Fluid-structure interaction dynamics simulation test method and system for canopy, and optimization method
By coupling a nonlinear mass-spring-damping model with the flow field, the problem of large simulation errors in parachute canopy simulation in traditional methods is solved, achieving high-precision dynamic simulation and reducing experimental costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-08
- Publication Date
- 2026-03-27
AI Technical Summary
Traditional methods struggle to balance computational efficiency and accuracy when simulating the fluid-structure interaction dynamics of parachute canopies. Linear models cannot accurately describe the nonlinear stiffness changes of the fabric, resulting in large simulation errors and severe numerical oscillations in complex aerodynamic environments.
A nonlinear mass-spring-damping model was adopted. By calibrating the nonlinear elastic coefficients and damping force terms, and combining flow field calculations, the governing equations were established to simulate the dynamic response of the umbrella canopy in the flow field.
It improves the accuracy and reliability of parachute dynamic behavior simulation, accurately predicts large deformation and nonlinear vibration, reduces the need for expensive wind tunnel tests and airdrop tests, and lowers development costs.
Smart Images
Figure CN121744969A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of parachute design and analysis, in particular to a kind of parachute's fluid-structure coupling dynamics simulation test method and system, optimization method. BACKGROUND
[0002] In the process of parachute opening, inflation and stable descent, the canopy, as a typical flexible fabric structure, will experience large deformation, strong nonlinearity and complex fluid-structure coupling. Traditional numerical methods face fundamental challenges in simulating such problems, such as the difficulty in balancing computational efficiency, numerical stability and physical accuracy. Specifically, the existing technology mainly has the following bottlenecks: when simulating extremely thin and large deformation structures such as fabrics, the continuous medium method (such as finite element method) is easily caused by grid distortion, resulting in calculation failure or sharp decline in accuracy. When modeling local anisotropic structures such as seams and reinforcing belts, high grid density is required, which is costly and difficult to apply to engineering-level overall canopy dynamics simulation.
[0003] In contrast, the classical particle-spring-damper model is usually applied to the parachute structure dynamics model and used for fluid-structure coupling calculation and analysis of the parachute. However, the classical mass-spring-damper model usually uses linear Hookean springs, and the force-deformation relationship is a simple linear proportion. This cannot describe the typical nonlinear constitutive relationship of real woven fabrics (such as parachute silk) under stress, such as low stiffness in the initial relaxation zone, subsequent linear or nonlinear stiffness transition in the working zone, and stiffness hardening or softening effect near failure. The linear model cannot accurately simulate the stiffness evolution of the fabric under large deformation, resulting in a fundamental deviation in predicting the canopy inflation shape, load transfer and stress distribution, especially under high dynamic load at the moment of opening. In a strong fluid-structure coupling environment, the structure model needs to withstand high-frequency and large-amplitude load excitation from the flow field. The linear spring system suitable for small deformation simulation is prone to non-physical numerical oscillation, abnormal energy accumulation or dissipation under such excitation, leading to coupling calculation instability.
[0004] In summary, there is an urgent need to provide a parachute's fluid-structure coupling dynamics simulation test method and system, optimization method that can significantly improve the accuracy, efficiency and reliability of the dynamics behavior simulation of flexible fabric systems such as parachutes in complex aerodynamic environments. SUMMARY
[0005] The purpose of the present application is to provide a parachute's fluid-structure coupling dynamics simulation test method and system, optimization method that can significantly improve the accuracy, efficiency and reliability of the dynamics behavior simulation of flexible fabric systems such as parachutes in complex aerodynamic environments.
[0006] The above object is achieved by the following technical solution: A fluid-structure coupling dynamics simulation test method of a canopy, comprising the following steps: S1, model discretization: for the flexible fabric structure of the parachute canopy, the flexible fabric structure is discretized into a grid model, and a mass-spring-damper model including discrete particles, spring units and damping units connecting adjacent particles is constructed; S2, nonlinear constitutive modeling: a nonlinear elastic force calculation expression is defined for the spring unit, the expression includes a linear elastic force term and a nonlinear elastic force term, and the linear elastic force term and the nonlinear elastic force term are respectively provided with a linear elastic coefficient and a nonlinear elastic coefficient; the linear elastic coefficient and the nonlinear elastic coefficient in the expression are calibrated by performing a material mechanics performance test on the flexible fabric of the canopy, and the calibrated values are assigned to the spring unit to form a nonlinear mass-spring-damper model; S3, establishment of control equation: based on Newton's second law, a control equation of the nonlinear mass-spring-damper model is established, the control equation at least includes an elastic force term determined by the nonlinear elastic force calculation expression, a damping force term and an external aerodynamic force term from the flow field; S4, fluid-structure coupling simulation: the nonlinear mass-spring-damper model is placed in a preset flow field calculation domain, the control equation is solved, the dynamic response process of the canopy in the flow field is simulated, and the kinetic behavior data and aerodynamic characteristic data of the parachute in the opening, inflation and stable descent process are obtained; S5, result output: based on the kinetic behavior data and aerodynamic characteristic data, the simulation test evaluation of the supersonic parachute structure performance and aerodynamic response is completed.
[0007] The present application overcomes the defect that the traditional linear model cannot accurately simulate the nonlinear mechanical behavior of the fabric large deformation by introducing a nonlinear spring constitutive model based on physical test calibration; the nonlinear model can more truly reflect the complex response of the canopy under the action of strong fluid-structure coupling, and more severe canopy asymmetric deformation and the corresponding unsteady flow field structure are observed in the simulation, which helps to study and predict the possible instability phenomena such as flutter and oscillation in practice, and the complex dynamic behavior capturing ability is enhanced.
[0008] Further technical solutions are that the mechanical property test is a uniaxial tensile test, and the linear elastic coefficient and the nonlinear elastic coefficient are calculated according to formula (1) and formula (2): (1) (2) Wherein, is the linear elastic coefficient, is the nonlinear elastic coefficient, Elastic modulus of material, Equivalent cross-sectional area, Original length of spring unit, Nonlinear coefficient of material, used to represent the nonlinear characteristics of the material.
