A stress analysis method and system for step stool cyclic loading test

Abstract

The present invention provides a stress analysis method and system for a step stool cyclic loading test, which belongs to the field of data processing. The friction probability difference degree of each preliminary grid is used to form a friction probability difference vector, and the elastic probability difference degree of each preliminary grid is used to form an elastic probability difference vector; the difference between the friction probability difference degree and the elastic probability difference degree of each preliminary grid is calculated to obtain the friction-elastic probability individual difference, and the difference between the friction probability difference vector and the elastic probability difference vector in the direction of the vector space is calculated to obtain the friction-elastic probability direction difference; by comparing the friction-elastic probability individual difference of each preliminary grid with the friction-elastic probability direction difference as a weight, the size of the preliminary grid is fine-tuned. By refining the grid in the stress concentration area, more accurate stress measurement points are captured, and potential stress concentration problems are discovered in time.

Description

Technical Field

[0001] The invention belongs to the field of data processing, and in particular relates to a stress analysis method and system for a step stool cyclic loading test. Background Art

[0002] In the stress simulation test of the step stool, the cyclic loading process refers to the process of repeatedly applying a specific load to the step stool to simulate the repeated load-bearing or impact conditions in actual use, thereby analyzing and calculating the stress distribution. This process is used to evaluate the durability of the step stool, that is, the structural stability and fatigue life of the step stool in long-term and repeated use. In the cyclic loading test of the step stool, the step stool structure usually undergoes repeated stress conditions, especially in the support points, pedal connection points and the area where the feet contact the ground. There will be complex stress concentration phenomena. Since the geometric shape of the step stool is irregular, in traditional finite element analysis (FEA), the division of the grid, the precise processing of the friction coefficient and the elastic modulus are crucial to the results of the overall analysis. However, traditional finite element technology has limitations in stress analysis and cannot fully reflect the stress distribution under the complex structure of the step stool, resulting in the failure to accurately identify the stress concentration area, which is prone to damage in actual testing.

[0003] In the cyclic loading stress analysis of the ladder stool, the finite element analysis method is usually used to model the whole or part of the surface of the ladder stool to be analyzed in three dimensions, divide its surface into grid areas on the three-dimensional model, and then simulate the three-dimensional model to apply multi-directional loads. Due to the different sizes, positions, angles, directions, etc. of each grid area, the loads received by each grid area in the force analysis are also different. Load and force surface are important factors in stress analysis. The size and density of the grid division will lead to the setting distribution of the force surface is not accurate and comprehensive, affecting the calculated stress value. However, since the ladder stool is a rod-shaped support structure, it is not like a large regular structure with a large and flat surface area such as a sphere or a cube. The surface force analysis of the ladder stool is relatively rugged, which is not convenient for normal regional division to receive load analysis, and the performance of finite element analysis will be limited.

[0004] In the existing step stool stress analysis technology, for example, the prestressed component simulation data processing method and system combined with finite element analysis provided in the patent document with announcement number CN116991981B, although the distribution characteristics of the stress monitoring text unit can be set, the finite element grid is usually divided at a fixed ratio, resulting in insufficient stress measurement accuracy in the stress concentration area, and unable to accurately capture the changes in local material properties. In addition, the existing technology cannot make adaptive adjustments based on the precise processing of the friction coefficient and elastic modulus in areas with complex stress distribution. Although the patent document with announcement number CN102222134B also provides a method for automatically generating mesh density suitable for finite element analysis of the forging process, this method is prone to missing potential stress concentration points in the step stool structure, and it is impossible to identify and reinforce the problem area in a timely manner.

[0005] The contact area between the front and rear feet of the step stool needs to consider the influence of friction and multi-degree-of-freedom motion on force analysis. In addition to the contact surface between the foot of the step stool and the ground, other parts of the step stool, including the connection points of different structural parts, the contact surface between the pedal and the support frame, etc., use conventional simple mesh segmentation, which will result in many subtle locations where stress is weak and not detected for reinforcement, leaving safety hazards caused by structural fragility, and conventional mesh segmentation methods are not suitable for stress analysis. After using the existing finite element analysis software to analyze the newly designed step stool model, it should have solved the high-risk stress areas in various places, but the step stool produced still often has defects in various subtle locations in actual testing, and it is necessary to improve the mesh style algorithm and its code in the existing finite element analysis software. Summary of the invention

[0006] The purpose of the present invention is to propose a stress analysis method and system for a step stool cyclic loading test to solve one or more technical problems existing in the prior art and at least provide a beneficial choice or create conditions.

[0007] In order to achieve the above object, according to one aspect of the present invention, a stress analysis method for a step stool cyclic loading test is provided, the method comprising the following steps:

[0008] The surface of the step stool is preliminarily segmented to obtain a preliminary regional grid, and the data of the friction coefficient and elastic modulus on each preliminary grid in the preliminary regional grid are obtained; each preliminary grid is compared with its adjacent preliminary grids in terms of the probability density of the friction coefficient and the probability density of the effective elastic modulus to obtain the friction probability difference and elastic probability difference of the preliminary grid; the friction probability difference of each preliminary grid is used to form a friction probability difference vector, and the elastic probability difference of each preliminary grid is used to form an elastic probability difference vector; the difference between the friction probability difference and the elastic probability difference of each preliminary grid is calculated to obtain the friction-elasticity individual difference, and the difference between the friction probability difference vector and the elastic probability difference vector in the direction of the vector space is calculated to obtain the friction-elasticity directional difference; the size of the preliminary grid is fine-tuned by comparing the friction-elasticity individual difference of each preliminary grid with the friction-elasticity directional difference as a weight.

[0009] Furthermore, according to the structure of the step stool, the surface of the step stool is preliminarily segmented with a preset initial grid size to obtain a preliminary regional grid.

[0010] Furthermore, a preliminary regional grid is formed by each preliminary grid, each preliminary regional grid does not overlap with each other, and the preliminary regional grid covers the surface of the step stool.

[0011] Furthermore, the friction coefficient data of various parts of the step stool surface are obtained by using a friction coefficient sensor and / or a friction coefficient tester; and the elastic modulus data of different parts of the step stool are obtained by dynamic thermomechanical analysis.

[0012] Furthermore, the method for obtaining the data of the friction coefficient and elastic modulus on each preliminary grid in the preliminary regional grid is:

[0013] Performing probability statistics on the values ​​of the friction coefficient on each preliminary grid, calculating the probability distribution of the values ​​of the friction coefficient on all preliminary grids, and obtaining the probability density of the values ​​of the friction coefficient on each preliminary grid appearing in the probability distribution of the values ​​of the friction coefficient on all preliminary grids, as the probability density of the friction coefficient of each preliminary grid;

[0014] The value of the effective elastic modulus on each preliminary grid is subjected to probability statistics, and the probability distribution of the values ​​of the effective elastic modulus on all preliminary grids is statistically calculated. The probability density of the value of the effective elastic modulus on each preliminary grid appearing in the probability distribution of the values ​​of the effective elastic modulus on all preliminary grids is obtained respectively as the probability density of the effective elastic modulus of each preliminary grid.

