A method and device for modeling high-order continuity of geometric boundaries of gradient lattice structure

Abstract

The present invention belongs to the technical field related to lattice structure design, and discloses a method and device for modeling high-order continuity of geometric boundaries of gradient lattice structures, comprising the following steps: (1) using a dual-parameter adjustable high-order continuous interpolation function to continuously interpolate the movable variable-width gradient boundaries of a microstructure unit cell to obtain a smooth transition block between two unit cells, and then using the smooth transition block to replace the structure of the original transition zone; (2) encrypting the level set function, and then discretizing the structure model into a triangular mesh model; (3) calculating and obtaining the maximum stress of the transition zone of the gradient lattice structure; (4) adjusting two parameters t e and t a , traverse other values ​​in the range of the two parameters; (5) Calculate the comprehensive force of the structure, establish the average value of the normal vectors of adjacent triangles and the parameter t e and t a The inverse mapping relationship; (6) Select the dual parameter t e and t a The present invention realizes high-order continuity modeling of geometric boundaries of gradient lattice structures through dual parameter adjustment.

Description

Technical Field

[0001] The present invention belongs to the technical field related to lattice structure design, and more specifically, relates to a method and device for modeling high-order continuity of geometric boundaries of a gradient lattice structure. Background Art

[0002] The gradient lattice structure is a non-homogeneous structure with gradually changing material properties. It is generally composed of unit cells with the same configuration and gradually changing size parameters along the gradient direction. The gradient lattice structure has excellent properties such as low relative density, high specific strength / stiffness, energy absorption and shock absorption. The material layout can be flexibly adjusted according to the actual load and boundary conditions to obtain the best performance. The gradient lattice structure is widely used in aerospace, vehicle and shipbuilding, biomedicine and other fields, such as aircraft heat dissipation structure, vehicle anti-collision energy absorption structure, bone implant structure, etc.

[0003] Since the size of the microstructure unit cell constituting the gradient lattice structure changes along the gradient direction, there is poor geometric continuity between the unit cells adjacent in space, and the low continuity of the unit cell geometric boundary will lead to local stress concentration, forming performance defects and other problems in the gradient lattice structure. Therefore, it is necessary to consider the continuity problem in the design stage of the gradient lattice structure. Summary of the invention

[0004] In response to the above defects or improvement needs of the prior art, the present invention provides a method and device for high-order continuity modeling of the geometric boundaries of a gradient lattice structure, which takes into account the comprehensive stress conditions of the microstructure in the macrostructure and the design error caused by the interpolation of the structural boundary, and realizes high-order continuity modeling of the geometric boundaries of the gradient lattice structure through dual parameter adjustment.

[0005] To achieve the above object, according to one aspect of the present invention, a method for modeling high-order continuity of geometric boundaries of a gradient lattice structure is provided, the method comprising the following steps:

[0006] (1) A dual-parameter adjustable high-order continuous interpolation function is used to continuously interpolate the movable variable-width gradient boundary of the microstructure unit cell to obtain a smooth transition block between two unit cells, and then the smooth transition block is used to replace the structure of the original transition zone; wherein the expression of the dual-parameter adjustable high-order continuous interpolation function is:

[0007]

[0008] Where t e is the interval width control parameter, t a is the interval starting control parameter, t e The selection interval is set to [0,20], t a The selection interval is set to [-t e ,t e ];

[0009] (2) encrypting the level set function corresponding to the structural model obtained after the transition block replacement, and then discretizing the structural model into a triangular mesh model;

[0010] (3) Based on the triangular mesh model, the normal vector angles of the two adjacent triangular facets on both sides of the connection line at the boundary between the two microstructure unit cells are calculated, and finite element simulation is performed on the current gradient lattice structure under three working conditions to obtain the maximum stress in the transition zone of the gradient lattice structure;