[0009] Further technical solutions are that the flexible fabric of the canopy has warp and weft anisotropy, the nonlinear term is a cubic power term with respect to the elongation of the spring, and for any internal reference particle (i, j) in the grid model, the spring unit connecting four adjacent particle points is explicitly divided into warp and weft directions, wherein the warp direction is i The force calculation of the spring unit adopts a nonlinear force elastic force formula, and in the nonlinear force mass-spring-damping model, the nonlinear force elastic force of the particle (i, j) and its adjacent particles corresponding to the four-direction spring is calculated according to the following formula: (3) (4) (5) (6) Wherein, is the elastic force of the warp spring at the position of the particle (i, j); is the elastic force of the warp spring at the position of the particle (i-1, j); is the elastic force of the weft spring at the position of the particle (i, j); is the elastic force of the weft spring at the position of the particle (i, j-1); is the linear elastic coefficient of the warp direction; is the nonlinear elastic coefficient of the warp direction; is the linear elastic coefficient of the weft direction; is the nonlinear elastic coefficient of the weft direction; is the complementary angle of the polar angle of the warp direction at the position of the particle (i, j); is the azimuth angle of the warp direction at the position of the particle (i, j); is the complementary angle of the polar angle of the warp direction at the position of the particle (i-1, j); is the azimuth angle of the warp direction at the position of the particle (i-1, j); is the complementary angle of the polar angle of the weft direction at the position of the particle (i, j); is the complementary angle of the polar angle of the weft direction at the position of the particle (i, j-1); is the azimuth angle of the weft direction at the position of the particle (i, j); is the azimuth angle of the weft direction at the position of the particle (i, j-1); is the displacement change amount of the warp direction at the position of the particle (i, j); is the displacement change amount of the warp direction at the position of the particle (i-1, j); The displacement change amount of the particle (i, j) in the longitudinal direction is The displacement change amount of the particle (i, j-1) in the longitudinal direction is The nonlinear elastic force of the four spring units is as follows: (7) The nonlinear elastic force of the four spring units is as follows: The nonlinear elastic force of the four spring units is as follows:
[0010] The present application distinguishes the spring units in the warp and weft directions, and uses experimentally calibrated and unequal elastic coefficients to construct an anisotropic force model, which for the first time reproduces the direction-dependent mechanical behavior of the canopy fabric in a mass-spring-damper framework with high calculation efficiency and high fidelity. This fundamentally overcomes the inherent defect of the traditional isotropic model that cannot accurately simulate the deformation difference between the warp and weft directions, and greatly improves the prediction accuracy of the large deformation and nonlinear vibration of the canopy.
[0011] Further, the particle (i, j) is connected to four adjacent particles (i-1, j), (i+1, j), (i, j-1), and (i, j+1) through four spring units, and a nonlinear force elastic force calculation expression is established for each of the four spring units, and the construction method is as follows: For the spring unit connecting the particles (i, j) and (i+1, j), and the spring unit connecting the particles (i-1, j) and (i, j), the linear elastic coefficient and the nonlinear elastic coefficient in the elastic force calculation formula are replaced by the warp linear elastic coefficient and the warp nonlinear elastic coefficient, respectively, and the calculation is performed in combination with the elongation and the geometric projection factor of the spring unit. For the spring unit connecting the particles (i, j) and (i, j+1), and the spring unit connecting the particles (i, j-1) and (i, j), the linear elastic coefficient and the nonlinear elastic coefficient in the elastic force calculation formula are replaced by the weft linear elastic coefficient and the weft nonlinear elastic coefficient, respectively, and the calculation is performed in combination with the elongation and the geometric projection factor of the spring unit.
[0012] The application realizes embedding of anisotropic constitutive relation at the most fundamental mechanical calculation unit level, ensures that the longitudinal mechanical path only uses the radial elastic coefficient and the weft mechanical path only uses the weft elastic coefficient, and thus forcibly realizes the direction dependence of mechanics at the algorithm root. Secondly, the topological logic of the structured grid is strictly followed, and the elongation and force of each spring are independently calculated, avoiding force calculation confusion that may occur under complex deformation. Meanwhile, the radial elastic coefficient and the weft elastic coefficient are separately calibrated, and the directional geometric projection factor is used, so that the model can still be physically self-consistent when simulating the longitudinal and weft coupling deformation, thereby ensuring the numerical stability of the whole process of fluid-structure coupling simulation under high nonlinearity working conditions.
[0013] Further technical solutions are that the longitudinal linear elastic coefficient, the longitudinal nonlinear elastic coefficient, the weft linear elastic coefficient are calculated by formula (1) and formula (2), the weft nonlinear elastic coefficient is obtained by multiplying the longitudinal nonlinear elastic coefficient by an anisotropic correction factor γ, and the value range of the anisotropic correction factor γ is 0.90 to 0.98.
[0014] Preferably, the anisotropic correction factor is 0.95. This technical solution establishes the correlation between the longitudinal and weft nonlinear elastic coefficients through a clear correction factor, which not only ensures the accurate adaptation of the model to the anisotropy of the fabric, but also simplifies the parameter determination process, reduces the complexity of model calibration, ensures the reasonableness of the simulation of weft mechanical properties, and improves the engineering practicability of the model.
[0015] Further technical solutions are that the control equation covers the force balance relationship of elastic force, damping force, pressure difference inside and outside the canopy, gravity and linkage structure tension, wherein the elastic force is determined by the nonlinear force-deformation relationship, and the damping force includes a tangential damping component and a normal damping component.
[0016] In this way, the application completely defines the physical laws and force balance relationships on which the simulation is based. The control equation integrates nonlinear elastic force, various external loads and constraints, and constitutes a physically complete dynamic system description. This is the mathematical basis for coupling and solving the nonlinear structure model and the real physical environment (flow field, gravity field), which ensures the mechanical correctness of the simulation process.
