CN114169187A - Design method of isotropic lattice structure - Google Patents

Design method of isotropic lattice structure Download PDF

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CN114169187A
CN114169187A CN202111331948.1A CN202111331948A CN114169187A CN 114169187 A CN114169187 A CN 114169187A CN 202111331948 A CN202111331948 A CN 202111331948A CN 114169187 A CN114169187 A CN 114169187A
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hollow
isotropic
cell structure
connecting rod
unit cell
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宋波
胡凯
张志�
史玉升
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Huazhong University of Science and Technology
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Abstract

The invention discloses a design method of an isotropic lattice structure, which belongs to the field of lattice structure design and comprises the following steps: selecting a plurality of hollow connecting rods, and combining the hollow connecting rods through Boolean union operation to obtain a single cell structure; creating a cubic structure coincident with the gravity center of the single cell structure, and deleting the overlapped part of the single cell structure and the cubic structure through Boolean difference set operation to obtain a hollow single cell structure; obtaining an anisotropic factor of a hollow single-cell structure, and obtaining an isotropic single-cell structure by adjusting the ratio of the diameter of a hollow structure inside a hollow connecting rod to the diameter of an external structure outside the hollow connecting rod; and carrying out three-dimensional repeated arrangement on the isotropic single-cell structure to obtain an isotropic lattice structure. According to the invention, isotropy is realized only by designing the hollow connecting rod through the isotropic lattice structure and changing the ratio between the inner hollow diameter and the outer complete connecting rod diameter, the adaptive single cell type is wide, the light weight degree is high, and the complexity of the isotropic single cell is reduced.

