Dynamic performance simulation test method and optimization method based on anisotropic canopy

Abstract

The invention relates to a parachute canopy dynamics simulation test method and optimization method based on anisotropic springs, and the method comprises the steps: dispersing a parachute canopy into a mass point-spring-damping grid model, dividing the springs into warp springs and weft springs according to the warp and weft directions of a fabric, respectively calibrating the elastic coefficients of the springs through a material test or an empirical formula, and calculating the elastic coefficient of the parachute canopy; an anisotropic elastic force calculation expression is constructed, and a mass-spring-damping model capable of accurately representing the directional characteristics of the fabric is formed; then the model and a computational fluid dynamics model are subjected to bidirectional real-time coupling simulation, the dynamic process of the canopy in a flow field is simulated, and deformation, resistance and flow field data are output. The optimization method comprises the steps of comparing a simulation result with a design index, and adjusting a local design parameter based on a diagnosis result and performing iteration until a requirement is met. According to the method, the prediction accuracy of the nonlinear deformation, aerodynamic performance and fluid-solid coupling effect of the canopy can be remarkably improved, and a reliable tool is provided for efficient digital design optimization.

Description

Technical Field

[0001] This invention relates to the field of parachute design and analysis technology, specifically to a dynamic performance simulation and optimization method based on anisotropic parachute canopy. Background Technology

[0002] During the parachute's deployment, inflation, and stable descent, the canopy, as a typical flexible fabric structure, undergoes large deformations, strong nonlinearity, and complex fluid-structure interaction.

[0003] Traditional numerical methods face a fundamental challenge in simulating such problems: the difficulty of simultaneously achieving computational efficiency, numerical stability, and physical accuracy. Specifically, existing technologies suffer from the following bottlenecks: when simulating extremely thin, highly deformable structures such as fabrics, continuous medium methods (such as the finite element method) are prone to computational failure or a sharp decline in accuracy due to mesh distortion. Furthermore, detailed modeling of locally anisotropic structures such as seams and reinforcing strips requires extremely high mesh densities, resulting in enormous computational costs and making it unsuitable for dynamic simulations of engineering-grade integral umbrella canopies.

[0004] In contrast, the traditional mass-spring-damped model is typically used in parachute structural dynamics models for fluid-structure interaction calculations and analyses. However, the traditional and standard mass-spring-damped model often employs isotropic spring elements, which cannot accurately characterize the inherent, strongly direction-dependent mechanical behavior of woven or nonwoven fabrics (such as different tensile stiffnesses in the warp and weft directions, shear deformation modes, and Poisson's ratio effect). Its simplified one-dimensional spring connection method struggles to naturally and stably capture the nonlinear deformation of the fabric, resulting in significant deviations between the simulated canopy shape, wrinkle evolution, and dynamic response and physical reality.

[0005] In summary, there is an urgent need to provide a simulation and testing method, optimization method, simulation system, and computer-readable storage medium based on anisotropic canopies that can significantly improve the accuracy, efficiency, and reliability of dynamic behavior simulation of flexible fabric systems such as parachutes in complex aerodynamic environments. Summary of the Invention

[0006] The purpose of this invention is to provide a simulation test method, optimization method, simulation system, and computer-readable storage medium based on anisotropic canopy dynamic performance that can significantly improve the accuracy, efficiency, and reliability of dynamic behavior simulation of flexible fabric systems such as parachutes in complex aerodynamic environments.

[0007] The above objective is achieved through the following technical solution: a dynamic performance simulation and testing method based on anisotropic umbrella canopies, comprising the following steps: S1, Basic Model Construction: For the flexible fabric structure of the parachute canopy, the flexible fabric structure is discretized into a mesh model, and a mass-spring-damping model is constructed, including discrete mass points and spring units connecting adjacent mass points. The mass points are discretely distributed according to the geometry of the parachute canopy. S2, Anisotropic Model Construction: The spring unit is divided into warp springs and weft springs according to the fiber orientation of the fabric, corresponding to the warp mechanical transmission path and weft mechanical transmission path of the fabric, respectively. By conducting a unidirectional tensile test on the umbrella canopy flexible fabric, the warp elastic coefficient and weft elastic coefficient are obtained and calibrated respectively. The warp elastic coefficient is not equal to the weft elastic coefficient. An anisotropic elastic force calculation expression is constructed to calculate the elastic force on the warp spring and the weft spring, forming an anisotropic mass-spring-damping model. S3, Fluid-structure Interaction Simulation: The anisotropic mass-spring-damping model is placed in a preset flow field calculation domain, and numerical calculations are performed through a fluid-structure interaction solver to simulate the dynamic process of the umbrella canopy in the flow field. S4. Result Output: Obtain and output the results of the simulation test, including at least the deformation time series of the canopy, the time history of the overall drag coefficient, and the flow field pressure distribution on the surface of the canopy.

[0008] This invention, by differentiating spring units according to warp and weft directions and constructing an anisotropic force model using experimentally calibrated, unequal elastic coefficients, for the first time reproduces the direction-dependent mechanical behavior of umbrella canopy fabrics with high fidelity within a computationally efficient mass-spring-damping framework. This fundamentally overcomes the inherent limitation of traditional isotropic models in accurately simulating warp-weft differential deformation, resulting in a qualitative improvement in the prediction accuracy of large deformations and nonlinear vibrations of umbrella canopies.