[0015] Furthermore, by comparing the individual difference of the friction-elasticity probability of each preliminary grid with the friction-elasticity probability directional difference as a weight, the method for fine-tuning the size of the preliminary grid may be:

[0016] The ratio of the individual difference in friction-elasticity probability to the directional difference in friction-elasticity probability is used, and a bias operator is combined in the comparison process to obtain a weight for grid adjustment, and the size of the preliminary grid is fine-tuned with the weight for grid adjustment.

[0017] Further, the method of calculating the difference between the friction probability difference and the elasticity probability difference of each preliminary grid to obtain the friction-elasticity probability individual difference, and calculating the difference between the friction probability difference vector and the elasticity probability difference vector in the direction of the vector space to obtain the friction-elasticity probability directional difference specifically includes:

[0018] For each preliminary grid, the absolute value of the difference between the friction probability difference of the preliminary grid and the elasticity probability difference of the preliminary grid is calculated as the friction-elasticity probability individual gap of the preliminary grid;

[0019] To calculate the directional difference between the probability density of the friction coefficient and the probability density of the effective elastic modulus in the vector space, the vector angle between the probability density of the friction coefficient and the probability density of the effective elastic modulus can be used to normalize the vector angle to obtain the friction-elasticity probability directional difference.

[0020] Furthermore, the method of forming a friction probability difference vector with the friction probability difference of each preliminary grid and forming an elasticity probability difference vector with the elasticity probability difference of each preliminary grid specifically includes:

[0021] Obtain the three-dimensional coordinates of the geometric center of each preliminary grid, obtain the three-dimensional coordinates of the geometric center of the step stool in the three-dimensional model for preliminary grid division, that is, the step stool center coordinates, and calculate the Euclidean distance of the three-dimensional coordinates of the geometric center of each preliminary grid relative to the step stool center coordinates as the center distance of each preliminary grid. Sort each preliminary grid in ascending order according to its center distance to form a preliminary grid sequence;

[0022] An array consisting of numerical values ​​of friction probability differences of each preliminary grid in the preliminary grid sequence is a friction probability difference vector;

[0023] An array consisting of numerical values ​​of elastic probability differences of each preliminary grid in the preliminary grid sequence is an elastic probability difference vector.

[0024] Furthermore, each preliminary grid is compared with its adjacent preliminary grids in terms of friction coefficient probability density and effective elastic modulus probability density, and the method for obtaining the friction probability difference and elastic probability difference of the preliminary grids is as follows:

[0025] For each preliminary grid, obtain the adjacent preliminary grids that have common edges with it as the adjacent preliminary grids of the preliminary grid;

[0026] For each preliminary grid, obtain the friction coefficient probability density of the preliminary grid, and respectively obtain the friction coefficient probability density of each adjacent preliminary grid of the preliminary grid, compare the friction coefficient probability density of the preliminary grid with the friction coefficient probability density of each adjacent preliminary grid, and take the average of the obtained ratios as the friction probability difference degree of the preliminary grid;

[0027] For each preliminary grid, the effective elastic modulus probability density of the preliminary grid is obtained, and the effective elastic modulus probability density of each adjacent preliminary grid of the preliminary grid is obtained respectively. The effective elastic modulus probability density of the preliminary grid is compared with the effective elastic modulus probability density of each adjacent preliminary grid, and the average of the obtained ratios is taken as the elastic probability difference of the preliminary grid.

[0028] The present invention also provides a stress analysis system for a step stool cyclic loading test, the stress analysis system for a step stool cyclic loading test comprising: a processor, a memory, and a computer program stored in the memory and executable on the processor, the processor implementing the steps in the stress analysis method for the step stool cyclic loading test when executing the computer program to control the grid segmentation size of the stress analysis software system, the stress analysis system for the step stool cyclic loading test can be run in computing devices such as desktop computers, laptop computers, mobile phones, PDAs, and cloud data centers, and the executable systems may include, but are not limited to, processors, memories, and server clusters, and the processor executing the computer program runs in the following system units:

[0029] A data acquisition unit, used for preliminarily segmenting the surface of the step stool to obtain a preliminary regional grid, and obtaining data of friction coefficient and elastic modulus on each preliminary grid in the preliminary regional grid;

[0030] The probability calculation unit is used to compare the friction coefficient probability density and the effective elastic modulus probability density of each preliminary grid with its adjacent preliminary grids, so as to obtain the friction probability difference and elastic probability difference of the preliminary grids;

[0031] A vector generating unit, used for forming a friction probability difference vector with the friction probability difference of each preliminary grid, and forming an elasticity probability difference vector with the elasticity probability difference of each preliminary grid;

[0032] a gap calculation unit, used for calculating the gap between the friction probability difference and the elasticity probability difference of each preliminary grid to obtain the friction-elasticity probability individual gap, and calculating the gap between the friction probability difference vector and the elasticity probability difference vector in the direction of the vector space to obtain the friction-elasticity probability direction gap;

[0033] The grid fine-tuning unit is used to fine-tune the size of the preliminary grid by comparing the individual gap of the friction-elasticity probability of each preliminary grid with the friction-elasticity probability direction gap as a weight.

[0034] The beneficial effects of the present invention are as follows: the present invention provides a stress analysis method and system for a step stool cyclic loading test, wherein the friction probability difference degree of each preliminary grid is used to form a friction probability difference vector, and the elastic probability difference degree of each preliminary grid is used to form an elastic probability difference vector; the difference between the friction probability difference degree and the elastic probability difference degree of each preliminary grid is calculated to obtain the friction-elastic probability individual difference, and the difference between the friction probability difference vector and the elastic probability difference vector in the direction of the vector space is calculated to obtain the friction-elastic probability direction difference; by comparing the friction-elastic probability individual difference of each preliminary grid with the friction-elastic probability direction difference as a weight, the size of the preliminary grid is fine-tuned. By refining the grid in the stress concentration area, more accurate stress measurement points are captured, potential stress concentration problems are discovered in time, and more accurate analysis results are ensured. The difference between the friction coefficient and the effective elastic modulus is used to identify changes in material properties, effectively dealing with complex geometric structures and uneven stress distributions. The grid density can be dynamically adjusted according to stress changes, the stress analysis process is continuously optimized, and the safety of the overall structure is ensured. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The above and other features of the present invention will become more obvious by describing in detail the embodiments shown in the accompanying drawings. The same reference numerals in the accompanying drawings of the present invention represent the same or similar elements. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other accompanying drawings can be obtained based on these accompanying drawings without creative work. In the accompanying drawings:

[0036] Figure 1 Shown is a flow chart of a stress analysis method for a step stool cyclic loading test;

[0037] Figure 2 Shown is a system structure diagram of a stress analysis system for a step stool cyclic loading test. DETAILED DESCRIPTION

[0038] The following will be combined with the embodiments and drawings to clearly and completely describe the concept, specific structure and technical effects of the present invention, so as to fully understand the purpose, scheme and effect of the present invention. It should be noted that the embodiments and features in the embodiments of this application can be combined with each other without conflict.