Description

Design method of isotropic lattice structure
Technical Field
The invention belongs to the field of lattice structure design, and particularly relates to a design method of an isotropic lattice structure.
Background
In industrial applications, the anisotropy of the structure is considered detrimental, particularly when the anisotropic structure is used as a support member or energy absorbing structure. For example, during a rear-end collision of an automobile, significant harm is caused to the passengers due to the low energy absorption capability in the direction of weak strength. Therefore, it is necessary to solve the problems of low directional strength of the structural part and reduced energy absorption effect due to the anisotropic structure.
At present, researchers begin to realize isotropy from the aspects of material selection and structural design, however, isotropic materials have the characteristic of being solid and cannot realize light weight. The isotropic cells are designed primarily by designing new cells or combining existing cells. However, designing new cells is time and labor consuming and costs are greatly increased. "Design of lattice structures with controlled and isotropic structure" describes that isotropic unit cells can be obtained by combining two unit cells with different stiffness orientations or by treating the unit cells as a combination of an outer structure and an inner structure, with varying the ratio of the connecting rod diameters of the outer structure to the inner structure. However, the isotropic unit cell designed by the above two methods has a complex shape, greatly increases the manufacturing difficulty, and has a small unit cell design application range and a low light weight degree. Therefore, it is necessary to provide a method for designing an isotropic cell having a high degree of weight reduction and a simple shape.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a design method of an isotropic lattice structure, aiming at realizing isotropy by changing the ratio of the inner hollow diameter and the outer solid diameter of a hollow connecting rod, thereby solving the technical problems of complicated shape and high manufacturing difficulty of an isotropic unit cell designed in the prior art.
To achieve the above object, according to one aspect of the present invention, there is provided a method for designing an isotropic lattice structure, the method comprising the steps of:
selecting a plurality of hollow connecting rods, and combining the hollow connecting rods through Boolean union operation to obtain a single cell structure;
creating a cubic structure coincident with the gravity center of the single cell structure, and deleting the overlapping part of the single cell structure and the cubic structure through Boolean difference set operation to obtain a hollow single cell structure;
obtaining an anisotropic factor of a hollow single-cell structure, and obtaining an isotropic single-cell structure by adjusting the ratio of the diameter of a hollow structure inside a hollow connecting rod to the diameter of an external structure outside the hollow connecting rod;
and (3) carrying out three-dimensional repeated arrangement on the isotropic unit cell structure to obtain an isotropic lattice structure.
Preferably, the obtaining of the anisotropy factor of the air core unit cell structure comprises the following steps:
applying periodic boundary conditions to the hollow unit cell structure, and calculating by adopting a finite element method to obtain an elastic matrix of the hollow unit cell structure;
and obtaining the anisotropy factor of the hollow unit cell structure according to the elastic matrix.
Preferably, the ratio of the diameter of the hollow structure in the hollow connecting rod to the diameter of the external structure of the connecting rod is a pore coefficient, and the value range of the pore coefficient is 0.5-1.
Preferably, the section of the hollow structure in the hollow connecting rod is obtained by scaling with the center of gravity of the section of the outer structure of the hollow connecting rod as the origin.
Preferably, the cross-sectional shape of the hollow connecting rod outer structure comprises a circle, an ellipse, a square or a hexagon.
Preferably, the center of the cross-sectional shape is the diameter of the outer structure of the hollow connecting rod.
Preferably, the isotropic unit cell structure is made of an isotropic material.
According to another aspect of the invention, an isotropic lattice structure is provided.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. according to the design method of the isotropic lattice structure, the isotropic lattice structure realizes isotropy by designing the hollow connecting rods and changing the ratio between the inner hollow diameter and the outer complete connecting rod diameter, is suitable for a wide range of single cell types, and can obtain the isotropic structure by using the existing single cell or the single cell with a simple structure without designing a novel lattice structure.
2. According to the design method of the isotropic lattice structure, part of the solid is removed from the middle of the connecting rod body of the solid single-cell structure to form the hollow lattice single cell, and compared with the traditional solid lattice structure, the lightweight degree is improved.
3. The design method of the isotropic lattice structure provided by the invention has the advantages that the designed isotropic lattice structure does not need various unit cell combinations with different rigidity orientations, the structure is simple to manufacture, and the manufacturing cost is low.
Drawings
FIG. 1 is a flow chart of a method of designing an isotropic lattice structure according to the present invention;
FIG. 2 is a schematic diagram of a hollow face-centered cubic (FCC) isotropic unit cell structure in one embodiment of the invention;
FIG. 3 is a schematic representation of a hollow octahedral isotropic unit cell structure in one embodiment of the present invention;
FIG. 4 is a schematic diagram of an isotropic unit cell structure of a hollow eight-fold truss in one embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1-4, the present invention provides a method for designing an isotropic lattice structure, comprising the following steps:
and S100, selecting a plurality of hollow connecting rods, and combining the hollow connecting rods through Boolean union operation to obtain a single cell structure.
S200, a cubic structure coincident with the gravity center of the single cell structure is created, and the overlapping part of the single cell structure and the cubic structure is deleted through Boolean difference set operation to obtain the hollow single cell structure.
S300, obtaining the anisotropy factor of the hollow single-cell structure, and obtaining the isotropic single-cell structure by adjusting the ratio of the diameter of the hollow structure in the hollow connecting rod to the diameter of the structure outside the hollow connecting rod.
Specifically, the method for acquiring the anisotropy factor of the hollow unit cell structure comprises the following steps:
s310, applying periodic boundary conditions to the hollow unit cell structure, and calculating by adopting a finite element method to obtain an elastic matrix of the hollow unit cell structure
And S320, obtaining the anisotropy factor of the hollow unit cell structure according to the elastic matrix.
And S400, carrying out three-dimensional repeated arrangement on the isotropic unit cell structure to obtain an isotropic lattice structure.
The technical solution of the present invention is further illustrated by the following specific examples.
Example one
The invention provides a design method of a hollow FCC isotropic structure, which comprises a plurality of hollow unit cells which are periodically and repeatedly arranged in a three-dimensional mode.
As shown in FIG. 2, a hollow FCC unit cell comprises 12 strips of length
Figure BDA0003349209990000041
The diameter of the periphery of the cylinder is 1.1mm, wherein, every 2 connecting rods are vertically crossed and combined at the midpoint of the connecting rods to form 6 quadrilateral surfaces. The 6 quadrilateral faces form a single cell according to the arrangement mode of 6 faces of the cube, and Boolean union operation is performed on the 12 semi-cylinder hollow connecting rods. And (3) creating a cubic structure with the side length of 5mm, wherein the cubic structure is superposed with the single cells at the gravity center, and 6 semi-cylinder cross surfaces are respectively superposed with 6 cubic surfaces. And (4) taking a Boolean difference set for operation to finally obtain the hollow FCC unit cell.
Example two
As shown in FIG. 3, the hollow octahedral unit cell includes 12 strips having a length of
Figure BDA0003349209990000042
The diameter of the periphery of the cylinder is 1.1mm, the hollow octahedron is a square formed by 4 connecting rods, the other 4 connecting rods are distributed on one side of the surface of the square, one end of each connecting rod is connected with 4 vertexes of the square respectively, and the other ends of the 4 hollow connecting rods are connected to one point; and then the remaining 4 hollow connecting rods are distributed on the other side of the plane where the square is located, one end of each connecting rod is respectively connected with 4 vertexes of the square, the other ends of the 4 hollow connecting rods are connected to one point, and Boolean union operation is performed on the 12 hollow connecting rods. And (3) creating a cubic structure with the side length of 5mm, wherein the cubic structure is superposed with the single cells at the center of gravity, and 6 vertexes are respectively superposed with the centers of 6 cubic surfaces. And taking a Boolean difference set for operation to finally obtain the hollow octahedral single cell.
EXAMPLE III
As shown in fig. 4, the hollow octaplex truss unit cell can be regarded as a hollow FCC unit cell and the octahedral unit cell coinciding on the gravity center, and the connecting rod connecting point of the hollow FCC unit cell coincides with the middle point of the connecting rod of the hollow octahedral unit cell, and is obtained by boolean union operation.
To explain further, the way of obtaining the unit cell anisotropy factor in the examples of the present invention is as follows:
1. obtaining an elastic matrix of the unit cell by adopting finite element calculation (FEM), wherein a material model selected from the three structures is Ti-6Al-4V, the Young modulus E is 110GPa, the Poisson ratio V is 0.34, applying periodic boundary conditions to the unit cell, and firstly applying axial strain to the unit cell in the directions of x, y and z, namely:
εx＝εy＝εz＝0.01
secondly, a shear strain is applied to the unit cell, namely:
εxy＝εxz＝εyz＝0.005
the following elastic matrix is finally obtained:
Figure BDA0003349209990000051
2. the anisotropy factor of the structure is obtained through the elastic matrix, and the calculation mode is as follows:
Figure BDA0003349209990000052
and A is an anisotropy factor, when A is equal to 1, the unit cell is isotropic, if A is not equal to 1, the porosity factor is readjusted to indirectly regulate the anisotropy factor of the unit cell, and finally the hollow unit cell with A being equal to 1, namely the isotropic unit cell, is obtained.
Obtaining an isotropic hollow FCC unit cell, a hollow octahedral unit cell and a hollow octal truss unit cell by means of FEM. The corresponding porosity coefficients of the three isotropic air cells are 0.61, 0.75 and 0.54 respectively.
It should be noted that the unit cell prepared from Ti-6Al-4V obtained by the FEM method is isotropic, and the Ti-6Al-4V material is replaced on the basis of the unit cell, that is, the unit cell is prepared from other materials and still is isotropic. The Ti-6Al-4V material is used only for endowing structural parameters, and thus an elastic matrix can be obtained, besides, the material type selection has no influence on the structural isotropy.
The FEM mode obtains a hollow isotropic unit cell with the dimension of a complete connecting rod of 1.1mm and the side length of 5mm, the unit cell is amplified or reduced in an equal proportion on the basis of the dimension, and the unit cell is still isotropic. The specific dimensions used are only to obtain the elastic matrix during FEM, except that scaling up or down the dimensions has no effect on the cell isotropy.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (8)

