Modeling method for lattice structure under tension and compression load conditions and derived lattice structures thereof

Abstract

The application provides a lattice structure modeling method under tensile and compressive load conditions and a derived lattice structure, and realizes lattice structure design under tensile and compressive load conditions. The method comprises the following steps: designing an original solid cell structure; performing generative topological optimization on the original solid cell to obtain a lattice topological configuration under multi-directional uniform tensile load and unidirectional dominant tensile load conditions; reconstructing the lattice structure obtained by the generative topological optimization; evaluating the manufacturability of the reconstructed lattice structure; performing derivative design on the reconstructed lattice structure to improve the manufacturability and bearing capacity thereof; and after the design is completed, preparing a corresponding lattice structure and performing performance testing. The application designs a lattice structure under tensile and compressive load conditions, and reduces the performance difference between the actual manufacturing structure and the design structure through structural adjustment, so that the obtained lattice structure has higher lightweight degree, specific stiffness and specific strength, and can be widely used in the fields of automobiles, aerospace and the like.

Description

Technical Field

[0001] This invention relates to the field of lightweight structural design, and in particular to a method for modeling lattice structures under tensile and compressive loads and its derived lattice structures. Background Technology

[0002] In the aerospace field, lightweighting of high-end transportation equipment can not only improve carrying capacity and reduce energy consumption, but also create more value. Lattice structures are spatial network structures formed by the periodic combination of basic units. They possess excellent characteristics such as high lightweighting, high specific strength, large specific surface area, and good specific energy absorption performance, and are used in aircraft load-bearing components, satellite supports, aerospace heat exchangers, and protective and shock-absorbing devices. Currently, the most widely studied lattice structure types include body-centered cubic structures, face-centered cubic structures, and rhombic dodecahedrons. However, many lattice structures still lack selection standards in practical applications, making it difficult to achieve function-oriented lattice structure design and application. Generative modeling is a lightweight structural design method that combines CAD structural design, smoothing topology optimization algorithms, and CAE simulation analysis. It can mimic the natural evolutionary process, based on the designer's optimization goals such as lightweighting and design rules such as loading methods, dimensional constraints, and stress constraints, to find the optimal material distribution within a given design space, thereby obtaining the best lightweight structural design scheme.

[0003] Traditional processing methods, such as stamping and three-dimensional weaving, produce limited types of lattice structures with simple structures, often failing to meet required mechanical properties. Additive manufacturing, as an advanced manufacturing technology, breaks through the limitations of traditional manufacturing techniques, granting designers greater design freedom and becoming the preferred process for fabricating lattice structures. However, when forming lattice structures using additive manufacturing techniques such as selective laser melting, if the angle between the slender rod and the horizontal plane is less than 40 degrees, the fabricated lattice structure suffers from poor dimensional accuracy, high surface roughness, and may even fail to form a complete structure. Excessive structural defects can also cause its mechanical properties to fall far below design values. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for modeling lattice structures under tensile and compressive loads and its derived lattice structures. The method adopts a generative topology optimization method to obtain the optimal material distribution of the original solid unit cell under two load conditions: multi-directional uniform tension and unidirectional dominant tension. The topology structure obtained by generative design is reconstructed to obtain a lattice structure with uniform structural distribution and few characteristic defects.

[0005] To address the above problems, this invention provides a method for modeling lattice structures under tensile and compressive load conditions, comprising the following steps:

[0006] S1. Use CAD software to design the original solid unit cell. The geometric structure of the original solid unit cell includes triangular prism, quadrangular prism and rhombic dodecahedron. The shape parameters of the original solid unit cell include side length and angle dimensions.

[0007] S2. Generative topology optimization with stress constraints is performed on the original solid unit cell. The mathematical model of generative topology optimization with stress constraints is expressed as follows:

[0008]

[0009] In the formula, t is the element topology design variable vector, N represents the number of element topology design variables, M is the total mass of the solid unit cell, and f m (t i ) is the unit quality filtering function. For the inherent mass of the element, σ ih Let f be the Von Mises stress of element i under operating condition h. σ (t i ) represents the element stress filtering function. The constraint stress is H, which represents the total number of working conditions.

[0010] Among them, f m (t i ) and f σ (t i The filtering function is in exponential form, i.e.:

[0011] f m (t i )=t i α

[0012] f σ (t i )=t i γ

[0013] In the formula, α and γ are constants;

[0014] S21. Import the original solid unit cell into the generative topology optimization system and define the material properties;

[0015] S22. Determine the applicable working condition h for the lattice unit cell, and apply loads and constraints.

[0016] S23. Set the loading and constraint locations to non-design space;

[0017] S24. Determine the constraint stress values ​​for generative topology optimization. Set generative topology optimization elements, including pillar density level and complexity, and perform model iterative calculations;

[0018] S3. The lattice structure obtained by generative topology optimization is reconstructed using methods including skeleton line reconstruction, surface model reconstruction, and volume invariance principle reconstruction.

[0019] S31. Extract skeleton lines based on the topology optimization model;

[0020] S32. Assign cross-sectional features to the skeleton lines to obtain the reconstructed model of the rod-shaped lattice structure. The cross-sectional shape includes circles and polygons, and the cross-sectional dimensions include uniform cross-sectional dimensions and variable gradient cross-sectional dimensions.

