A design method of high-rigidity high-strength three-dimensional lattice structure

Abstract

This invention discloses a design method for a high-stiffness, high-strength three-dimensional lattice structure: A truss lattice structure is established using 3D modeling software as the initial lattice structure; the unit cells of the lattice model are mirrored and combined to obtain usable novel unit cells; these novel unit cells are then arrayed to obtain a novel lattice structure. This invention yields a structure with performance superior to most traditional truss lattices, which can be effectively applied to the lightweight design of high-stiffness, high-strength structures.

Description

Technical Field

[0001] This invention belongs to the field of lightweight structural design technology, specifically a design method for a high-stiffness, high-strength three-dimensional lattice structure. Background Technology

[0002] Three-dimensional lattice structures are a new type of lightweight and multifunctional structure with excellent mechanical properties. The center of the lattice is a hollow structure. Due to its many excellent mechanical properties such as high specific strength, high specific stiffness, high energy absorption and lightweight, it is widely used in many fields such as aerospace, weapons and ammunition, biomedicine, vehicle engineering, and sports equipment, and has attracted much attention in recent years.

[0003] Traditional three-dimensional lattice structures mainly include rod-shaped cells with limited configurations such as body-centered cubic, face-centered cubic, pyramid, and Kagome. The rod structure within these cells is simple, the design space is limited, and it reduces the compressive strength of the material. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for a high-rigidity, high-strength three-dimensional lattice structure to solve the problems of insufficient rigidity and load-bearing capacity of traditional design cells.

[0005] The technical solution for achieving the objective of this invention is: a design method for a high-stiffness, high-strength three-dimensional lattice structure, comprising:

[0006] S1: Use 3D modeling software to create a truss lattice structure as the initial lattice structure, and classify the rods;

[0007] S2: The lattice model unit cell is mirrored and combined to obtain a usable new unit cell;

[0008] S3: Combine and array the novel unit cells to obtain a novel lattice structure.

[0009] Preferably, when establishing a truss lattice structure as the initial lattice structure, the lattice type, unit cell size, lattice scale, relative density, rod diameter, and elastic modulus E of the material used in the structure are determined. c Poisson's ratio υ, density ρ, the bottom of the structure is completely fixed, and the top is uniformly subjected to a vertically downward displacement load F.

[0010] Preferably, the design principle of the initial lattice structure is as follows:

[0011] Remove the face-centered atoms from the top and bottom surfaces of the face-centered cubic unit cell; extend the diagonal length of the central four-membered ring to be equal to the diagonal length of the four-membered rings on the top and bottom surfaces; connect adjacent atoms sequentially from top to bottom;

[0012] The quadrilateral truss lattice structure was used as the initial lattice structure.

[0013] Preferably, the initial lattice established has the following structural features:

[0014] The initial lattice has two types of rods according to different forces: 12 horizontal rods l1 of the same length and 16 diagonal rods l2 of the same length. At the intersection of the axes of all rods, there is a sphere centered on the intersection point.

[0015] Preferably, the specific method for using quadrilaterals to extract the truss lattice structure as the initial lattice structure is as follows:

[0016] Create a cube as the minimum boundary of the lattice. Divide the horizontal bars into 3 groups, with the axes of the 4 bars in each group forming small squares: The 4 vertices of the first group of small squares are located on the 4 sides of the square on the upper surface of the cube of the minimum boundary of the lattice, and the two sides of each small square vertex form acute angles of 22.5° and 67.5° with the sides of the square on the upper surface where the vertex is located, respectively; The 4 vertices of the second group of small squares are located on the 4 sides of the squares intercepted by the planes of symmetry of the upper and lower surfaces of the cube of the minimum boundary of the lattice. The squares are obtained by projecting the small squares on the upper surface onto the planes of symmetry and rotating them 45° clockwise from the geometric center of the projection; The third group of small squares is symmetrical to the first group of small squares about the planes of symmetry of the upper and lower surfaces of the cube of the minimum boundary of the lattice.