[0017] Further technical solutions are that the control equation is: ; Wherein, is the displacement change amount of the particle (i, j) position, m is the mass of the particle, t is the time, and are the tangential and normal damping coefficients respectively, represents the change of the spring unit, represents the unit vector of adjacent mass points, represents the velocity of the mass point, represents the normal vector of the flexible fabric surface, , and respectively represent the pressure difference inside and outside the flexible fabric, the gravity and the tension of the connecting structure.
[0018] The present application ensures the completeness and accuracy of the control equation by comprehensively covering the key force types of parachute dynamics behavior, enables the model to fully characterize the dynamic response of the mass point in the fluid-structure coupling environment, effectively avoids the simulation error caused by force omission, and further improves the reliability of the simulation of key processes such as parachute opening impact and steady-state descent; and by setting the damping coefficient in different directions, the difference in damping characteristics of the canopy fabric in the tangential and normal directions is accurately matched, effectively suppressing the non-physical numerical oscillation caused by high-frequency and large-amplitude load excitation in the fluid-structure coupling environment, avoiding abnormal energy accumulation or dissipation, and improving the stability of the coupling calculation.
[0019] To achieve the above-mentioned purpose, the present application also provides an optimization method of a canopy, first using the fluid-structure coupling dynamics simulation test method of the canopy described above to perform simulation test, and then performing the following steps: S6, performance evaluation: comparing the simulation test results with the preset performance indicators; S7, design iteration: if the comparison result does not meet the requirements, adjusting at least one design parameter of the canopy based on the analysis of the simulation test results, and returning to execute step S1 until the requirements are met.
[0020] Further technical solutions are that in the step S7, at least one evaluation index related to the structure performance of the canopy is extracted, and based on the distribution or value of the index, the weak area or optimization point of the canopy design is diagnosed, and according to the diagnosis result, the local design variable of the canopy corresponding to the weak area or optimization point in the initial design parameter is adjusted, and then the step S1 is returned to perform iterative simulation until the evaluation index meets the preset design requirements.
[0021] The method of the present application allows extraction of multiple evaluation indexes of different properties (such as static strength indexes and dynamic characteristic indexes), and diagnosis of the corresponding weak areas respectively. This enables the designer to handle multiple engineering problems of different properties in parallel in the same iteration (such as solving local strength deficiency and excessive vibration at the same time), and to evaluate the mutual influence between different adjustment measures. Since the diagnosis is clear and the adjustment is accurate, the design modification in each iteration is local and small in scope, avoiding overall changes. This not only reduces the model modification and calculation cost of each iteration, but more importantly, it enables the optimization process to converge quickly along a clear path, avoiding the oscillation or divergence in the traditional trial-and-error method.
[0022] To achieve the above object, the present application also provides a fluid-structure coupling dynamics simulation test system of canopy, for realizing the dynamics performance simulation test method of anisotropic canopy based on any of the above, comprising: A model discretization module is configured to discretize the flexible fabric structure of the supersonic parachute canopy into a grid model; A nonlinear constitutive modeling module is configured to build a nonlinear mass-spring-damper model; A control equation establishment module is configured to establish a control equation of the nonlinear mass-spring-damper model based on Newton's second law; A fluid-structure coupling simulation module is configured to solve the control equation in the preset flow field calculation domain of the nonlinear mass-spring-damper model by a time marching algorithm, and simulate the dynamic process of the canopy in the flow field; A result output module is configured to acquire and output the results of the simulation test.
[0023] The present application greatly reduces the technical threshold through modular design, enabling ordinary engineering designers to conveniently and normatively carry out high-precision simulation test of the dynamics performance of the canopy without deep understanding of all the details of anisotropic modeling and fluid-structure coupling algorithms, greatly promoting the popularization and application of advanced simulation technology in engineering.
[0024] Compared with the prior art, the present application has the following technical advantages: (1) The present application can reproduce the complete nonlinear constitutive relationship of the fabric from the initial relaxation, the linear working section to the large deformation stage with high fidelity. Numerical experiments show that the relative error of the drag coefficient in the stable section calculated by the nonlinear model is only 5.0%, which is better than the linear model of 6.0%, proving that the prediction result is closer to the physical actuality, and significantly improving the simulation accuracy of the nonlinear mechanical behavior of the canopy; (2) The application can more truly simulate the severe response of the canopy under the action of strong non-steady airflow, successfully simulate the asymmetric large deformation of the canopy and the complex asymmetric flow field structure coupled therewith, and the test proves that the application has a higher dominant response frequency, can more accurately reflect the rapid response characteristics of the system under dynamic load, and enhances the capturing ability of complex fluid-structure coupling dynamics phenomena; (3) The application can effectively predict the load and evaluate the stability in the design stage, thereby reducing the dependence on expensive and high-risk wind tunnel tests and air drop tests, optimizing the design process, reducing the development cost and period, and having important engineering application prospects. BRIEF DESCRIPTION OF DRAWINGS
[0025] The drawings that form a part of the present application are used to provide a further understanding of the present application, the illustrative embodiments of the present application and the description thereof serve to explain the present application, and do not constitute an improper limitation on the present application.
[0026] Figure 1 The schematic diagram of the anisotropic mass-spring-damper model involved in an embodiment of the present application; Figure 2 The resistance coefficient-time curve of different examples of the experimental group in an embodiment of the present application; Figure 3 The resistance coefficient-time curve of different examples of the experimental group in an embodiment of the present application; Figure 2 The enlarged schematic diagram of the resistance coefficient-time curve in the 0.005s-0.01s interval in the figure; Figure 4 The instantaneous flow field nephogram of the linear elastic coefficient example in an embodiment of the present application, wherein (a), (c) and (e) are the Mach number nephograms at t=0.05s, 0.01s and 0.015s respectively, and (b), (d) and (f) are the pressure nephograms at t=0.05s, 0.01s and 0.015s respectively; Figure 5 The instantaneous flow field nephogram of the nonlinear elastic coefficient example in an embodiment of the present application, wherein (a), (c) and (e) are the Mach number nephograms at t=0.05s, 0.01s and 0.015s respectively, and (b), (d) and (f) are the pressure nephograms at t=0.05s, 0.01s and 0.015s respectively; Figure 6 The FFT analysis result graph of the resistance coefficient of different examples of the experimental group in an embodiment of the present application.