[0009] Based on the high-precision simulation of this method, this invention can simulate the shift in the dominant frequency of umbrella canopy vibration, the increase in amplitude, and the more localized and asymmetric wrinkling deformation modes caused by anisotropy. At the same time, it can also simulate the asymmetric flow field structure and wake oscillation caused by this, and can capture and analyze complex physical phenomena that traditional models cannot reveal.

[0010] This invention can significantly improve the accuracy, efficiency and reliability of dynamic behavior simulation of flexible fabric systems such as parachutes in complex aerodynamic environments, and provide advanced numerical simulation tools for parachute design, performance prediction and optimization.

[0011] A further technical solution is that the force calculation of the spring unit adopts the anisotropic elastic force formula. In the anisotropic mass-spring-damping model, the elastic force of the spring in the four directions corresponding to mass point (i,j) and its adjacent mass points is calculated according to the following formula: ; ; ; ; in, Let be the elastic force of the spring along the direction at the position of mass (i,j); The elastic force of the spring at the position (i-1,j) is the radial force. Let be the elastic force of the spring in the latitudinal direction at the position of mass (i,j); The elastic force of the spring in the latitudinal direction at the position of mass (i,j-1); The longitudinal linear elastic coefficient; The linear elastic coefficient is in the latitudinal direction; It is the complementary angle of the polar angle of the particle (i,j) along the meridional direction; Let be the azimuth angle of the particle (i,j) along the meridional direction; It is the complementary angle of the polar angle of the particle (i-1,j) along the meridional direction; Let be the azimuth angle of the particle (i-1,j) along the meridional direction; It is the complementary angle of the polar angle in the latitudinal direction of the particle (i,j); It is the complementary angle of the polar angle in the latitudinal direction of the particle (i,j-1); Let be the azimuth angle of the particle (i,j) in the latitudinal direction; Let be the azimuth angle of the particle (i,j-1) in the latitudinal direction; Let be the change in displacement of the particle (i,j) along the meridional direction; This represents the change in displacement of the particle at position (i-1,j) along the meridional direction. Let be the change in displacement of the particle (i,j) in the latitudinal direction; This represents the latitudinal displacement change of the particle at position (i,j-1).

[0012] In this way, the anisotropic mechanical response of the umbrella canopy fabric was accurately characterized by the quantitative elastic force calculation formula, which solved the engineering problem that traditional models could not capture the nonlinear deformation of the fabric, and made the simulation results of complex behaviors such as umbrella canopy wrinkle evolution and asymmetric deformation more in line with engineering reality.

[0013] A further technical solution is that, for any reference mass point (i, j) in the mesh model, it is connected to four adjacent mass points (i-1, j), (i+1, j), (i, j-1), and (i, j+1) respectively through four spring elements. Anisotropic elastic force calculation expressions are established for each of the four spring elements, and the construction method is as follows: For the spring unit connecting mass (i, j) and (i+1, j), and the spring unit connecting mass (i-1, j) and (i, j), the isotropic elastic coefficient in its elastic force calculation formula is replaced with the meridional elastic coefficient, and the calculation is performed in conjunction with the elongation and geometric projection factor of the spring unit. For the spring unit connecting mass (i, j) and (i, j+1), and the spring unit connecting mass (i, j-1) and (i, j), the isotropic elastic coefficient in its elastic force calculation formula is replaced with the latitudinal elastic coefficient, and the calculation is performed in conjunction with the elongation and geometric projection factor of the spring unit.

[0014] This invention embeds anisotropic constitutive relations at the most fundamental mechanical calculation unit level, ensuring that the meridional mechanical path uses only the radial elastic coefficient, and the zonal mechanical path uses only the zonal elastic coefficient, thus forcing the directional dependence of mechanics at the algorithm's root. Secondly, it strictly adheres to the topological logic of the structured mesh and calculates the elongation and force of each spring independently, avoiding potential force calculation confusion under complex deformations. Simultaneously, by using separately calibrated radial and zonal elastic coefficients, along with directional geometric projection factors, the model maintains physical self-consistency when simulating meridional coupled deformation, thereby ensuring the numerical stability of the entire fluid-structure interaction simulation under highly nonlinear conditions.

[0015] A further technical solution is that the warp elastic coefficient and the weft elastic coefficient are correlated through an anisotropy factor, whereby the anisotropy factor is the ratio of the weft elastic coefficient to the warp elastic coefficient, and the anisotropy factor ranges from 0.90 to 0.98. This matches the mechanical properties of the umbrella canopy fabric, ensuring that the warp bears the principal stress and the weft maintains morphological stability. By precisely adapting the anisotropy factor to the inherent mechanical properties of the umbrella canopy fabric, simulation deviations caused by mismatches in warp and weft stiffness parameters are avoided, further improving the fit between simulation results and actual engineering conditions, and reducing the parameter adjustment costs of engineering simulations.

[0016] A further technical solution is that the anisotropy factor is set to 0.94. This value can meet the simulation requirements of nylon supersonic parachutes without additional experimental calibration, greatly improving the engineering versatility and convenience of the method, and can be directly applied to the engineering research and development of nylon canopy parachutes.

[0017] A further technical solution is that, in step S2, the fluid-structure interaction simulation is performed using an autonomous solver, which performs bidirectional real-time coupling solution of the structural dynamics equations of the anisotropic mass-spring-damped model and the flow control equations of the computational fluid dynamics model.

[0018] To achieve the above objectives, the present invention also provides an optimization method based on anisotropic parachute canopy. First, simulation testing is performed using any of the aforementioned dynamic performance simulation testing methods based on anisotropic parachute canopy, followed by the following steps: S5, Performance Evaluation: Compare the simulation test results with the preset performance indicators; S6, Design Iteration: If the comparison results do not meet the requirements, adjust at least one design parameter of the canopy based on the analysis of the simulation test results, and return to step S1 until the requirements are met.