[0017] The diagonal bars are divided into two groups of eight bars each. The axes of the bars are respectively the straight lines connecting each vertex of the small square in the first group to the two vertices of the nearest small square in the second group, and the straight lines connecting each vertex of the small square in the third group to the two vertices of the nearest small square in the second group.

[0018] The structure within the smallest external boundary is taken as the initial structure.

[0019] Preferably, the rod diameter is 2mm.

[0020] Preferably, the diameter of the sphere is 5 mm.

[0021] Preferably, the specific method for obtaining a usable novel unit cell by mirror transformation and combination design of the lattice model unit cell is as follows:

[0022] S21: While preserving the initial structure, take any one of the four faces other than the top and bottom surfaces of the minimum boundary cube of the initial structure as the mirror symmetry face, perform a mirror transformation, and perform a logical OR operation on the transformed model to obtain the secondary structure.

[0023] S22: While retaining the secondary structure, take any one of the two surfaces other than the upper and lower surfaces adjacent to the selected mirror symmetry plane in step 1 as the new mirror symmetry plane, perform a mirror transformation on the secondary structure, and perform a logical OR operation on the transformed model to obtain a new cell structure.

[0024] Preferably, the array size when combining the novel unit cells is n×n×2n, where n>0 and n is an integer.

[0025] Compared with the prior art, the significant advantages of this invention are: this invention obtains a cell that is superior to traditional truss lattice in terms of strength and stiffness, and can be effectively applied to most pressure-bearing lattice structures. Attached Figure Description

[0026] Figure 1 This is a flowchart of the present invention.

[0027] Figure 2 This serves as the design basis for the truss structure unit cell and a schematic diagram of the extracted initial unit cell structure.

[0028] Figure 3 A schematic diagram of the stress analysis of the initial unit cell structure under compression.

[0029] Figure 4 The process of obtaining a unit cell by combining mirror designs and its array in 3×3×6.

[0030] Figure 5 For traditional truss cell 1 and its constituent elements Figure 4 Arrays of the same size.

[0031] Figure 6 For traditional truss cell 2 and its composition and Figure 4 Arrays of the same size.

[0032] Figure 7 Stress diagrams were simulated and analyzed for arrays of the same size composed of novel unit cells and traditional truss unit cells.

[0033] Figure 8 The stress-strain curves are for three different structures. Detailed Implementation

[0034] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0035] like Figure 1 As shown, a design method for a high-stiffness, high-strength three-dimensional lattice structure includes:

[0036] S1: Use 3D modeling software to create a truss lattice structure as the initial lattice structure;

[0037] Following the design guidelines, the initial truss lattice structure was constructed in the CREO PARAMETRIC software, as shown in the attached figure. Figure 2 As shown.

[0038] Specifically, when establishing a truss lattice structure as the initial lattice structure, the lattice type, unit cell size, lattice scale, relative density, rod diameter, and elastic modulus E of the material used in the structure are determined. c Poisson's ratio υ, density ρ, the bottom of the structure is completely fixed, and the top is uniformly subjected to a vertically downward displacement load F.

[0039] Specifically, the design process is as follows:

[0040] Remove the face-centered atoms on the top and bottom surfaces of the face-centered cubic unit cell; extend the diagonal length of the central quaternary ring to be equal to the diagonal length of the quaternary rings on the top and bottom surfaces; connect adjacent atoms sequentially from top to bottom; use quadrilaterals to extract the truss lattice structure as the initial lattice structure.

[0041] S2: Perform mirror transformation and combination design on the lattice model unit cell to obtain a usable new unit cell.

[0042] In some embodiments, mirror-image combination and merging design a unit cell with a size of 2×2×1, as shown in the attached figure. Figure 4 As shown;

[0043] Specifically, the method for obtaining usable novel unit cells by mirror transformation and combination design of lattice model unit cells is as follows:

[0044] S21: While preserving the initial structure, take any one of the four faces other than the top and bottom surfaces of the minimum boundary cube of the initial structure as the mirror symmetry face, perform a mirror transformation, and perform a logical OR operation on the transformed model to obtain the secondary structure.

