Method, system, medium and software product for calculating contribution of tire component to radial rigidity

Abstract

The invention relates to the technical field of tire finite element simulation design, in particular to a method, a system, a medium and a software product for calculating contribution of a tire part to radial rigidity. The method comprises the steps that a two-dimensional tire finite element model is established, inflation pressure is applied, a three-dimensional model is generated, a load is applied, and the radial rigidity of a complete tire is calculated; the Young modulus of the target part is reduced to 0.01%-5% of a design value, simulation is repeated, and rigidity after modification is calculated; and calculating a rigid contribution value and a contribution rate of the component through a difference value between the two values. The system comprises a finite element modeling module, a simulation module, an attribute adjustment module and a rigidity analysis module. On the premise of ensuring the continuity of a simulation structure and the consistency of working conditions, the method can accurately peel off the contribution of the component, is suitable for different tire structures, and has the advantages of high precision, high universality, low cost and the like.

Description

Technical Field

[0001] This invention relates to the field of tire finite element simulation design technology, and in particular to a method, system, medium, and software product for calculating the contribution of tire components to radial stiffness. Background Technology

[0002] As the sole contact medium between a car and the road, the tire's structural design and performance play a decisive role in the vehicle's power, safety, comfort, and fuel efficiency. Especially against the backdrop of the automotive industry's accelerated transformation towards intelligent, electric, and lightweight designs, higher technical requirements are being placed on tire performance design, analysis, and optimization. To achieve precise tire performance control, understanding the influence of various structural components on overall tire performance, particularly key mechanical performance indicators such as radial stiffness, has become an indispensable part of tire research and development.

[0003] Radial stiffness, defined as the tire's radial displacement response under a unit radial load, is a crucial parameter for evaluating tire performance, including load-bearing capacity, deformation response, rolling resistance, and ride comfort. Excessive radial stiffness leads to decreased ride comfort, while insufficient radial stiffness may reduce steering stability and tread contact area, thus impacting driving safety. Tires are constructed from multiple layers of structural units, including tread rubber, belt layers, carcass layers, sidewall rubber, inner liner, base rubber, and airtight layer. The material properties, geometry, and location of each component significantly influence radial stiffness. Therefore, understanding the specific contribution of different components to radial stiffness not only helps researchers optimize material selection and structural design but also enables targeted performance improvements.

[0004] However, under conventional technical conditions, the analysis of the contribution of tire components to radial stiffness mainly relies on the following two methods:

[0005] (i) Static estimation methods based on empirical formulas. These methods are typically based on simplified mechanical models, estimating parameters based on the geometric parameters and material moduli of components. These models often assume the tire is an ideal circular ring, neglecting the mutual coupling between components. Although computationally simple, they have significant errors in handling the synergistic effects between multilayer composite materials, failing to meet the demands of the increasingly complex structures of modern tires.

[0006] (II) Physical Testing Method. This method involves loading tests on a physical tire under different component modification conditions to measure changes in radial stiffness. For example, replacing the target component with a low-modulus material or completely removing the component and comparing the changes in stiffness before and after testing can infer its contribution. However, this method has serious limitations: First, tire manufacturing costs are high, and repeated experiments are expensive; second, preparing test tires requires modifications to molds and vulcanization processes, resulting in long experimental cycles; third, it is difficult to change the characteristics of individual components without compromising the overall structure of the tire, leading to poor experimental accuracy and controllability.

[0007] With the development of simulation technology, especially the widespread application of Finite Element Analysis (FEA), tire structural performance prediction is gradually shifting from the traditional experience-based approach of "prototyping-testing-adjustment" to an intelligent process of "modeling-simulation-optimization." FEA-based tire performance analysis can not only efficiently and accurately predict key indicators such as tire deformation, stress, temperature rise, and durability, but also provide a theoretical basis for structural optimization design. In the finite element environment, the material models, geometry, and contact relationships of each component can be customized, and performance evaluations under various working conditions can be quickly completed without actually manufacturing the tire.