[0019] A further technical solution is that, in step S6, at least one evaluation index related to the performance of the canopy structure is extracted, and based on the distribution or value of the index, weak areas or points to be optimized in the canopy design are diagnosed. According to the diagnosis results, the local design variables of the canopy corresponding to the weak areas or points to be optimized in the initial design parameters are adjusted, and then the process returns to step S1 for iterative simulation until the evaluation index meets the preset design requirements.

[0020] This invention allows for the extraction of multiple evaluation indices of different properties (such as static strength indices and dynamic characteristic indices) and the diagnosis of their corresponding weak areas. This enables designers to address multiple engineering problems of different natures in parallel within the same iteration (such as simultaneously solving local strength deficiencies and excessive vibrations) and assess the interactions between different adjustment measures. Because the diagnosis is clear and the adjustments are precise, the design modifications in each iteration are local and small-scale, avoiding complete overhauls. This not only reduces model modifications and computational costs in each iteration, but more importantly, it allows the optimization process to converge quickly along a clear path, avoiding the oscillations or divergences found in traditional trial-and-error methods.

[0021] To achieve the above objectives, the present invention also provides a dynamic performance simulation and testing system based on anisotropic umbrella canopies, used to implement any of the above-described dynamic performance simulation and testing methods based on anisotropic umbrella canopies, comprising: The basic model building module is used to discretize the flexible fabric structure of the transsupersonic parachute canopy into a mesh model. Anisotropic model building module, used to build anisotropic mass-spring-damping models; The fluid-structure interaction simulation module is used to place the anisotropic mass-spring-damping model in a preset supersonic flow field calculation domain, and perform numerical calculations through the fluid-structure interaction solver to simulate the dynamic process of the umbrella canopy in the flow field. The result output module is used to acquire and output the results of the simulation test.

[0022] This invention significantly lowers the technical barrier to entry through modular design, enabling ordinary engineering designers to conduct high-precision umbrella dynamic performance simulation tests conveniently and systematically without needing to master all the details of anisotropic modeling and fluid-structure interaction algorithms. This greatly promotes the engineering popularization and application of advanced simulation technology.

[0023] To achieve the above objectives, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements any of the above-described methods for simulating and testing the dynamic performance of anisotropic umbrella canopies.

[0024] Compared with existing technologies, the present invention has the following technical advantages: (1) By differentiating the spring network according to the warp and weft directions of the fabric and assigning different elastic coefficients calibrated by uniaxial tensile tests, this model embeds the anisotropic constitutive relation of the material at the algorithm level. Comparative simulation results show that this model can not only more realistically capture the nonlinear large deformation and complex wrinkle morphology of the umbrella canopy, but also that the anisotropy causes the main frequency of the umbrella canopy vibration to shift and the amplitude to increase significantly, and induces an asymmetric flow field structure and wake oscillation, thus simulating the fluid-structure interaction dynamics of the umbrella canopy more accurately.

[0025] (2) The present invention can effectively and accurately simulate the nonlinear deformation of the canopy of a supersonic parachute, and can observe more complex anisotropic / nonlinear behavior, as well as correspondingly more intense deformation and more unstable flow field changes, effectively filling the current engineering needs for parachute fluid-structure interaction simulation and aerodynamic characteristic prediction and analysis. (3) Through the iterative process of simulation, diagnosis, adjustment and verification, this invention can transform design optimization from macro-adjustment that relies on experience to precise improvement of local design variables based on physical mechanisms, thereby significantly improving design efficiency and product reliability, and reducing R&D costs and risks. Attached Figure Description

[0026] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0027] Figure 1 This is a schematic diagram of an anisotropic mass-spring-damping model according to one embodiment of the present invention; Figure 2 This is a curve showing the change of drag coefficient over time for different examples in an experimental group according to one embodiment of the present invention; Figure 3 This is a graph showing the FFT analysis results of the drag coefficients of different examples in an experimental group according to one embodiment of the present invention. Figure 4This is a schematic diagram comparing the deformation of the umbrella canopy in different calculation examples of an embodiment of the present invention. Among them, (a) is a schematic diagram of the deformation of the isotropic umbrella canopy at t=0.01 s, (b) is a schematic diagram of the deformation of the anisotropic umbrella canopy at t=0.01 s, (c) is a schematic diagram of the deformation of the isotropic umbrella canopy at t=0.0134 s, and (d) is a schematic diagram of the deformation of the anisotropic umbrella canopy at t=0.0134 s. Figure 5 This is a schematic diagram comparing the Mach number distribution cloud map and pressure distribution of the experimental group at t=0.01s in one embodiment of the present invention. Among them, (a) is an isotropic Mach number distribution cloud map, (b) is an isotropic pressure distribution schematic diagram, (c) is an anisotropic Mach number distribution cloud map, and (d) is an anisotropic pressure distribution schematic diagram. Figure 6 The diagram shows the Mach number distribution cloud map and pressure distribution comparison diagram for the experimental group at t=0.0134s in one embodiment of the present invention. (a) is an isotropic Mach number distribution cloud map, (b) is an isotropic pressure distribution diagram, (c) is an anisotropic Mach number distribution cloud map, and (d) is an anisotropic pressure distribution diagram.