1. A method of designing an isotropic lattice structure, the method comprising the steps of:
selecting a plurality of hollow connecting rods, and combining the hollow connecting rods through Boolean union operation to obtain a single cell structure;
creating a cubic structure coincident with the gravity center of the single cell structure, and deleting the overlapping part of the single cell structure and the cubic structure through Boolean difference set operation to obtain a hollow single cell structure;
obtaining an anisotropic factor of a hollow single-cell structure, and obtaining an isotropic single-cell structure by adjusting the ratio of the diameter of a hollow structure inside a hollow connecting rod to the diameter of an external structure outside the hollow connecting rod;
and (3) carrying out three-dimensional repeated arrangement on the isotropic unit cell structure to obtain an isotropic lattice structure.
2. The method of claim 1, wherein the step of obtaining the anisotropy factor of the air-core unit cell structure comprises the steps of:
applying periodic boundary conditions to the hollow unit cell structure, and calculating by adopting a finite element method to obtain an elastic matrix of the hollow unit cell structure;
and obtaining the anisotropy factor of the hollow unit cell structure according to the elastic matrix.
3. The method for designing the isotropic lattice structure according to claim 2, wherein the ratio of the diameter of the hollow structure inside the hollow connecting rod to the diameter of the structure outside the connecting rod is a porosity factor, and the value range of the porosity factor is 0.5-1.
4. The method as claimed in claim 3, wherein the cross-section of the hollow structure inside the hollow connecting rod is scaled by using the center of gravity of the cross-section of the outer structure of the hollow connecting rod as the origin.
5. The method as claimed in claim 4, wherein the cross-sectional shape of the outer structure of hollow connecting rods comprises a circle, an ellipse, a square or a hexagon.
6. A design method of isotropic lattice structure as claimed in claim 5, wherein the center of the cross-sectional shape is the diameter of the outer structure of the hollow connecting rod.
7. The method of claim 1, wherein the isotropic unit cell structure is made of isotropic material.
8. An isotropic lattice structure of the isotropic lattice structure designing method as set forth in any one of claims 1 to 7.
CN202111331948.1A 2021-11-11 2021-11-11 Design method of isotropic lattice structure Pending CN114169187A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116386788A (en) * 2023-04-10 2023-07-04 精创石溪科技(成都)有限公司 Variable density porous grid structure parameterized modeling method based on multi-objective optimization

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116386788A (en) * 2023-04-10 2023-07-04 精创石溪科技(成都)有限公司 Variable density porous grid structure parameterized modeling method based on multi-objective optimization
CN116386788B (en) * 2023-04-10 2023-11-21 精创石溪科技(成都)有限公司 Variable density porous grid structure parameterized modeling method based on multi-objective optimization

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