[0011] (4) Controlling the two parameters of the high-order continuous interpolation function can be controlled by adjusting the two parameters t e and t a , traverse other values ​​in the range of the two parameters to obtain the average value of the normal vectors of adjacent triangles of the discrete triangular mesh model and the maximum stress value of the transition area of ​​the gradient lattice structure under three working conditions;

[0012] (5) The weight factor is introduced, and the comprehensive stress of the structure is calculated based on the average value of the normal vectors of adjacent triangles of all discrete triangular mesh models and the maximum stress value of the transition area of ​​the corresponding gradient lattice structure; at the same time, the average value of the normal vectors of adjacent triangles of all discrete triangular mesh models and the corresponding parameter t e and t a , and then establish the average value of the normal vectors of adjacent triangles in the discrete triangle mesh model and the parameter t e and t a The inverse mapping relationship of

[0013] (6) Select the dual parameter t based on the material of the gradient lattice structure to be designed and its corresponding comprehensive stress e and t a , and then the gradient lattice structure is obtained.

[0014] Furthermore, the comprehensive stress determines the magnitude of the vector product, which is inversely mapped to the corresponding dual parameter t e and t a .

[0015] Furthermore, an implicit level set function is used to construct the microstructure unit cell of the gradient lattice structure to be designed, and the expression of the implicit level set function is:

[0016]

[0017] Where φ(x) is the level set function, t is the microstructure configuration control parameter, the area where φ(x)>t represents the solid area in the microstructure, and the area where φ(x)<t represents the void area in the microstructure. It is the boundary between the solid area and the void area of ​​the microstructure.

[0018] Furthermore, a dual-parameter controllable high-order continuous interpolation function is constructed based on the Beta growth function and the microstructure unit cell.

[0019] Furthermore, the formula corresponding to the smooth transition block is:

[0020] φ=μ(X)φ1(X1)+(1-μ(X))φ2(X2)

[0021] In the formula, and is the level set scalar field of two adjacent unit cells.

[0022] Furthermore, the encryption formula is:

[0023]

[0024] P x (xx i )=a 0x +a 1x (xx i )+a 2x (xx i ) 2 +a 3x (xx i ) 3

[0025] P y (yy j )=a 0y +a 1y (yy j )+a 2y (yy j ) 2 +a 3y (yy j ) 3

[0026] P z (zz k )=a 0z +a 1z (zz k )+a 2z (zz k ) 2 +a 3z (zz k ) 3

[0027] in P is the fine grid point for interpolation encryption. x ,P y ,P zThey are the weight coefficients in the x, y, and z directions respectively.

[0028] Furthermore, the triangular facets on both sides of the connecting line of adjacent unit cells are extracted, and then the inner product of the normal vectors of the triangular facets on both sides with a common edge on the connecting line of the unit cells is calculated to characterize whether the microstructure transition is smooth.

[0029] Furthermore, the boundary line of the gradient structure is extracted, the triangular facets with an edge on the boundary line are detected, and the triangular facets on the connecting line are extracted; the triangular facets sharing the same edge line on both sides of the boundary line are matched in pairs, the normal vectors of the triangular facets are obtained, and then the normal vectors are multiplied in pairs, and the average of the results is calculated. The corresponding formula is:

[0030] d=n1·n2=(x1,y1,z1)·(x2,y2,z3)=x1x2+y1y2+z1z2

[0031] Compute the average of each pair of vector products:

[0032]

[0033] Where n1 is the normal vector of the triangle on the left side of the boundary line; n2 is the normal vector of the triangle on the right side of the boundary line; (x1, y1, z1) is the coordinate of the normal vector of the triangle on the left side of the boundary line; (x2, y2, z2) is the coordinate of the normal vector of the triangle on the right side of the boundary line; n is the total number of triangles on the structure boundary line; d i is the inner product of the normal vectors of the i-th pair of triangles on the boundary line of the structure.