[0028] In the picture: 1. Meridian spring unit 2. Weft spring unit 3. Damping Detailed Implementation

[0029] The present invention will now be described in detail with reference to the accompanying drawings. This description is merely illustrative and explanatory, and should not be construed as limiting the scope of protection of the present invention. Furthermore, those skilled in the art can combine the features in the embodiments described herein and in different embodiments accordingly based on the description in this document.

[0030] To better understand the technical solution of this invention, a dynamic performance simulation and testing method based on anisotropic umbrella canopy includes the following steps: S1, Basic Model Construction: For the flexible fabric structure of the parachute canopy, the flexible fabric structure is discretized into a mesh model, and a mass-spring-damping model is constructed, including discrete mass points and spring units connecting adjacent mass points. The mass points are discretely distributed according to the geometry of the parachute canopy. S2, Anisotropic Model Construction: The spring unit is divided into warp springs and weft springs according to the fiber orientation of the fabric, corresponding to the warp mechanical transmission path and weft mechanical transmission path of the fabric, respectively. By conducting a unidirectional tensile test on the umbrella canopy flexible fabric, the warp elastic coefficient and weft elastic coefficient are obtained and calibrated respectively. The warp elastic coefficient is not equal to the weft elastic coefficient. An anisotropic elastic force calculation expression is constructed to calculate the elastic force on the warp spring and the weft spring, forming an anisotropic mass-spring-damping model. S3, Fluid-structure Interaction Simulation: The anisotropic mass-spring-damping model is placed in a preset flow field calculation domain, and numerical calculations are performed through a fluid-structure interaction solver to simulate the dynamic process of the umbrella canopy in the flow field. S4. Result Output: Obtain and output the results of the simulation test, including at least the deformation time series of the canopy, the time history of the overall drag coefficient, and the flow field pressure distribution on the surface of the canopy.

[0031] In practical applications, for parachute canopies, preprocessing software is used to discretize the canopy surface into a regular structured quadrilateral mesh. Each node of the mesh is considered a discrete mass point, and each mass point has mass properties. Subsequently, spring elements are established between adjacent mass points; specifically, the mesh edges connecting each pair of adjacent mass points constitute a spring element. Simultaneously, a damper is connected in parallel to each spring element to characterize the material's internal resistance, collectively forming the basic mass-spring-damping model.

[0032] Based on the actual fiber weaving direction of the umbrella canopy fabric, the spring units established within it are classified. Specifically, the spring units corresponding to the grid edges aligned with the warp direction of the fabric are defined as warp springs; the spring units corresponding to the grid edges aligned with the weft direction of the fabric are defined as weft springs.

[0033] Uniaxial tensile tests were conducted on the nylon fabric used to make the umbrella canopy. Specimens were cut along both the warp and weft directions, loaded onto a material testing machine, and stress-strain curves were obtained. In the linear elastic stage, the warp and weft elastic moduli were calculated. Combined with the equivalent area and length represented by the spring elements in the discrete mesh, the warp and weft elastic coefficients were converted and calibrated. These coefficients were then assigned to all warp and weft springs in the model.

[0034] For any reference mass (i, j) in the model, the elastic force it experiences is contributed by the four spring elements connected to it. Traditional isotropic models use uniform elastic coefficients to calculate forces in all directions. An anisotropic elastic force calculation expression is constructed by embedding it into the model's dynamic equations, thus ultimately forming an anisotropic mass-spring-damped model that accurately reflects the directional characteristics of the fabric.

[0035] The constructed anisotropic structural model is imported into the fluid dynamics calculation software. A predefined flow field computational domain is set, for example, simulating supersonic flow conditions at an altitude of 30 km (Mach number Ma=2.0). In the fluid-structure interaction solver, a two-way coupling algorithm is configured: First, the Computational Fluid Dynamics (CFD) module solves the flow field, transferring the pressure loads acting on the canopy surface to the structural model; then, the structural dynamics module (based on the aforementioned anisotropic model) calculates the displacement and deformation of the canopy based on the received loads; finally, the updated canopy shape is returned to the CFD module as the new boundary to update the flow field. This process is iterated to simulate the complete dynamic process of the canopy from its initial state to stable inflation.

[0036] After the simulation is completed, the post-processing module automatically extracts and outputs key result data. These results include at least: Deformation sequence of the umbrella canopy: It can generate shape diagrams of the umbrella canopy at different times (such as t=0.01s, 0.0134s), which can intuitively show the process of wrinkle generation and development.

[0037] Overall drag coefficient time history: The curve of the output drag coefficient Cd changing over time, used to evaluate the deceleration performance of the parachute.

[0038] Pressure distribution of the flow field on the surface of the canopy: Outputs a pressure cloud map of the space around the canopy to analyze the distribution of aerodynamic loads.

[0039] In addition, it can output data such as vibration spectrum and paracord tension for further analysis.

[0040] This invention, by differentiating spring units according to warp and weft directions and constructing an anisotropic force model using experimentally calibrated, unequal elastic coefficients, for the first time reproduces the direction-dependent mechanical behavior of umbrella canopy fabrics with high fidelity within a computationally efficient mass-spring-damping framework. This fundamentally overcomes the inherent limitation of traditional isotropic models in accurately simulating warp-weft differential deformation, resulting in a qualitative improvement in the prediction accuracy of large deformations and nonlinear vibrations of umbrella canopies.

[0041] Based on the high-precision simulation of this method, this invention can simulate the shift in the dominant frequency of umbrella canopy vibration, the increase in amplitude, and the more localized and asymmetric wrinkling deformation modes caused by anisotropy. At the same time, it can also simulate the asymmetric flow field structure and wake oscillation caused by this, and can capture and analyze complex physical phenomena that traditional models cannot reveal.

