A finite element modeling method and system for a trampoline net

Abstract

The application relates to the technical field of electric digital data processing, in particular to a trampoline net surface finite element modeling method and system. The method comprises the following steps: respectively performing dynamic and static pressure tests on target landing points of the trampoline net surface by using trampolines of various specifications to obtain stress loads of the target landing points; determining the load directions of the target landing points by using unit vectors of deflection springs, static tension values and pressure gradients of the target landing points; dividing the trampoline net surface into multiple load areas by using the stress loads and the load directions of the target landing points, obtaining load area sequences by using mean values of stress loads of the load areas; and obtaining a finite element model of the trampoline net surface by using the number of landing points of each load area in the load area sequences to determine the unit sizes corresponding to the load areas. Through the technical scheme, the simulation and analysis accuracy of the finite element model for complex working conditions such as asymmetric impact and multi-point stress is improved, and the reliability of trampoline net surface deformation analysis and safety evaluation is enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of digital data processing, in particular to a trampoline net finite element modeling method and system. BACKGROUND

[0002] Trampoline is a competitive sport in which the human body on the elastic net surface obtains the height of the air through the net to complete various difficult movements, and the research on the trampoline net surface is not only a necessary means of engineering design, but also a key technical support for improving sports performance and scientific research level, so in order to further study the trampoline net surface, some researches on modeling by combining finite element analysis technology have appeared.

[0003] Because the trampoline net surface needs to bear dynamic impact load (such as periodic impact when the athlete jumps) and interact with the human body during the movement of the athlete on the trampoline, but in practice there are complex dynamic loads such as asymmetric impact and multi-point stress, which cause the trampoline net surface to be in a complex physical field, and the existing finite element model elements are usually fixed shape, which fails to consider the differences in stress size and direction of different areas of the net surface in the complex physical field, so that the fixed shape elements affect the accuracy of the final finite element analysis results using the finite element model of the trampoline net surface. SUMMARY

[0004] In order to solve the technical problem that the existing fixed shape elements make the finite element analysis result using the finite element model of the trampoline net surface less accurate, the purpose of the present application is to provide a trampoline net finite element modeling method and system, and the technical scheme adopted is as follows:

[0005] The present application provides a trampoline net finite element modeling method, which comprises:

[0006] The target landing point of the trampoline net surface is tested by using each specification weight containing multiple weight factors, and the stress load of the target landing point is obtained;

[0007] The position coordinates of the target landing point and its adjacent pressure detection points on the trampoline net surface are used to obtain the landing point horizontal interval and the landing point vertical interval, and the trampoline springs outside the landing point horizontal interval and the landing point vertical interval are used as the deflection springs;

[0008] The unit vector of the deflection spring, the static tension value and the pressure gradient of the target landing point are used to determine the load direction of the target landing point;

[0009] The trampoline net surface is divided into multiple load areas by using the stress load and the load direction of the target landing point, and the load area sequence is obtained by using the average stress load of the load area;

[0010] By utilizing the number of landing points in each load region of the load region sequence, the element size corresponding to each load region is determined to obtain the finite element model of the trampoline net surface.

[0011] Furthermore, the dynamic and static pressure tests on the target landing point of the trampoline net using various specifications of counterweights with multiple weight factors are conducted to obtain the force load on the target landing point, including:

[0012] Pressure detection points that are consecutively adjacent to the target landing point and have a pressure value that is not 0 are considered as adjacent pressure detection points of the target landing point.

[0013] Dynamic and static pressure tests were conducted on the target landing point of the trampoline net using various weights of different specifications that include multiple weight factors. Dynamic pressure data, dynamic tension data, static pressure data, and static tension data were obtained at adjacent pressure testing points.

[0014] By using dynamic pressure data, dynamic tension data, static pressure data, and static tension data, the force load at the target landing point is determined.

[0015] Furthermore, determining the force load at the target landing point using dynamic pressure data, dynamic tension data, static pressure data, and static tension data includes:

[0016] Determine the dynamic pressure maximum value sequence and dynamic tension maximum value sequence corresponding to the dynamic pressure data maximum value point and dynamic tension data maximum value point of each adjacent pressure detection point;

[0017] By using the difference between the maximum values ​​of dynamic pressure and the maximum values ​​of dynamic tension, the attenuation coefficient of each specification of counterweight at the target landing point is determined under the target counterweight factor value.

[0018] The average attenuation coefficient of each weight specification at the target landing point under the target weight factor value is used as the attenuation factor of the target weight factor, and the attenuation factor sequence under each target weight factor value is obtained.

[0019] Determine the weight factor sequence for each weight factor, and determine the Pearson correlation coefficient between the weight factor sequence and the corresponding attenuation factor sequence;

[0020] The load attenuation parameters at the target landing point are calculated using the Pearson correlation coefficient and the mean value of elements in the attenuation factor sequence.

[0021] By using load attenuation parameters, dynamic and static pressure data from adjacent pressure detection points, and combined with dynamic and static tension data from the trampoline springs, the force load at the target landing point is determined.

[0022] Furthermore, the determination of the force load at the target landing point using load attenuation parameters, dynamic and static pressure data from adjacent pressure detection points, combined with the dynamic and static tension data of the trampoline spring, includes:

[0023] The pressure load characteristic value of the target impact point is calculated by using the maximum peak value of the dynamic pressure data and the static pressure values ​​and average static pressure values ​​in the static pressure data of adjacent pressure detection points.

[0024] The trampoline springs in the horizontal and vertical sections of the landing point are taken as straight springs. The maximum peak value in the dynamic tension data of the bias spring, as well as the dynamic and static tension data of the straight spring, are used to calculate the characteristic value of the tension load at the target landing point.

[0025] The load-related parameters of the target landing point are determined by using the characteristic values ​​of the compressive load and the characteristic values ​​of the tensile load, and the force load at the target landing point is determined by using the load attenuation parameter and the load-related parameters.

[0026] Furthermore, the step of obtaining the horizontal and vertical intervals of the landing point using the position coordinates of the target landing point and its adjacent pressure detection points on the trampoline net includes:

[0027] The set of coordinates of the target landing point and its adjacent pressure detection points on the trampoline net is used as the local coordinate set of the landing point.

[0028] The interval formed by the maximum and minimum values ​​of the horizontal coordinates in the local coordinate set of the landing point is taken as the horizontal interval of the landing point, and the interval formed by the maximum and minimum values ​​of the vertical coordinates in the local coordinate set of the landing point is taken as the vertical interval of the landing point.

[0029] Furthermore, the method of determining the load direction at the target landing point using the unit vector and static tension value of the deflection spring and the pressure gradient at the target landing point includes:

[0030] The unit vector of the deflection spring is determined by using the angle between the target landing point and the line containing the deflection spring and the horizontal axis of the two-dimensional coordinate system containing the trampoline net.

[0031] By using the static tension values ​​of the deflection springs corresponding to the target landing point in the lateral and longitudinal directions, the static tension components in the lateral and longitudinal directions are determined respectively.

[0032] The load direction at the target impact point is determined by utilizing the static tensile force components in the lateral and longitudinal directions and the pressure gradient at the target impact point.