[0027] In the figure: 1 linear warp spring unit 2 nonlinear warp spring unit 3 linear weft spring unit 4 nonlinear weft spring unit 5 damping unit DETAILED DESCRIPTION
[0028] The present application is described in detail below with reference to the accompanying drawings. The description in this part is only exemplary and explanatory, and should not have any limiting effect on the protection scope of the present application. In addition, those skilled in the art can combine the features in the embodiments in the present document and the features in different embodiments according to the description in the present document.
[0029] In order to better understand the technical solutions of the present application, a fluid-structure coupling dynamics simulation test method of a canopy includes the following steps: S1, model discretization: for the flexible fabric structure of the parachute canopy, the flexible fabric structure is discretized into a grid model, and a mass-spring-damper model including discrete particles, spring units and damping units connecting adjacent particles is constructed; S2, nonlinear constitutive modeling: a nonlinear elastic force calculation expression is defined for the spring unit, the expression includes a linear elastic force term and a nonlinear elastic force term, and the linear elastic force term and the nonlinear elastic force term are respectively provided with a linear elastic coefficient and a nonlinear elastic coefficient; the linear elastic coefficient and the nonlinear elastic coefficient in the expression are calibrated by material mechanics performance test of the canopy flexible fabric, and the calibrated values are assigned to the spring unit to form a nonlinear mass-spring-damper model; S3, establishing control equation: based on Newton's second law, a control equation of the nonlinear mass-spring-damper model is established, the control equation at least includes an elastic force term determined by the nonlinear elastic force calculation expression, a damping force term and an external aerodynamic force term from the flow field; S4, fluid-structure coupling simulation: the nonlinear mass-spring-damper model is placed in a preset flow field calculation domain, the control equation is solved, the dynamic response process of the canopy in the flow field is simulated, and the dynamic behavior data and aerodynamic characteristic data of the parachute in the opening, inflation and stable descent process are obtained; S5, result output: based on the dynamic behavior data and aerodynamic characteristic data, the simulation test evaluation of the supersonic parachute structure performance and aerodynamic response is completed.
[0030] The core of the present application is to construct a mass-spring-damper model that can accurately represent the nonlinear mechanical behavior of the canopy fabric, and to couple it with the computational fluid dynamics method to realize the dynamic simulation of the whole process from the opening impact to the stable descent of the parachute.
[0031] In the specific application process, for the parachute canopy, the pre-processing software is used to discretize the canopy curved surface into a regular structured quadrilateral mesh, and the nodes of the mesh are regarded as discrete particles. Each particle has a mass attribute, and the mass of the particle can be allocated according to the surface density of the canopy fabric and the unit area represented by the node. Then, spring elements are established between adjacent particles, specifically: the mesh edge connecting each pair of adjacent particles constitutes a spring element. At the same time, a damping element is connected in parallel to each spring element to represent the internal damping of the material or the damping effect caused by air, which together constitute the basic mass-spring-damper model.
[0032] Define the nonlinear elastic force expression: define the elastic force F generated by each spring element, which no longer follows the simple linear Hooke's law, but adopts the following nonlinear expression: ; Wherein is the linear elastic coefficient, is the nonlinear elastic coefficient, is the elongation of the spring element; is a small parameter (which can be positive or negative), representing the stiffness characteristics of the spring When , it is called a hard spring, and the stiffness gradually increases with the increase of deformation (such as the force resisting deformation of a compression spring increases superlinearly). When , it is called a soft spring, and the stiffness decreases with large deformation, showing a softening characteristic (such as the large deformation stage of rubber material).
[0033] Parameter calibration: in order to obtain the linear and nonlinear elastic coefficients, the standard material mechanics performance test of the flexible fabric of the canopy (such as nylon silk, polyester fabric, etc.) needs to be carried out. The linear and nonlinear elastic coefficients in the expression are calibrated and assigned to the spring elements to form a nonlinear mass-spring-damper model.
[0034] Based on Newton's second law, a motion control equation is established for each particle in the nonlinear mass-spring-damper model, and then the nonlinear mass-spring-damper model is placed in a predetermined flow field calculation domain to solve the control equation and perform fluid-structure coupling simulation. After the simulation calculation is completed, the post-processing module automatically extracts and outputs the key result data. These results at least include: Canopy deformation time sequence: the shape diagram of the canopy at different times (such as t=0.005s, 0.01s) can be generated, which intuitively shows the process of wrinkle generation and development.
[0035] Overall drag coefficient time history: output the curve of the change of drag coefficient Cd with time, which is used to evaluate the deceleration performance of the parachute.
[0036] The flow field pressure distribution of the canopy surface: output the pressure nephogram of the space around the canopy, for analyzing the distribution of the aerodynamic load.
[0037] In addition, vibration spectrum, umbrella rope tension and other data can be further output for in-depth analysis.
[0038] The present application fundamentally overcomes the defects of the traditional linear model that cannot accurately simulate the nonlinear mechanical behavior of the fabric large deformation by introducing a nonlinear spring constitutive model based on physical test calibration, Figure 1 The nonlinear model can more truly reflect the complex response of the canopy under the strong fluid-structure interaction, and more severe asymmetric deformation of the canopy and the corresponding unsteady flow field structure are observed in the simulation, which helps to study and predict the possible instability phenomena such as flutter and oscillation in practice, and the complex dynamic behavior capturing ability is enhanced.
[0039] On the basis of the above embodiment, in another embodiment of the present application, the mechanical property test is a uniaxial tensile test, and the linear elastic coefficient and the nonlinear elastic coefficient are calculated according to formula (1) and formula (2): (1) (2) Wherein, is the linear elastic coefficient, is the nonlinear elastic coefficient, is the material elastic modulus, is the equivalent cross-sectional area, is the original length of the spring unit, is the material nonlinear coefficient, used to represent the nonlinear characteristics of the material.
