Three-dimensional superposition construction method of adaptive structures of minimal surfaces subjected to multiple sets of stresses

Abstract

The present invention discloses a three-dimensional superposition construction method of a minimal surface adaptive structure subjected to multiple groups of stresses, including: S1. Determine the relationship between the volume fraction control parameter and the yield stress value of the minimal surface structure; S2. Perform stress decomposition on the solid structure subjected to multiple groups of stresses to obtain a plurality of substructures; S3. Obtain all node coordinates of each substructure and the stress value corresponding to the node coordinates; S4. Obtain all node coordinates of each substructure and the volume fraction control parameters corresponding to the node coordinates; S5. Fit all node coordinates of each substructure and the volume fraction control parameters corresponding to the node coordinates to generate the minimal surface structure corresponding to each substructure; S6. Perform Boolean operation on the minimal surface structure corresponding to each substructure to obtain a three-dimensional superimposed minimal surface adaptive structure. The present invention can make the strength of the minimal surface structure at different positions in the three-dimensional space meet the mechanical requirements, while realizing the lightweight of the structure.

Description

Technical Field

[0001] The invention relates to the field of structural design, and in particular to a three-dimensional superposition construction method of a minimal surface adaptive structure subjected to multiple groups of stresses. Background Art

[0002] With the rapid development of aerospace, aerospace parts are also gradually improving and changing. Parts need to be lightweight while meeting mechanical requirements. Similarly, in the field of biological implants, biological bone implants also need to be as lightweight as possible while meeting mechanical requirements. Therefore, minimal surface structures are widely used.

[0003] However, in general, the stress patterns of parts and implants are relatively complex, and it is difficult to match the stress values ​​of different stress-bearing areas of the structure with the volume fractions of the corresponding structures. Therefore, it is difficult to obtain a minimal surface structure model that conforms to the stress characteristics of the structure. Summary of the invention

[0004] In view of this, the purpose of the present invention is to overcome the defects in the prior art and provide a three-dimensional superposition construction method for a minimal surface adaptive structure subjected to multiple sets of stresses, which can design the volume fraction control parameters of the minimal surface structure at different positions in the three-dimensional space, so that the strength at different positions meets the mechanical requirements while achieving the lightweight of the structure.

[0005] The three-dimensional superposition construction method of the minimal surface adaptive structure subjected to multiple sets of stresses of the present invention comprises the following steps:

[0006] S1. Determine the relationship between the volume fraction control parameter of the minimal surface structure and the yield stress value G;

[0007] S2. performing stress splitting on the solid structure subjected to multiple groups of stresses to obtain a number of substructures;

[0008] S3. Perform finite element simulation on several substructures respectively to obtain all node coordinates of each substructure and stress values ​​corresponding to the node coordinates;

[0009] S4. taking the stress value as the yield stress value, and calculating the volume fraction control parameter corresponding to the stress value according to the relational expression G; based on the processing result of step S3, replacing the stress value corresponding to the node coordinate with the volume fraction control parameter corresponding to the node coordinate, and obtaining all the node coordinates of each substructure and the volume fraction control parameter corresponding to the node coordinate;

[0010] S5. fitting all node coordinates of each substructure and the volume fraction control parameters corresponding to the node coordinates to generate minimal surface structures corresponding to each substructure;

[0011] S6. Perform a union process of Boolean operations on the minimal surface structures corresponding to each substructure to obtain a three-dimensional superimposed minimal surface adaptive structure subjected to multiple groups of stresses.

[0012] Further, the step S1 specifically includes:

[0013] S11. Calibrate the volume fraction of the minimal surface structure to obtain a relationship A between the volume fraction and the volume fraction control parameter;

[0014] S12. Fitting calculation to obtain the relationship between the yield stress value and volume fraction of the minimal surface structure (B);

[0015] S13. Combining equations A and B, we obtain equation G between the volume fraction control parameter and the yield stress value of the minimal surface structure.

[0016] Furthermore, the volume fraction of the minimal surface structure is calibrated, specifically including: performing linear fitting between the volume fraction control parameter of the minimal surface structure and the volume fraction corresponding to the volume fraction control parameter.

[0017] Furthermore, the step S3 further includes: performing interpolation fitting processing on all node coordinates of each substructure and stress values ​​corresponding to the node coordinates to obtain processed node coordinates and stress values ​​corresponding to the node coordinates.

[0018] Furthermore, step S4 further includes: setting a value range for the stress value, and when the stress value is not within the value range, reassigning the stress value so that the stress value is equal to the critical value of the value range that is closest to it.