[0008] While FEA performs exceptionally well in predicting overall stiffness, current mainstream finite element analysis methods still struggle to accurately and directly quantify the independent contribution of a specific tire component to the overall radial stiffness. This technical bottleneck stems from the fact that a tire is a highly coupled multibody system. Components are tightly connected through adhesive layers or vulcanization, and the deformation of different components during stress not only affects their own stiffness response but also significantly couples with and influences the stress transfer and deformation modes of the surrounding structure. Therefore, it is impossible to isolate the component contribution using traditional parameter sensitivity analysis methods. Furthermore, tire finite element models typically employ a global solution approach in simulations, making it difficult to decompose the response influence of individual components without altering the overall boundary conditions or load configuration.

[0009] The applicant's Chinese invention patent application (Publication No.: CN116451479A, Publication Date: 2023-07-18) discloses a method for rapidly generating a mesh for a two-dimensional tire geometric model. This method includes the following steps: First, drawing auxiliary lines; second, exporting the file; third, reading the mesh.dxf file generated in the second step; fourth, geometrically repairing the lines in the TireLines from the second step; fifth, generating closed regions for components; sixth, generating closed regions for elements; and seventh, identifying precise element information. This invention adds mesh auxiliary lines to a two-dimensional tire geometric model and then directly and accurately extracts mesh data using a program. It is not only fast (estimated to take 5 minutes) but also eliminates reliance on third-party software, greatly improving the efficiency of mesh generation for tire geometric models and providing technical support for tire numerical simulation.

[0010] The applicant's Chinese invention patent application (Publication No.: CN117171882A, Publication Date: 2023-12-05) discloses an automatic identification method for tire pretreatment components. This method includes the following steps: First, defining the names of tire components; second, specifying the number of component layers; third, identifying the geometric outline of the tire structure; fourth, identifying the names of components in the tire crown area; fifth, identifying sidewall components; sixth, identifying the steel wire bead; seventh, identifying the triangular rubber component; and eighth, identifying the outer protective rubber. This method automatically identifies and names tire components, greatly improving pretreatment efficiency and ensuring that tire numerical simulations performed by different engineers have the same component names, providing technical support for tire numerical simulation.

[0011] Although the two patents mentioned above have realized the finite element model of the tire, they have not disclosed the subsequent applications after modeling. In particular, they have not disclosed a reliable method to quantify the contribution of each tire component to radial stiffness directly through the finite element simulation model without relying on physical experiments or destroying the structural continuity. Summary of the Invention

[0012] To address the aforementioned technical problems, the present invention aims to provide a method for calculating the contribution of tire components to radial stiffness. This method not only maintains the structural integrity and boundary condition consistency of the tire finite element model, ensuring simulation stability, but also possesses significant advantages such as high efficiency, low cost, and scalability, greatly improving the accuracy and efficiency of tire structure optimization.

[0013] To achieve the above objectives, the present invention adopts the following technical solution:

[0014] A method for calculating the contribution of a tire component to radial stiffness includes the following steps:

[0015] 1) Establish a finite element model of the tire and perform inflation analysis, including:

[0016] a) Perform two-dimensional axisymmetric modeling and mesh generation based on the tire structure diagram, and assign material properties to each component, including Young's modulus and Poisson's ratio;

[0017] b) Establish a rigid rim model and define the contact pair and friction coefficient between the tire and the rim;

[0018] 2) Apply the rated inflation pressure to the inner wall of the tire and perform inflation analysis;

[0019] 3) Based on the inflation analysis, rotate the two-dimensional axisymmetric model one revolution to generate a three-dimensional tire model, construct a rigid road surface model, and define the contact pairs and friction coefficients between the tire and the road surface; fix the rim and apply a load F to the rigid road surface. z Perform tire load analysis;

[0020] 4) Output the distance d that the road surface moves in the load direction. z1 Calculate the radial stiffness K of the complete tire. z1 =F z / d z1 ;

[0021] 5) Reduce the Young's modulus of the target component to a preset threshold, which is 0.01% to 5% of the design value, while keeping its Poisson's ratio unchanged. Other component properties and boundary conditions remain unchanged. Repeat steps 2) to 4) to obtain the radial stiffness K of the modified model. z2 =F z / d z2 ;

[0022] 6) Calculate the contribution value and contribution rate of the target component to radial stiffness:

[0023] ΔK=∣K z1 -K z2 | / n,

[0024] η=ΔK / K z1 ,

[0025] Where n is the number of times the target component appears in the tire structure.