[0040] In the above nonlinear mass-spring-damper model, because the canopy is a fabric or flexible material, regarding the nonlinear elastic coefficient of the canopy material, it should be noted that the mechanical behavior of the canopy material as a high polymer exhibits significant nonlinear viscoelasticity, which means that its stress-strain relationship is very complex. However, in the above nonlinear mass-spring-damper model, when the system deforms, the linear elastic spring and the nonlinear spring will be compressed by the same amount. The total force provided by the system is the sum of the respective forces. And the equivalent stiffness of the system will become harder. Its force-displacement curve is "force superposition", which is equivalent to superimposing the force-displacement curves of the linear spring and the nonlinear spring along the force axis (vertical axis) on the graph. Therefore, the initial stiffness of the system is the sum of the stiffness of the two springs. If the nonlinear spring is very soft at the initial stage, the characteristics of the linear spring will dominate; when the deformation increases, the force of the nonlinear spring rises sharply, and it will become dominant, making the overall stiffness increase significantly. Therefore, how to design the elastic coefficients of the two spring parts becomes particularly important.
[0041] To obtain the mechanical parameters for a specific design, it is usually possible to determine experimentally, i.e. by performing specific mechanical property tests on the canopy material. However, the present application employs a simple non-linear function of stress and strain in the non-linear elastic theory to describe. For example, for a simple non-linear elastic model, the relationship between stress and strain can be expressed as: ; Convert it to force-displacement relationship, as shown below: ; ; The above formula can obtain the calculation formula (1) and (2) of linear elastic coefficient and nonlinear elastic coefficient.
[0042] On the basis of the above embodiment, in another embodiment of the present application, the flexible fabric of the canopy has warp and weft anisotropy, and the non-linear term is a cubic power term about the elongation of the spring. For any internal reference particle (i, j) in the grid model, the spring element connecting the four adjacent particles is clearly divided into warp and weft, wherein the warp is the i direction, and the weft is the j direction. The force calculation of the spring element adopts the non-linear force elastic force formula. In the non-linear mass-spring-damping model, the non-linear force elastic force of the particle (i, j) and its adjacent particles corresponding to the four direction springs is calculated according to the following formula: i (3) (4) (5) (6) Wherein, is the elastic force of the warp spring at the position of the particle (i, j); is the elastic force of the warp spring at the position of the particle (i-1, j); is the elastic force of the weft spring at the position of the particle (i, j); is the elastic force of the weft spring at the position of the particle (i, j-1); is the linear elastic coefficient of the warp; is the nonlinear elastic coefficient of the warp; is the linear elastic coefficient of the weft; is the nonlinear elastic coefficient of the weft; is the complementary angle of the polar angle of the warp at the position of the particle (i, j); is the azimuth angle of the warp at the position of the particle (i, j); is the complementary angle of the polar angle of the warp at the position of the particle (i-1, j); is the azimuth angle of the longitudinal direction of the position of the particle (i, j); is the complementary angle of the polar angle of the latitudinal direction of the position of the particle (i, j); is the complementary angle of the polar angle of the latitudinal direction of the position of the particle (i, j-1); is the azimuth angle of the latitudinal direction of the position of the particle (i, j); is the azimuth angle of the latitudinal direction of the position of the particle (i, j-1); is the displacement change of the longitudinal direction of the position of the particle (i, j); is the displacement change of the longitudinal direction of the position of the particle (i-1, j); is the displacement change of the latitudinal direction of the position of the particle (i, j); is the displacement change of the latitudinal direction of the position of the particle (i, j-1); The nonlinear elastic force of the parachute center axis (z-axis) direction composed of the nonlinear forces of the above four direction springs is as follows: (7) The is the nonlinear elastic resultant force of the parachute center axis (z-axis) direction.
[0043] In the mass-spring-damper model of the application, in the original linear elastic force part, the elastic force of one direction of the particle (i, j) is corrected to nonlinear elastic force as shown in the following formula: ; In this item, represents the displacement change, that is, the elongation of the spring. represents the complementary angle of the polar angle in the spherical coordinate system, represents the azimuth angle in the spherical coordinate system, , is the geometric projection factor corresponding to the direction.
[0044] In order to introduce anisotropy, we need to replace each isotropic term, but we need to note that the displacement change of each term in the original expression is calculated independently, and corresponds to the displacement difference between the 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): corresponding to one edge of the i, j position in the i direction; corresponding to one edge of the i-1, j position in the i direction; corresponding to one edge of the i, j position in the j direction; , the one edge in the j direction corresponding to the i, j-1 position; Now, for each term, we need to replace the linear force with a nonlinear force. But note that the displacement change of each term is different. Then the force of each term becomes (3)~(6); in the original expression, the four terms are all positive terms, while the second and fourth terms have negative signs in front of them, and the elastic force of the above four edges forms the nonlinear elastic force in the z direction as formula (7).
[0045] The present application reproduces the direction-dependent mechanical behavior of the canopy fabric with high fidelity in the mass-spring-damper framework with higher calculation efficiency by distinguishing the spring units in the warp and weft directions and constructing an anisotropic force model using experimentally calibrated and unequal elastic coefficients. This fundamentally overcomes the inherent defect of the traditional isotropic model that cannot accurately simulate the warp and weft difference deformation, so that the prediction accuracy of the canopy large deformation and nonlinear vibration is improved in quality.
[0046] On the basis of the above embodiment, in another embodiment of the present application, as Figure 1 The particle (i, j) is connected to four adjacent particles (i-1, j), (i+1, j), (i, j-1), and (i, j+1) through four spring units, and a nonlinear force elastic force calculation expression is established for the four spring units, and the construction method is as follows: For the spring unit connecting the particles (i, j) and (i+1, j), and the spring unit connecting the particles (i-1, j) and (i, j), replace the linear elastic coefficient and the nonlinear elastic coefficient in the elastic force calculation formula with the warp linear elastic coefficient and the warp nonlinear elastic coefficient respectively, and calculate in combination with the elongation of the spring unit and the geometric projection factor; For the spring unit connecting the particles (i, j) and (i, j+1), and the spring unit connecting the particles (i, j-1) and (i, j), replace the linear elastic coefficient and the nonlinear elastic coefficient in the elastic force calculation formula with the weft linear elastic coefficient and the weft nonlinear elastic coefficient respectively, and calculate in combination with the elongation of the spring unit and the geometric projection factor.