[0039] In the description of the present invention, "several" means one or more, "more" means more than two, "greater than", "less than", "exceed" etc. are understood as not including the number itself, and "above", "below", "within" etc. are understood as including the number itself. If there is a description of "first" or "second", it is only used for the purpose of distinguishing the technical features, and cannot be understood as indicating or implying the relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0040] like Figure 1 The flowchart of the stress analysis method of the step stool cyclic loading test according to the present invention is shown below. Figure 1 A stress analysis method and system for a step stool cyclic loading test according to an embodiment of the present invention will be described.

[0041] The present invention provides a stress analysis method for a step stool cyclic loading test, the method specifically comprising the following steps:

[0042] Performing preliminary segmentation on the surface of the step stool to obtain preliminary regional grids, and obtaining data on the friction coefficient and elastic modulus on each preliminary grid in the preliminary regional grid;

[0043] Each preliminary grid is compared with its adjacent preliminary grids in terms of friction coefficient probability density and effective elastic modulus probability density, and the friction probability difference and elastic probability difference of the preliminary grids are obtained;

[0044] The friction probability difference degree of each preliminary grid is used to form a friction probability difference vector, and the elasticity probability difference degree of each preliminary grid is used to form an elasticity probability difference vector;

[0045] The difference between the friction probability difference and the elasticity probability difference of each preliminary grid is calculated to obtain the friction-elasticity probability individual difference, and the difference between the friction probability difference vector and the elasticity probability difference vector in the direction of the vector space is calculated to obtain the friction-elasticity probability direction difference;

[0046] The size of the preliminary grid is fine-tuned by comparing the individual gap of the friction-elasticity probability of each preliminary grid with the directional gap of the friction-elasticity probability as a weight.

[0047] Furthermore, according to the structure of the step stool, the surface of the step stool is preliminarily segmented with a preset initial grid size to obtain a preliminary regional grid.

[0048] In some embodiments, in a cyclic loading test of a step stool, an initial mesh size of stress adaptive meshing may be set according to structural characteristics of the step stool and requirements for stress analysis.

[0049] For the step stool support frame (main structure), the step stool support frame is usually the area that bears the main vertical load, but the stress distribution is relatively uniform over a large range. The initial mesh size can be set to 10-20 mm. This mesh size is sufficient to capture the overall stress distribution trend of the support frame under cyclic loading. Since the force on the support frame is relatively dispersed, this range of meshes can achieve a balance between efficiency and accuracy, providing a basis for subsequent mesh refinement.

[0050] Stress concentration usually occurs at the connection between the step stool tread and the supporting frame, especially when repeated load bearing and cyclic loading occur, and these parts may be the early occurrence points of fatigue cracks and plastic deformation. The initial mesh size is recommended to be set to 5-10mm. At the connection part, the mesh needs to be smaller than the frame to capture the detailed stress changes and facilitate the observation of the local stress distribution at the stress concentration point. In addition, this mesh size can be further refined to 1-2mm during the adaptive encryption process to improve the accuracy of local stress analysis.

[0051] The contact area between the front and rear legs of the step stool and the ground is a key part for support and fixation. This part will be subjected to uneven force during repeated cyclic loading, so a higher stress analysis accuracy is required. The recommended initial mesh size is 2-5mm. Since the front and rear leg contact area needs to consider the effects of friction and multi-degree-of-freedom motion, a smaller mesh helps to improve the accuracy of force distribution. If the stress concentration is severe later, the mesh can be further encrypted to 0.5-1mm to ensure that the stress changes in the ground contact area are captured in detail.

[0052] Furthermore, a preliminary regional grid is formed by each preliminary grid, each preliminary regional grid does not overlap with each other, and the preliminary regional grid covers the surface of the step stool.

[0053] Furthermore, the friction coefficient data of various parts of the step stool surface are obtained by using a friction coefficient sensor and / or a friction coefficient tester; and the elastic modulus data of different parts of the step stool are obtained by dynamic thermomechanical analysis.

[0054] In some embodiments, in order to comprehensively measure the friction coefficient of different parts of the step stool, a combined friction measuring instrument and a micro sensor arrangement method can be used. In an embodiment using a micro friction coefficient sensor / friction coefficient tester, micro friction coefficient sensors can be installed on the surface of various parts of the step stool to accurately measure the friction coefficient of different contact points. The embodiments using a surface scanning friction coefficient analyzer, such as an AFT friction coefficient tester, a surface friction coefficient meter, a friction coefficient tester, etc., are suitable for measuring and recording the changes in the friction coefficient of each contact surface area, and can be used to scan different contact parts of the step stool in steps, including the foot of the step stool, the pedal, the support frame connection point, etc.

[0055] Micro friction sensors can be attached to different contact points of the step stool, such as the pedal and frame, support rod joints, and connection points to measure tiny changes in friction and calculate the real-time friction coefficient. The friction coefficient of each contact point can also be gradually recorded by scanning the friction coefficient analyzer under no load or light load to form preliminary friction distribution data; under loading or cyclic loading, the dynamic changes of the friction coefficient can be monitored in real time using sensors to record the values ​​of the friction coefficient under different loading conditions and moving states. The measured friction coefficient data can be integrated through the data acquisition system to generate a distribution map of the friction coefficient, which can be used to analyze the impact of friction in different parts on stress distribution.

[0056] In some embodiments, in addition to the effective elastic modulus of the overall structure of the step stool, it is also necessary to pay attention to the changes in the elastic modulus of different contact surfaces, connectors and other parts under multiple temperature and humidity environments. A variety of instruments can be used to collaboratively detect the effective elastic modulus, such as a dynamic mechanical analyzer, which can detect the elastic modulus of materials at different parts of the step stool, including key structures such as pedals and support frames, to evaluate the impact of temperature and humidity changes on the elastic modulus of each part. Ultrasonic detectors can also be used at each contact point and connection to detect the effective elastic modulus of different parts, especially parts that are susceptible to environmental influences, such as areas of high humidity or significant temperature changes.

[0057] The effective elastic modulus data of each part can then be uploaded to the central data acquisition system to form a distribution map of the elastic modulus. In the simulation, different elastic moduli can be set for each part based on these data to simulate the subtle effects of environmental changes on the stress and deformation of the step stool.

