbrella model changed. For the folded canopy mesh model, the reference geometric information of the corresponding nodes of the canopy after folding was set according to the spatial positions of the nodes of each mesh before folding, based on the numerical calculation of the canopy's original position, to restore the geometric dimensions of each unit of the canopy. For each mesh unit of the folded line system, the expansion and contraction of each unit of the line system after folding was set according to the difference in length of the mesh units before and after folding, based on the numerical calculation of the line system's original length, to restore the length of the line system. Thus, the longitudinal and latitudinal numerical folding simulation model of the cross-shaped umbrella was achieved.

[0050] Step Six: Use the ALE algorithm to verify whether the cross-shaped umbrella folding simulation model can open correctly. If mesh nodes are incorrectly stuck together during the canopy inflation process, causing the canopy to not fully inflate, then start the folding modeling again from Step Three.

[0051] The governing equations for the solution required in this process are as follows:

[0052] The flow field governing equations consist of the mass equation, momentum equation, and energy equation, and their tensor forms are as follows:

[0053]

[0054]

[0055]

[0056] In the formula: ρ is density; v i The velocity of matter; u i Indicates the speed of the grid; w i For relative velocity, w i =v i -u i w j Meaning and w i Similar; x i Let i be the Euler coordinates, x j Let J be the Euler coordinates; E be the energy; σ be the scalar coordinates. ij,j σ is the divergence of the flow field stress tensor; ij The stress tensor of the flow field, σ ij =-pδ ij +μ(v i,j +v j,i ), p is the fluid pressure, μ is the aerodynamic viscosity, and v alone i,j or v j,i Let v be the angular deformation rate in a certain direction. i,j With v j,i The sum of these values ​​represents the angular deformation rate of the corresponding plane; b i δ represents the force per unit volume. ijThis represents the Kronecker delta function.

[0057] The grid governing equations are:

[0058]

[0059] In the formula: X i Represents Lagrange grid coordinates; x i Represents Euler coordinates; w i t represents relative velocity, and t represents time.

[0060] The structural governing equations are:

[0061]

[0062] The velocity of the material is determined by the structural dynamics of the membrane. Here, M, C, and K represent the element mass, damping modulus, and elastic modulus, respectively, F is the resultant force on the membrane element, and ω is the nodal displacement.

[0063] The scope of protection of this invention is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its scope. If such modifications and variations fall within the scope of the claims of this invention and their equivalents, then the intent of this invention also includes these modifications and variations.

Claims

1. A multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation, characterized in that, Includes the following steps: Step 1, geometric modeling of the cross-shaped umbrella: Based on the size characteristics of the cross-shaped umbrella canopy, establish the geometric surface of a single canopy section and the geometric edge model of all the umbrella cords in the bundle form; Step 2: Grid the umbrella canopy geometry and the parachute cord system geometry established in Step 1 to create a mesh model; Step 3: Fold the individual umbrella canopy mesh model from Step 2 in the warp direction, and establish a complete umbrella canopy warp folded mesh model by copying, translating, selecting, and stitching nodes. Step four involves performing latitudinal numerical folding modeling of the parachute canopy and parachute rope system based on the mesh model of the parachute rope system in step two and the warp folding mesh model of the parachute canopy in step three. In step four, a rigid material plate structure is established, and a force or velocity is applied to it as the driving force for the latitudinal folding deformation of the parachute canopy mesh model established in step three and the parachute rope mesh model established in step two. Constraint boundaries are established based on the parachute size to limit the deformation range of the parachute canopy and parachute ropes. After the force or velocity is applied and the boundaries are set, the simulation calculation is submitted to the finite element solver. Step 5: Correct the mesh elements of the multi-dimensional numerical folding simulation model of the cross-shaped umbrella obtained in Step 4; In Step 5, for the folded umbrella canopy mesh model, calculate the spatial position of each mesh node before folding according to the umbrella canopy numerical calculation, and set the reference geometric information of each node of the folded umbrella canopy for restoring the geometric dimensions of each unit of the umbrella canopy; For each mesh element of the folded paracord system, calculate the difference in length of the mesh element before and after folding according to the paracord system numerical calculation, and set the extension and retraction of each unit of the folded paracord system for restoring the length of the paracord system. Step Six: Verify the opening of the cross-shaped umbrella multi-dimensional numerical folding simulation model obtained in Step Five. If the umbrella cannot be fully opened due to incorrect merging of mesh nodes, re-fold and model from Step Three.

2. The multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation as described in claim 1, characterized in that, In step one, the geometric model of the canopy is a flat surface result, and the geometric model of the paracord is a geometric model of a "bundled" straight paracord system with a geometric edge structure.

3. The multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation as described in claim 1, characterized in that, In step two, the quadrilateral shell element in the finite element preprocessing software is used to mesh the geometric surfaces representing the geometric features of the umbrella canopy established in step one; the seat belt element in the finite element preprocessing software is used to mesh the geometric edge structure representing the geometric features of the umbrella cord system established in step one.

4. The multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation as described in claim 1, characterized in that, In step three, the mesh element copying function in the finite element preprocessing software is used to copy a single umbrella canopy twice. The copied umbrella canopy mesh is then translated, rotated, and stitched together to obtain a complete warp folded mesh model of the umbrella canopy.

5. The multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation as described in claim 1, characterized in that, After completing the longitudinal and latitudinal numerical folding simulation model of the cross-shaped umbrella, the ALE algorithm is used to verify whether the cross-shaped umbrella folding simulation model can open the umbrella correctly. If the mesh nodes are incorrectly stuck together during the inflation process, resulting in the umbrella not being fully inflated, the folding modeling is restarted from step three.

6. The multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation as described in claim 3, characterized in that, Finite element preprocessing software includes HyperMesh and LS-PrePost.

7. The multi-dimensional numerical folding modeling method for a cross-shaped umbrella based on finite element simulation as described in claim 1, characterized in that, The finite element solver used is LS-DYNA.

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