[0026] Preferably, in step 1), the coefficient of friction between the tire and the rim is set to be between 0.01 and 1.0.

[0027] Preferably, in step 3), the coefficient of friction between the tire and the rigid road surface is set to be between 0.1 and 1.0.

[0028] Preferably, in step 5), the target component is any one or more of the tread, belt layer, or sidewall rubber.

[0029] Preferably, in step 5), the material properties of the target component are replaced with an equivalent low-modulus material in the finite element model, with a Young's modulus value of 0.01% to 5% of the original value, while keeping the Poisson's ratio consistent with the original material.

[0030] Preferably, in step 5), the Young's modulus of the target component is gradually reduced until the radial stiffness change rate after changing the Young's modulus of the target component tends to stabilize.

[0031] Furthermore, the present invention also provides a system for calculating the contribution of a tire component to radial stiffness, the system implementing the method comprising:

[0032] The finite element modeling module is used to generate a two-dimensional tire model, mesh it, and set material properties and contact conditions.

[0033] The inflation simulation module is used to apply the rated inflation pressure to the model and output the stress and deformation results of the tire after inflation.

[0034] The 3D modeling and load analysis module is used to rotate a 2D model to generate a 3D tire model, set a rigid road surface, apply loads, and output the tire sinkage.

[0035] The property adjustment module is used to adjust the Young's modulus of the target part to 0.01% to 5% of the design value and update the model's material properties;

[0036] The rigidity calculation module is used to calculate the radial rigidity Kz1 and Kz2 of the unadjusted and adjusted models respectively, and to calculate the contribution value ΔK and contribution rate η.

[0037] Preferably, the property adjustment module further includes control logic for setting the termination condition for Young's modulus adjustment based on the radial stiffness change rate.

[0038] And / or, the finite element modeling module sets parameters for the rubber material based on the Neo-Hookean model and sets linear elastic properties for the reinforcing material;

[0039] And / or, the rigidity calculation module records the output displacement and load in real time and automatically calculates the radial stiffness and the contribution rate of each component.

[0040] Furthermore, the present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement the method.

[0041] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the method.

[0042] By employing the aforementioned technical solution, this invention introduces a "target component low-modulus degradation strategy," accurately extracting the mechanical contribution of the target component to the tire's radial stiffness without compromising the overall structural continuity and boundary condition consistency of the tire's finite element model. This enables quantitative analysis of the influence of the tire's local structure on its overall stiffness. The method and system achieve significant technical effects in the following aspects:

[0043] 1. Achieved quantitative stripping analysis of the contribution of tire components to radial stiffness: This invention reduces the Young's modulus of the target component to 0.01%–5% of its original design value in finite element simulation, degenerating it into a mechanically ineffective component that is approximately "rigid." This strategy effectively avoids the model instability caused by directly deleting or completely removing the component, while significantly reducing the component's impact on overall stiffness, thus enabling comparative analysis. By comparing the radial stiffness difference between the complete model and the degenerated model under the same simulation conditions, the component's contribution value (ΔK) and contribution rate (η) can be accurately calculated, providing a reproducible, visualized, and comparable scientific basis for the quantitative influence of the component on stiffness for the first time.

[0044] 2. Improved targeting and efficiency of tire structure optimization design: The component contribution calculation results provided by this invention can be used as input parameters for tire structure optimization. Designers can adjust material parameters, geometric dimensions, or arrangement structures according to the contribution rate of each component, thereby achieving a more goal-oriented optimization strategy. For example, for components with high contribution rates, their stiffness-damping ratio can be further optimized; while components with low contribution rates can be prioritized for weight reduction and cost reduction designs, thereby accelerating the iteration speed and improving design efficiency.

[0045] 3. Balancing accuracy and computational stability to enhance simulation controllability: Compared to traditional sensitivity analysis or trial-and-error methods involving direct structural modification, this invention employs a continuous parameter adjustment strategy. By gradually adjusting the Young's modulus of the target component within a range of 0.01% to 5%, the changing trend of the radial stiffness output by the model is monitored, achieving stable convergence of the results. This method significantly improves the numerical stability and computational repeatability of the simulation while ensuring the validity of the physical meaning. The error can be controlled within ±2%, meeting the accuracy requirements of engineering applications.