[0042] This invention can significantly improve the accuracy, efficiency and reliability of dynamic behavior simulation of flexible fabric systems such as parachutes in complex aerodynamic environments, and provide advanced numerical simulation tools for parachute design, performance prediction and optimization.

[0043] Based on the above embodiments, in another embodiment of the present invention, the force calculation of the spring unit adopts the anisotropic elastic force formula. In the anisotropic mass-spring-damping model, the elastic force of the springs in the four directions corresponding to mass point (i,j) and its adjacent mass points is calculated according to the following formula: (1) (2) (3) (4) in, Let be the elastic force of the spring along the direction at the position of mass (i,j); The elastic force of the spring at the position (i-1,j) is the radial force. Let be the elastic force of the spring in the latitudinal direction at the position of mass (i,j); The elastic force of the spring in the latitudinal direction at the position of mass (i,j-1); The longitudinal linear elastic coefficient; The linear elastic coefficient is in the latitudinal direction; It is the complementary angle of the polar angle of the particle (i,j) along the meridional direction; Let be the azimuth angle of the particle (i,j) along the meridional direction; It is the complementary angle of the polar angle of the particle (i-1,j) along the meridional direction; Let be the azimuth angle of the particle (i-1,j) along the meridional direction; It is the complementary angle of the polar angle in the latitudinal direction of the particle (i,j); It is the complementary angle of the polar angle in the latitudinal direction of the particle (i,j-1); Let be the azimuth angle of the particle (i,j) in the latitudinal direction; Let be the azimuth angle of the particle (i,j-1) in the latitudinal direction; Let be the change in displacement of the particle (i,j) along the meridional direction; This represents the change in displacement of the particle at position (i-1,j) along the meridional direction. Let be the change in displacement of the particle (i,j) in the latitudinal direction; This represents the latitudinal displacement change of the particle at position (i,j-1).

[0044] In this way, the anisotropic mechanical response of the umbrella canopy fabric was accurately characterized by the quantitative elastic force calculation formula, which solved the engineering problem that traditional models could not capture the nonlinear deformation of the fabric, and made the simulation results of complex behaviors such as umbrella canopy wrinkle evolution and asymmetric deformation more in line with engineering reality.

[0045] Based on the above embodiments, in another embodiment of the present invention, for any reference mass point (i, j) of the mesh model, it is connected to four adjacent mass points (i-1, j), (i+1, j), (i, j-1), and (i, j+1) respectively through four spring elements. Anisotropic elastic force calculation expressions are established for each of the four spring elements, and the construction method is as follows: For the spring unit connecting mass (i, j) and (i+1, j), and the spring unit connecting mass (i-1, j) and (i, j), the isotropic elastic coefficient in its elastic force calculation formula is replaced with the meridional elastic coefficient, and the calculation is performed in conjunction with the elongation and geometric projection factor of the spring unit. For the spring unit connecting mass (i, j) and (i, j+1), and the spring unit connecting mass (i, j-1) and (i, j), the isotropic elastic coefficient in its elastic force calculation formula is replaced with the latitudinal elastic coefficient, and the calculation is performed in conjunction with the elongation and geometric projection factor of the spring unit.

[0046] In practical applications, within the mesh model, the focus is on any reference point located inside the mesh (not at the boundary), with index coordinates (i, j). This point is connected to its four nearest neighboring points via four spring elements: point (i, j+1), point (i, j-1), point (i-1, j), and point (i+1, j).

[0047] For each spring element connected to the reference mass point (i, j), a formula for calculating its elastic force is established. The core operation is to select the corresponding elastic coefficient according to the direction of the spring and replace the general coefficient in the original isotropic formula.

[0048] In the existing mass-spring-damped structural dynamics model, the spring force follows Huke's law, and its expression is: ;in, It is the linear elastic coefficient. This represents the elongation of the spring (i.e., the change in displacement). In this patent, in the mass-spring-damping model (such as...) Figure 1 In the original linear elastic force component, the elastic force of particle (i, j) in one direction. For example, to illustrate the correction of linear elastic force to anisotropic elastic force, , This indicates the change in displacement, that is, the elongation of the spring. This represents the complementary angle of the polar angle in spherical coordinates. Represents the azimuth angle in a spherical coordinate system. , It is the geometric projection factor in the corresponding direction.

[0049] To introduce anisotropy, we need to replace each term with isotropic one. However, it's important to note that the displacement change of each term in the original expression is calculated independently, corresponding to the displacement difference between four adjacent points (i.e., the four edges). Specifically, the original expression should have four terms, corresponding to the four directions (two edges in the i-direction and two edges in the j-direction): , which corresponds to an edge at position i, j in the direction i; , corresponding to an edge at position i-1, j in the direction i; , which corresponds to an edge at position i, j in the j direction; , corresponding to an edge at position i, j-1 in the j direction; For each term, we need to replace isotropic with anisotropic. However, note that the displacement change is different for each term. Then, after anisotropic correction, the force for each term becomes formulas (1) to (4); each direction may have different characteristics (meridian and latitudinal), so we can specify the coefficients for direction i (meridian) and direction j (latitudinal) respectively, then, The elastic modulus in the i-direction (meridian direction); The elastic coefficient is in the j-direction (latitudinal direction).

[0050] Simultaneously assume and The constant displacement change (i.e., the elongation of the spring) can be either positive or negative.

[0051] The elastic forces of all particles calculated in this way, along with the damping forces and external aerodynamic forces, are assembled into the system's dynamic equations, thus completing the core construction of the anisotropic mass-spring-damped model at the mechanical calculation level. This model is then fed into a fluid-structure interaction solver for dynamic simulation.