[0033] Furthermore, determining the load direction at the target impact point using the static tensile force components in the lateral and longitudinal directions and the pressure gradient at the target impact point includes:

[0034] Determine the static pressure values ​​and distances between the endpoints of multiple consecutive adjacent pressure detection points in both the horizontal and vertical directions where the target impact point is located.

[0035] By using the static pressure values ​​and endpoint distances of multiple adjacent pressure detection points in the horizontal and vertical directions, the pressure gradients of the target landing point in the horizontal and vertical directions are obtained respectively.

[0036] The load direction at the target impact point is calculated by using the static tensile force components and pressure gradients in the lateral and longitudinal directions of the target impact point.

[0037] Furthermore, the trampoline net surface is divided into multiple load regions using the force load and load direction at the target landing point, and a load region sequence is obtained using the average force load value of each load region, including:

[0038] Using the force load, load direction, and coordinate position between target landing points as similarity criteria, the trampoline net surface is divided into multiple load regions using a regional growth algorithm.

[0039] The average load of all points in the load region is used as the overall load parameter of the load region. The load regions are arranged in descending order of the normalized overall load parameter to obtain the load region sequence.

[0040] Furthermore, the step of determining the element size corresponding to each load region by utilizing the number of landing points in each load region sequence to obtain the finite element model of the trampoline net surface includes:

[0041] The intervals corresponding to the load region sequence are divided into an equal number of sub-intervals based on the number of load regions in the load region sequence.

[0042] The proportional relationship between the number of landing points in each load region in the load region sequence is determined as the range proportional relationship between each sub-interval.

[0043] By using the preset maximum unit size and preset minimum unit size, as well as the range ratio, the unit size allocated to the load region corresponding to the sub-interval is determined;

[0044] The finite element model of the trampoline surface is obtained by generating an unstructured mesh according to the element size allocated to each load region.

[0045] The present invention also provides a finite element modeling system for trampoline net surfaces, the system being used to implement the finite element modeling method for trampoline net surfaces as described in any of the preceding claims; the system includes:

[0046] The force testing module is used to perform dynamic and static pressure tests on the target landing point of the trampoline net using various specifications of counterweights with multiple weight factors to obtain the force load on the target landing point; it uses the position coordinates of the target landing point and its adjacent pressure detection points on the trampoline net to obtain the lateral and longitudinal intervals of the landing point, and uses the trampoline springs outside the lateral and longitudinal intervals of the landing point as bias springs; it uses the unit vector and static tension value of the bias springs and the pressure gradient of the target landing point to determine the load direction of the target landing point;

[0047] The load planning module is used to divide the trampoline net into multiple load regions using the force load and load direction at the target landing point, and to obtain the load region sequence using the average force load of the load region.

[0048] The model adjustment module is used to determine the element size of each load region by utilizing the number of landing points in each load region in the load region sequence, thereby obtaining the finite element model of the trampoline net surface.

[0049] The present invention has the following beneficial effects:

[0050] This invention introduces load vectors to comprehensively represent the magnitude and direction of force at each impact point, and combines this with a regional growth algorithm to divide load regions with similar mechanical properties. Based on the normalized sorting of the average load modulus of the regions, intervals are dynamically divided according to the proportion of impact points, establishing a decreasing element size mapping relationship. This enables adaptive meshing of fine meshes in high-load regions and coarse meshes in low-load regions, effectively avoiding shear lock-up and computational divergence. This improves the accuracy of finite element models in simulating complex conditions such as asymmetric impacts and multi-point stress, and enhances the reliability of trampoline surface deformation analysis and safety assessment. Attached Figure Description

[0051] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 A flowchart illustrating the steps of a finite element modeling method for a trampoline mesh surface provided in an embodiment of the present invention;

[0053] Figure 2 This is a detailed flowchart of step S1 in a finite element modeling method for a trampoline mesh provided in an embodiment of the present invention.

[0054] Figure 3 This is a detailed flowchart of step S13 in a finite element modeling method for a trampoline mesh provided in an embodiment of the present invention.

[0055] Figure 4 This is a detailed flowchart of step S3 in a finite element modeling method for a trampoline mesh provided in an embodiment of the present invention.

[0056] Figure 5 This is a detailed flowchart of step S33 in a finite element modeling method for a trampoline mesh provided in an embodiment of the present invention.

[0057] Figure 6 A detailed flowchart of step S4 in a finite element modeling method for a trampoline mesh provided in an embodiment of the present invention;

[0058] Figure 7 A detailed flowchart of step S5 in a finite element modeling method for a trampoline mesh surface provided in an embodiment of the present invention;

[0059] Figure 8 This is a schematic diagram of the hardware operating environment of the finite element modeling equipment for the trampoline net surface involved in the embodiments of the present invention;

[0060] Figure 9 This is a schematic diagram of the framework structure of the finite element modeling system for the trampoline net surface involved in the embodiment of the present invention;

[0061] Figure 10 This is a schematic diagram of the two-dimensional coordinate system of the trampoline net surface in the finite element modeling method of the trampoline net surface involved in the embodiment of the present invention;

[0062] Figure 11 This is a schematic diagram of the minimum diameter of the counterweight in the finite element modeling method for the trampoline mesh surface involved in the embodiments of the present invention;

[0063] Figure 12 This is a schematic diagram illustrating the relationship between the size of the sub-interval and the number of landing points within the load area in the finite element modeling method for the trampoline net surface involved in the embodiments of the present invention. Detailed Implementation

[0064] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a finite element modeling method for a trampoline mesh surface proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0065] It should be noted that, in order to ensure that the calculation results are meaningful, when performing fractional operations, if the denominator is 0, a parameter adjustment factor greater than 0 needs to be added to the denominator to prevent the denominator from being 0. The value of the parameter adjustment factor shall be set by the implementer according to the actual situation, and this application does not impose any special restrictions.

[0066] It should be noted that, for ease of calculation, all indicator data involved in the calculation in this embodiment of the invention have undergone data preprocessing to eliminate the influence of dimensions. The specific methods for eliminating the influence of dimensions are well known to those skilled in the art and are not limited here.

[0067] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0068] The specific scenarios targeted by the various embodiments of this invention can be as follows:

[0069] Because the stress and deformation process of trampoline netting in reality is quite complex, the matching between the element shape type of the finite element model and the physical behavior is often insufficient. For example, when the elements of the finite element model are low-order elements (such as linear triangular elements), "shear lock-up" or "volume lock-up" is likely to occur, resulting in excessive stiffness and inability to accurately simulate the large deformation characteristics of the netting. Furthermore, in large deformation regions (such as when the netting is stretched violently), elements with fixed shapes may become singular in the Jacobian matrix due to excessive twisting, leading to calculation divergence.

[0070] The following describes in detail, with reference to the accompanying drawings, a specific scheme of the finite element modeling method for trampoline mesh provided by the present invention.

[0071] Example 1:

[0072] For the finite element modeling method of trampoline mesh provided by this invention, please refer to [link / reference]. Figure 1 The diagram illustrates a finite element modeling method for a trampoline mesh surface according to an embodiment of the present invention.