[0034] Furthermore, the three working conditions are compression condition, shear condition and torsion condition; the boundary conditions are: ① Compression condition: the left end of the structure is fixed, and the right end face moves to the right by a% of the structure width; ② Shear condition: the left end of the structure is fixed, and the right end face moves downward by b% of the structure height; ③ Torsion condition: the left end of the structure is fixed, and the right end face rotates by γ°.

[0035] The present invention also provides a device for modeling high-order continuity of geometric boundaries of a gradient lattice structure, the device comprising a memory and a processor, the memory storing a computer program, and the processor executing the method for modeling high-order continuity of geometric boundaries of a gradient lattice structure as described above when executing the computer program.

[0036] In general, compared with the prior art, the above technical solution conceived by the present invention has the following advantages in the method and device for modeling the geometric boundary high-order continuity of the gradient lattice structure provided by the present invention:

[0037] Beneficial effects:

[0038] 1. The present invention takes into account the comprehensive stress conditions of the microstructure in the macrostructure and the design error caused by the structural boundary interpolation, and realizes the high-order continuity modeling of the geometric boundary of the gradient lattice structure through dual parameter adjustment.

[0039] 2. A dual-parameter adjustable high-order continuous interpolation function is used to continuously interpolate the movable variable-width gradient boundary of the microstructure unit cell to obtain a smooth transition block between two unit cells. The smooth transition block is then used to replace the structure of the original transition zone, thereby realizing high-order continuous gradient microstructure modeling and improving the continuity of the designed gradient lattice structure.

[0040] 3. The present invention introduces a weight factor and comprehensively considers the stress conditions of the gradient microstructure under three working conditions, so that the method is suitable for the design of gradient microstructures under different working conditions and has wide applicability.

[0041] 4. The present invention uses the spatial position relationship of the triangular facets at the boundary of adjacent microstructures as a geometric criterion to more simply and directly determine the degree of smoothness of the gradient microstructure connection. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of a method for modeling high-order continuity of geometric boundaries of a gradient lattice structure provided by the present invention;

[0043] Figure 2 and Figure 3 They are schematic diagrams of two microstructure unit cells provided by embodiments of the present invention;

[0044] Figure 4 The embodiment of the present invention takes e =8,t a =4 corresponding function graph;

[0045] Figure 5 The embodiment of the present invention takes e =8,t a = -4 corresponding function graph;

[0046] Figure 6 is a schematic diagram of a smooth transition block obtained in an embodiment of the present invention;

[0047] Figure 7 It is a schematic diagram of the original transition region structure of the present invention;

[0048] Figure 8 It is a schematic diagram of the updated transition area structure of the present invention;

[0049] Fig. 9 is the gradient structure boundary line map extracted by the present invention;

[0050] Fig.10is a schematic diagram of triangular facets on connecting lines extracted by the present invention;

[0051] Fig.11 is a schematic diagram of the normal vector of the triangular facet obtained by the present invention;

[0052] Fig.12 is the parameter t of the present invention e ,t a Schematic diagram of the value of ;

[0053] Fig.13 It is a schematic diagram of the mapping relationship between the geometric boundary transition angle and the boundary comprehensive stress obtained by the present invention;

[0054] Fig.14 is the product of the average normal vector of the structural transition boundary obtained in the embodiment of the present invention and the parameter t e and t a Schematic diagram of the inverse mapping relationship;

[0055] Fig.15 It is a schematic diagram of the gradient lattice structure obtained by the present invention. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0057] See also Figure 1 The present invention provides a method for modeling high-order continuity of geometric boundaries of a gradient lattice structure, the method mainly comprising the following steps:

[0058] S1, using implicit level set function to construct the microstructure unit cell of the gradient lattice structure to be designed.

[0059] Among them, the expression of the implicit level set function is:

[0060]

[0061] Where φ(x) is the level set function, t is the microstructure configuration control parameter, the area where φ(x)>t represents the solid area in the microstructure, and the area where φ(x)<t represents the void area in the microstructure. It is the boundary between the solid area and the void area of ​​the microstructure. By adjusting the parameter t, microstructure configurations with different volume fractions can be obtained.