[0046] 4. The method is highly versatile and applicable to tires of different specifications and structures: The method proposed in this invention does not depend on specific tire sizes, configurations, or material types, and is applicable to various structures such as conventional radial tires, passenger car tires, truck and bus tires, and lightweight high-performance tires; it is also applicable to various tire components such as tread, belt layers, sidewall rubber, base rubber, and carcass ply. By simply modifying the input model parameters, it can be transferred and applied to different scenarios, demonstrating good engineering scalability and commercial value.

[0047] 5. Eliminates the dependence of physical experiments on tire manufacturing and testing resources, significantly reducing R&D costs: Compared to traditional methods of comparative experiments through physical prototype tire manufacturing, this invention is entirely based on a finite element simulation platform, eliminating the need for multiple rounds of tire manufacturing, disassembly, and testing. This avoids the high costs associated with mold remaking, material waste, and long-cycle experiments. The method allows for reuse of a single model for contribution evaluation of multiple components, significantly lowering the R&D threshold and shortening the design cycle.

[0048] 6. Seamless integration with existing tire simulation platforms and structural databases facilitates implementation: The calculation method of this invention can be implemented on existing mainstream finite element platforms (such as Abaqus, ANSYS, or MSC.Marc), and can also be combined with tire modeling automation tools for fully automated simulation analysis. It supports modular integration of processes such as structural modeling, parameter replacement, boundary application, batch analysis, and contribution visualization. It possesses excellent system integration and scalability, making it easy for industrial deployment and engineering applications.

[0049] 7. Providing a data foundation for intelligent tire design and AI-assisted modeling: The contribution values ​​and contribution rates of each component output by this invention can serve as important label data for training structural performance correlation models in intelligent design systems, laying a crucial data foundation for intelligent tire design based on big data or machine learning. Through linkage with performance prediction models, automatic deduction of tire structures and closed-loop performance optimization can be further realized.

[0050] In summary, the "method and system for calculating the contribution of tire components to radial stiffness" proposed in this invention not only has significant innovation in methodology, but also demonstrates extremely high accuracy, versatility, and economy in practical engineering applications. It can effectively promote the transformation of tire structure design from experience-driven to data-driven and performance-fine control, and has broad prospects for industrial promotion and patent protection value. Attached Figure Description

[0051] Figure 1 This is a material distribution diagram for a 215 / 50R15 tire.

[0052] Figure 2 For 215 / 50R15 tire cross-section grid and material components;

[0053] Figure 3 The deformation results of a 215 / 50R15 tire after inflation;

[0054] Figure 4 The result of three-dimensional circumferential mesh generation for a 215 / 50R15 tire;

[0055] Figure 5 Load-displacement curve for a 215 / 50R15 tire;

[0056] Figure 6 This defines the tire coordinate system and boundary conditions. Detailed Implementation

[0057] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0058] like Figure 1 As shown, a method for calculating the contribution of a tire component to radial stiffness includes the following steps:

[0059] The first step is to establish a finite element model of the tire and perform a two-dimensional axisymmetric inflation analysis: mesh the tire design drawings (material distribution diagram) and assign material properties (designed Young's modulus); establish a rigid rim model and define the contact pair between the tire and the rim and its friction coefficient as between 0.01 and 1.0.

[0060] The second step is to apply the rated inflation pressure to the inner boundary layer of the tire and perform an inflation analysis.

[0061] The third step, based on the inflation analysis, involves rotating the two-dimensional axisymmetric model one revolution to generate a three-dimensional tire model; establishing a rigid road surface model, positioned 1 mm above the lower surface of the tire; defining the contact pair between the tire and the road surface and their coefficients of friction; setting the coefficient of friction between the tire and the rigid road surface to between 0.1 and 1.0; fixing the tire rim and applying the rated load F to the rigid road surface. z Perform tire load analysis;

[0062] The fourth step is to output the total distance d that the road surface moves in the load direction. z1 , (d z1 The radial stiffness is calculated from the initial load on the tire until the load reaches the rated load (i.e., the settling).

