CN117231659A - Body-centered cubic lattice structure and calculation method for variable cross-section rod diameter thereof - Google Patents
Body-centered cubic lattice structure and calculation method for variable cross-section rod diameter thereof Download PDFInfo
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- 210000003537 structural cell Anatomy 0.000 claims abstract description 18
- 238000000034 method Methods 0.000 claims abstract description 15
- 238000005452 bending Methods 0.000 claims abstract description 11
- 230000007704 transition Effects 0.000 claims abstract description 5
- 238000004458 analytical method Methods 0.000 claims description 14
- 210000004027 cell Anatomy 0.000 claims description 9
- 230000006835 compression Effects 0.000 claims description 9
- 238000007906 compression Methods 0.000 claims description 9
- 239000000463 material Substances 0.000 claims description 4
- 241000486463 Eugraphe sigma Species 0.000 claims description 3
- 230000000737 periodic effect Effects 0.000 claims description 3
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- 238000010521 absorption reaction Methods 0.000 abstract description 6
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- 230000000052 comparative effect Effects 0.000 description 3
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- 230000000694 effects Effects 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
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- 238000000280 densification Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
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- 229910001220 stainless steel Inorganic materials 0.000 description 1
- 239000010935 stainless steel Substances 0.000 description 1
- 239000002699 waste material Substances 0.000 description 1
Abstract
The invention belongs to the field of light energy absorbing structures, and particularly discloses a body-centered cubic lattice structure and a method for calculating the diameter of a variable cross-section rod thereof, wherein the body-centered cubic lattice structure comprises a plurality of structural cells which are periodically arranged in an array manner; the structural cell comprises two subunits, the two subunits are distributed in a central symmetry mode, each subunit comprises four variable cross-section rods, and eight variable cross-section rods of the structural cell are fixedly connected at the same node; the diameter of the center of the variable cross-section rod is minimum, the diameters of the two ends of the variable cross-section rod are maximum, and the variable cross-section rod is in smooth transition. Aiming at the traditional BCC structure, the invention provides the EBCC structure with optimal design based on the equal strength theory under the bending combination deformation, and compared with the traditional BCC structure, the EBCC structure has higher elastic modulus, yield strength and energy absorption, effectively improves the stress concentration problem at the node and improves the bearing capacity of the structure.
Description
Technical Field
The invention belongs to the field of light energy absorption structures, and particularly relates to a body-centered cubic lattice structure and a method for calculating the diameter of a variable cross-section rod thereof.
Background
Lightweight design and manufacture are a permanent subject pursued by high-end equipment such as aerospace, aviation, weapons, engineering machinery and the like. The BCC lattice structure (body centered cubic lattice structure) is used as a novel light high-strength energy-absorbing structure, has high symmetry of geometric structure, good mechanical property and energy-absorbing property, and is widely applied to the fields of light design, aerospace, biomedical treatment, automobile ships and the like.
However, the conventional BCC lattice structure has the disadvantages of stress concentration at the nodes, easy fracture failure, uneven stress, etc., which may result in a reduction of the structural load-bearing capacity. Therefore, there is a need to optimally design the BCC lattice structure cell to solve this problem.
Disclosure of Invention
In order to solve the technical problems, the invention provides a body-centered cubic lattice structure and a method for calculating the diameter of a variable cross-section rod thereof, and aims to solve or improve at least one of the technical problems.
To achieve the above object, in one aspect, the present invention provides a body centered cubic lattice structure (denominated EBCC lattice structure) comprising a plurality of structural cells arranged in a periodic array; the structural cell comprises two subunits, the two subunits are distributed in a central symmetry mode, each subunit comprises four variable cross-section rods, and eight variable cross-section rods of the structural cell are fixedly connected at the same node; the diameter of the center of the variable cross-section rod is minimum, the diameters of the two ends of the variable cross-section rod are maximum, and the variable cross-section rod is in smooth transition.
Preferably, the method comprises the steps of, the lattice structure is formed by periodically arranging 5 multiplied by 5 structural cells.
Preferably, the terminal connection lines of the four variable-section bars on the same subunit are square.
Preferably, the cross section of the variable cross section rod is circular.
Preferably, the diameter at any point on the variable cross-section bar may be determined byCalculated, where d 0 And x is the distance from any point to the center of the variable cross-section rod, and θ is the included angle between the variable cross-section rod and the horizontal plane.