[0052] This invention embeds anisotropic constitutive relations at the most fundamental mechanical calculation unit level, ensuring that the meridional mechanical path uses only the radial elastic coefficient, and the zonal mechanical path uses only the zonal elastic coefficient, thus forcing the directional dependence of mechanics at the algorithm's root. Secondly, it strictly adheres to the topological logic of the structured mesh and calculates the elongation and force of each spring independently, avoiding potential force calculation confusion under complex deformations. Simultaneously, by using separately calibrated radial and zonal elastic coefficients, along with directional geometric projection factors, the model maintains physical self-consistency when simulating meridional coupled deformation, thereby ensuring the numerical stability of the entire fluid-structure interaction simulation under highly nonlinear conditions.

[0053] Based on the above embodiments, in another embodiment of the present invention, the warp elastic coefficient and the weft elastic coefficient are correlated through an anisotropy factor, wherein the anisotropy factor is the ratio of the weft elastic coefficient to the warp elastic coefficient, and the anisotropy factor ranges from 0.90 to 0.98. This matches the mechanical properties of the umbrella canopy fabric, ensuring that the warp bears the principal stress and the weft maintains morphological stability. By precisely adapting the anisotropy factor to the inherent mechanical properties of the umbrella canopy fabric, simulation deviations caused by mismatch in warp and weft stiffness parameters are avoided, further improving the fit between simulation results and actual engineering conditions, and reducing the parameter adjustment costs of engineering simulations.

[0054] Based on the above embodiments, in another embodiment of the present invention, the anisotropy factor is set to 0.94. This value can meet the simulation requirements of nylon supersonic parachutes without additional experimental calibration, greatly improving the engineering versatility and convenience of the method, and can be directly applied to the engineering research and development of nylon canopy parachutes.

[0055] Because umbrella canopies are made of fabric or flexible material, the relationship between the linear elastic coefficients in the warp and weft directions can indeed be described using an anisotropy factor. The anisotropy factor is defined as the ratio of the weft elastic coefficient to the warp elastic coefficient. For umbrella canopy materials, the elastic properties in the warp and weft directions typically differ due to variations in weave structure and fiber orientation. For example, the warp (longitudinal) direction bears the principal stress and has higher stiffness, while the weft (transverse) direction maintains shape stability and has slightly lower stiffness. The anisotropy factor is usually less than 1. The selection of the anisotropy factor for umbrella canopy materials should be based on actual material test data or empirical values. The anisotropy factor range for nylon fabrics is 0.90 to 0.98; in this study, a value of 0.94 was used.

[0056] Based on the above embodiments, in another embodiment of the present invention, in step S2, the fluid-structure interaction simulation is performed using an autonomous solver, which performs bidirectional real-time coupling solution of the structural dynamics equations of the anisotropic mass-spring-damped model and the flow control equations of the computational fluid dynamics model.

[0057] Based on the above-mentioned anisotropic elastic composition mass-spring-damped structure dynamic model, a self-defined solver was used to solve the problem. Two sets of experiments were set up, including an isotropic comparison group (using only the longitudinal linear elastic coefficient) and an anisotropic comparison group (including both longitudinal and latitudinal elastic coefficients), as shown in Table 1.

[0058] Table 1. Working conditions and parameters of the parachute structure dynamics model in the embodiment.

[0059] like Figure 2As shown, the average drag coefficients for the initial stages of "-k1k (isotropic)" and "-kik (anisotropic)" are 0.3393 and 0.3389, respectively. The average drag coefficients for the steady-state stage only include the first two examples, which are 0.4265 and 0.4072, respectively, with a relative error of less than 5%. This indicates that the influence of isotropic and anisotropic elastic coefficients on the average drag coefficient is not significant.

[0060] like Figure 3 As shown, FFT analysis was performed on the drag coefficients of the two sets of experiments. The graph shows that the first dominant frequency of "-k1k" is 51.52 Hz, the second dominant frequency is 257.61 Hz, and the third dominant frequency is 412.17 Hz, while the first dominant frequency of "-kik" is 45.24 Hz, the second dominant frequency is 271.45 Hz, and the third dominant frequency is 497.65 Hz. It can also be seen that the amplitude of "-kik" (anisotropic) is significantly higher than that of "-k1k" (isotropic).

[0061] The original model of isotropic materials exhibits identical mechanical properties (linear elastic coefficients) in all directions. In airflow, the deformation of the canopy is relatively "regular" and "uniform." Due to its homogeneity, the canopy's vibration modes are relatively simple, with the dominant frequency typically being concentrated and well-defined. The drag coefficient also fluctuates relatively regularly, although the amplitude may be relatively small (e.g., ...). Figure 3 (As shown). In summary, the isotropic model provides a baseline, idealized dynamic response. Its fluctuations mainly stem from the coupling between the unsteady properties of the fluid itself and the overall stiffness of the structure. In contrast, the dynamic behavior of the entire system becomes more complex when anisotropic materials (improved model) affect it. Materials have different mechanical properties in different directions. For a parasol, the stiffness (elastic coefficient) differs in the warp and weft directions. Deformation in the warp direction "drives" or "suppresses" deformation in the weft direction. That is, under the influence of different stiffnesses in different directions, the natural frequencies of the parasol differ in the warp and weft directions. This causes the overall dominant frequency to shift relative to the isotropic model, and even multiple close dominant frequencies (such as...) are observed. Figure 3 (As shown). Meanwhile, the elastic modulus is relatively small in the latitudinal direction of the material, making it more prone to large, localized deformations (such as...). Figure 4 This will increase the instantaneous fluctuation amplitude of the drag coefficient (e.g.) Figure 3 As shown), and this will cause the canopy to undergo asymmetric deformation and corresponding significant asymmetric flow field distribution and wake oscillation during operation (such as...). Figure 5 and 6 (As shown).