[0073] The finite element modeling method for the trampoline mesh includes:

[0074] Step S1: Using various weights of different specifications that include multiple weight factors, dynamic and static pressure tests are conducted on the target landing point of the trampoline net to obtain the force load on the target landing point.

[0075] Before conducting dynamic and static pressure tests on the target landing point of the trampoline net using various weights of different specifications that incorporate multiple counterweight factors, preliminary work may include:

[0076] Sensors are installed on the trampoline to obtain force data: Due to the interaction between the athlete and the trampoline, the trampoline net is subjected to various forces such as pressure, tension, and elasticity. The magnitude and direction of these forces also differ in different areas. Therefore, in order to understand the force situation on the trampoline net in detail, it is necessary to install multiple sensors on the trampoline to monitor the force and obtain force data.

[0077] Specifically, please refer to Figure 10 , Figure 10 This is a schematic diagram of the two-dimensional coordinate system of the trampoline net surface in the finite element modeling method of the trampoline net surface involved in the embodiment of the present invention.

[0078] Selecting a trampoline for competition: The specifications of a professional competition trampoline are as follows: the overall frame of the trampoline is 5.05 meters long, 2.91 meters wide, and 1.15 meters high; the net is 4.28 meters long and 2.14 meters wide. In addition, the trampoline contains a total of 118 springs. A two-dimensional coordinate system is established on the trampoline net on a horizontal plane. The origin of the two-dimensional coordinate system is the center of the first small grid at the lower left corner of the net (0,0). The horizontal and vertical sides of the net are regarded as the X-axis and Y-axis, respectively. Thus, each spring on the trampoline net also has a corresponding position coordinate in the two-dimensional coordinate system.

[0079] Sensors are installed on the trampoline: corresponding sensor data is obtained through the sensors, which are mainly divided into pressure data and tension data.

[0080] Specifically, a high-density pressure sensor array is arranged on the trampoline mesh, and the location of each pressure sensor is used as a pressure detection point to obtain pressure data at each pressure detection point on the trampoline mesh. Force gauges are installed on the springs around the trampoline to obtain the tension data of the springs at different locations.

[0081] In this embodiment, dynamic and static tests are performed on the trampoline mesh to obtain sensor data from the dynamic and static tests, and the collected sensor data is then standardized.

[0082] Specifically, several pressure detection points are evenly selected on the horizontal surface of the trampoline net as landing points. Weights of different sizes and weights are statically placed at each landing point (referred to as the target landing point) on the trampoline net, and sensor data is recorded. Weights of different sizes and weights are dropped freely at different heights above each landing point on the trampoline net, and sensor data is recorded.

[0083] Additionally, please refer to Figure 11 , Figure 11This is a schematic diagram of the minimum diameter of the counterweight in the finite element modeling method of the trampoline mesh involved in the embodiment of the present invention. For the convenience of subsequent analysis, the minimum diameter of the counterweight should be greater than or equal to the distance between the two ends of the pressure detection points in three consecutive adjacent pressure detection points, i.e., the distance L in the figure.

[0084] Thus, we have obtained the force data at different positions on the trampoline net, the tension data of each spring of the trampoline, and the size (i.e., volume), weight, drop height, and landing point of the counterweight. The size, weight, and drop height of the counterweight are called the counterweight factors.

[0085] The stress data of the trampoline net surface are used to perform multiphysics stress analysis on different areas of the trampoline net surface, and the element shape of the finite element model of the trampoline net surface is set using the results of the multiphysics stress analysis.

[0086] The stress process on a trampoline net is a multi-physics process, and the stress process exhibits different characteristics under static and dynamic stress conditions. Furthermore, the effect of the counterweight on the trampoline net varies depending on the location of the test (dynamic or static). Therefore, the stress conditions differ across different areas of the trampoline net. To ensure that the finite element model of the trampoline net effectively reflects the stress and deformation characteristics of different areas, facilitating further finite element analysis, this embodiment analyzes the sensor data generated during dynamic and static tests to adjust the finite element model of different areas of the trampoline net.

[0087] In this embodiment, for any landing point (target landing point), force analysis is performed using sensor data obtained during dynamic and static tests at the landing point to determine the load vector of the landing point. The load vector includes the vector magnitude and direction. The vector magnitude is the load vector, and the direction is the load direction.

[0088] The process of obtaining the load vector mainly includes:

[0089] The pressure detection points that are consecutively adjacent to the target landing point and whose pressure values ​​are not zero are obtained as the adjacent pressure detection points of the landing point. The pressure data corresponding to each adjacent pressure detection point is obtained, and the pressure data detected during dynamic and static tests are respectively used as dynamic pressure data and static pressure data. Similarly, the tension data of each spring around the trampoline during dynamic and static tests are respectively used as dynamic tension data and static tension data.

[0090] For the process of performing dynamic and static tests on a counterweight of arbitrary size and weight, when it is dropped from an arbitrary height above an arbitrary landing point, the load vector at the landing point is obtained by using the static pressure data of the adjacent pressure detection points at the landing point to reflect the pressure level, the fluctuation process of the dynamic pressure data, the tensile force data reflected by the static tensile force data, the fluctuation process of the dynamic tensile force data, and the positional characteristics of the landing point.

[0091] The magnitude of the load vector is used to describe the mechanical properties of a local area at the corresponding landing point (i.e., the area formed by the landing point and the adjacent pressure detection point) under different sizes and weights of counterweights in different ways (i.e., dynamic and static tests) during dynamic and static tests. The larger the magnitude of the load vector, the more likely the mechanical properties at the landing point are to cause a greater degree of deformation of the trampoline net surface. Therefore, it is more necessary to reduce the size of the elements in the corresponding area in the finite element model during subsequent finite element modeling.

[0092] Specifically, please refer to Figure 2 Step S1 includes:

[0093] Step S11: The pressure detection points that are continuously adjacent to the target landing point and whose pressure value is not 0 are taken as the adjacent pressure detection points of the target landing point.

[0094] Step S12: Using various weights of different specifications that include multiple weight factors, dynamic and static pressure tests are conducted on the target landing point of the trampoline net to obtain dynamic pressure data, dynamic tension data, static pressure data, and static tension data of adjacent pressure test points.

[0095] Step S13: Using dynamic pressure data, dynamic tension data, static pressure data, and static tension data, determine the force load at the target landing point.

[0096] Please refer to Figure 3 Step S13 specifically includes:

[0097] Step S131: Determine the dynamic pressure maximum value sequence and dynamic tension maximum value sequence corresponding to the dynamic pressure data maximum value point and dynamic tension data maximum value point of each adjacent pressure detection point;

[0098] Step S132: Using the difference between the maximum values ​​of dynamic pressure and the maximum values ​​of dynamic tension, determine the attenuation coefficient of each specification of counterweight at the target landing point under the target counterweight factor value;

[0099] Step S133: Take the average attenuation coefficient of each specification of counterweight at the target landing point under the target counterweight factor value as the attenuation factor of the target counterweight factor, and obtain the attenuation factor sequence under each target counterweight factor value.