Compared with the prior art, the invention has the following advantages and technical effects:
according to the high-strength body-centered cubic lattice structure, the structural stress distribution under the compression load is used for optimally designing the rod pieces of the structural cells, so that the problem of stress concentration at the joints is solved, the elastic modulus, the yield strength and the energy absorption of the structure are improved under the condition of the same quality, and the bearing capacity of the structure is effectively improved.
In another aspect, the present invention also provides a method for calculating a diameter of a variable cross-section rod in a body-centered cubic lattice structure, where the method is applied to any one of the above body-centered cubic lattice structures, and the method includes:
taking 1/4 structural cells near the nodes of any node area as an analysis unit, simplifying the analysis unit into a cantilever beam structure for stress analysis;
assuming that the vertical compression load is F, each variable cross section rod in the analysis unit bears an axial force F x And tangential force F y The included angle between the variable cross section rod and the bottom surface is theta; decomposing the load F, the axial force and the tangential force borne by the variable cross-section rod are respectively as follows:
based on the equal strength theory under the bending combination deformation, the stress sigma of the variable cross-section rod can be expressed as:
wherein A (x) is the cross-sectional area at x,
m (x) is the bending moment at x, M (x) =F y x；
W z (x) The bending resistance section coefficient of the round section is that
And (3) finishing to obtain:
the stress value at any x is equal to the allowable stress value of the parent material, i.e. sigma (x) =sigma max ＝[σ]The following steps are:
wherein l is 1/2 of the length of the variable cross-section rod, d 0 D is the diameter of the center of the variable cross-section rod 1 Is the diameter of the node of the variable cross-section rod;
when x=0, it is possible to obtainSubstituting it into σ (x) =σ max ＝[σ]The method can obtain:
further, the functional relation of the diameter d of the variable cross-section rod with respect to x is obtained as follows:
the functional relation is a calculation formula of the diameter of the variable cross-section rod in the body-centered cubic lattice structure.
The invention applies the equal strength theory under the bending combination deformation to the optimal design of the BCC structure to obtain the rod diameter calculation formula of the structural cells. Compared with the previous experience design, the equal strength theory provides corresponding theoretical support for the optimal design of the structure. Under the condition of the same mass, the elastic modulus, the yield strength, the energy absorption and other mechanical properties of the structure are improved, the bearing capacity of the structure is effectively improved, and the composite material can be widely applied to bearing structures such as light design, aerospace, automobiles, ships and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a body centered cubic lattice structure according to the present invention;
FIG. 2 is a schematic diagram of a cell of the structure of FIG. 1;
FIG. 3a is a diagram illustrating a stress analysis of a conventional BCC lattice structure under a compressive load;
FIG. 3b is a schematic diagram illustrating stress analysis of an arbitrary node region of a conventional BCC lattice structure;
FIG. 3c is a schematic diagram illustrating a force analysis of an arbitrary rod at a node of a conventional BCC lattice structure;
FIG. 4a is a stress cloud of a conventional BCC lattice structure during axial compression;
FIG. 4b is a stress cloud of the structure of the body centered cubic lattice structure of the present invention during axial compression;
fig. 5 is a compressive stress-strain curve of the body centered cubic lattice structure before and after modification.
Wherein: 1. a structural cell; 2. a subunit; 3. a variable cross-section rod.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1:
the body centered cubic lattice structure of the present invention is described below with reference to fig. 1 to 5.
Under the action of compression load, the traditional BCC lattice structure has the phenomena of stress concentration, uneven stress and the like at the node, the node is easy to damage and lose efficacy, and the stress at the edge of the rod piece is smaller, so that the quality waste exists. If a novel BCC lattice structure can be designed, the structural rod pieces can bear the stress with the same size everywhere, so that the cost is saved, and meanwhile, the bearing capacity of the lattice structure can be effectively improved.
Referring to fig. 1, fig. 1 shows a schematic structure of a body-centered cubic lattice structure of embodiment 1 of the present invention, the structure comprises a plurality of structure cells 1, and can be formed by periodically arranging 5 multiplied by 5 structure cells 1; the structural cell 1 comprises two subunits 2, wherein the two subunits 2 are distributed in a central symmetry manner, each subunit 2 comprises four variable cross-section rods 3, and the eight variable cross-section rods 3 are fixedly connected at the same node; the diameter of the center of the variable cross section rod 3 is minimum, the diameter of the rod gradually increases from the center to the nodes at two ends, the rod is in smooth transition, and the cross section of the variable cross section rod 3 is circular; wherein the connecting lines of the tail ends of the four variable cross-section rods 3 on the same subunit 2 are square.