[0063] Step 5: Change the Young's modulus of the target components, including the tread, belt layer, and sidewall rubber. Reduce the Young's modulus of the target components to a preset threshold (e.g., 0.01% to 5% of the design value) to ignore their mechanical contribution to radial stiffness, while keeping the material properties of other components and boundary conditions unchanged. Repeat steps 2 to 4 to calculate the radial stiffness after changing the target components, and denote the calculated radial stiffness after changing the target components as K. z2 ;

[0064] Step 6: Calculate the contribution value and contribution rate of the tire components to radial stiffness:

[0065] ΔK=∣Kz1-Kz2∣ / n, eta=ΔK / Kz1,

[0066] Define the variable n as the number of times the target component appears in the tire structure. For example, for components that appear only once, such as the tread or base rubber, n = 1; while for components that appear twice, such as the sidewall rubber, n = 2. In this way, we can quantify and compare the specific contribution values ​​and contribution rates of different components to the overall radial stiffness of the tire.

[0067] The optimal embodiment of the present invention will be described in detail below using a 215 / 50R15 tire as an example.

[0068] Step 1: Establishing the finite element model of the tire

[0069] 1. The tire material distribution map (carcass only) was meshed using self-developed finite element software (CN116451479A, a method, application, and computer program product for rapidly generating two-dimensional geometric model meshes of tires; CN117171882A, an automatic identification method, application, and computer program product for tire pre-processing components). The mesh size was ensured to be appropriate, accurately reflecting the tire's geometric characteristics while maintaining computational efficiency.

[0070] 2. Material Property Assignment: Based on the material information provided by the designer, the mesh is assigned corresponding material properties such as Young's modulus and Poisson's ratio. When selecting a material model, the Neo-Hookean model was used to describe the constitutive relationship of the rubber material, and the parameters required for the Neo-Hookean model were accurately calculated based on actual material test data. Simultaneously, the material properties of the reinforcing materials (including carcass steel wire, belt layer, and crown layer) were also defined, including Young's modulus and Poisson's ratio.

[0071] 3. Boundary condition settings: Defines the contact relationship between the tire and the rim, with the friction coefficient set to 0.03.

[0072] Step 2: Inflation Analysis

[0073] 1. Rated inflation pressure: The rated inflation pressure of the tire is set to 250 kPa.

[0074] 2. Simulation calculation and analysis results: Inflation analysis was performed to obtain the deformation and stress distribution of the tire under the rated inflation pressure.

[0075] Step 3: Tire Load Analysis

[0076] 1. 3D Model Generation: Based on the inflation analysis, the 2D axisymmetric model is rotated one revolution to generate a 3D model of the tire.

[0077] 2. Establish a rigid, flat road surface model: Place a rigid, flat road surface 1 mm away from the tire surface to simulate the contact between the tire and the ground.

[0078] 3. Friction coefficient setting: The friction coefficient between the tire and the rim is set to 0.03, and the friction coefficient between the tire and the road surface is set to 0.5.

[0079] 4. Apply rated load: Fix the tire rim and apply the rated load (e.g., 4802N) to a rigid road surface to simulate the load conditions of the tire.

[0080] 5. Analysis Results: Tire load analysis was performed.

[0081] Step 4: Radial stiffness calculation

[0082] 1. Total travel distance output: Outputs the total travel distance (sinking) of the road surface in the load direction from 0 load to rated load.

[0083] 2. Radial stiffness calculation: Based on the deflection and rated load, the actual radial stiffness of the tire is calculated (condition 1):

[0084]

[0085] Step 5: Changes in Young's modulus of the target component and repeatability analysis

[0086] 1. Target component selection: Select a key component of the tire as the target component. In this case, the target component is the tire tread.

[0087] 2. Change of Young's modulus: Change the Young's modulus of the target component. In this case, the Young's modulus of the tread component will be reduced to 1% of the designed Young's modulus, while keeping the material properties of other components unchanged.