[0062] Experiments have shown that structural dynamics models that consider the influence of anisotropic elastic coefficients can effectively and accurately simulate the nonlinear deformation of the canopy of a supersonic parachute, and can observe more complex anisotropic / nonlinear behavior, as well as correspondingly more intense deformation and more unstable flow field changes.

[0063] This invention also provides an optimization method based on anisotropic umbrella canopies, with the following embodiment: First, simulation testing is performed using any of the above-described dynamic performance simulation testing methods based on anisotropic umbrella canopies, and then the following steps are performed: S5, Performance Evaluation: Compare the simulation test results with the preset performance indicators; S6, Design Iteration: If the comparison results do not meet the requirements, adjust at least one design parameter of the canopy based on the analysis of the simulation test results, and return to step S1 until the requirements are met.

[0064] The simulation testing method of this invention is used to conduct simulation tests on the initial canopy design. The simulation conditions simulate its target working environment (e.g., 30km altitude, Ma=2.0). After the test, a comprehensive result dataset is obtained, including: the time history curve of the overall drag coefficient of the canopy, the transient equivalent stress distribution cloud map of the canopy surface, the displacement and acceleration time history of canopy feature points (e.g., the canopy top, canopy edge), and the dominant frequency and amplitude of canopy vibration obtained through spectrum analysis. Through in-depth analysis and diagnosis of these results, the above diagnostic results are compared with the preset, more optimized performance index system. If the comparison results do not meet the requirements, at least one design parameter of the canopy is adjusted based on the analysis of the simulation test results, and the design is iterated until the requirements are met.

[0065] Based on the above embodiments, in another embodiment of the present invention, in step S6, at least one evaluation index related to the performance of the umbrella canopy structure is extracted, and based on the distribution or value of the index, weak areas or points to be optimized in the umbrella canopy design are diagnosed. According to the diagnosis results, the local design variables of the umbrella canopy corresponding to the weak areas or points to be optimized in the initial design parameters are adjusted, and then the process returns to step S1 for iterative simulation until the evaluation index meets the preset design requirements.

[0066] This invention allows for the extraction of multiple evaluation indices of different properties (such as static strength indices and dynamic characteristic indices) and the diagnosis of their corresponding weak areas. This enables designers to address multiple engineering problems of different natures in parallel within the same iteration (such as simultaneously solving local strength deficiencies and excessive vibrations) and assess the interactions between different adjustment measures. Because the diagnosis is clear and the adjustments are precise, the design modifications in each iteration are local and small-scale, avoiding complete overhauls. This not only reduces model modifications and computational costs in each iteration, but more importantly, it allows the optimization process to converge quickly along a clear path, avoiding the oscillations or divergences found in traditional trial-and-error methods.

[0067] This invention also provides a dynamic performance simulation and testing system based on anisotropic umbrella canopies, with the following embodiment: It is used to implement any of the above-described dynamic performance simulation and testing methods based on anisotropic umbrella canopies, comprising: The basic model building module is used to discretize the flexible fabric structure of the transsupersonic parachute canopy into a mesh model. Anisotropic model building module, used to build anisotropic mass-spring-damping models; The fluid-structure interaction simulation module is used to place the anisotropic mass-spring-damping model in a preset supersonic flow field calculation domain, and perform numerical calculations through the fluid-structure interaction solver to simulate the dynamic process of the umbrella canopy in the flow field. The result output module is used to acquire and output the results of the simulation test.

[0068] This invention significantly lowers the technical barrier to entry through modular design, enabling ordinary engineering designers to conduct high-precision umbrella dynamic performance simulation tests conveniently and systematically without needing to master all the details of anisotropic modeling and fluid-structure interaction algorithms. This greatly promotes the engineering popularization and application of advanced simulation technology.

[0069] The present invention also provides a computer-readable storage medium, wherein a computer program is stored thereon, and when the computer program is executed by a processor, it implements any of the above-described methods for simulating and testing the dynamic performance of anisotropic umbrella canopies.

[0070] For those skilled in the art, various improvements and modifications can be made without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention.

Claims

1. A method for simulating and testing the dynamic performance of anisotropic umbrella canopies, characterized in that, Includes the following steps: S1, Basic Model Construction: For the flexible fabric structure of the parachute canopy, the flexible fabric structure is discretized into a mesh model, and a mass-spring-damping model is constructed, including discrete mass points and spring units connecting adjacent mass points. The mass points are discretely distributed according to the geometry of the parachute canopy. S2, Anisotropic Model Construction: The spring unit is divided into warp springs and weft springs according to the fiber orientation of the fabric, corresponding to the warp mechanical transmission path and weft mechanical transmission path of the fabric, respectively. By conducting a unidirectional tensile test on the umbrella canopy flexible fabric, the warp elastic coefficient and weft elastic coefficient are obtained and calibrated respectively. The warp elastic coefficient is not equal to the weft elastic coefficient. An anisotropic elastic force calculation expression is constructed to calculate the elastic force on the warp spring and the weft spring, forming an anisotropic mass-spring-damping model. S3, Fluid-structure Interaction Simulation: The anisotropic mass-spring-damping model is placed in a preset flow field calculation domain, and numerical calculations are performed through a fluid-structure interaction solver to simulate the dynamic process of the umbrella canopy in the flow field. S4. Result Output: Obtain and output the results of the simulation test, including at least the deformation time series of the canopy, the overall drag coefficient time history, and the flow field pressure distribution on the surface of the canopy.