[0058] Furthermore, the data of the friction coefficient and elastic modulus on each preliminary grid in the preliminary regional grid are obtained, specifically:

[0059] Performing probability statistics on the values ​​of the friction coefficient on each preliminary grid, calculating the probability distribution of the values ​​of the friction coefficient on all preliminary grids, and obtaining the probability density of the values ​​of the friction coefficient on each preliminary grid appearing in the probability distribution of the values ​​of the friction coefficient on all preliminary grids, as the probability density of the friction coefficient of each preliminary grid;

[0060] The value of the effective elastic modulus on each preliminary grid is subjected to probability statistics, and the probability distribution of the values ​​of the effective elastic modulus on all preliminary grids is statistically calculated. The probability density of the value of the effective elastic modulus on each preliminary grid appearing in the probability distribution of the values ​​of the effective elastic modulus on all preliminary grids is obtained respectively as the probability density of the effective elastic modulus of each preliminary grid.

[0061] In the embodiments of the prior art, the values ​​of the friction coefficient and the effective elastic modulus on each preliminary grid are usually compressed uniformly using a min-max homogenization algorithm, and compressed into floating point numbers of 0 to 1, as the probability density of the friction coefficient and the probability density of the effective elastic modulus on each preliminary grid. However, this is actually inaccurate, because the homogenized floating point numbers only represent the proportion of the values ​​of the friction coefficient and the effective elastic modulus on each preliminary grid in the overall numerical distribution, and are not accurate for representing the frequency at which the values ​​of the friction coefficient and the effective elastic modulus on each preliminary grid appear on the surface of the step stool.

[0062] In the prior art, the min-max normalization algorithm is usually used to compress the friction coefficient and the effective elastic modulus into floating point numbers between 0 and 1. However, normalization only represents the relative proportion of the data, rather than the probability of occurrence of the actual physical quantity on the surface of the structure. This makes it difficult to reflect the true stress distribution for complex structures such as step stools. Moreover, the structure of step stools is diverse. For example, the stress conditions at the contact surface between the foot and the ground and the connection between the pedals are completely different. A simple normalization method cannot capture the local stress concentration in different parts.

[0063] In a preferred embodiment, a more accurate processing is achieved by using a probability density function to calculate the distribution of the friction coefficient and the effective elastic modulus. Such a calculation can capture the actual frequency and probability density of the physical quantity on each preliminary grid, ensuring that the stress characteristics in the complex structure of the step stool are accurately reflected. Especially at the contact point between the supporting foot and the ground, the local change of the friction coefficient is particularly important for stress analysis. Through the processing method of probability density, stress concentration in areas with large friction coefficients (such as the feet) and areas with small elastic modulus, such as connection points, can be better identified.

[0064] The statistical basis of the probability density function is based on the continuous distribution model, which can more accurately describe the distribution characteristics of the friction coefficient and elastic modulus in different grid areas in the structure, rather than simple relative values. For complex geometric bodies such as step stools, the use of probability density can more clearly express the force characteristics of different structural parts. In complex structures, local stress concentration phenomena often depend on the distribution characteristics of physical quantities. By using the probability density function method for stress analysis, these stress concentration points on the step stool can be better identified and analyzed and improved.

[0065] In some preferred embodiments, the friction coefficient probability density and the effective elastic modulus probability density on each preliminary grid are obtained in the preliminary regional grid.

[0066] Probability statistics are performed on the values ​​of the friction coefficient on each preliminary grid, and the probability distribution of the values ​​of the friction coefficient on all the preliminary grids is statistically calculated. The probability density of the value of the friction coefficient on each preliminary grid appearing in the probability distribution of the values ​​of the friction coefficient on all the preliminary grids is obtained as the probability density of the friction coefficient of each preliminary grid.

[0067] The value of the effective elastic modulus on each preliminary grid is subjected to probability statistics, and the probability distribution of the values ​​of the effective elastic modulus on all preliminary grids is statistically calculated. The probability density of the value of the effective elastic modulus on each preliminary grid appearing in the probability distribution of the values ​​of the effective elastic modulus on all preliminary grids is obtained respectively as the probability density of the effective elastic modulus of each preliminary grid.

[0068] In one embodiment provided, the probability density can be obtained by performing probability statistics through the probability density function module in the Scipy software.

[0069] Furthermore, the friction coefficient probability density and the effective elastic modulus probability density of each preliminary grid are compared with those of its adjacent preliminary grids to obtain the friction probability difference and elastic probability difference of the preliminary grids, which are specifically:

[0070] In the embodiment of the prior art, the convolution kernel of the convolution neural network can be used to locally compare the friction coefficient probability density and the effective elastic modulus probability density of each preliminary grid with its adjacent preliminary grids. However, the convolution neural network cannot be used right away. Its convolution kernel needs to accumulate a large amount of data for training and fitting. Then the model designed and produced at the beginning will become its test data, resulting in a large amount of waste of production materials.

[0071] In the existing technology, convolutional neural networks (CNNs) are used to compare the probability density of friction coefficient and effective elastic modulus locally. However, CNNs require a large amount of training data in stress analysis. However, in the early design stage of a new structure such as a step stool, there is a lack of sufficient actual test data, which easily leads to material waste. The convolution kernel of CNNs is fixed, which makes it impossible to flexibly deal with the different force characteristics of different parts (such as the feet and the joints) during stress analysis.

[0072] In a preferred embodiment, the approach of replacing the convolutional neural network with the probability density difference comparison of adjacent grids can avoid the limitation of large data accumulation. Directly calculating the difference in friction coefficient and effective elastic modulus between the preliminary grid and its adjacent grids reduces the need for data accumulation and is suitable for the early design stage. In particular, at the connection between the step and frame of the step stool, potential stress concentration problems can be quickly identified through simple adjacent grid difference analysis.

[0073] In addition, compared with CNN, this analysis based on adjacent grids is more flexible and suitable for areas with large local stress changes in complex structures, such as support points and locations where friction is concentrated in the foot. The probability difference of adjacent grids reflects the difference in stress distribution in adjacent areas, which can directly reflect the local stress concentration or inconsistency of material properties. Especially in complex structures such as step stools, potential stress problems can be discovered through this local comparison. In step stool stress analysis, local stress concentration is usually the cause of structural failure. The comparison method of adjacent grids can quickly identify these areas and improve the efficiency of stress analysis on them.

[0074] In some preferred embodiments, for each preliminary grid, adjacent preliminary grids having common edges with the preliminary grid are obtained as adjacent preliminary grids of the preliminary grid.

[0075] For each preliminary grid, the friction coefficient probability density of the preliminary grid is obtained, and the friction coefficient probability density of each adjacent preliminary grid of the preliminary grid is obtained respectively. The friction coefficient probability density of the preliminary grid is compared with the friction coefficient probability density of each adjacent preliminary grid, and the average of the obtained ratios is taken as the friction probability difference of the preliminary grid.