[0100] Step S134: Determine the weight factor sequence of each weight factor, and determine the Pearson correlation coefficient between the weight factor sequence and the corresponding attenuation factor sequence;

[0101] Step S135: Calculate the load attenuation parameters at the target landing point using the Pearson correlation coefficient and the mean value of elements within the attenuation factor sequence.

[0102] Step S136: Using the load attenuation parameter, the dynamic pressure data and static pressure data of adjacent pressure detection points, and the dynamic tension data and static tension data of the trampoline spring, determine the force load at the target landing point.

[0103] Based on the above embodiments, the process of obtaining the load attenuation parameter is as follows:

[0104] When a counterweight of any size and weight is dropped freely from different heights, the maximum values ​​of dynamic pressure and dynamic tension data at each adjacent pressure detection point are obtained when the dynamic test is performed. These data are then arranged in chronological order to obtain the dynamic pressure maximum value sequence and the dynamic tension maximum value sequence.

[0105] Obtain the backward difference sequence of the maximum dynamic pressure sequence and the maximum dynamic tension sequence. Based on the rate of change of the element values ​​in the maximum dynamic pressure sequence and the maximum dynamic tension sequence, calculate the attenuation coefficient of the counterweight at the landing point corresponding to the size, weight and height.

[0106] The specific calculation process for obtaining the attenuation coefficient is as follows:

[0107] ;

[0108] in, This indicates that with a counterweight of size v, weight m, and drop height h, the th The attenuation coefficient at each landing point; This indicates that with a counterweight of size v, weight m, and a falling height h, the th... The a-th difference value in the sequence of maximum dynamic pressure values ​​at each landing point; This indicates that with a counterweight of size v, weight m, and a falling height h, the th... The a-th difference value in the sequence of maximum dynamic tension values ​​at each landing point; This represents the time corresponding to the a-th difference value. A represents the total number of difference values ​​in the sequence of dynamic pressure maxima and dynamic tension maxima that are equal.

[0109] Furthermore, all counterweights are sorted in ascending order by size, weight, and height to obtain corresponding sequences, namely the counterweight size sequence, counterweight weight sequence, and counterweight height sequence (collectively referred to as the counterweight factor sequence). Additionally, the average attenuation coefficient of all weights and heights under any counterweight size is obtained as the size-attenuation factor for the corresponding counterweight size. The sequence formed by the size-attenuation factors under all counterweight sizes is called the size-attenuation factor sequence. Similarly, the weight-attenuation factor sequence and the height-attenuation factor sequence are obtained. The sequence formed by the size-attenuation factor, the weight-attenuation factor sequence, and the height-attenuation factor sequence are collectively referred to as the factor-attenuation factor sequence (each counterweight factor corresponds to its own attenuation factor sequence). For ease of analysis, a target counterweight factor value is first fixed, and then the various specifications of counterweights are obtained after changing the values ​​of other counterweight factors under that target counterweight factor value.

[0110] Pearson correlation coefficients were obtained for the counterweight size sequence and size-attenuation factor sequence, counterweight weight sequence and weight-attenuation factor sequence, and counterweight height sequence and height-attenuation factor sequence, respectively. These results yielded Pearson correlation coefficients under different counterweight factors. As the load attenuation parameter at this landing point, Indicates the first Pearson correlation coefficient for the i-th weight factor at each landing point Indicates the first The mean of all elements in the factor-attenuation factor sequence corresponding to the i-th weight factor at each landing point; This represents the sigmoid normalization function.

[0111] When the counterweight is tested on the trampoline net, it undergoes a process of converting the counterweight's gravitational potential energy into elastic potential energy. During this process, as energy dissipates, the counterweight gradually stabilizes on the trampoline net. This causes the pressure generated by the counterweight at the landing point and the tension generated by the springs around the trampoline driven by the trampoline net to fluctuate and decrease continuously. The faster the pressure and tension decrease, the greater and faster the deformation of the trampoline net caused by the counterweight landing at that point due to energy conversion.

[0112] Further, step S136 specifically includes:

[0113] The pressure load characteristic value of the target impact point is calculated by using the maximum peak value of the dynamic pressure data and the static pressure values ​​and average static pressure values ​​in the static pressure data of adjacent pressure detection points.

[0114] The trampoline springs in the horizontal and vertical sections of the landing point are taken as straight springs. The maximum peak value in the dynamic tension data of the bias spring, as well as the dynamic and static tension data of the straight spring, are used to calculate the characteristic value of the tension load at the target landing point.

[0115] The load-related parameters of the target landing point are determined by using the characteristic values ​​of the compressive load and the characteristic values ​​of the tensile load, and the force load at the target landing point is determined by using the load attenuation parameter and the load-related parameters.

[0116] Based on the above embodiments, the process of obtaining load-related parameters in this embodiment is as follows:

[0117] The coordinates of the landing point and its adjacent pressure detection points on the trampoline mesh are collected as a set, which serves as the local coordinate set of the landing point. The maximum value of the x-coordinate in the local coordinate set of the landing point is then obtained. and minimum value The formed interval This serves as the horizontal interval of the landing point; similarly, the interval formed along the vertical axis... , which serves as the vertical interval of the landing point.

[0118] The springs within the horizontal and vertical ranges of the landing point are identified as the straight springs, and the springs other than the straight springs are identified as the deflection springs at that landing point.

[0119] Taking into account the weights of all sizes, weights, and drop heights during the descent at the landing point, the load-related parameters at the landing point are calculated using the directional angle formed by the landing point on the spring mesh surface and the deflection spring, combined with the spring tension data, the pressure data at the landing point, and the pressure data from adjacent pressure detection points. The specific calculation method is as follows:

[0120]

[0121] in, Indicates the first Load-related parameters at each landing point; This represents the set of all counterweights, including their size, weight, and drop height. This indicates that the average value is obtained.

[0122] This indicates that with a counterweight of size v, weight m, and a falling height h, the th... The characteristic value of the pressure load at each landing point; This indicates that with a counterweight of size v, weight m, and a falling height h, the th... The first landing point The maximum peak value among the dynamic pressure data of adjacent pressure detection points; This indicates that during a static test with a counterweight of size v and weight m, the first... The average static pressure value of all adjacent pressure detection points at each landing point; Indicates the first The number of all adjacent pressure detection points of each landing point.

[0123] This indicates that with a counterweight of size v, weight m, and a falling height h, the th... Characteristic values ​​of tensile load at each landing point; This indicates that with a counterweight of size v, weight m, and a falling height h, the th... The maximum peak value in the dynamic tension data of the u-th deflection spring at each landing point; This indicates that with a counterweight of size v, weight m, and a falling height h, the th... The average of the maximum peak values ​​of the dynamic tension data of all straight springs on the side edge of the trampoline net corresponding to the u-th deflection spring at the landing point; This indicates that with a counterweight of size v, weight m, and a falling height h, the th... The number of deflection springs at each landing point; This indicates that during a static test with a counterweight of size v and weight m, the first... The average static tension of all straight springs at each landing point;

[0124] Load-related parameters describe the influence of the correlation between different sensor data and the positional information of the landing point on the deformation of the trampoline mesh during dynamic and static testing with counterweights. A higher load-related parameter value indicates a greater degree of deformation caused by the multi-physics coupling between different sensor data at the landing point. In other words, a higher load-related parameter value indicates that the local area formed by the landing point and adjacent pressure detection points is more prone to deformation and exhibits a higher degree of deformation. (Pressure load characteristic value) This value represents the ratio of dynamic pressure response to static pressure. It reflects the instantaneous relative pressure of a local area to which a dynamic impact load is equivalent to static pressure. The larger the ratio, the more significant the pressure fluctuation caused by the dynamic impact, and the more likely the local area is to undergo severe deformation. This characteristic value captures the nonlinear response of the local pressure field during energy transfer by comparing dynamic and static pressure, providing a basis for dynamic deformation sensitivity for finite element element division.