[0045] S22: While retaining the secondary structure, take any one of the two surfaces other than the upper and lower surfaces adjacent to the selected mirror symmetry plane in step 1 as the new mirror symmetry plane, perform a mirror transformation on the secondary structure, and perform a logical OR operation on the transformed model to obtain a new cell structure.

[0046] S3: Combine and array the novel unit cells to obtain a novel lattice structure.

[0047] In some embodiments, an array size of 3×3×6 is used as an example; as shown in the appendix. Figure 4 As shown.

[0048] To verify the effectiveness of the invention, a stress analysis was performed on each rod of the initial structure.

[0049] (1) Perform stress analysis on the lattice structure, classify the rods obtained after compression according to different forces, and calculate the deformation force of each type of rod;

[0050] (2) Calculate the stress based on the force applied and the strain based on the deformation.

[0051] (3) Calculate the uniaxial compressive stiffness based on stress and strain, and obtain the formula for calculating uniaxial stiffness.

[0052] The uniaxial stiffness E of the initial lattice structure oct The derivation process is as follows:

[0053] (a) Classify the members in the tilted lattice under compression according to the different forces applied, and calculate the deformation force of each type of member:

[0054]

[0055]

[0056] (b) Calculate the stress based on the applied forces and the strain based on the deformation:

[0057]

[0058]

[0059] (c) Calculate the uniaxial compressive stiffness based on stress and strain:

[0060]

[0061] Substituting, we get:

[0062]

[0063] Wherein, the rod lengths are l1 and l2; F1 and F2 are the deformation forces of l1 and l2 after compression, respectively; I is the moment of inertia of the circular rod; δ is the strain of each rod after compression; E is the elastic modulus of the base material; r is the rod radius; γ is the spatial angle of the rod; rod lengths are l1 and l2; σ is the overall equivalent stress of the lattice; A is the cross-sectional area of ​​the lattice in the compression direction; ε is the overall equivalent strain of the lattice; H is the initial height of the lattice in the compression direction; E is the equivalent elastic modulus in the compression direction; E oct The equivalent elastic modulus in the compression direction of the lattice structure; the aforementioned spatial angle γ was obtained from the modeling software. (See attached...) Figure 3 As shown.

[0064] For this invention, r = 1 mm, l1 = 7.65 mm, l2 = 6.46 mm, γ = 50.361°, and A = 100 mm. 2 H = 10 mm, theoretically E can be calculated. oct ≈0.112E.

[0065] The three-dimensional lattice structure and commonly used unit cells designed in this invention are imported into topology optimization software. The lower surface is fixed and a dynamic displacement of 0.25H is applied to the upper surface. The stress-strain curve of the structure is analyzed. The stress-strain curve of the traditional truss structure is simulated and analyzed using the same method. The elastic modulus and specific modulus of the two are calculated and the differences between them are compared.

[0066] Both structures here have dimensions of 60×60×60mm.

[0067] Due to limitations in computing power, only a dynamic displacement of 0.25H is applied to the upper surface of the structure.

[0068] Based on the simulation results, it can be calculated that when using titanium alloy as the same material, the elastic modulus of the new unit cell is about 14.19 GPa, while the elastic modulus of the traditional truss structure 1 is about 4.49 GPa, and the elastic modulus of the traditional truss structure 2 is 8.69 GPa.

[0069] This invention uses titanium alloy material TC4, with an elastic modulus of approximately 110 GPa. Therefore, the specific elastic modulus of the novel structure is:

[0070] E 新 =14.19÷110=0.129E

[0071] The simulation results are slightly better than the theoretical derivation results. This may be because the longitudinal deformation of the unit cells is constrained by the transverse compression of the cells during actual pressure application, resulting in a larger uniaxial compressive stiffness. The simulation results are acceptable.

[0072] The traditional structure is:

[0073] E 传1 =4.49 ÷ 110 = 0.041E

[0074] E 传2 =8.69 ÷ 110 = 0.079E

[0075] As can be seen from the figure, when the strain ε is 0.025, the traditional structure 1 has already been crushed and failed, while the new structure has not yet exceeded the proportional limit.