[0076] For each preliminary grid, the effective elastic modulus probability density of the preliminary grid is obtained, and the effective elastic modulus probability density of each adjacent preliminary grid of the preliminary grid is obtained respectively. The effective elastic modulus probability density of the preliminary grid is compared with the effective elastic modulus probability density of each adjacent preliminary grid, and the average of the obtained ratios is taken as the elastic probability difference of the preliminary grid.

[0077] Furthermore, the friction probability difference degree of each preliminary grid is used to form a friction probability difference vector, and the elasticity probability difference degree of each preliminary grid is used to form an elasticity probability difference vector, specifically:

[0078] In an embodiment of the prior art, a convolutional neural network can be used to extract the numerical distribution characteristics of the friction coefficient probability density and the effective elastic modulus probability density of the preliminary grid on the step stool surface, and respectively extract the representation vectors of the numerical distribution of the friction coefficient probability density and the effective elastic modulus probability density, which are respectively used as the friction probability difference vector and the elastic probability difference vector. However, the dimensions of these representation vectors are fixed in the model hyperparameters, such as 500 dimensions, 300 dimensions, etc., which lacks specific targeting for each specific preliminary grid and is not convenient for subsequent inspection and investigation. Moreover, even if the dimensional size of the model's fully connected layer output is adjusted to the number of preliminary grids, the numerical value of the dimension output by the fully connected layer is unexplainable, and the numerical value of the corresponding dimension number is not for a specific preliminary grid, and the order of its dimensions is disturbed in the fully connected layer, and the validity of each dimension is difficult to trace and verify.

[0079] In the prior art, the use of convolutional neural networks for feature extraction has the problem of dimensional confusion in the fully connected layer and the limitation of flexibility due to fixed dimensions. The fully connected layer of the convolutional neural network easily confuses the features of different preliminary grids, resulting in the inability to accurately track the stress of a specific grid during the stress analysis of the step stool. The output dimension of CNN is usually fixed, lacking the flexibility to handle different grids.

[0080] In a preferred embodiment, it is proposed to calculate the Euclidean distance of the geometric center of each preliminary grid relative to the center of the step stool and sort the grids. Sorting by geometric center can enhance logic. Sorting by Euclidean distance of geometric center ensures that the grid arrangement has a certain spatial logic, can track the stress characteristic changes of each preliminary grid, and avoid the confusion caused by using a fully connected layer. The calculation of friction and elastic difference vectors can effectively identify the material performance mismatch problem in different grid areas through the probability difference vector analysis of friction coefficient and elastic modulus, and help optimize grid division.

[0081] Since the Euclidean distance measures the distance between two points, that is, on the surface of a step stool with complex geometric structures, the geometric center sorting can better help analyze the spatial distribution characteristics of the structural force, especially to effectively compare different stress areas. Moreover, by calculating the probability difference of the friction coefficient and elastic modulus, the material performance difference can be effectively identified, which helps to optimize the structural strength and safety in the future.

[0082] In some preferred embodiments, the three-dimensional coordinates of the geometric center of each preliminary grid are obtained, the three-dimensional coordinates of the geometric center of the step stool in the three-dimensional model for preliminary grid division, i.e., the center coordinates of the step stool, are obtained, and the Euclidean distance of the three-dimensional coordinates of the geometric center of each preliminary grid relative to the center coordinates of the step stool is calculated as the center distance of each preliminary grid. Each preliminary grid is sorted from small to large according to its center distance, to form a preliminary grid sequence.

[0083] An array consisting of numerical values ​​of friction probability differences of each preliminary grid in the preliminary grid sequence is a friction probability difference vector;

[0084] An array consisting of numerical values ​​of elastic probability differences of each preliminary grid in the preliminary grid sequence is an elastic probability difference vector.

[0085] Furthermore, the difference between the friction probability difference and the elasticity probability difference of each preliminary grid is calculated to obtain the friction-elasticity probability individual difference, and the difference between the friction probability difference vector and the elasticity probability difference vector in the direction of the vector space is calculated to obtain the friction-elasticity probability direction difference, specifically:

[0086] For each preliminary grid, the absolute value of the difference between the friction probability difference of the preliminary grid and the elasticity probability difference of the preliminary grid is calculated as the friction-elasticity probability individual gap of the preliminary grid;

[0087] To calculate the directional difference between the probability density of the friction coefficient and the probability density of the effective elastic modulus in the vector space, the vector angle between the probability density of the friction coefficient and the probability density of the effective elastic modulus can be used to normalize the vector angle to obtain the friction-elasticity probability directional difference.

[0088] The friction-elastic probability individual gap calculates the degree of difference in the friction coefficient and effective elastic modulus within each preliminary grid. These two physical quantities directly affect the force situation in the grid area. By analyzing their gaps, it is possible to accurately identify areas where material properties change, especially in stress concentration areas or where material properties are uneven. For such areas with large local property differences, using this gap as a weight can ensure that the mesh in this area is refined to capture more potential stress concentration points.

[0089] The friction-elastic probability directional difference reflects whether the change direction of the friction coefficient and the effective elastic modulus is consistent. If the two quantities change in the same direction, it means that the material properties in this area are relatively stable and uniform; on the contrary, if the directional difference is large, it means that the material properties in this area change dramatically. Therefore, using the directional difference can better reflect the trend of stress change, thereby optimizing the directionality of mesh division and making stress analysis more accurate.

[0090] Using the friction-elastic probability individual gap and direction gap as weights, it is possible to achieve differentiated mesh adjustments in areas with different material properties and stress characteristics. This adaptive adjustment method allows the mesh to be refined in areas such as stress concentration points and connection points, while the mesh is coarsened in areas with relatively uniform stress, thereby avoiding the waste of mesh resources and improving computational efficiency. This weight calculation method can automatically identify areas with significant differences in local material properties (such as support points and connection points of step stools), without relying on manual intervention for regional division, and improving the intelligence of mesh adjustment.

[0091] By weighting the individual gaps and directional gaps in friction-elasticity probability, the mesh adjustment can be dynamically adjusted according to the actual conditions of material performance differences and stress changes. In areas where stress is concentrated, the mesh is refined, and the analysis accuracy is greatly improved; while in areas where stress is relatively dispersed, the mesh is moderately coarsened to reduce unnecessary consumption of computing resources. This can significantly improve the computational efficiency of finite element analysis while ensuring accuracy.

[0092] The Friction-Elastic Probability Individual Difference is calculated based on the difference in probability densities between the friction coefficient and the effective elastic modulus. This probability density reflects the actual distribution of the physical quantity within the mesh, rather than just a simple value. Therefore, the difference in probability density can more accurately capture the distribution of material properties in different mesh areas. This calculation method is particularly suitable for analyzing objects with complex structures and uneven forces such as step stools, and can reflect minor stress concentrations or material inconsistencies.

