Cellular equivalent parameter simulation method based on probability distribution

Abstract

The invention belongs to the field of structural strength testing, and particularly relates to a honeycomb equivalent parameter simulation method based on probability distribution. At present, the research on honeycomb equivalent parameter simulation does not fully consider the probability distribution problem caused by dispersity. The method comprises the following steps: scanning random N honeycombs, and measuring structural parameters of each honeycomb; performing statistical analysis on each structural parameter measurement value of the honeycomb to obtain a corresponding probability density function; performing Monte Carlo simulation based on the obtained probability density function to generate a random number sequence; in combination with the random number sequence and a cellular equivalent parameter formula, simulating to obtain a cellular equivalent parameter simulation value; and carrying out probability statistical analysis, establishing a frequency distribution histogram of the honeycomb equivalent parameters, obtaining a probability density function of the honeycomb equivalent parameters, and obtaining corresponding honeycomb equivalent parameter values in combination with given reliability. Experiments are simple and cost is low.

Description

Technical Field

[0001] This invention belongs to the field of structural strength testing, specifically relating to a method for simulating cellular equivalent parameters based on probability distribution. Background Technology

[0002] Bionic honeycomb structures, such as aluminum honeycomb or Nomex honeycomb, draw heavily on the hexagonal structure of natural honeycombs. While ensuring structural strength, they can save materials and space to the maximum extent, achieving a combination of lightweight and high performance.

[0003] Honeycomb structures are widely used in engineering due to their lightweight, high strength, high flame retardancy, high corrosion resistance, and excellent wave transmission properties. However, due to the discrete and non-uniform nature of honeycomb structures, it is necessary to calculate their equivalent parameters in practical engineering applications to transform the discrete honeycomb structure into a uniform solid structure.

[0004] Due to material dispersion and errors in the processing and fabrication process, the equivalent parameters of a honeycomb structure are not ideal constants; instead, they follow a specific probability distribution. However, current research on the simulation of the equivalent parameters of a honeycomb structure has not fully considered the probability distribution problem caused by dispersion, resulting in a significant discrepancy between the calculated and actual values. Therefore, there is an urgent need to develop a method for simulating the equivalent parameters of a honeycomb structure based on probability distribution, and to determine the numerical values ​​of the equivalent parameters of a honeycomb structure under a given reliability condition. Summary of the Invention

[0005] Current research on cellular equivalent parameter simulation does not adequately consider the probability distribution problem caused by dispersion, resulting in significant discrepancies between the calculated equivalent parameter values ​​and the actual values, making it difficult to meet the requirements for accurate cellular analysis. This invention provides a probability distribution-based method for simulating cellular equivalent parameters, taking into account the dispersion of the cellular structure. This method achieves accurate simulation of cellular equivalent parameters under given reliability, thus meeting the needs for accurate cellular analysis.

[0006] This invention proposes a method for simulating cellular equivalent parameters based on probability distribution, which includes the following steps: S1. Scan N random honeycombs (N≥50) using a scanning electron microscope and measure the structural parameters of each honeycomb, including the adhesive thickness. Length of straight walls in honeycomb Length of inclined wall The angle between the inclined wall and the x-axis direction and honeycomb wall thickness ; S2. Perform statistical analysis on the measured values ​​of each structural parameter of the cell to obtain the frequency distribution histogram of each structural parameter, and perform data fitting to obtain the corresponding probability density function; S3. Perform Monte Carlo simulation based on the obtained probability density function to generate a series of random number sequences that obey the probability density function; S4. Combining the random number sequence and the cellular equivalent parameter formula, a series of simulated values ​​of cellular equivalent parameters are obtained through simulation; S5. Perform probabilistic statistical analysis on the simulated values ​​of cellular equivalent parameters, establish a frequency distribution histogram of cellular equivalent parameters, obtain the probability density function of cellular equivalent parameters, and obtain the corresponding cellular equivalent parameter values ​​in combination with the given reliability.

[0007] Advantageously, the cellular equivalent parameters described in S4 include the cellular equivalent elastic modulus along the x-direction. Equivalent elastic modulus along the y-direction Equivalent shear modulus in the xy plane Out-of-plane equivalent shear modulus in the xz plane Out-of-plane equivalent shear modulus in the yz plane Out-of-plane equivalent elastic modulus in the z-direction and equivalent density .