[0076] Calculations clearly show that the new structure has better compressive strength than the traditional structure.

[0077] All technical solutions falling within the scope of this invention are protected by this invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of this invention should be considered within the scope of protection of this invention.

Claims

1. A method of designing a high stiffness high strength three-dimensional lattice structure, characterized by, include: S1: Use 3D modeling software to create a truss lattice structure as the initial lattice structure. The design principle of the initial lattice structure is as follows: Remove the face-centered atoms from the top and bottom surfaces of a face-centered cubic unit cell; The diagonal length of the central four-membered ring is extended to be equal to the diagonal length of the four-membered rings on the upper and lower surfaces; adjacent atoms are connected sequentially from top to bottom; a quadrilateral is used to extract the truss lattice structure as the initial lattice structure, specifically: Create a cube as the minimum boundary of the lattice. Divide the horizontal bars into 3 groups, with the axes of the 4 bars in each group forming small squares: The 4 vertices of the first group of small squares are located on the 4 sides of the square on the upper surface of the cube of the minimum boundary of the lattice, and the two sides of each small square vertex form acute angles of 22.5° and 67.5° with the sides of the square on the upper surface where the vertex is located, respectively; The 4 vertices of the second group of small squares are located on the 4 sides of the squares intercepted by the planes of symmetry of the upper and lower surfaces of the cube of the minimum boundary of the lattice. The squares are obtained by projecting the small squares on the upper surface onto the planes of symmetry and rotating them 45° clockwise from the geometric center of the projection; The third group of small squares is symmetrical to the first group of small squares about the planes of symmetry of the upper and lower surfaces of the cube of the minimum boundary of the lattice. The diagonal bars are divided into two groups of eight bars each. The axes of the bars are respectively the straight lines connecting each vertex of the small square in the first group to the two vertices of the nearest small square in the second group, and the straight lines connecting each vertex of the small square in the third group to the two vertices of the nearest small square in the second group. The structure within the smallest external boundary is taken as the initial structure; S2: By performing mirror transformation and combination design on the lattice model unit cell, a usable novel unit cell is obtained. The specific method is as follows: S21: While preserving the initial structure, take any one of the four faces other than the top and bottom surfaces of the minimum boundary cube of the initial structure as the mirror symmetry face, perform a mirror transformation, and perform a logical OR operation on the transformed model to obtain the secondary structure. S22: While retaining the secondary structure, take any one of the two surfaces other than the upper and lower surfaces adjacent to the selected mirror symmetry plane in step S21 as the new mirror symmetry plane and perform a mirror transformation on the secondary structure. Then, perform a logical OR operation on the transformed model to obtain a new cell structure. S3: Combine and array the novel unit cells to obtain a novel lattice structure.

2. The design method for a high-stiffness, high-strength three-dimensional lattice structure according to claim 1, characterized in that, When establishing a truss lattice structure as the initial lattice structure, determine the lattice type, unit cell size, lattice scale, relative density, bar diameter, and elastic modulus of the materials used in the structure. E c Poisson's ratio υ ,density ρ The bottom of the structure is completely fixed, and the top is uniformly subjected to a vertically downward displacement load F.

3. The design method for a high-stiffness, high-strength three-dimensional lattice structure according to claim 1, characterized in that, The initial lattice established has the following structural features: The initial lattice has 12 horizontal bars of the same length according to the different forces applied. l 1 and 16 diagonal bars of the same length l 2 Both types of rods have a sphere centered at the intersection of all rod axes.

4. The design method for a high-stiffness, high-strength three-dimensional lattice structure according to claim 3, characterized in that, The rod diameter is 2mm.

5. The design method for a high-stiffness, high-strength three-dimensional lattice structure according to claim 3, characterized in that, The diameter of the sphere is 5mm.

6. The design method for a high-stiffness, high-strength three-dimensional lattice structure according to claim 1, characterized in that, The array size when combining novel unit cells into an array is , n>0 and n is an integer.

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