[0125] Therefore, based on the method for calculating the magnitude of the load vector mentioned in the above embodiments, the first... Force load at each landing point:

[0126] ,in, Indicates the first The magnitude of the load vector at each landing point (as the target landing point) (force load). Indicates the first Load attenuation parameters at each landing point; Indicates the first Load-related parameters for each landing point.

[0127] Step S2: Use the position coordinates of the target landing point and its adjacent pressure detection points on the trampoline net to obtain the horizontal and vertical landing ranges of the landing point, and use the trampoline springs outside the horizontal and vertical landing ranges of the landing point as deflection springs.

[0128] Specifically, step S2, which uses the position coordinates of the target landing point and its adjacent pressure detection points on the trampoline net to obtain the horizontal and vertical intervals of the landing point, includes:

[0129] The set of coordinates of the target landing point and its adjacent pressure detection points on the trampoline net is used as the local coordinate set of the landing point.

[0130] The interval formed by the maximum and minimum values ​​of the horizontal coordinates in the local coordinate set of the landing point is taken as the horizontal interval of the landing point, and the interval formed by the maximum and minimum values ​​of the vertical coordinates in the local coordinate set of the landing point is taken as the vertical interval of the landing point.

[0131] In this embodiment, the position coordinates of the landing point and its adjacent pressure detection points on the trampoline mesh are obtained as a set, which serves as the local coordinate set of the landing point. The maximum value of the abscissa in the local coordinate set of the landing point is then obtained. and minimum value The formed interval This serves as the horizontal interval of the landing point; similarly, the interval formed along the vertical axis... , which serves as the vertical interval of the landing point.

[0132] Step S3: Determine the load direction at the target landing point using the unit vector and static tension value of the deflection spring and the pressure gradient at the target landing point;

[0133] Specifically, please refer to Figure 4 Step S3 includes:

[0134] Step S31: Determine the unit vector of the deflection spring by using the angle between the target landing point and the straight line where the deflection spring is located and the horizontal axis of the two-dimensional coordinate system where the trampoline net is located.

[0135] Step S32: Using the static tension values ​​of the deflection springs corresponding to the target landing point in the lateral and longitudinal directions respectively, determine the static tension components in the lateral and longitudinal directions respectively.

[0136] Step S33: Determine the load direction of the target landing point by utilizing the static tensile force components in the lateral and longitudinal directions and the pressure gradient at the target landing point.

[0137] Please refer toFigure 5 Step S33 specifically includes:

[0138] Step S331: Determine the static pressure values ​​and endpoint distances of multiple consecutive adjacent pressure detection points in the horizontal and vertical directions of the target landing point.

[0139] Step S332: Using the static pressure values ​​and endpoint distances of multiple adjacent pressure detection points in the horizontal and vertical directions, the pressure gradients of the target landing point in the horizontal and vertical directions are obtained respectively.

[0140] Step S333: Calculate the load direction of the target impact point by using the static tensile force components and pressure gradients of the target impact point in the lateral and longitudinal directions.

[0141] In this embodiment, the angle between the straight line containing the k-th landing point and the i-th deflection spring and the X-axis of the two-dimensional coordinate system containing the trampoline net is obtained. Thus, the unit vector is obtained. ,in Represents the cosine function. This represents the sine function.

[0142] Combining the unit vector of the deflection spring and the static tension value, calculate the static tension components in different directions (lateral and longitudinal). Specifically, the static tension component in the longitudinal direction is... ,in This represents the static tension value of the y-th deflection spring along the vertical axis corresponding to the k-th landing point; This represents the unit vector of the y-th deflection towards the spring along the vertical axis corresponding to the k-th landing point; similarly, the static tension component in the lateral direction is obtained. .

[0143] The pressure gradients at the impact point are obtained in the horizontal and vertical directions, respectively. and The calculation results are denoted as lateral pressure gradients. and longitudinal pressure gradient ,in This represents the static pressure value of the (i+1)th adjacent pressure detection point in the horizontal direction of the k-th impact point. This represents the difference between the static pressure value of the (i+1)th adjacent pressure detection point and the static pressure value of the (i-1)th adjacent pressure detection point in the horizontal direction of the kth landing point. These two static pressure values ​​are the endpoint static pressure values ​​of the three consecutive adjacent pressure detection points, i-1, i, and i+1, respectively. Indicates the distance between pressure detection points. This represents the distance between the endpoints of three adjacent pressure detection points in the horizontal direction. Similarly, This represents the static pressure value of the (j+1)th adjacent pressure detection point in the longitudinal direction of the k-th impact point. This shows the static pressure value of the (j-1)th adjacent pressure detection point in the longitudinal direction of the k-th impact point. This indicates the distance between the endpoints of three adjacent pressure detection points in the longitudinal direction.

[0144] Combined with the The pressure gradients in the lateral and longitudinal directions at each impact point, along with the static tensile force components in different directions, yield the vector direction of the load vector at the impact point (load direction). :

[0145]

[0146] in, Indicates the first The direction of the load vector at each landing point, i.e., the load direction; Represents the arctangent function; Indicates the lateral pressure gradient. Indicates the longitudinal pressure gradient; , These represent the static tension components of the deflecting spring in the lateral direction and in the longitudinal direction, respectively.

[0147] Step S4: Divide the trampoline net into multiple load areas using the force load and load direction at the target landing point, and obtain the load area sequence using the average force load of the load areas.

[0148] In this embodiment, it is necessary to analyze the force data of the trampoline net and divide the trampoline net area.

[0149] When a weight falls freely or an athlete jumps, the stress wave propagation path and energy dissipation rate differ in different areas of the trampoline, leading to significant differences in local deformation rates. Furthermore, the edges of the net are fixed to the frame, restricting deformation in these areas, while the central area can stretch freely, creating a distinct stiffness gradient. Additionally, when the counterweight is statically placed, the net deformation is mainly concentrated around the load application point, with a relatively gentle stress gradient. However, when the counterweight falls freely, localized areas of the net experience high-frequency vibrations and stress wave propagation due to the impact force, causing a sudden surge in tension in the edge springs. Therefore, different areas experience different stress states and exhibit varying mechanical properties in different directions. Thus, regional analysis of the trampoline net is necessary to avoid incompatibility between the element properties used in finite element modeling and the corresponding mechanical properties, which could lead to shear locking and volumetric self-locking.