[0047] The application realizes the embedding of anisotropic constitutive relation at the most fundamental mechanical calculation unit level, ensures that the meridional mechanical path only uses the radial elastic coefficient and the weft mechanical path only uses the weft elastic coefficient, and thus forcibly realizes the direction dependence of mechanics at the algorithm root. Secondly, the topological logic of the structured grid is strictly followed, and the elongation and force of each spring are calculated independently, avoiding the confusion in force calculation under complex deformation. At the same time, the radial elastic coefficient and the weft elastic coefficient are separately calibrated, and the directional geometric projection factor is used, so that the model can still maintain physical self-consistency when simulating the meridional and weft coupling deformation, thereby ensuring the numerical stability of the whole process of fluid-structure coupling simulation under high nonlinearity working conditions.
[0048] On the basis of the above-mentioned embodiment, in another embodiment of the application, the meridional linear elastic coefficient, the meridional nonlinear elastic coefficient, the weft linear elastic coefficient are calculated by formula (1) and formula (2), and the weft nonlinear elastic coefficient is obtained by multiplying the meridional nonlinear elastic coefficient by an anisotropic correction factor γ, the value range of the anisotropic correction factor γ is 0.90 to 0.98.
[0049] Preferably, the anisotropic correction factor is 0.95. This technical solution establishes the correlation between the meridional and weft nonlinear elastic coefficients through a clear correction factor, which not only ensures the accurate adaptation of the model to the anisotropy of the fabric, but also simplifies the parameter determination process, reduces the complexity of model calibration, ensures the reasonableness of the simulation of weft mechanical properties, and improves the engineering practicability of the model.
[0050] For canopy materials, due to the difference in weaving structure and fiber orientation, the elastic properties in the warp and weft directions are usually different. For example, the warp direction (longitudinal direction) bears the principal stress and has higher stiffness, while the weft direction (transverse direction) maintains shape stability and has slightly lower stiffness. The anisotropic factor is usually less than 1. For canopy materials, the selection of the anisotropic factor should be based on the test data or empirical values of the actual material.
[0051] On the basis of the above-mentioned embodiment, in another embodiment of the application, the control equation covers the force balance relationship of elastic force, damping force, pressure difference inside and outside the canopy, gravity and linkage structure tension, wherein the elastic force is determined by the nonlinear force-deformation relationship, and the damping force includes a tangential damping component and a normal damping component.
[0052] In addition, it is noted that the cubic term in the nonlinear term may cause numerical instability, especially when the displacement change is large. Therefore, it is necessary to ensure that the time step is small enough, or an implicit method is used. At the same time, if the displacement change is large, the cubic term will increase rapidly, which may cause numerical problems. Therefore, in practical application, it may be necessary to limit the range of displacement change, or use a more complex constitutive model.
[0053] Here we assume and The displacement change (i.e. the elongation of the spring) can be positive or negative, and is usually positive for parachute canopy fabric, which is generally stretched but not compressed, due to the stress characteristics of the canopy fabric.
[0054] If a piecewise linear-nonlinear model is considered (for example, linear when the displacement change is less than a certain threshold, and nonlinear when it is greater), then a judgment needs to be made at each position, which would make the calculation more complex. Here we use a unified cubic nonlinear model.
[0055] In summary, this is the process of extending the linear spring model to include linear and nonlinear elastic changes, and the control equation is based on Newton's second law acting on each control point. The control equation covers the force balance relationship of elastic force, damping force, pressure difference inside and outside the canopy, gravity, and the tension of the linking structure, where the elastic force is determined by the nonlinear force-deformation relationship, and the damping force includes the tangential and normal damping components.
[0056] In this way, the invention completely defines the physical laws and force balance relationships on which the simulation is based. The control equation integrates nonlinear elastic force, various external loads, and constraints, forming a physically complete description of the dynamic system. This is the mathematical basis for coupling the nonlinear structure model with the real physical environment (flow field, gravitational field) for solving, ensuring the mechanical correctness of the simulation process.
[0057] Further technical solutions are that the control equation is: ; where, is the displacement change of the particle (i, j) position, m is the mass of the particle, t is the time, and are the tangential and normal damping coefficients, respectively, represents the change of the spring element, represents the unit vector of the adjacent particle, represents the velocity of the particle, represents the normal vector of the flexible fabric surface, , and represent the pressure difference inside and outside the flexible fabric, the gravity, and the tension of the linking structure, respectively.
[0058] The present application ensures the completeness and accuracy of the control equation by comprehensively covering the key stress types of parachute dynamics behavior, enables the model to completely characterize the dynamic response of the mass point in the fluid-structure coupling environment, effectively avoids the simulation error caused by the omission of stress, and further improves the reliability of the simulation of key processes such as parachute opening impact and steady descent; and by setting the damping coefficient in different directions, the difference in damping characteristics of the canopy fabric in the tangential and normal directions is accurately matched, effectively suppressing the non-physical numerical oscillation caused by high-frequency and large-amplitude load excitation in the fluid-structure coupling environment, avoiding abnormal energy accumulation or dissipation, and improving the stability of the coupling calculation.
[0059] Based on the characteristics of the self-developed solver and the solving process of the nonlinear elastic coefficient, the possible problems are optimized, such as reducing the calculation step and weakening the influence of nonlinear elasticity. It should be noted that if the nonlinear elastic coefficient is strictly calculated according to the above formula, the superposition effect of the two spring units will inevitably cause the total stiffness of the spring to increase sharply. Therefore, the elastic coefficient of the nonlinear spring is greatly weakened, and further refinement design is carried out in the subsequent research.
[0060] Based on the above nonlinear mass-spring-damper structure dynamics model, the self-owned solver is used for solving, and numerical experiments are set, including linear spring comparison group (only using the longitudinal linear elastic coefficient, “-k1k” represents) and nonlinear spring comparison (including longitudinal and latitudinal linear elastic coefficient and nonlinear coefficient, “-knl” represents), as shown in Table 1.