[0062] In this implementation, the I-WP structure is selected as the basic unit cell, and the implicit expression of the unit cell is ΦIWP as follows:

[0063] Φ IWP =[cos(2x)+cos(2y)+cos(2z)]-2[cos(x)cos(y)+cos(y)cos(z)+cos(z)cos(x)]+t

[0064] By adjusting the parameter t, the unit cell configuration size can be adjusted to construct microstructures of different sizes. In this embodiment, two unit cells are selected, corresponding to t of 0 and 10, respectively, denoted as t1=0, t2=10, and the unit cell size is 40*40*40. Figure 2 and Figure 3 shown.

[0065] S2, using a dual-parameter adjustable high-order continuous interpolation function to continuously interpolate the movable variable-width gradient boundary of the microstructure unit cell to obtain a smooth transition block between two unit cells, and then using the smooth transition block to replace the structure of the original transition zone; wherein the expression of the dual-parameter adjustable high-order continuous interpolation function is:

[0066]

[0067] Where t e is the interval width control parameter, t a is the interval starting control parameter, t e The selection interval is set to [0,20], t a The selection interval is set to [-t e ,t e ]. e ,t a <Unit cell size. By adjusting two parameters, the control range of the interpolation function can be adjusted, thereby controlling the high-order continuity modeling strategy of the gradient lattice structure.

[0068] Among them, a dual-parameter adjustable high-order continuous interpolation function is constructed based on the Beta growth function and the microstructure unit cell; when the microstructure changes along the y direction, t is selected e =8,t a =4, the function graph is as follows Figure 4 As shown, select t e =8,t a = -4, the function graph is as follows Figure 5 shown.

[0069] The movable variable width gradient boundary continuous interpolation is completed, and the formula corresponding to the smooth transition block is:

[0070] φ=μ(X)φ1(X1)+(1-μ(X))φ2(X2)

[0071] Adjacent unit cells are interpolated by this formula to obtain a smooth transition block between two unit cells. The obtained structure is as follows: Figure 6 As shown, the original transition area of ​​the structure is replaced by the newly constructed smooth transition block, and the updated Figure 7 The transition region structure shown in Figure 2 is updated as follows: Figure 8 shown.

[0072] In one embodiment, the gradient microstructure transition block is constructed by constructing the μ function

[0073]

[0074] and is the level set scalar field of two adjacent unit cells. The adjacent unit cells are interpolated through this formula to obtain the smooth transition block between the two unit cells, and then the original transition area of ​​the unit cell is replaced by the newly constructed smooth transition block to complete the modeling of high-order continuous gradient microstructure.

[0075] S3, using a cubic convolution interpolation method to encrypt the level set function corresponding to the structural model obtained after the transition block is replaced, and then discretizing the structural model into a triangular mesh model.

[0076] The encryption formula is:

[0077]

[0078] P x (xx i )=a 0x +a 1x (xx i )+a 2x (xx i ) 2 +a 3x (xx i ) 3

[0079] P y (yy j )=a 0y +a 1y (yy j )+a 2y (yy j ) 2 +a 3y (yy j ) 3

[0080] P z (zz k )=a 0z +a1z (zz k )+a 2z (zz k ) 2 +a 3z (zz k ) 3

[0081] in P is the fine grid point for interpolation encryption. x ,P y ,P z are weight coefficients in the x, y, and z directions respectively. After mesh encryption, the Delaunay method is used to triangulate the zero isosurface of the level set function to derive a discrete triangular mesh model. The derived model is shown in Figure 8 shown.

[0082] S4, based on the triangular mesh model, calculates the normal vector angles of the two adjacent triangular facets on both sides of the connection line at the boundary of the two microstructure unit cells, and performs finite element simulation on the current gradient lattice structure under three working conditions to obtain the maximum stress in the transition zone of the gradient lattice structure.