Further, the diameter at any point on the variable cross-section bar 3 can be calculated by the formula one;
equation one:
wherein d 0 The diameter of the center of the variable cross-section rod is x, the distance from the point to the center of the variable cross-section rod (3), and theta, the included angle between the variable cross-section rod (3) and the horizontal plane.
In order to derive the formula one, the present invention also provides another embodiment, and details of the embodiment 2 are described in detail.
Example 2:
the method for calculating the diameter of the variable cross-section rod in the body-centered cubic lattice structure according to the present invention will be described with reference to fig. 3a to 3 c.
The embodiment 2 of the invention provides a method for calculating the diameter of a variable cross-section rod in a body-centered cubic lattice structure, which is applied to the body-centered cubic lattice structure of the embodiment 1, and comprises the following steps:
as shown in fig. 3a, the BCC lattice structure is selected as the original model; the bottom surface of the structural cell 1 has the size of L multiplied by L and the height of H, and the bottom surface of the structure adopts fixed constraint; when the BCC lattice structure is subjected to an axial compressive load, each node is subjected to the same load, and any node area S may be taken for analysis, as shown in fig. 3 b. Because the structure has geometric symmetry, 1/4 of any branch structure cell 1 near the node is taken as an analysis unit, and the analysis unit is simplified into a cantilever structure for stress analysis, as shown in figure 3 c.
Assuming a vertical compressive load F, each rod is subjected to an axial force F x And tangential force F y The included angle between the variable cross section rod 3 and the bottom surface is theta. When the acting load F is decomposed, the axial force and the tangential force born by the rod piece are respectively as follows:
based on the equal strength theory under the press bending combined deformation, the stress σ of the variable cross-section rod 3 can be expressed as:
wherein A (x) is the cross-sectional area at x,m (x) is the bending moment at x, M (x) =F y x，W z (x) The bending resistance of the circular section is +.>And (3) finishing to obtain:
the stress value at any x is equal to the allowable stress value of the parent material, i.e. sigma (x) =sigma max ＝[σ]The following steps are:
wherein l is 1/2 of the length of the variable cross-section rod 3, d 0 Is the initial diameter (diameter at the center of the rod), d 1 Is the largest diameter (diameter at the node).
When x=0, it is possible to obtainSubstituting it into σ (x) =σ max ＝[σ]The method can obtain:
and then the functional relation of the rod diameter d with respect to x is obtained as follows:
the diameter formula of the variable cross section rod 3 in the body-centered cubic lattice structure is the above formula.
The specific implementation and verification steps of the body-centered cubic lattice structure (EBCC lattice structure) of the invention are as follows:
s1, calculating the diameter of a variable cross section rod 3 according to a calculation formula of the diameter of the variable cross section rod 3, drawing a longitudinal section curve of the variable cross section rod 3 from the center to a node in CAD software, mirroring the longitudinal section curve of the variable cross section rod 3 according to symmetry characteristics of a structure, adding a round angle of R=3mm in the center for transition, rotating and stretching to generate the variable cross section rod 3, and filling the variable cross section rod 3 into a cube to generate a structural cell 1;
s2, generating a 5 multiplied by 5 lattice structure in the x, y and z directions respectively;
and S3, performing grid division by using Hypermesh software, and importing the model into Ls-Dyna software to perform quasi-static compression simulation verification.
The embodiment designs a group of examples for compression experiment simulation verification, wherein:
comparison example: the pre-modified BCC lattice structure (conventional BCC lattice structure);
example 1: an improved EBCC lattice structure (an improved body-centered cubic lattice energy absorbing structure);
the comparative examples contained a comparative model prior to modification of the same volume as example 1, the number of the cells is 5 multiplied by 5; wherein the initial diameter d of the BCC lattice variable cross-section rod 3 of example 1 (modified EBCC lattice structure) 0 The diameter of the BCC lattice variable cross-section rod of the comparison example (BCC lattice structure before modification) is 0.3mm and 1.025mm; the overall dimensions of the lattice structure are 30mm multiplied by 30mm, the material is 316L stainless steel, the elastic modulus is 67GPa, the yield strength is 551.63MPa, and the Poisson ratio is 0.3.
Fig. 4a and fig. 4b show the compressive stress distribution of the two, respectively, and it can be observed that the stress distribution of the BCC lattice structure is uneven before modification, the stress concentration phenomenon exists at the node, and the stress at the midpoint of the rod is smaller. The improved body-centered cubic lattice energy absorbing structure has larger stress at the center of the variable cross-section rod 3, the overall stress distribution of the structure is more uniform, and the stress concentration at the node is effectively improved.