[0061] Table 1 Research conditions and parameters of parachute structure dynamics model of the embodiment
[0062] In order to better study the influence of nonlinear elastic coefficient, the experimental group adopts a smaller elastic coefficient, that is, a softer material. Therefore, for this case, the resistance coefficient of the Polyester material with the largest flexibility in the reference (AIAA-2015-2133) is selected as a comparison, and the resistance coefficient of the wind tunnel verification test is 0.69. From Figure 2 and Figure 3 ( Figure 2 the local enlarged view) can be seen, the resistance coefficient change trend of the two comparison groups includes an initial stage, followed by a stable stage, but it can be seen that the resistance coefficient changes of the stable stage of the two examples basically coincide. However, from Figure 4(d) It can be seen that the canopy appears asymmetric deformation after 0.01s in the late stable stage, and the flow field also appears asymmetric, which is consistent with the flow phenomenon observed in the prior art document (K. Hatanaka, et al. Numerical investigations on shock oscillations ahead of a hemispherical shell in supersonic flow, Shock waves, 2016, 26:299-310).
[0063] It should be noted that in order to compare with the above wind tunnel test document (AIAA-2015-2133), the average drag force results of the stable stage of the flow field are selected for evaluation, and the linear elastic coefficient and the nonlinear elastic coefficient are calculated as shown in Figure 2 The average values are 0.6483 and 0.6554, respectively, and the relative errors with the wind tunnel test value 0.69 are 6.0% and 5.0%, respectively. It can be seen that the two groups can obtain reasonable drag coefficient results, but the nonlinear elastic coefficient can be closer to the test value.
[0064] In addition, Figure 6 The FFT analysis of the drag coefficient changes of the two groups of examples is given, and it can be seen that the first main frequency of the linear elastic coefficient example is 183.3Hz, and the second main frequency is 504.1Hz, and the first main frequency of the nonlinear elastic coefficient example is 565.6Hz. Therefore, the first main frequency of the nonlinear elastic coefficient example is higher, and it can be seen that it responds faster in the flow field. It is worth noting that the first main frequency of the nonlinear elastic coefficient example is close to the second main frequency of the linear elastic coefficient example, which shows that the canopy of the linear elastic coefficient may cause unreasonable drag coefficient fluctuations.
[0065] Overall, the structural dynamics model considering the influence of the nonlinear elastic coefficient (nonlinear spring) can effectively and more accurately simulate the nonlinear deformation of the canopy of the supersonic parachute, and more complex nonlinear behavior, and more severe deformation and more unstable flow field changes can be observed.
[0066] From the above content, it can be seen that the structural dynamics model of the parachute composed of the nonlinear spring proposed in the present application can effectively and accurately simulate the nonlinear deformation of the canopy of the supersonic parachute, and more complex nonlinear behavior, and more severe deformation and more unstable flow field changes can be observed, effectively filling the current engineering needs for fluid-structure coupling simulation and aerodynamic characteristic prediction and analysis of the parachute, and providing necessary theoretical support and technical reserves for parachute structure design and development under different task requirements.
[0067] The application further provides an optimization method of the canopy, which is implemented as follows: first, the fluid-structure coupling dynamic simulation test method of any one of the above-mentioned canopies is used for simulation test, and then the following steps are performed: S6, performance evaluation: the simulation test result is compared with the preset performance index; S7, design iteration: if the comparison result does not meet the requirement, at least one design parameter of the canopy is adjusted based on the analysis of the simulation test result, and step S1 is returned to be executed until the requirement is met.
[0068] Based on the above-mentioned embodiments, in another embodiment of the application, in the step S7, at least one evaluation index related to the structural performance of the canopy is extracted, and based on the distribution or value of the index, a weak area or optimization point of the canopy design is diagnosed, and according to the diagnosis result, a local design variable of the canopy corresponding to the weak area or optimization point in the initial design parameter is adjusted, and then step S1 is returned to be iteratively simulated until the evaluation index meets the preset design requirement.
[0069] The method of the application allows extraction of multiple evaluation indexes of different properties (such as static strength index and dynamic characteristic index), and diagnosis of the corresponding weak areas. This enables the designer to handle multiple engineering problems of different properties in parallel (such as simultaneously solving local strength deficiency and excessive vibration) in the same iteration, and to evaluate the mutual influence between different adjustment measures. Since the diagnosis is clear and the adjustment is accurate, the design modification in each iteration is local and small in scope, avoiding overall modification. This not only reduces the model modification and calculation cost of each iteration, but more importantly, it enables the optimization process to converge quickly along a clear path, avoiding the oscillation or divergence in the traditional trial-and-error method.
[0070] The application further provides a fluid-structure coupling dynamic simulation test system of the canopy, which is implemented as follows and is used to implement the dynamic performance simulation test method of the anisotropic canopy, and comprises: A model discretization module is configured to discretize the flexible fabric structure of the supersonic parachute canopy into a grid model; A nonlinear constitutive modeling module is configured to construct a nonlinear mass-spring-damper model; A control equation establishing module is configured to establish a control equation of the nonlinear mass-spring-damper model based on Newton's second law; A fluid-structure coupling simulation module is configured to solve the control equation in a preset flow field calculation domain of the nonlinear mass-spring-damper model by a time marching algorithm to simulate the dynamic process of the canopy in the flow field; A result output module is configured to obtain and output the result of the simulation test.
[0071] The application greatly reduces the technical use threshold through the modular design, so that ordinary engineering designers do not need to deeply master all details of anisotropic modeling and fluid-structure coupling algorithm, and can conveniently and normatively carry out high-precision simulation test of umbrella clothing dynamics performance, greatly promoting popularization and application of engineering of advanced simulation technology.
[0072] For those skilled in the art of the present technology, several improvements and refinements can be made without departing from the principles of the present application, and these improvements and refinements should also be considered within the scope of protection of the present application.