[0088] 3. Repeat steps: Repeat steps two through four to obtain the radial stiffness after changing the Young's modulus of the target component (condition two):

[0089]

[0090] Step 6: Calculation of the radial stiffness contribution value of the tire tread

[0091] 1. Contribution value calculation:

[0092]

[0093] 2. Contribution rate calculation:

[0094]

[0095] Step 7: Results and Analysis

[0096] contrast Figure 5 The two curves show that after the tread modulus decreased, the sinking increased by 10.1%, indicating that its radial stiffness contribution was effectively stripped away.

[0097] Through the above implementation examples, this invention successfully calculated the contribution value and contribution rate of the tire tread to radial stiffness. These results can provide important reference information for tire designers, helping them to better understand the impact of various tire components on overall performance, thereby enabling more precise tire design and optimization.

[0098] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

Claims

1. A method for calculating the contribution of a tire component to radial stiffness, characterized in that, Includes the following steps: 1) Establish a finite element model of the tire and perform inflation analysis, including: a) Perform two-dimensional axisymmetric modeling and mesh generation based on the tire structure diagram, and assign material properties to each component, including Young's modulus and Poisson's ratio; b) Establish a rigid rim model and define the contact pair and friction coefficient between the tire and the rim; 2) Apply the rated inflation pressure to the inner wall of the tire and perform inflation analysis; 3) Based on the inflation analysis, rotate the two-dimensional axisymmetric model one revolution to generate a three-dimensional tire model, construct a rigid road surface model, and define the contact pairs and friction coefficients between the tire and the road surface; fix the rim and apply a load F to the rigid road surface. z Perform tire load analysis; 4) Output the distance d that the road surface moves in the load direction. z1 Calculate the radial stiffness K of the complete tire. z1 =F z / d z1 ; 5) Reduce the Young's modulus of the target component to a preset threshold, which is 0.01% to 5% of the design value, while keeping its Poisson's ratio unchanged. Other component properties and boundary conditions remain unchanged. Repeat steps 2) to 4) to obtain the radial stiffness K of the modified model. z2 =F z / d z2 ; 6) Calculate the contribution value and contribution rate of the target component to radial stiffness: ΔK=∣K z1 −K z2 ∣ / n, η=ΔK / K z1 , Where n is the number of times the target component appears in the tire structure.

2. The method according to claim 1, characterized in that, In step 1), the coefficient of friction between the tire and the rim is set to be between 0.01 and 1.

0.

3. The method according to claim 1, characterized in that, In step 3), the coefficient of friction between the tire and the rigid road surface is set to be between 0.1 and 1.

0.

4. The method according to claim 1, characterized in that, In step 5), the target component is any one or more of the tread, belt layer, or sidewall rubber.

5. The method according to claim 1, characterized in that, In step 5), in the finite element model, the material properties of the target component are replaced with an equivalent low-modulus material, whose Young's modulus is 0.01% to 5% of the original value, while keeping the Poisson's ratio consistent with the original material.

6. The method according to claim 1, characterized in that, In step 5), the Young's modulus of the target component is gradually reduced until the radial stiffness change rate after changing the Young's modulus of the target component tends to stabilize.

7. A system for calculating the contribution of a tire component to radial stiffness, characterized in that, The system implements the method according to any one of claims 1-6, comprising: The finite element modeling module is used to generate a two-dimensional tire model, mesh it, and set material properties and contact conditions. The inflation simulation module is used to apply the rated inflation pressure to the model and output the stress and deformation results of the tire after inflation. The 3D modeling and load analysis module is used to rotate a 2D model to generate a 3D tire model, set a rigid road surface, apply loads, and output the tire sinkage. The property adjustment module is used to adjust the Young's modulus of the target component to 0.01% to 5% of the design value and update the model's material properties; The rigidity calculation module is used to calculate the radial stiffness K of the unadjusted and adjusted models, respectively. z1 ,K z2 And calculate the contribution value ΔK and contribution rate η.

8. The system according to claim 7, characterized in that, The property adjustment module further includes control logic for setting the termination condition for Young's modulus adjustment based on the radial stiffness change rate. And / or, the finite element modeling module sets parameters for the rubber material based on the Neo-Hookean model and sets linear elastic properties for the reinforcing material; And / or, the rigidity calculation module records the output displacement and load in real time and automatically calculates the radial stiffness and the contribution rate of each component.

9. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1-6.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1-6.

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