[0150] Specifically, please refer to Figure 6 Step S4 includes:

[0151] Step S41: Using the force load, load direction, and coordinate position between target landing points as similarity criteria, the trampoline net surface is divided into multiple load regions using a regional growth algorithm.

[0152] Step S42: Take the average load of all landing points in the load region as the overall load parameter of the load region, and arrange the load regions in descending order of the normalized overall load parameter to obtain the load region sequence.

[0153] In this embodiment, the load vector reflects the load direction and magnitude of the trampoline net at the corresponding landing point. The vector direction of the load vector is the load direction, and the magnitude of the load vector is the load magnitude.

[0154] Then, using the load vector and the position information of the landing point, the trampoline net is divided into several load regions. The specific method is as follows: select seed points from all landing points, and use the load vector and coordinate position information of the landing point as similarity criteria. The distance similarity and load vector similarity between landing points can be calculated, and the regions can be divided using a regional growth algorithm (existing algorithms will not be explained in detail here) to obtain several regions as load regions.

[0155] The mechanical properties of trampoline netting are similar in the same load area. Therefore, by dividing the load area, the element properties in the area with similar mechanical characteristics can be adjusted more effectively, which can improve the efficiency of finite element modeling. Furthermore, after adjusting the element properties of each area, the occurrence of shear lock-up and volume self-locking in the finite element model is reduced.

[0156] For areas that are prone to deformation and have a high degree of deformation, in order to avoid inaccurate analysis results when using the finite element model for subsequent finite element analysis due to shear locking or volumetric self-locking in these areas, this invention adjusts the relevant properties of the elements in the finite element model using load vectors from different load regions, thereby improving the ability of the finite element model to describe the actual deformation of the trampoline net.

[0157] More specifically, firstly, the average load vector magnitude of all points in any load region is obtained, i.e., the average force load, as the overall load parameter of the load region. Then, a linear normalization function is used to normalize the overall load parameter of all load regions to... Within the range, the corresponding load regions are arranged in descending order of the normalized overall load parameters of the load regions to obtain the load region sequence.

[0158] Step S5: Using the number of landing points in each load region in the load region sequence, determine the element size corresponding to each load region to obtain the finite element model of the trampoline net surface.

[0159] Specifically, please refer to Figure 7 Step S5 includes:

[0160] Step S51: Divide the intervals corresponding to the load region sequence into an equal number of sub-intervals using the number of load regions in the load region sequence;

[0161] Step S52: The proportional relationship between the number of landing points of each load region in the load region sequence is determined as the range proportional relationship between each sub-interval;

[0162] Step S53: Using the preset maximum unit size, the preset minimum unit size, and the range ratio relationship, determine the unit size allocated to the load area corresponding to the sub-interval;

[0163] Step S54: Generate an unstructured mesh according to the element size allocated to each load region to obtain the finite element model of the trampoline mesh.

[0164] Please refer to Figure 12 , Figure 12 This is a schematic diagram illustrating the relationship between the size of the sub-interval and the number of landing points within the load area in the finite element modeling method for the trampoline net surface involved in the embodiments of the present invention.

[0165] In this embodiment, the number of load regions is obtained. and the interval Divided into The sub-intervals are divided into several sub-intervals, and their sizes are arranged in descending order. At the same time, the size relationship of the sub-intervals satisfies the number relationship of landing points in each load region in the load region sequence.

[0166] like Figure 12 As shown in the figure, the ratio of the number of landing points within the load region sequence is 2:1:3:4. Similarly, the same ratio is present in the relationship between the size of the sub-intervals.

[0167] Finally, let the maximum element size be... (e.g., 0.3m), the minimum unit size is (e.g., 0.1m), for each subinterval Define the unit size Any load area Corresponding normalized global load parameters At that time, the size of the allocated unit is determined. .

[0168] Thus, the element shape setting results in the finite element model of the trampoline mesh are obtained.

[0169] The finite element model of the trampoline net is then visualized and used for subsequent finite element analysis.

[0170] First, use PyVista or Abaqus CAE software and input the following data: mesh geometry parameters (length 4.28m, width 2.14m, spring distribution coordinates); element attribute table (including region number, element type, element size, orientation, and material properties); sensor data (pressure / tension distribution, dynamic load time series).

[0171] Then, based on the load region division results, the trampoline mesh is divided into S load regions. Within each load region, an unstructured mesh is generated according to the allocated element size, resulting in the finite element model of the trampoline mesh for subsequent finite element analysis. This completes the finite element modeling of the trampoline mesh.

[0172] This invention introduces load vectors to comprehensively represent the magnitude and direction of force at each impact point, and combines this with a regional growth algorithm to divide load regions with similar mechanical properties. Based on the normalized sorting of the average load modulus of the regions, intervals are dynamically divided according to the proportion of impact points, establishing a decreasing element size mapping relationship. This enables adaptive meshing of fine meshes in high-load regions and coarse meshes in low-load regions, effectively avoiding shear lock-up and computational divergence. This improves the accuracy of finite element models in simulating complex conditions such as asymmetric impacts and multi-point stress, and enhances the reliability of trampoline surface deformation analysis and safety assessment.

[0173] Example 2:

[0174] This invention also proposes a finite element modeling device for trampoline net surfaces. The device can be a computer, server, or other data analysis and computing equipment, or a combination of multiple devices.

[0175] like Figure 8 As shown, Figure 8 This is a schematic diagram of the hardware operating environment of the finite element modeling device for the trampoline net surface involved in the embodiments of the present invention.

[0176] like Figure 8As shown, the finite element modeling device for the trampoline net surface may include: a processor 1001, such as a CPU, a network interface 1004, a user interface 1003, a memory 1005, and a communication bus 1002. The communication bus 1002 is used to establish communication between these components. The user interface 1003 may include a display or an input unit such as a control panel; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1005 may be a high-speed RAM or a stable, non-volatile memory, such as a disk drive. Optionally, the memory 1005 may also be a storage device independent of the aforementioned processor 1001. The memory 1005, as a computer storage medium, may contain the finite element modeling program for the trampoline net surface.

[0177] Those skilled in the art will understand that Figure 8 The hardware structure shown does not constitute a limitation on the device and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0178] Continue to refer to Figure 8 , Figure 8 The memory 1005, which is a computer-readable storage medium, may include an operating system, a user interface module, a network communication module, and a finite element modeling program for the trampoline surface.

[0179] exist Figure 8 In this embodiment, the network communication module is mainly used to connect to the server and can communicate with the server for data; while the processor 1001 can call the finite element modeling program of the trampoline net surface stored in the memory 1005 and execute the steps in the above embodiments.

[0180] The hardware structure of the finite element modeling device for the trampoline net surface described above is used to implement various embodiments of the finite element modeling method for the trampoline net surface of the present invention.

[0181] In addition, the present invention also provides a finite element modeling system for trampoline mesh surfaces, please refer to... Figure 9 The finite element modeling system for the trampoline mesh includes:

[0182] The force testing module A10 is used to perform dynamic and static pressure tests on the target landing point of the trampoline net using various specifications of counterweights with multiple weight factors to obtain the force load on the target landing point; it uses the position coordinates of the target landing point and its adjacent pressure detection points on the trampoline net to obtain the lateral and longitudinal intervals of the landing point, and uses the trampoline springs outside the lateral and longitudinal intervals of the landing point as bias springs; it uses the unit vector and static tension value of the bias springs and the pressure gradient of the target landing point to determine the load direction of the target landing point;

[0183] The load planning module A20 is used to divide the trampoline net into multiple load areas using the force load and load direction of the target landing point, and to obtain the load area sequence using the average force load of the load area.