[0019] The beneficial effects of the present invention are as follows: a three-dimensional superposition construction method of a minimal surface adaptive structure subjected to multiple groups of stresses disclosed by the present invention, by determining the relationship between the volume fraction control parameter and the yield stress value of the minimal surface structure, and by performing stress decomposition analysis on the solid structure, the node coordinates of each substructure and the volume fraction control parameters corresponding to the node coordinates are obtained, and finally the minimal surface structures corresponding to each substructure are generated, and the minimal surface structures corresponding to each substructure are processed by the union of Boolean operations to obtain the minimal surface adaptive structure subjected to multiple groups of stresses in three-dimensional superposition. The present invention can design the volume fraction control parameters of different positions of the minimal surface structure in three-dimensional space, so that the strength at different positions meets the mechanical requirements, while achieving the lightweight of the structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0021] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0022] Figure 2 It is a schematic diagram of stress splitting analysis of the entity structure of the present invention;

[0023] Figure 3 It is a schematic diagram of an IWP type minimal surface structure b2 that complies with the stress distribution of a solid structure of the present invention;

[0024] Figure 4 It is a schematic diagram of an IWP type minimal surface structure c2 that complies with the stress distribution of a solid structure of the present invention;

[0025] Figure 5 It is a schematic diagram of the adaptive structure of a three-dimensional superimposed minimal surface subjected to multiple groups of stresses of the present invention. DETAILED DESCRIPTION

[0026] The present invention is further described below in conjunction with the accompanying drawings, as shown in the drawings:

[0027] The three-dimensional superposition construction method of the minimal surface adaptive structure subjected to multiple sets of stresses of the present invention comprises the following steps:

[0028] S1. Determine the relationship between the volume fraction control parameter of the minimal surface structure and the yield stress value G;

[0029] S2. performing stress splitting on the solid structure subjected to multiple groups of stresses to obtain a number of substructures;

[0030] S3. Perform finite element simulation on several substructures respectively to obtain all node coordinates of each substructure and stress values ​​corresponding to the node coordinates;

[0031] S4. taking the stress value as the yield stress value, and calculating the volume fraction control parameter corresponding to the stress value according to the relational expression G; based on the processing result of step S3, replacing the stress value corresponding to the node coordinate with the volume fraction control parameter corresponding to the node coordinate, and obtaining all the node coordinates of each substructure and the volume fraction control parameter corresponding to the node coordinate;

[0032] S5. fitting all node coordinates of each substructure and the volume fraction control parameters corresponding to the node coordinates to generate minimal surface structures corresponding to each substructure;

[0033] S6. Perform a union process of Boolean operations on the minimal surface structures corresponding to each substructure to obtain a three-dimensional superimposed minimal surface adaptive structure subjected to multiple groups of stresses.

[0034] The present invention determines the relationship between the volume fraction control parameter and the yield stress value of the minimal surface structure, and obtains the node coordinates of each substructure and the volume fraction control parameter corresponding to the node coordinates by performing stress decomposition analysis on the solid structure, and finally generates the minimal surface structure corresponding to each substructure. By performing a union processing of Boolean operations on the minimal surface structures corresponding to each substructure, a three-dimensionally superimposed minimal surface adaptive structure subjected to multiple groups of stresses is obtained, so that the strength of the minimal surface structure at different positions in the three-dimensional space meets the mechanical requirements, and at the same time, the lightweight structure is achieved.

[0035] In this embodiment, the step S1 specifically includes:

[0036] S11. Perform volume fraction calibration on the minimal surface structure to obtain a relational expression A between the volume fraction and the volume fraction control parameter; that is, perform linear fitting between the volume fraction control parameter of the minimal surface structure and the volume fraction corresponding to the volume fraction control parameter to obtain a relational expression A between the volume fraction and the volume fraction control parameter; wherein, an IWP type minimal surface structure is selected, and the volume fraction is calibrated according to the mathematical formula (1) of the minimal surface structure to obtain a relational expression A between the volume fraction V and the volume fraction control parameter t; the mathematical formula (1) is: cos(2x)+cos(2y)+cos(2z)-2*(cos(x)*cos(y)+cos(y)*cos(z)+cos(z)*cos(x))-t=0; wherein x, y and z are the node coordinate values ​​of the minimal surface structure; the relational expression A is: V=0.1467*t+0.5;

[0037] S12. The relationship between the yield stress value and the volume fraction of the minimal surface structure is obtained by fitting and calculation. Specifically, a compression test is performed on the selected minimal surface structure to collect the yield stress values ​​σ corresponding to the minimal surface structures with different volume fractions. s , refer to the Gibson–Ashby theory, and calculate the relative stress value by fitting and volume fraction (the volume fraction Said is the relative density) relation (3):

[0038]

[0039] Among them, σ0 and ρ0 are the stress value and density value of the solid structure respectively, σ s , s are the yield stress and density of the selected minimal surface structure, C σ and m σare all parameter values ​​related to the material and component shape. The solid structure can be made of titanium alloy material, and its stress value and density value can be determined according to the selected material; for the IWP type minimal surface structure, according to the relationship (3), the relationship B between the yield stress value and the volume fraction of the IWP type minimal surface structure can be obtained as: s =1186*V 2.11 ;

[0040] S13. Combine the relationship A and the relationship B to obtain the relationship G between the volume fraction control parameter and the yield stress value of the minimal surface structure. In this embodiment, the relationship A and the relationship B corresponding to the IWP type minimal surface structure are calculated together to obtain the relationship G:

[0041] In this embodiment, Figure 2 As shown in the figure, the stress of the solid structure subjected to multiple stresses is split, that is, Figure 2 In (a), the two stresses applied to the solid structure are split to form two separate stress-bearing structures, respectively. Figure 2 (b) and Figure 2 (c) as shown.