[0008] Advantageously, the equivalent elastic modulus of the honeycomb along the x-direction for:

[0009] in, For the elastic modulus of honeycomb core material, For honeycomb wall thickness, The angle between the inclined wall and the x-axis direction. For the length of the inclined wall, This represents the length of the straight wall of the honeycomb.

[0010] Advantageously, the equivalent elastic modulus along the y-direction for:

[0011] in, The angle between the inclined wall and the x-axis direction. For the length of the inclined wall, For the length of the straight wall of the honeycomb, For honeycomb wall thickness, For the elastic modulus of honeycomb core material, For the elastic modulus of adhesive materials, This refers to the thickness of the adhesive.

[0012] Advantageously, the equivalent shear modulus in the xy plane :

[0013] in, For the length of the inclined wall, For the length of the straight wall of the honeycomb, The angle between the inclined wall and the x-axis direction. For honeycomb wall thickness, For adhesive thickness, For the elastic modulus of honeycomb core material, This refers to the elastic modulus of the adhesive material.

[0014] Advantageously, the out-of-plane equivalent shear modulus in the xz plane :

[0015] in, For the length of the inclined wall, For the length of the straight wall of the honeycomb, The angle between the inclined wall and the x-axis direction. For honeycomb wall thickness, This represents the shear modulus of the honeycomb core material.

[0016] Advantageously, the out-of-plane equivalent shear modulus in the yz plane :

[0017] in, For honeycomb wall thickness, For adhesive thickness, For the length of the straight wall of the honeycomb, For the length of the inclined wall, The angle between the inclined wall and the x-axis direction. For the shear modulus of honeycomb core material, This refers to the shear modulus of the adhesive material.

[0018] Advantageously, the out-of-plane equivalent elastic modulus in the z-direction :

[0019] in, For the elastic modulus of honeycomb core material, For the elastic modulus of adhesive materials, For honeycomb wall thickness, For adhesive thickness, For the length of the straight wall of the honeycomb, For the length of the inclined wall, It is the angle between the inclined wall and the x-axis.

[0020] Advantageously, equivalent density :

[0021] in, For the density of honeycomb core material, For the density of adhesive materials, For honeycomb wall thickness, For adhesive thickness, For the length of the straight wall of the honeycomb, For the length of the inclined wall, It is the angle between the inclined wall and the x-axis.

[0022] Beneficial effects: 1. The invention proposes a method for simulating equivalent parameters of a cellular structure based on probability distribution. This method only requires conducting experiments to determine the cellular structure parameters and obtain the corresponding structural parameters. The experiment is simple and low-cost. 2. The invention proposes a method for simulating cellular equivalent parameters based on probability distribution, which takes into account the dispersion problem introduced in the material and processing, and is a more scientific method; 3. The invention proposes a cellular equivalent parameter simulation method based on probability distribution, which can determine the magnitude of cellular equivalent parameters under a given reliability, thus meeting the needs of subsequent cellular performance analysis. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the parameters of the Nomex honeycomb structure in the embodiment; Figure 2 It is the thickness of the adhesive. Frequency distribution histogram; Figure 3 It is the length of the straight wall of the honeycomb. Frequency distribution histogram; Figure 4 It is the length of the inclined wall. Frequency distribution histogram; Figure 5 It is the angle between the inclined wall and the x-axis. Frequency distribution histogram; Figure 6 It is the thickness of the honeycomb wall. Frequency distribution histogram; Figure 7 It is the thickness of the adhesive. Probability density function data fitting plot; Figure 8 It is the length of the straight wall of the honeycomb. Probability density function data fitting plot; Figure 9 It is the length of the inclined wall. Probability density function data fitting plot; Figure 10 It is the angle between the inclined wall and the x-axis. Probability density function data fitting plot; Figure 11 It is the thickness of the honeycomb wall. Probability density function data fitting plot; Figure 12 Cellular equivalent parameters Probability distribution statistics graph; Figure 13 Cellular equivalent parameters Probability distribution statistics graph; Figure 14 Cellular equivalent parameters Probability distribution statistics graph; Figure 15 Cellular equivalent parameters Probability distribution statistics graph; Figure 16 Cellular equivalent parameters Probability distribution statistics graph; Figure 17 Cellular equivalent parameters Probability distribution statistics graph; Figure 18 Cellular equivalent parameters Statistical graph of probability distribution. Detailed Implementation

[0024] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings. The present invention can be better understood through the embodiments. The specific material ratios, process conditions, and results described in the embodiments are for illustrative purposes only and should not, and will not, limit the present invention as described in detail in the claims.