[0093] The friction-elastic probability directional gap can identify the changing trend of material properties in the mesh area by analyzing the directional changes of the friction coefficient and the effective elastic modulus. If the change direction of the friction coefficient and the elastic modulus is consistent, it indicates that the material properties in the area are relatively stable; conversely, a large directional gap means that the material has inconsistent changes in the area, which may indicate the risk of stress concentration or material performance failure. The calculation method of the directional gap can better help optimize the distribution of the mesh and ensure sufficient mesh density in the local stress mutation area.

[0094] Complex geometric structures often contain multiple different stress surfaces and stress points, and material properties will also change locally with stress distribution. By analyzing individual differences and directional differences, it is possible to adapt to these complex changes and provide a more flexible mesh adjustment mechanism. This calculation method avoids the shortcomings of traditional uniform meshing that cannot effectively capture local stress problems, making stress analysis more adaptable to complex structures.

[0095] For each preliminary grid, the probability density of its friction coefficient and effective elastic modulus is obtained, and the individual gap between the friction probability difference and the elastic probability difference of the preliminary grid is calculated as the friction-elasticity probability individual gap of the preliminary grid.

[0096] The friction probability difference is the probability density of the friction coefficient, and the elastic probability difference is the probability density of the effective elastic modulus. The difference indicates the local inconsistency of the friction coefficient and the elastic modulus in the grid area. In some preferred embodiments, for each preliminary grid, the absolute value of the difference between the friction probability difference of the preliminary grid and its elastic probability difference can be calculated as the friction-elastic probability individual difference of the preliminary grid.

[0097] The friction-elasticity probability direction difference is a numerical value that can be used to represent the difference in direction between the friction probability difference vector and the elasticity probability difference vector in the vector space.

[0098] The difference between the friction probability difference vector and the elasticity probability difference vector in the direction of the vector space can be calculated as the friction-elasticity probability difference. Preferably, the difference between the friction coefficient probability density and the effective elastic modulus probability density in the direction of the vector space can be calculated, and the vector angle between the friction coefficient probability density and the effective elastic modulus probability density can be used to normalize the vector angle to represent the degree of difference in direction. For example, the maximum vector angle can be set to 180. When the vector angle is 60, 60 / 180 is 1 / 3, which is about 0.33.

[0099] Furthermore, by comparing the individual difference of the friction-elasticity probability of each preliminary grid with the directional difference of the friction-elasticity probability as a weight, the size of the preliminary grid is fine-tuned, specifically:

[0100] The ratio of the individual difference in friction-elasticity probability to the directional difference in friction-elasticity probability is used, and a bias operator is combined in the comparison process to obtain a weight for grid adjustment, and the size of the preliminary grid is fine-tuned with the weight for grid adjustment.

[0101] In some embodiments, the weight M of the grid adjustment is calculated based on the ratio of the individual difference of the friction-elasticity probability and the directional difference of the friction-elasticity probability. In one embodiment provided, the ratio of the individual difference of the friction-elasticity probability to the directional difference of the friction-elasticity probability can be used as the weight M of the grid adjustment. In another embodiment provided, the weight M of the grid adjustment can also be multiplied by an adjustment coefficient α, α can be a value between 0 and 1, and α can be obtained based on the numerical statistics of the individual difference of the friction-elasticity probability and the directional difference of the friction-elasticity probability. When calculating the ratio of the individual difference of the friction-elasticity probability and the directional difference of the friction-elasticity probability, the values ​​of the two can also be indexed before comparison.

[0102] The grid adjustment weight M is added with a bias operator bias as the denominator, and the bias operator bias is used as the numerator to obtain the grid fine-tuning weight L. The bias operator bias is a value greater than zero and not greater than one, and preferably, bias is 1. The grid fine-tuning weight L is used to adjust the original size of the preliminary grid. When the weight M is large, the grid is refined; when M is small, the grid maintains its original size or increases appropriately.

[0103] When the friction-elastic individual gap is significantly larger than the directional gap, the mesh is refined and suitable for stress concentration areas, such as step stool support points and pedal-frame connections. When the individual gap is smaller than the directional gap, the mesh is coarsened and suitable for areas with uniform stress distribution. In the transition area, gradient mesh adjustment can be used to ensure smooth changes in mesh density and avoid stress calculation errors caused by mutations. During the simulation process, the weights are dynamically adjusted according to the real-time stress distribution changes to automatically optimize the mesh size.

[0104] By introducing the probability gap between the friction coefficient and the effective elastic modulus as weights, the grid density in different areas can be precisely controlled, and the analysis accuracy of stress concentration areas can be improved. The weight-based dynamic adjustment method can adjust the grid size in time according to the real-time stress analysis results, making the grid division more flexible and the allocation of computing resources more reasonable. This method is particularly suitable for structures with complex geometric shapes such as step stools, and can deal with local stress concentration and material property differences to improve the reliability of stress analysis. This method is used for finite element stress analysis of various complex structures, and is particularly suitable for stress analysis of structural parts with large variations in friction coefficients and uneven material properties, such as step stools, frame structures, and bridge supports.

[0105] In the prior art, mechanized meshing is often used, such as dividing the mesh into 1 / 2, 1 / 4, etc. However, this method lacks flexibility and is not suitable for the complex structure of the step stool. Mechanical segmentation cannot reflect the actual situation of the local stress concentration area, resulting in excessive mesh encryption or unnecessary mesh refinement. In addition, for complex shapes such as step stools, mechanized meshing cannot accurately capture the stress characteristics of complex geometric areas, especially local support points and connection points.

[0106] In a preferred embodiment, a flexible grid fine-tuning method based on the friction-elasticity probability gap is proposed. By calculating the friction-elasticity difference of each preliminary grid, the density of the grid is dynamically adjusted so that the stress concentration area can be accurately processed. In particular, the support points and connection points can be fine-tuned by gap fine-tuning.

[0107] The present invention uses an adaptive grid fine-tuning method to fine-tune the size of the local grid and adaptively adjust the grid, thereby adjusting the number of corresponding stress measurement points and their further accuracy, so as to more comprehensively capture the stress distribution of each area of ​​the step stool, thereby discovering potential problems as early as possible and reinforcing the areas with stress problems on the step stool. In the test experiment, the changes in the grid size before and after adjustment and the corresponding changes in stress values ​​in the finite element analysis of the step stool were recorded. The test recording points included the support feet, connection point 1, pedal, connection point 2 and support rods, and the data records showed:

[0108] At the support foot, before adjustment, the mesh size of the support foot was 10 mm, and the measured stress value was 150 MPa. However, due to the large initial mesh, the measured stress data was relatively rough and may not reflect the true stress distribution in the area. After adaptive mesh fine-tuning, the mesh of the support foot was refined to 5 mm, and more measurement points were added. After adjustment, the measured stress value was 140 MPa, indicating that the stress distribution in the area was captured more finely, and the originally missed stress concentration area was detected more accurately, so that potential problems can be discovered in time and measures can be taken to strengthen it.