Claims
1. A fluid-structure interaction dynamics simulation and testing method for an umbrella canopy, characterized in that, Includes the following steps: S1, Model Discretization: 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 and damping units connecting adjacent mass points. S2, Nonlinear Constitutive Modeling: Define a nonlinear elastic force calculation expression for the spring element. The expression includes a linear elastic force term and a nonlinear elastic force term, with linear elastic coefficients and nonlinear elastic coefficients respectively. By testing the material mechanical properties of the umbrella canopy flexible fabric, the linear elastic coefficients and nonlinear elastic coefficients in the expression are calibrated and the calibrated values are assigned to the spring element to form a nonlinear mass-spring-damping model. S3, Establish the governing equations: Based on Newton's second law, establish the governing equations of the nonlinear mass-spring-damped model. The governing equations shall include at least the elastic force term, the damping force term, and the external aerodynamic force term from the flow field, which are determined by the nonlinear elastic force calculation expression. S4, Fluid-structure Interaction Simulation: The nonlinear mass-spring-damping model is placed in a preset flow field calculation domain, the control equation is solved, the dynamic response process of the parachute canopy in the flow field is simulated, and the dynamic behavior data and aerodynamic characteristic data of the parachute during the opening, inflation and stable descent processes are obtained. S5. Results Output: Based on the aforementioned dynamic behavior data and aerodynamic characteristic data, complete the simulation test and evaluation of the structural performance and aerodynamic response of the supersonic parachute.
2. The fluid-structure interaction dynamics simulation and testing method for umbrella canopies according to claim 11, characterized in that, The mechanical property test is a uniaxial tensile test, and the linear elastic coefficient and nonlinear elastic coefficient are calculated according to formula (1) and formula (2): （1） （2） in, The linear elastic coefficient is... The elastic coefficient is a nonlinear elastic coefficient. The elastic modulus of the material. For equivalent cross-sectional area, The original length of the spring unit This is the material nonlinearity coefficient, used to represent the nonlinear characteristics of a material.
3. The fluid-structure interaction dynamics simulation and testing method for umbrella canopies according to claim 2, characterized in that, The flexible fabric of the umbrella canopy exhibits warp and weft anisotropy, and the nonlinear term is a cubic power of the spring elongation. For any internal reference mass point (i, j) in the mesh model, the spring elements connecting its four neighboring mass points are explicitly divided into warp and weft directions, where the warp direction is... i The direction, with the latitudinal direction being the j-direction, is used for force calculation of the spring unit using a nonlinear force elastic force formula. In the nonlinear force mass-spring-damping model, the nonlinear force elastic force of the spring in the four directions corresponding to mass point (i,j) and its adjacent mass points is calculated using 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 elastic coefficient is the meridional nonlinear elastic coefficient. The linear elastic coefficient is in the latitudinal direction; The nonlinear 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); The nonlinear elastic forces of the springs in the four directions mentioned above constitute the nonlinear elastic resultant force along the central axis of the parachute. The calculation formula is as follows: ； The The resultant force is the nonlinear elastic force along the central axis of the parachute.
4. The fluid-structure interaction dynamics simulation and testing method for umbrella canopies according to claim 3, characterized in that, A particle (i,j) is connected to four adjacent particles (i-1,j), (i+1,j), (i,j-1), and (i,j+1) via four spring units. Nonlinear elastic force calculation expressions are established for each of the four spring units, and their 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 linear elastic coefficient and nonlinear elastic coefficient in their elastic force calculation formula are replaced with the meridional linear elastic coefficient and meridional nonlinear elastic coefficient, respectively, 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 linear elastic coefficient and nonlinear elastic coefficient in their elastic force calculation formula are replaced with the latitudinal linear elastic coefficient and latitudinal nonlinear elastic coefficient, respectively, and the calculation is performed in conjunction with the elongation and geometric projection factor of the spring unit.
5. The fluid-structure interaction dynamics simulation and testing method for umbrella canopies according to claim 4, characterized in that, The meridional linear elastic coefficient, the meridional nonlinear elastic coefficient, and the zonal linear elastic coefficient are calculated by formulas (1) and (2). The zonal nonlinear elastic coefficient is obtained by multiplying the meridional nonlinear elastic coefficient by an anisotropy correction factor γ, and the value of the anisotropy correction factor γ ranges from 0.90 to 0.
98.
6. The fluid-structure interaction dynamics simulation test method for umbrella canopies according to claim 3, characterized in that, The governing equations cover the force balance relationship of elastic force, damping force, pressure difference between the inside and outside of the canopy, gravity, and tension of the connecting structure. The elastic force is determined by the nonlinear force-deformation relationship, and the damping force includes tangential damping components and normal damping components.
7. The fluid-structure interaction dynamics simulation and testing method for umbrella canopies according to claim 4, characterized in that, The governing equation is: ； in, Let be the change in displacement of the particle at position (i,j). m For the mass of the point mass, t For time, and These are the damping coefficients in the tangential and normal directions, respectively. This indicates the change in the spring unit. Represents the unit vector of adjacent particles. Represents the velocity of a particle. This represents the normal vector of the flexible fabric surface. , and These represent the pressure difference between the inside and outside of the flexible fabric, gravity, and the tensile force of the connecting structure, respectively.
8. An optimization method for umbrella canopies, characterized in that, First, the fluid-structure interaction dynamics simulation test method for the umbrella canopy as described in any one of claims 1 to 7 is used for simulation testing, and then the following steps are performed: S6, Performance Evaluation: Compare the simulation test results with the preset performance indicators; S7, 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.
9. The method for optimizing the umbrella canopy according to claim 8, characterized in that, In step S7, 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.
10. A fluid-structure interaction dynamics simulation and testing system for an 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 7 includes: The model discretization module is used to discretize the flexible fabric structure of the supersonic parachute canopy into a mesh model. The nonlinear basic modeling module is used to construct nonlinear mass-spring-damped models; Control equation establishment module: used to establish the control equations of the nonlinear mass-spring-damped model based on Newton's second law; The fluid-structure interaction simulation module is used to solve the control equations in the preset flow field calculation domain of the nonlinear mass-spring-damping mode using a time-progression algorithm, thereby simulating 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.