[0025] In one embodiment, the structural parameters of the Nomex cell are as follows: Figure 1 As shown, this includes adhesive thickness. Length of straight walls in honeycomb Length of inclined wall The angle between the inclined wall and the x-axis direction Honeycomb wall thickness These structural parameters provide parameter inputs for the simulation of equivalent parameters of the cellular structure. The x-axis is perpendicular to the straight wall, and the y-axis is parallel to the straight wall.

[0026] Applying the probability distribution-based cellular equivalent parameter simulation method of the present invention to the Nomex cellular equivalent parameter simulation process includes the following steps: (1) Conduct Nomex honeycomb structure parameter determination experiments. The honeycomb structure parameters, including adhesive thickness, were determined using a scanning electron microscope. Length of straight walls in honeycomb Length of inclined wall The angle between the inclined wall and the x-axis direction Honeycomb wall thickness The five parameters, including the structural parameters, were measured 60 times each, and the numerical results of each measurement were recorded, as shown in Table 1.

[0027] Table 1. Structural parameter measurement results

[0028] (2) Statistical analysis was performed on the measurement results of the Nomex cellular structure parameters, and frequency distribution histograms of each structural parameter were plotted, such as... Figures 2 to 6 As shown in the table, the frequency distribution histogram shows that the structural parameters approximately follow a normal distribution. Therefore, a normal distribution function is used for data fitting, and the mean and standard deviation of the normal distribution probability density function expression for the structural parameters are shown in Table 2. The probability density function data fitting graph for the structural parameters is shown in the table below. Figure 7-11 As shown.

[0029] Table 2. Statistical table of probability density function parameters of structural parameters

[0030] (3) Conduct Monte Carlo simulations, sample the probability density functions of each structural parameter, and generate a series of random number sequences that follow the probability density functions of the cellular structural parameters. Considering simulation efficiency and accuracy, the number of random numbers selected for each structural parameter is 200.

[0031] (4) According to the Nomex cell equivalent parameter calculation formula, including the equivalent elastic modulus of the cell along the x-direction. The equivalent elastic modulus of the honeycomb along the y-direction The equivalent shear modulus of the honeycomb in the xy plane Out-of-plane equivalent shear modulus of the honeycomb in the xz plane Out-of-plane equivalent shear modulus of the honeycomb in the yz plane out-of-plane equivalent elastic modulus in the z-direction of the honeycomb Cellular equivalent density ,Right now:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] Combined with the material parameters provided by the material supplier , , , , , The thickness of the adhesive Length of straight walls in honeycomb Length of inclined wall The angle between the inclined wall and the x-axis direction Honeycomb wall thickness The random numbers generated by the Monte Carlo simulation were substituted into the equivalent parameter calculation formula to obtain 200 simulated values ​​corresponding to each cell equivalent parameter, as shown in Table 3.

[0039] Table 3. Statistical Table of Simulated Values ​​of Cellular Equivalent Parameters

[0040] (5) Perform probability distribution statistics on the simulated values ​​of the above-mentioned cellular equivalent parameters, and draw a probability distribution histogram, such as... Figures 12-18 As shown in the histogram, the probability distribution of the simulated equivalent parameters approximately follows a normal distribution. Therefore, the normal probability density function is used for fitting, and the fitting parameters are shown in Table 4. The fitting curve is also shown in... Figures 12-18 .

[0041] Table 4. Statistical table of probability density function parameters of cellular equivalent parameters

[0042] Based on the probability density function of the cellular equivalent parameters, the numerical values ​​of the Nomex cellular equivalent parameters can be determined under any given reliability. For example, when the given reliability is 84%, the Nomex cellular equivalent parameters are determined as follows: , , , , , , .