[0184] The model adjustment module A30 is used to determine the element size of each load region by utilizing the number of landing points in each load region in the load region sequence, thereby obtaining the finite element model of the trampoline net surface.

[0185] Furthermore, the force testing module A10 is also used for:

[0186] Pressure detection points that are consecutively adjacent to the target landing point and have a pressure value that is not 0 are considered as adjacent pressure detection points of the target landing point.

[0187] Dynamic and static pressure tests were conducted on the target landing point of the trampoline net using various weights of different specifications that include multiple weight factors. Dynamic pressure data, dynamic tension data, static pressure data, and static tension data were obtained at adjacent pressure testing points.

[0188] By using dynamic pressure data, dynamic tension data, static pressure data, and static tension data, the force load at the target landing point is determined.

[0189] Furthermore, the force testing module A10 is also used for:

[0190] Determine the dynamic pressure maximum value sequence and dynamic tension maximum value sequence corresponding to the dynamic pressure data maximum value point and dynamic tension data maximum value point of each adjacent pressure detection point;

[0191] By using the difference between the maximum values ​​of dynamic pressure and the maximum values ​​of dynamic tension, the attenuation coefficient of each specification of counterweight at the target landing point is determined under the target counterweight factor value.

[0192] The average attenuation coefficient of each weight specification at the target landing point under the target weight factor value is used as the attenuation factor of the target weight factor, and the attenuation factor sequence under each target weight factor value is obtained.

[0193] Determine the weight factor sequence for each weight factor, and determine the Pearson correlation coefficient between the weight factor sequence and the corresponding attenuation factor sequence;

[0194] The load attenuation parameters at the target landing point are calculated using the Pearson correlation coefficient and the mean value of elements in the attenuation factor sequence.

[0195] By using load attenuation parameters, dynamic and static pressure data from adjacent pressure detection points, and combined with dynamic and static tension data from the trampoline springs, the force load at the target landing point is determined.

[0196] Furthermore, the force testing module A10 is also used for:

[0197] The pressure load characteristic value of the target impact point is calculated by using the maximum peak value of the dynamic pressure data and the static pressure values ​​and average static pressure values ​​in the static pressure data of adjacent pressure detection points.

[0198] The trampoline springs in the horizontal and vertical sections of the landing point are taken as straight springs. The maximum peak value in the dynamic tension data of the bias spring, as well as the dynamic and static tension data of the straight spring, are used to calculate the characteristic value of the tension load at the target landing point.

[0199] The load-related parameters of the target landing point are determined by using the characteristic values ​​of the compressive load and the characteristic values ​​of the tensile load, and the force load at the target landing point is determined by using the load attenuation parameter and the load-related parameters.

[0200] Furthermore, the force testing module A10 is also used for:

[0201] The set of coordinates of the target landing point and its adjacent pressure detection points on the trampoline net is used as the local coordinate set of the landing point.

[0202] The interval formed by the maximum and minimum values ​​of the horizontal coordinates in the local coordinate set of the landing point is taken as the horizontal interval of the landing point, and the interval formed by the maximum and minimum values ​​of the vertical coordinates in the local coordinate set of the landing point is taken as the vertical interval of the landing point.

[0203] Furthermore, the force testing module A10 is also used for:

[0204] The unit vector of the deflection spring is determined by using the angle between the target landing point and the line containing the deflection spring and the horizontal axis of the two-dimensional coordinate system containing the trampoline net.

[0205] By using the static tension values ​​of the deflection springs corresponding to the target landing point in the lateral and longitudinal directions, the static tension components in the lateral and longitudinal directions are determined respectively.

[0206] The load direction at the target impact point is determined by utilizing the static tensile force components in the lateral and longitudinal directions and the pressure gradient at the target impact point.

[0207] Furthermore, the force testing module A10 is also used for:

[0208] Determine the static pressure values ​​and distances between the endpoints of multiple consecutive adjacent pressure detection points in both the horizontal and vertical directions where the target impact point is located.

[0209] By using the static pressure values ​​and endpoint distances of multiple adjacent pressure detection points in the horizontal and vertical directions, the pressure gradients of the target landing point in the horizontal and vertical directions are obtained respectively.

[0210] The load direction at the target impact point is calculated by using the static tensile force components and pressure gradients in the lateral and longitudinal directions of the target impact point.

[0211] Furthermore, the load planning module A20 is also used for:

[0212] Using the force load, load direction, and coordinate position between target landing points as similarity criteria, the trampoline net surface is divided into multiple load regions using a regional growth algorithm.

[0213] The average load of all points in the load region is used as the overall load parameter of the load region. The load regions are arranged in descending order of the normalized overall load parameter to obtain the load region sequence.

[0214] Furthermore, the model adjustment module A30 is also used for:

[0215] The intervals corresponding to the load region sequence are divided into an equal number of sub-intervals based on the number of load regions in the load region sequence.

[0216] The proportional relationship between the number of landing points in each load region in the load region sequence is determined as the range proportional relationship between each sub-interval.

[0217] By using the preset maximum unit size and preset minimum unit size, as well as the range ratio, the unit size allocated to the load region corresponding to the sub-interval is determined;

[0218] The finite element model of the trampoline surface is obtained by generating an unstructured mesh according to the element size allocated to each load region.

[0219] The specific implementation of the finite element modeling system for trampoline netting of the present invention is basically the same as the embodiments of the finite element modeling method for trampoline netting described above, and will not be repeated here.

[0220] Furthermore, the present invention also provides a computer-readable storage medium. The computer-readable storage medium of the present invention stores a finite element modeling program for a trampoline mesh surface, wherein, when executed by a processor, the finite element modeling program for the trampoline mesh surface implements the steps of the finite element modeling method for the trampoline mesh surface as described above.

[0221] The method implemented when the finite element modeling program for the trampoline net surface is executed can be referred to in various embodiments of the finite element modeling method for the trampoline net surface of the present invention, and will not be repeated here.

[0222] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0223] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0224] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0225] The above description is only a preferred embodiment of the present invention and does not limit the scope of protection of the present invention. All equivalent structural / method transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the scope of protection of the present invention.