[0042] Then, the split entity structures are subjected to finite element simulation to obtain the stress distribution cloud diagram of each entity structure. According to the simulation results, the coordinate points of all nodes of each entity structure and the stress values ​​corresponding to the coordinate points are derived, and then the stress distribution cloud diagram of each entity structure is obtained. Figure 2 (b) The corresponding node coordinates and stress values ​​are: (x b ,y b ,z b ,σ b ), Figure 2 (c) The corresponding node coordinates and stress values ​​are: (x c ,y c ,z c ,σ c ), and b,c=1,2,3….

[0043] The structure Figure 2 (b) Figure 2 (c) The node coordinates and corresponding stress values ​​are imported into MATLAB, and interpolation fitting is performed through the interpolation function to obtain more accurate coordinate points and corresponding stress values: (x' b ,y' b ,z' b ,σ' b )、(x' c ,y' c ,z' c ,σ' c), and b, c = 1, 2, 3... According to the volume fraction control parameter t and yield stress value σ s The relationship G is used to match the node coordinates obtained by fitting with the volume fraction control parameter t, and then (x' b ,y' b ,z' b ,t' b )、(x' c ,y' c ,z' c ,t' c ), and b,c=1,2,3….

[0044] In this embodiment, in order to eliminate the situation where the node stress is too large or too small, resulting in the generated structure not meeting the actual requirements, a maximum and minimum volume fraction interval Vmin≤V≤Vmax of the structure is also set, and its corresponding volume fraction control parameter tmin≤t≤tmax, and its corresponding stress value σmin≤σ≤σmax;

[0045] That is, a value range is set for the stress value, and when the stress value is not within the value range, the stress value is reassigned so that the stress value is equal to the critical value of the value range that is closest to it.

[0046] According to the matched coordinate points and volume fraction control parameters, the coordinate points and volume fraction control parameters are fitted to generate a structure that conforms to the entity. Figure 2 (b) Figure 2 (c) IWP type minimal surface structures b2 and c2 with stress distribution, respectively. Figure 3 as well as Figure 4 shown.

[0047] Finally, the IWP type minimal surface structures b2 and c2 are processed by Boolean operation to achieve the superposition of structures, and then a three-dimensional superimposed minimal surface adaptive structure subjected to multiple sets of stress is obtained, such as Figure 5 shown.

[0048] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A three-dimensional superposition construction method of a minimal surface adaptive structure subjected to multiple sets of stresses, characterized in that: The steps include: S1. Determine the relationship G between the volume fraction control parameter of the minimal surface structure and the yield stress value, specifically including: S11. Calibrate the volume fraction of the minimal surface structure to obtain a relationship A between the volume fraction and the volume fraction control parameter; S12. Fitting calculation to obtain the relationship between the yield stress value and volume fraction of the minimal surface structure (B); S13. By combining equation A and equation B, we obtain equation G of relationship between the volume fraction control parameter and the yield stress value of the minimal surface structure; S2. performing stress splitting on the solid structure subjected to multiple groups of stresses to obtain a number of substructures; S3. Perform finite element simulation on several substructures respectively to obtain all node coordinates of each substructure and stress values ​​corresponding to the node coordinates; S4. taking the stress value as the yield stress value, and calculating the volume fraction control parameter corresponding to the stress value according to the relational expression G; based on the processing result of step S3, replacing the stress value corresponding to the node coordinate with the volume fraction control parameter corresponding to the node coordinate, and obtaining all the node coordinates of each substructure and the volume fraction control parameter corresponding to the node coordinate; S5. fitting all node coordinates of each substructure and the volume fraction control parameters corresponding to the node coordinates to generate minimal surface structures corresponding to each substructure; S6. Perform a union process of Boolean operations on the minimal surface structures corresponding to each substructure to obtain a three-dimensional superimposed minimal surface adaptive structure subjected to multiple groups of stresses.

2. The three-dimensional superposition construction method of the minimal surface adaptive structure subjected to multiple sets of stresses according to claim 1 is characterized in that: The volume fraction calibration of the minimal surface structure specifically includes: performing linear fitting between the volume fraction control parameter of the minimal surface structure and the volume fraction corresponding to the volume fraction control parameter.

3. The three-dimensional superposition construction method of the minimal surface adaptive structure subjected to multiple sets of stresses according to claim 1 is characterized in that: The step S3 further includes: performing interpolation fitting processing on all node coordinates of each substructure and stress values ​​corresponding to the node coordinates to obtain processed node coordinates and stress values ​​corresponding to the node coordinates.

4. The three-dimensional superposition construction method of the minimal surface adaptive structure subjected to multiple sets of stresses according to claim 1 is characterized in that: Step S4 further includes: setting a value range for the stress value, and when the stress value is not within the value range, reassigning the stress value so that the stress value is equal to the critical value of the value range that is closest to it.

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