[0109] At connection point 1, before adjustment, the mesh size of connection point 1 was 8 mm, corresponding to a stress value of 320 MPa. However, the coarser meshing may have masked the local stress concentration phenomenon. After adjustment, the mesh was refined to 4 mm, generating more stress measurement points. The adjusted stress value was 290 MPa, indicating that the stress hotspot areas that were not accurately captured were more accurately identified through denser meshing. This allows possible structural problems to be identified at an early stage and reinforced in time.

[0110] In the pedal area, the initial mesh size was 12 mm and the measured stress value was 180 MPa. Since the stress distribution in this area was relatively uniform, the adjusted mesh size remained unchanged at 12 mm and the stress value did not change significantly. However, the adaptive mesh adjustment allowed other possible stress distribution anomalies to be identified, ensuring that no potential problems were overlooked.

[0111] At connection point 2, before adjustment, the mesh size of connection point 2 was 8 mm, and the measured stress value was 310 MPa. After refining the mesh to 4 mm, the detection obtained a more accurate stress distribution, and the adjusted stress value was 285 MPa. This adjustment helped to discover stress concentration points in local areas that may not have been accurately detected, so that potential structural problems in this area can be strengthened at an early stage.

[0112] The mesh size of the support rod area before adjustment was 10 mm, and the measured stress value was 170 MPa. After adjustment, the mesh size was reduced to 8 mm, and the measured stress value was 160 MPa. By increasing the stress measurement points, more stress distribution information was obtained, especially in the edges or small areas, which made it possible to detect potential stress problems in the area earlier and perform preventive reinforcement.

[0113] By fine-tuning the mesh, such as adding stress measurement points at key area support feet and connection points, and coarsening the mesh in non-key areas, more detailed stress distribution data can be provided. Through more accurate stress analysis, potential structural problems can be discovered early, and reinforcement measures can be taken before production problems on the assembly line deteriorate after the step stool is designed. In this way, the accuracy of finite element analysis can be significantly improved, thereby improving the safety, reliability and energy efficiency of the step stool structure.

[0114] The stress analysis system for the step stool cyclic loading test runs in any computing device such as a desktop computer, a laptop computer, a mobile phone, a PDA or a cloud data center. The computing device includes: a processor, a memory and a computer program stored in the memory and running on the processor. When the processor executes the computer program, the steps in the stress analysis method for the step stool cyclic loading test are implemented. The executable system may include, but is not limited to, a processor, a memory, and a server cluster.

[0115] An embodiment of the present invention provides a stress analysis system for a step stool cyclic loading test, such as Figure 2As shown, a stress analysis system for a step stool cyclic loading test of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the stress analysis method embodiment of the step stool cyclic loading test are implemented. The processor executes the computer program to run in the following system units:

[0116] A data acquisition unit, used for preliminarily segmenting the surface of the step stool to obtain a preliminary regional grid, and obtaining data of friction coefficient and elastic modulus on each preliminary grid in the preliminary regional grid;

[0117] The probability calculation unit is used to compare the friction coefficient probability density and the effective elastic modulus probability density of each preliminary grid with its adjacent preliminary grids, so as to obtain the friction probability difference and elastic probability difference of the preliminary grids;

[0118] A vector generating unit, used for forming a friction probability difference vector with the friction probability difference of each preliminary grid, and forming an elasticity probability difference vector with the elasticity probability difference of each preliminary grid;

[0119] a gap calculation unit, used for calculating the gap between the friction probability difference and the elasticity probability difference of each preliminary grid to obtain the friction-elasticity probability individual gap, and calculating the gap between the friction probability difference vector and the elasticity probability difference vector in the direction of the vector space to obtain the friction-elasticity probability direction gap;

[0120] The grid fine-tuning unit is used to fine-tune the size of the preliminary grid by comparing the individual gap of the friction-elasticity probability of each preliminary grid with the friction-elasticity probability direction gap as a weight.

[0121] Among them, preferably, all undefined variables in the present invention, if not clearly defined, can be manually set thresholds.

[0122] In order to unify the numerical distribution relationship between the numerical values ​​of physical quantities in different units, dimensionless numerical calculation is adopted between physical quantities in different units.

[0123] The stress analysis system for the step stool cyclic loading test can be run in computing devices such as desktop computers, laptops, mobile phones, PDAs, and cloud data centers. The stress analysis system for the step stool cyclic loading test includes, but is not limited to, a processor and a memory. Those skilled in the art will understand that the example is merely an example of a stress analysis method and system for a step stool cyclic loading test, and does not constitute a limitation on a stress analysis method and system for a step stool cyclic loading test, and may include more or fewer components than the example, or a combination of certain components, or different components. For example, the stress analysis system for the step stool cyclic loading test may also include input and output devices, network access devices, buses, etc.

[0124] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete component gate circuits or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the stress analysis system for the step stool cyclic loading test, and uses various interfaces and lines to connect the various sub-areas of the entire stress analysis system for the step stool cyclic loading test.

[0125] The memory can be used to store the computer program and / or module, and the processor realizes various functions of the stress analysis method and system of the step stool cyclic loading test by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory. The memory can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, an application required for at least one function (such as a sound playback function, an image playback function, etc.), etc.; the data storage area can store data created according to the use of the mobile phone (such as audio data, a phone book, etc.), etc. In addition, the memory can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0126] The present invention provides a stress analysis method and system for a step stool cyclic loading test, wherein the friction probability difference degree of each preliminary grid is used to form a friction probability difference vector, and the elastic probability difference degree of each preliminary grid is used to form an elastic probability difference vector; the difference between the friction probability difference degree and the elastic probability difference degree of each preliminary grid is calculated to obtain the friction-elastic probability individual difference, and the difference between the friction probability difference vector and the elastic probability difference vector in the direction of the vector space is calculated to obtain the friction-elastic probability direction difference; by comparing the friction-elastic probability individual difference of each preliminary grid with the friction-elastic probability direction difference as a weight, the size of the preliminary grid is fine-tuned. By refining the grid of the stress concentration area, more accurate stress measurement points are captured, potential stress concentration problems are discovered in time, and more accurate analysis results are ensured. The difference between the friction coefficient and the effective elastic modulus is used to identify changes in material properties, effectively coping with complex geometric structures and uneven stress distributions. The grid density can be dynamically adjusted according to stress changes, the stress analysis process is continuously optimized, and the safety of the overall structure is ensured.