FIG. 5 is a compressive stress-strain curve of the BCC lattice structure before and after modification, and the gray scale region of FIG. 5 shows the equivalent stress by color change, which is only a comparative illustration of one implementation effect, and does not constitute a limitation or reference to the structure of the embodiment of the present invention. And the observation shows that the initial line elastic stage of the improved EBCC lattice structure is steeper, the stress of the platform stage is higher, and the densification stage is reached faster. Under the same strain, the stress of the improved EBCC lattice structure is improved compared with that of the BCC lattice structure before improvement.
Table 1 shows the mechanical properties of the improved front and rear BCC lattice structures under compression. Under the condition of the same quality, compared with the traditional BCC lattice structure before improvement, the elastic modulus, the yield strength and the energy absorption of the EBCC lattice structure after improvement are respectively improved by 61.80%, 53.72% and 11.89%. The equal-strength design effectively improves the bearing capacity and the energy absorption characteristic of the structure, and provides a new idea for the design optimization of the light high-strength structure.
TABLE 1
The present invention is not limited to the conventional technical means known to those skilled in the art.
In the description of the present invention, it should be understood that the terms "longitudinal," "transverse," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like indicate or are based on the orientation or positional relationship shown in the drawings, merely to facilitate description of the present invention, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus should not be construed as limiting the present invention.
The above embodiments are only illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solutions of the present invention should fall within the protection scope defined by the claims of the present invention without departing from the design spirit of the present invention.
Claims (6)
1. A body centered cubic lattice structure, characterized in that the lattice structure comprises a plurality of structural cells (1), the plurality of structural cells (1) being arranged in a periodic array; the structure cell (1) comprises two subunits (2), wherein the two subunits (2) are distributed in a central symmetry mode, each subunit (2) comprises four variable cross-section rods (3), and the eight variable cross-section rods (3) of the structure cell (1) are fixedly connected at the same node; the diameter of the center of the variable cross-section rod (3) is minimum, the diameters of the two ends of the variable cross-section rod are maximum, and the variable cross-section rod is in smooth transition.
2. A body centred cubic lattice structure according to claim 1, wherein the lattice structure is formed by a periodic array of 5 x 5 cells (1) of the structure.
3. A body centred cubic lattice structure according to claim 2, wherein the end connections of four variable cross-section bars (3) on the same subunit (2) are square.
4. A body centred cubic lattice structure according to claim 1, wherein the variable cross section rods (3) are circular in cross section.
5. A body centred cubic lattice structure according to claim 4, wherein the diameter at any point on the variable cross-section bar (3) can be defined by d 3 (x)-d 0 2 d(x)＝8cotθd 0 2 x is calculated, wherein d 0 And x is the distance from any point to the center of the variable cross-section rod (3), and θ is the included angle between the variable cross-section rod (3) and the horizontal plane.
6. A method of calculating a diameter of a variable cross-section rod in a body-centered cubic lattice structure, the method being applied to the body-centered cubic lattice structure as claimed in any one of claims 1 to 5, the method comprising:
taking 1/4 of structural cells (1) near any node area node as an analysis unit, simplifying the structural cells into a cantilever beam structure, and carrying out stress analysis; assuming that the vertical compression load is F, each variable cross section rod (3) in the analysis unit bears an axial force F x And tangential force F y The included angle between the variable cross section rod (3) and the bottom surface is theta; the load F is decomposed, and then the axial force and the tangential force borne by the variable cross-section rod (3) are respectively as follows:
based on the equal strength theory under the bending combination deformation, the stress sigma of the variable cross-section rod (3) can be expressed as:
wherein A (x) is the cross-sectional area at x,
m (x) is the bending moment at x, M (x) =F y x；
W z (x) The bending resistance section coefficient of the round section is that
And (3) finishing to obtain:
let stress at arbitrary xThe value being equal to the allowable stress value of the parent material, i.e. sigma (x) =sigma max ＝[σ]The following steps are:
wherein l is 1/2 of the length of the variable cross section rod (3), d 0 Is the diameter d of the center of the variable cross-section rod (3) 1 Is the diameter of the node of the variable cross-section rod (3);
when x=0, it is possible to obtainSubstituting it into σ (x) =σ max ＝[σ]The method can obtain:
further, the functional relation of the diameter d of the variable cross-section rod (3) with respect to x is obtained as follows:
the functional relation is a calculation formula of the diameter of the variable cross-section rod (3) in the body-centered cubic lattice structure.
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