[0083] The geometric spatial position relationship of the boundary structure of the unit cell connection is calculated. The spatial geometric angle relationship of the adjacent triangular facets on both sides of the boundary connection is positively correlated with the smoothness of the gradient microstructure transition. Therefore, the triangular facets on both sides of the adjacent unit cell connection line are extracted, and then the inner product of the normal vectors of the triangular facets on both sides with a common edge on the unit cell connection line is calculated to characterize whether the microstructure transition is smooth.

[0084] In one embodiment, the boundary line of the gradient structure is first extracted, and the triangular facets having an edge on the boundary line are detected, such as Fig. 9 As shown in the green part of , extract the triangular facets on the connecting line, such as Fig.10 As shown. The triangular facets sharing the same edge line on both sides of the boundary line are matched pairwise to obtain the normal vector of the triangular facet, as shown in Fig.11 As shown, we then multiply them two by two and find the average of the results. The calculation formula is as follows:

[0085] d=n1·n2=(x1,y1,z1)·(x2,y2,z3)=x1x2+y1y2+z1z2

[0086] Compute the average of each pair of vector products:

[0087]

[0088] Where n1 is the normal vector of the triangle on the left side of the boundary line; n2 is the normal vector of the triangle on the right side of the boundary line; (x1, y1, z1) is the coordinate of the normal vector of the triangle on the left side of the boundary line; (x2, y2, z2) is the coordinate of the normal vector of the triangle on the right side of the boundary line; n is the total number of triangles on the structure boundary line; d i is the inner product of the normal vectors of the i-th pair of triangles on the boundary line of the structure.

[0089] The calculation result of the mean inner product of the normal vectors of the triangle patches at the connection of this structure is:

[0090] In another embodiment, the three working conditions are compression, shear and torsion, and the boundary conditions are: ① compression condition: the left end of the structure is fixed, and the right end face moves rightward by a% of the structure width; ② shear condition: the left end of the structure is fixed, and the right end face moves downward by a distance of b% of the structure height; ③ torsion condition: the left end of the structure is fixed, and the right end face rotates by γ°, specifically:

[0091] Compression condition: the left end face of the gradient lattice structure is fixed, and the right end face moves 0.016mm to the right;

[0092] Shearing condition: the left end of the structure is fixed, and the right end moves downward by 0.016mm;

[0093] Torsion condition: the left end of the structure is fixed, and the right end is rotated 200KN. The maximum stress in the transition area under the three conditions is recorded respectively.

[0094] The structural material selected in this embodiment is structural steel, with a Young's modulus of 200 GPa and a Poisson's ratio of 0.3. e =8,t a When =4, the stresses of the structure under the above three working conditions are 1644.44MPa, 104.6MPa and 168.3MPa respectively.

[0095] S5, regulating the two parameters of the high-order continuous interpolation function t e and t a , traverse other values ​​in the value range of the two parameters to obtain the average value of the normal vectors of adjacent triangles in the discrete triangular mesh model and the maximum stress value in the transition area of ​​the gradient lattice structure under three working conditions.

[0096] See also Fig.12 , regulating the interpolation function t e and t a Two parameters (both positive integers) are used to change the width and starting area of ​​the transition region between two adjacent unit cells, calculate the average value of the normal vectors of adjacent triangles of the discrete triangular mesh model under various strategies, and count the maximum stress values ​​of the structure under three working conditions.

[0097] S6, introduce the weight factor, and interpolate the average value of the normal vectors of adjacent triangles of all discrete triangular mesh models and the maximum stress value of the transition area of ​​the corresponding gradient lattice structure through the proxy model to obtain the comprehensive stress of the structure; at the same time, based on the average value of the normal vectors of adjacent triangles of all discrete triangular mesh models and the corresponding parameter t e and t a , the average value of the normal vectors of adjacent triangles of the discrete triangular mesh model and the parameter t are established by the Kriging interpolation method e and t a The inverse mapping relationship of .