Claims

1. A finite element modeling method for trampoline mesh, characterized in that, The method includes: Dynamic and static pressure tests were conducted on the target landing point of the trampoline net using various specifications of counterweights with multiple counterweight factors to obtain the force load at the target landing point. The horizontal and vertical intervals of the landing point are obtained by using the position coordinates of the target landing point and its adjacent pressure detection points on the trampoline mesh. The trampoline springs outside the horizontal and vertical intervals of the landing point are used as deflection springs. The load direction at the target impact point is determined by using the unit vector and static tension value of the deflection spring and the pressure gradient at the target impact point; The trampoline net is divided into multiple load regions by using the force load and load direction at the target landing point, and the load region sequence is obtained by using the average force load of the load region. By utilizing the number of landing points in each load region in the load region sequence, the element size corresponding to each load region is determined to obtain the finite element model of the trampoline net surface. Methods for determining the load direction include: The unit vector of the deflection spring is determined by using the angle between the target landing point and the line containing the deflection spring and the horizontal axis of the two-dimensional coordinate system containing the trampoline net. By using the static tension values ​​of the deflection springs corresponding to the target landing point in the lateral and longitudinal directions, the static tension components in the lateral and longitudinal directions are determined respectively. The load direction at the target impact point is determined by utilizing the static tensile force components in the lateral and longitudinal directions and the pressure gradient at the target impact point.

2. The finite element modeling method for trampoline netting according to claim 1, characterized in that, The method involves using various weights of different specifications, incorporating multiple counterweight factors, to conduct dynamic and static pressure tests on the target landing point of the trampoline net, thereby obtaining the force load at the target landing point, including: Pressure detection points that are consecutively adjacent to the target landing point and have a pressure value that is not 0 are considered as adjacent pressure detection points of the target landing point. Dynamic and static pressure tests were conducted on the target landing point of the trampoline net using various weights of different specifications that include multiple weight factors. Dynamic pressure data, dynamic tension data, static pressure data, and static tension data were obtained at adjacent pressure testing points. By using dynamic pressure data, dynamic tension data, static pressure data, and static tension data, the force load at the target landing point is determined.

3. The finite element modeling method for trampoline netting according to claim 2, characterized in that, The method of determining the force load at the target landing point using dynamic pressure data, dynamic tension data, static pressure data, and static tension data includes: Determine the dynamic pressure maximum value sequence and dynamic tension maximum value sequence corresponding to the dynamic pressure data maximum value point and dynamic tension data maximum value point of each adjacent pressure detection point; By using the difference between the maximum values ​​of dynamic pressure and the maximum values ​​of dynamic tension, the attenuation coefficient of each specification of counterweight at the target landing point is determined under the target counterweight factor value. The average attenuation coefficient of each weight specification at the target landing point under the target weight factor value is used as the attenuation factor of the target weight factor, and the attenuation factor sequence under each target weight factor value is obtained. Determine the weight factor sequence for each weight factor, and determine the Pearson correlation coefficient between the weight factor sequence and the corresponding attenuation factor sequence; The load attenuation parameters at the target landing point are calculated using the Pearson correlation coefficient and the mean value of elements in the attenuation factor sequence. By using load attenuation parameters, dynamic and static pressure data from adjacent pressure detection points, and combined with dynamic and static tension data from the trampoline springs, the force load at the target landing point is determined.

4. The finite element modeling method for trampoline netting according to claim 3, characterized in that, The method of determining the force load at the target landing point by utilizing load attenuation parameters, dynamic and static pressure data from adjacent pressure detection points, and combining them with the dynamic and static tension data of the trampoline springs includes: The pressure load characteristic value of the target impact point is calculated by using the maximum peak value of the dynamic pressure data and the static pressure values ​​and average static pressure values ​​in the static pressure data of adjacent pressure detection points. The trampoline springs in the horizontal and vertical sections of the landing point are taken as straight springs. The maximum peak value in the dynamic tension data of the bias spring, as well as the dynamic and static tension data of the straight spring, are used to calculate the characteristic value of the tension load at the target landing point. The load-related parameters of the target landing point are determined by using the characteristic values ​​of the compressive load and the characteristic values ​​of the tensile load, and the force load at the target landing point is determined by using the load attenuation parameter and the load-related parameters.

5. The finite element modeling method for trampoline netting according to claim 1, characterized in that, The method of obtaining the horizontal and vertical intervals of the landing point using the position coordinates of the target landing point and its adjacent pressure detection points on the trampoline net includes: The set of coordinates of the target landing point and its adjacent pressure detection points on the trampoline net is used as the local coordinate set of the landing point. The interval formed by the maximum and minimum values ​​of the horizontal coordinates in the local coordinate set of the landing point is taken as the horizontal interval of the landing point, and the interval formed by the maximum and minimum values ​​of the vertical coordinates in the local coordinate set of the landing point is taken as the vertical interval of the landing point.

6. The finite element modeling method for trampoline netting according to claim 1, characterized in that, The method of determining the load direction at the target impact point by utilizing the static tensile force components in the lateral and longitudinal directions and the pressure gradient at the target impact point includes: Determine the static pressure values ​​and distances between the endpoints of multiple consecutive adjacent pressure detection points in both the horizontal and vertical directions where the target impact point is located. By using the static pressure values ​​and endpoint distances of multiple adjacent pressure detection points in the horizontal and vertical directions, the pressure gradients of the target landing point in the horizontal and vertical directions are obtained respectively. The load direction at the target impact point is calculated by using the static tensile force components and pressure gradients in the lateral and longitudinal directions of the target impact point.

7. The finite element modeling method for trampoline netting according to claim 1, characterized in that, The trampoline net surface is divided into multiple load regions using the force load and load direction at the target landing point. A load region sequence is obtained using the average force load value of each load region, including: Using the force load, load direction, and coordinate position between target landing points as similarity criteria, the trampoline net surface is divided into multiple load regions using a regional growth algorithm. The average load of all points in the load region is used as the overall load parameter of the load region. The load regions are arranged in descending order of the normalized overall load parameter to obtain the load region sequence.

8. The finite element modeling method for trampoline netting according to claim 7, characterized in that, The step of determining the element size of each load region by utilizing the number of landing points in each load region sequence to obtain the finite element model of the trampoline net surface includes: The intervals corresponding to the load region sequence are divided into an equal number of sub-intervals based on the number of load regions in the load region sequence. The proportional relationship between the number of landing points in each load region in the load region sequence is determined as the range proportional relationship between each sub-interval. By using the preset maximum unit size and preset minimum unit size, as well as the range ratio, the unit size allocated to the load region corresponding to the sub-interval is determined; The finite element model of the trampoline surface is obtained by generating an unstructured mesh according to the element size allocated to each load region.

9. A finite element modeling system for a trampoline mesh, characterized in that, The system is used to implement the finite element modeling method for trampoline net surfaces as described in any one of claims 1 to 8; the system includes: The force testing module is used to perform dynamic and static pressure tests on the target landing point of the trampoline net using various specifications of counterweights with multiple weight factors to obtain the force load on the target landing point; it uses the position coordinates of the target landing point and its adjacent pressure detection points on the trampoline net to obtain the lateral and longitudinal intervals of the landing point, and uses the trampoline springs outside the lateral and longitudinal intervals of the landing point as bias springs; it uses the unit vector and static tension value of the bias springs and the pressure gradient of the target landing point to determine the load direction of the target landing point; The load planning module is used to divide the trampoline net into multiple load regions using the force load and load direction at the target landing point, and to obtain the load region sequence using the average force load of the load region. The model adjustment module is used to determine the element size of each load region by utilizing the number of landing points in each load region in the load region sequence, thereby obtaining the finite element model of the trampoline net surface.

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