[0127] Although the description of the present invention has been quite detailed and has been described in particular with respect to several described embodiments, it is not intended to be limited to any of these details or embodiments or any particular embodiment, so as to effectively cover the intended scope of the present invention. In addition, the present invention is described above with the embodiments foreseeable by the inventors, and its purpose is to provide a useful description, and those non-substantial changes to the present invention that are not currently foreseen may still represent equivalent changes of the present invention.

Claims

1. A stress analysis method for a step stool cyclic loading test, characterized in that: The method comprises the following steps: The surface of the step stool is preliminarily segmented to obtain a preliminary regional grid, and the data of the friction coefficient and elastic modulus on each preliminary grid in the preliminary regional grid are obtained; each preliminary grid is compared with its adjacent preliminary grids in terms of the probability density of the friction coefficient and the probability density of the effective elastic modulus to obtain the friction probability difference and elastic probability difference of the preliminary grid; the friction probability difference of each preliminary grid is used to form a friction probability difference vector, and the elastic probability difference of each preliminary grid is used to form an elastic probability difference vector; the difference between the friction probability difference and the elastic probability difference of each preliminary grid is calculated to obtain the friction-elasticity individual difference, and the difference between the friction probability difference vector and the elastic probability difference vector in the direction of the vector space is calculated to obtain the friction-elasticity directional difference; the size of the preliminary grid is fine-tuned by comparing the friction-elasticity individual difference of each preliminary grid with the friction-elasticity directional difference as a weight; The method of fine-tuning the size of the preliminary grid by comparing the individual difference of the friction-elasticity probability of each preliminary grid with the friction-elasticity probability directional difference as a weight is as follows: using the ratio of the individual difference of the friction-elasticity probability to the directional difference of the friction-elasticity probability, combining the bias operator in the comparison process, obtaining the weight of the grid adjustment, and fine-tuning the size of the preliminary grid with the weight of the grid adjustment; The method of calculating the difference between the friction probability difference and the elasticity probability difference of each preliminary grid to obtain the individual difference of friction-elasticity probability, and calculating the difference between the friction probability difference vector and the elasticity probability difference vector in the direction in the vector space to obtain the directional difference of friction-elasticity probability, specifically comprises: for each preliminary grid, calculating the absolute value of the difference obtained by subtracting the friction probability difference of the preliminary grid from the elasticity probability difference of the preliminary grid, as the individual difference of friction-elasticity probability of the preliminary grid; calculating the directional difference between the probability density of friction coefficient and the probability density of effective elastic modulus in the vector space, using the vector angle between the probability density of friction coefficient and the probability density of effective elastic modulus to normalize the vector angle to obtain the directional difference of friction-elasticity probability.

2. A stress analysis method for a step stool cyclic loading test according to claim 1, characterized in that: According to the structure of the step stool, the initial mesh size is preset, and the surface of the step stool is preliminarily segmented to obtain a preliminary regional mesh.

3. The stress analysis method for a step stool cyclic loading test according to claim 1, characterized in that: in, A preliminary regional grid is composed of various preliminary grids, each preliminary grid in the preliminary regional grid does not overlap with each other, and the preliminary regional grid covers the surface of the step stool.

4. The stress analysis method for a step stool cyclic loading test according to claim 1, characterized in that: in, Obtaining data on the coefficient of friction at various locations on the step stool surface by using a coefficient of friction sensor and / or a coefficient of friction tester; The data of elastic modulus at different parts of the step stool were obtained by dynamic thermomechanical analysis.

5. The stress analysis method for a step stool cyclic loading test according to claim 1, characterized in that: The method for obtaining the data of the friction coefficient and elastic modulus on each preliminary grid in the preliminary regional grid is: Performing probability statistics on the values ​​of the friction coefficient on each preliminary grid, calculating the probability distribution of the values ​​of the friction coefficient on all preliminary grids, and obtaining the probability density of the values ​​of the friction coefficient on each preliminary grid appearing in the probability distribution of the values ​​of the friction coefficient on all preliminary grids, as the probability density of the friction coefficient of each preliminary grid; The value of the effective elastic modulus on each preliminary grid is subjected to probability statistics, and the probability distribution of the values ​​of the effective elastic modulus on all preliminary grids is statistically calculated. The probability density of the value of the effective elastic modulus on each preliminary grid appearing in the probability distribution of the values ​​of the effective elastic modulus on all preliminary grids is obtained respectively as the probability density of the effective elastic modulus of each preliminary grid.

6. The stress analysis method for a step stool cyclic loading test according to claim 1, characterized in that: The method of forming a friction probability difference vector with the friction probability difference of each preliminary grid and forming an elasticity probability difference vector with the elasticity probability difference of each preliminary grid specifically includes: Obtain the three-dimensional coordinates of the geometric center of each preliminary grid, obtain the three-dimensional coordinates of the geometric center of the step stool in the three-dimensional model for preliminary grid division, that is, the center coordinates of the step stool, calculate the Euclidean distance of the three-dimensional coordinates of the geometric center of each preliminary grid relative to the center coordinates of the step stool as the center distance of each preliminary grid; sort each preliminary grid in ascending order according to its center distance to form a preliminary grid sequence; An array consisting of numerical values ​​of friction probability differences of each preliminary grid in the preliminary grid sequence is a friction probability difference vector; An array consisting of numerical values ​​of elastic probability differences of each preliminary grid in the preliminary grid sequence is an elastic probability difference vector.

7. The stress analysis method for step stool cyclic loading test according to claim 1, characterized in that: Each preliminary grid is compared with its adjacent preliminary grids in terms of friction coefficient probability density and effective elastic modulus probability density. The method to obtain the friction probability difference and elastic probability difference of the preliminary grids is as follows: For each preliminary grid, obtain the adjacent preliminary grids that have common edges with it as the adjacent preliminary grids of the preliminary grid; For each preliminary grid, obtain the friction coefficient probability density of the preliminary grid, and respectively obtain the friction coefficient probability density of each adjacent preliminary grid of the preliminary grid, compare the friction coefficient probability density of the preliminary grid with the friction coefficient probability density of each adjacent preliminary grid, and take the average of the obtained ratios as the friction probability difference degree of the preliminary grid; For each preliminary grid, the effective elastic modulus probability density of the preliminary grid is obtained, and the effective elastic modulus probability density of each adjacent preliminary grid of the preliminary grid is obtained respectively. The effective elastic modulus probability density of the preliminary grid is compared with the effective elastic modulus probability density of each adjacent preliminary grid, and the average of the obtained ratios is taken as the elastic probability difference of the preliminary grid.

8. A stress analysis system for a step stool cyclic loading test, characterized in that: The stress analysis system for the step stool cyclic loading test runs in any computing device such as a desktop computer, a laptop computer or a cloud data center. The computing device includes: a processor, a memory and a computer program stored in the memory and running on the processor. When the processor executes the computer program, the steps in the stress analysis method for the step stool cyclic loading test as described in any one of claims 1 to 7 are implemented.

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