[0098] According to the proportion of the three stresses actually suffered by the microstructure in the macrostructure, a weight factor is introduced to construct a comprehensive stress evaluation index:

[0099] σ z =k·σ+p·τ1+q·τ2

[0100] Where k, p, q are weight coefficients, and σ, τ1, τ2 are the maximum stresses in the transition area of ​​the structure under the three working conditions, respectively.

[0101] The size of the vector product is determined according to the comprehensive stress, and the vector product is inversely mapped to the corresponding optimal boundary high-order continuity modeling interpolation scheme.

[0102] In one embodiment, a weight factor is introduced to calculate the comprehensive stress of the structure. In this example, torsion accounts for 50%, compression accounts for 20%, and shear accounts for 30%. A mapping relationship between the geometric boundary transition angle and the boundary comprehensive stress is established. The mapping relationship is as follows: Fig.13 shown.

[0103] The Kriging interpolation method is used to establish the average normal vector product of the structural transition boundary and the parameter t e and t a The inverse mapping relationship of Fig.14 shown.

[0104] S7, select the dual parameter t based on the material of the gradient lattice structure to be designed and its corresponding comprehensive stress e and t a , and then the gradient lattice structure is obtained.

[0105] In this embodiment, the optimal boundary continuity interpolation scheme is determined according to the structural material properties. e =8,t a =8, the comprehensive structural stress is 180.2MPa, which ensures that the structural stress does not exceed the yield strength of the material when the transition area is the shortest. Fig.15 as shown.

[0106] The present invention also provides a device for modeling high-order continuity of geometric boundaries of a gradient lattice structure, the device comprising a memory and a processor, the memory storing a computer program, and the processor executing the method for modeling high-order continuity of geometric boundaries of a gradient lattice structure as described above when executing the computer program.

[0107] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for modeling high-order continuity of geometric boundaries of gradient lattice structures, characterized in that: The method comprises the following steps: (1) A dual-parameter adjustable high-order continuous interpolation function is used to continuously interpolate the movable variable-width gradient boundary of the microstructure unit cell to obtain a smooth transition block between two unit cells, and then the smooth transition block is used to replace the structure of the original transition zone; wherein the expression of the dual-parameter adjustable high-order continuous interpolation function is: Where t e is the interval width control parameter, t a is the interval starting control parameter, t e The selection interval is set to (0,20], t a The selection interval is set to [-t e ,t e ]; (2) encrypting the level set function corresponding to the structural model obtained after the smooth transition block replacement, and then discretizing the structural model into a triangular mesh model; (3) Based on the triangular mesh model, the normal vector angles of the two adjacent triangular facets on both sides of the connection line at the boundary between the two microstructure unit cells are calculated, and finite element simulation is performed on the current gradient lattice structure under three working conditions to obtain the maximum stress in the transition zone of the gradient lattice structure; (4) Controlling the two parameters of the high-order continuous interpolation function can be controlled by adjusting the two parameters t e and t a , traverse other values ​​in the range of the two parameters to obtain the average value of the normal vectors of adjacent triangles of the discrete triangular mesh model and the maximum stress value of the transition area of ​​the gradient lattice structure under three working conditions; (5) The weight factor is introduced, and the comprehensive stress of the structure is calculated based on the average value of the normal vectors of adjacent triangles of all discrete triangular mesh models and the maximum stress value of the transition area of ​​the corresponding gradient lattice structure; at the same time, the average value of the normal vectors of adjacent triangles of all discrete triangular mesh models and the corresponding parameter t e and t a , and then establish the average value of the normal vectors of adjacent triangles in the discrete triangle mesh model and the parameter t e and t a The inverse mapping relationship of (6) Select the dual parameter t based on the material of the gradient lattice structure to be designed and its corresponding comprehensive stress e and t a , and then the gradient lattice structure is obtained.

2. The method for modeling high-order continuity of geometric boundaries of a gradient lattice structure according to claim 1, characterized in that: The comprehensive stress determines the size of the vector product, which is inversely mapped to the corresponding dual parameter t e and t a .