2. The dynamic performance simulation and testing method based on anisotropic umbrella canopy according to claim 1, characterized in that, The force calculation of the spring unit adopts the anisotropic elastic force formula. In the anisotropic mass-spring-damping model, the elastic force of the spring in the four directions corresponding to mass point (i,j) and its adjacent mass points is calculated according to the following formula: ； ； ； ； in, Let be the elastic force of the spring along the direction at the position of mass (i,j); The elastic force of the spring at the position (i-1,j) is the radial force. Let be the elastic force of the spring in the latitudinal direction at the position of mass (i,j); Let be the elastic force of the spring in the latitudinal direction at the position of mass (i,j-1); The longitudinal linear elastic coefficient; The linear elastic coefficient is in the latitudinal direction; It is the complementary angle of the polar angle of the particle (i,j) along the meridional direction; Let be the azimuth angle of the particle (i,j) along the meridional direction; It is the complementary angle of the polar angle of the particle (i-1,j) along the meridional direction; Let be the azimuth angle of the particle (i-1,j) along the meridional direction; It is the complementary angle of the polar angle in the latitudinal direction of the particle (i,j); It is the complementary angle of the polar angle in the latitudinal direction of the particle (i,j-1); Let be the azimuth angle of the particle (i,j) in the latitudinal direction; Let be the azimuth angle of the particle (i,j-1) in the latitudinal direction; Let be the change in displacement of the particle (i,j) along the meridional direction; This represents the change in displacement of the particle at position (i-1,j) along the meridional direction. Let be the change in displacement of the particle (i,j) in the latitudinal direction; This represents the latitudinal displacement change of the particle at position (i,j-1).

3. The dynamic performance simulation and testing method based on anisotropic umbrella canopy according to claim 2, characterized in that, For any reference mass point (i, j) in the mesh model, it is connected to four adjacent mass points (i-1, j), (i+1, j), (i, j-1), and (i, j+1) through four spring elements. Anisotropic elastic force calculation expressions are established for each of the four spring elements. The construction method is as follows: For the spring unit connecting mass (i, j) and (i+1, j), and the spring unit connecting mass (i-1, j) and (i, j), the isotropic elastic coefficient in its elastic force calculation formula is replaced with the meridional elastic coefficient, and the calculation is performed in conjunction with the elongation and geometric projection factor of the spring unit. For the spring unit connecting mass (i, j) and (i, j+1), and the spring unit connecting mass (i, j-1) and (i, j), the isotropic elastic coefficient in its elastic force calculation formula is replaced with the latitudinal elastic coefficient, and the calculation is performed in conjunction with the elongation and geometric projection factor of the spring unit.

4. The method for simulating and testing the dynamic performance of anisotropic umbrella canopies according to claim 1 or 2, characterized in that, The warp elasticity coefficient and the latitudinal elasticity coefficient are related by an anisotropy factor, which is the ratio of the latitudinal elasticity coefficient to the warp elasticity coefficient, and the anisotropy factor ranges from 0.90 to 0.

98.

5. The method for simulating and testing the dynamic performance of anisotropic umbrella canopies according to claim 4, characterized in that, The anisotropy factor is set to 0.

94.

6. The dynamic performance simulation and testing method based on anisotropic umbrella canopy according to claim 5, characterized in that, In step S2, the fluid-structure interaction simulation is performed using an autonomous solver, which performs bidirectional real-time coupling solution of the structural dynamics equations of the anisotropic mass-spring-damped model and the flow control equations of the computational fluid dynamics model.

7. An optimization method based on anisotropic parachute canopy, characterized in that, First, the dynamic performance simulation test method based on anisotropic umbrella canopy as described in any one of claims 1 to 6 is used for simulation testing, and then the following steps are performed: S5, Performance Evaluation: Compare the simulation test results with the preset performance indicators; S6, Design Iteration: If the comparison results do not meet the requirements, adjust at least one design parameter of the canopy based on the analysis of the simulation test results, and return to step S1 until the requirements are met.

8. The optimization method based on anisotropic umbrella canopy according to claim 7, characterized in that, In step S6, at least one evaluation index related to the performance of the canopy structure is extracted, and based on the distribution or value of the index, weak areas or points to be optimized in the canopy design are diagnosed. According to the diagnosis results, the local design variables of the canopy corresponding to the weak areas or points to be optimized in the initial design parameters are adjusted, and then the process returns to step S1 for iterative simulation until the evaluation index meets the preset design requirements.

9. A dynamic performance simulation and testing system based on anisotropic umbrella canopy, characterized in that, The method for simulating and testing the dynamic performance of anisotropic umbrella canopies as described in any one of claims 1 to 6 includes: The basic model building module is used to discretize the flexible fabric structure of the transsupersonic parachute canopy into a mesh model. Anisotropic model building module, used to build anisotropic mass-spring-damping models; The fluid-structure interaction simulation module is used to place the anisotropic mass-spring-damping model in a preset supersonic flow field calculation domain, and perform numerical calculations through the fluid-structure interaction solver to simulate the dynamic process of the umbrella canopy in the flow field. The result output module is used to acquire and output the results of the simulation test.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the dynamic performance simulation test method based on anisotropic umbrella canopy as described in any one of claims 1 to 6.

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