[0043] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0044] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0045] Note: The above data is for reference only.

Claims

1. A method for probabilistic distribution based simulation of equivalent parameters of a cell, characterized in that, The method includes the following steps: S1, scan random N honeycombs by scanning electron microscope, N≥50, and measure the structure parameters of each honeycomb, including adhesive thickness , length of straight wall of honeycomb , length of inclined wall , included angle between inclined wall and x-axis direction , and honeycomb wall thickness ; S2. Perform statistical analysis on the measured values ​​of each structural parameter of the cell to obtain the frequency distribution histogram of each structural parameter, and perform data fitting to obtain the corresponding probability density function; S3. Perform Monte Carlo simulation based on the obtained probability density function to generate a series of random number sequences that obey the probability density function; S4. Combining the random number sequence and the cellular equivalent parameter formula, a series of simulated values ​​of cellular equivalent parameters are obtained through simulation; S5. Perform probabilistic statistical analysis on the simulated values ​​of cellular equivalent parameters, establish a frequency distribution histogram of cellular equivalent parameters, obtain the probability density function of cellular equivalent parameters, and obtain the corresponding cellular equivalent parameter values ​​in combination with the given reliability.

2. The method for simulating cellular equivalent parameters according to claim 1, characterized in that: The cellular equivalent parameters in S4 include an equivalent elastic modulus of the cellular structure in the x direction an equivalent elastic modulus in the y direction an equivalent shear modulus in the x-y plane an equivalent shear modulus out of the x-z plane an equivalent shear modulus out of the y-z plane an equivalent elastic modulus out of the z direction and an equivalent density .

3. The method for simulating cellular equivalent parameters according to claim 2, characterized in that: Equivalent elastic modulus of the honeycomb along the x-direction for: in, For the elastic modulus of honeycomb core material, For honeycomb wall thickness, The angle between the inclined wall and the x-axis direction. For the length of the inclined wall, This represents the length of the straight wall of the honeycomb.

4. The method for simulating cellular equivalent parameters according to claim 2, characterized in that: Equivalent elastic modulus along the y-direction for: in, The angle between the inclined wall and the x-axis direction. For the length of the inclined wall, For the length of the straight wall of the honeycomb, For honeycomb wall thickness, For the elastic modulus of honeycomb core material, For the elastic modulus of adhesive materials, This refers to the thickness of the adhesive.

5. The method for simulating cellular equivalent parameters according to claim 2, characterized in that: Equivalent shear modulus in the xy plane : in, For the length of the inclined wall, For the length of the straight wall of the honeycomb, The angle between the inclined wall and the x-axis direction. For honeycomb wall thickness, For adhesive thickness, For the elastic modulus of honeycomb core material, This refers to the elastic modulus of the adhesive material.

6. The method for simulating cellular equivalent parameters according to claim 2, characterized in that: Out-of-plane equivalent shear modulus in the xz plane : in, For the length of the inclined wall, For the length of the straight wall of the honeycomb, The angle between the inclined wall and the x-axis direction. For honeycomb wall thickness, This represents the shear modulus of the honeycomb core material.

7. The method for simulating cellular equivalent parameters according to claim 2, characterized in that: Out-of-plane equivalent shear modulus in the yz plane : in, For honeycomb wall thickness, For adhesive thickness, For the length of the straight wall of the honeycomb, For the length of the inclined wall, The angle between the inclined wall and the x-axis direction. For the shear modulus of honeycomb core material, This refers to the shear modulus of the adhesive material.

8. The method for simulating cellular equivalent parameters according to claim 2, characterized in that: Out-of-plane equivalent elastic modulus in the z-direction : in, For the elastic modulus of honeycomb core material, For the elastic modulus of adhesive materials, For honeycomb wall thickness, For adhesive thickness, For the length of the straight wall of the honeycomb, For the length of the inclined wall, It is the angle between the inclined wall and the x-axis.

9. The method for simulating cellular equivalent parameters according to claim 2, characterized in that: equivalent density : in, For the density of honeycomb core material, For the density of adhesive materials, For honeycomb wall thickness, For adhesive thickness, For the length of the straight wall of the honeycomb, For the length of the inclined wall, It is the angle between the inclined wall and the x-axis.

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