3. The method for modeling high-order continuity of geometric boundaries of a gradient lattice structure according to claim 1, characterized in that: The microstructure unit cell of the gradient lattice structure to be designed is constructed using an implicit level set function, and the expression of the implicit level set function is: In the formula, φ(x) is the level set function, t is the microstructure configuration control parameter. The region where φ(x) > t represents the solid region in the microstructure, and the region where φ(x) < t represents the void region in the microstructure. is the boundary between the solid region and the void region of the microstructure.

4. The method for modeling high-order continuity of geometric boundaries of a gradient lattice structure according to claim 1, characterized in that: The dual-parameter adjustable high-order continuous interpolation function is constructed based on the Beta growth function and the microstructure unit cell.

5. The method for modeling high-order continuity of geometric boundaries of a gradient lattice structure according to claim 1, characterized in that: The formula corresponding to the smooth transition block is: In the formula, and is the level set scalar field of two adjacent unit cells.

6. The method for modeling high-order continuity of geometric boundaries of a gradient lattice structure according to claim 5, characterized in that: The encryption formula is: P x (x-x i )=a 0x +a 1x (x-x i )+a 2x (x-x i ) 2 +a 3x (x-x i ) 3 P y (yy j )=a 0y +a 1y (yy j )+a 2y (yy j ) 2 +a 3y (yy j ) 3 P z (from) k )=a 0z +a 1z (from) k )+a 2z (from) k ) 2 +a 3z (from) k ) 3 in P is the fine grid point for interpolation encryption. x ,P y ,P z They are the weight coefficients in the x, y, and z directions respectively.

7. The method for modeling high-order continuity of geometric boundaries of a gradient lattice structure according to claim 5, characterized in that: The triangular facets on both sides of the connecting line of adjacent unit cells are extracted, and then the inner product of the normal vectors of the triangular facets on both sides with a common edge on the connecting line of the unit cells is calculated to characterize whether the microstructure transition is smooth.

8. The method for modeling high-order continuity of geometric boundaries of a gradient lattice structure according to claim 7, characterized in that: Extract the boundary line of the gradient structure, detect the triangular facets with an edge on the boundary line, and extract the triangular facets on the connecting line; match the triangular facets that share the same edge line on both sides of the boundary line, obtain the normal vector of the triangular facets, and then multiply them two by two, and calculate the average of the results. The corresponding formula is: d=n1·n2=(x l1 ,y l1 ,z l1 )·(x l2 ,y l2 ,z l2 )=x l1 x l2 +y l1 y l2 +z l1 z l2 Compute the average of each pair of vector products: Where n1 is the normal vector of the triangle on the left side of the boundary line; n2 is the normal vector of the triangle on the right side of the boundary line; (x l1 ,y l1 ,z l1 ) is the normal vector coordinate of the triangle patch on the left side of the boundary line; (x l2 ,y l2 ,z l2 ) is the normal vector coordinate of the triangle on the right side of the boundary line; n is the total number of triangles on the structure boundary line; d g is the inner product of the g-th pair of normal vectors of triangles on the boundary line of the structure.

9. The method for modeling high-order continuity of geometric boundaries of a gradient lattice structure according to any one of claims 1 to 8, characterized in that: The three working conditions are compression, shear and torsion. The boundary conditions are as follows: ① Compression condition: the left end of the structure is fixed, and the right end moves to the right by a% of the structure width; ② Shear condition: the left end of the structure is fixed, and the right end moves downward by b% of the structure height; ③ Torsion condition: the left end of the structure is fixed, and the right end rotates by γ°.

10. A device for modeling high-order continuity of geometric boundaries of a gradient lattice structure, characterized by: The device includes a memory and a processor, the memory stores a computer program, and the processor executes the gradient lattice structure geometric boundary high-order continuity modeling method described in any one of claims 1-9 when executing the computer program.

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