[0021] S4. Determine the manufacturability of the lattice structure;

[0022] When additive manufacturing is used to form a rod-shaped lattice structure with a circular cross-section, the area overlap ratio R between the nth and (n+1)th layer slices is introduced. A And let R A Greater than 95%, of which:

[0023]

[0024] In the formula, β is the inclination angle of the rod, d is the diameter of the rod, and t is the diameter of the rod. s Let A(β,d,t) be the slice layer thickness. s ) represents the overlap area between the nth and (n+1)th slice layers;

[0025] Where A(β,d,t) s () is about β, d, and t s Functions:

[0026]

[0027] S5. Perform derivative design on the reconstructed lattice structure;

[0028] S51, Perform derivative replacement of rod elements;

[0029] S52. Add connecting rods to enhance the connectivity between free rods and establish a lattice structure model for tensile and compressive load conditions.

[0030] Furthermore, the material properties mentioned in step S21 include density ρ s Elastic modulus E s Poisson's ratio μ and yield strength σ S .

[0031] Furthermore, in step S22, the applicable working conditions for the lattice unit cell include multi-directional uniform tension and unidirectional dominant tension. The loading position is the vertex of the original solid unit cell, and the constraint position is the centroid of the unit cell. Under the multi-directional uniform tension load condition, a constraint stress gradient is set, and the influence of different constraint stress values ​​on the optimization results of the lattice structure is analyzed. Under the unidirectional dominant tension load condition, a unidirectional dominant load gradient is set, and the influence of different unidirectional dominant load magnitudes on the optimization results of the lattice structure is analyzed.

[0032] Preferably, in step S5, parallel diagonals and cross diagonals are introduced into the member derivative design, and the connectivity between the free members of the lattice structure is increased by adding horizontal short members and members parallel to the bearing direction.

[0033] Preferably, the performance characteristics of the lattice structure before and after optimization are verified through experimental verification steps. The verification parameters for these experimental verification steps include:

[0034] Specific stiffness:

[0035] In the formula, E is the elastic modulus of the lattice structure. The relative density of the lattice structure;

[0036] Specific strength:

[0037] In the formula, σ' s The yield strength of the lattice structure;

[0038] Energy absorption:

[0039] In the formula, ε0 is the energy absorption cutoff strain;

[0040] Specific energy absorption:

[0041] In the formula, ρ s denoted as the density of the matrix material of the lattice structure.

[0042] In a second aspect, the present invention provides a BCC-derived lattice structure, comprising a parallel body-centered cubic lattice structure P-BCC and a cross-body-centered cubic lattice structure C-BCC; wherein the body diagonal direction of the parallel body-centered cubic lattice structure P-BCC is a set of mutually parallel rods; and the body diagonal direction of the cross-body-centered cubic lattice structure C-BCC is a set of mutually intersecting rods.

[0043] Furthermore, a BCC-derived lattice structure includes P-BCCXY and C-BCCXY lattice structures; the P-BCCXY and C-BCCXY lattice structures are respectively based on the P-BCC and C-BCC lattice structures by adding horizontal short rods to connect free nodes, thereby improving the connectivity between free rods and increasing the stiffness and strength of the lattice structure.

[0044] Furthermore, a BCCZ-derived lattice structure includes P-BCCXYZ and C-BCCXYZ lattice structures. The P-BCCXYZ and C-BCCXYZ lattice structures respectively add rods parallel to the dominant force direction Z on the basis of the P-BCCXY and C-BCCXY lattice structures, thereby enhancing the load-bearing capacity in the dominant force direction.

[0045] Compared with existing technologies, the technical effects of this solution are as follows:

[0046] 1. This invention adopts generative topology optimization technology and proposes a modeling method for lattice structures under tensile and compressive load conditions. It provides the material distribution forms of lattice structures under two load conditions: multi-directional uniform tension and unidirectional dominant tension. It also gives the influence law of constraint stress and dominant load on the topology optimization results for lattice structure designers to refer to.

[0047] 2. The topology optimization lattice structure reconstruction method proposed in this invention includes reconstruction based on skeleton lines, reconstruction based on surface models, and reconstruction based on the principle of volume invariance, so that the reverse reconstruction of topology optimization results is based on evidence.

[0048] 3. Based on the reconstructed lattice structure, this invention introduces parallel diagonals and intersecting diagonals into the rod replacement derivative design of the lattice structure, which not only increases the manufacturability of the lattice structure, but also improves its load-bearing performance.

[0049] 4. This invention improves the load-bearing capacity of the lattice structure by increasing the connectivity between the members, especially the connecting members along the dominant force direction, which significantly increase the elastic modulus of the lattice structure. Under the same compression conditions, the mechanical properties of the derived structure proposed in this invention are significantly improved compared to the original lattice structure, providing a good design solution for improving the mechanical properties of existing lattice structures. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method for modeling lattice structures under tensile and compressive loads according to the present invention;

[0051] Figure 2a This is a schematic diagram of the loading method of the original solid unit cell and the non-designed space division under triaxial uniform tension conditions;

[0052] Figure 2bThis is a schematic diagram of the loading method of the original solid unit cell and the non-design space division under unidirectional dominant tension conditions;

[0053] Figure 3 A schematic diagram of the topology optimization process with a constraint stress of 110 MPa under triaxial uniform force.

[0054] Figure 4a A schematic diagram of the skeleton lines of the BCC lattice structure;

[0055] Figure 4b A schematic diagram of the skeleton lines of the BCCZ lattice structure;

[0056] Figure 5a A schematic diagram of the reconstructed rod-shaped lattice structure BCC;

[0057] Figure 5b A schematic diagram of the reconstructed rod-shaped lattice structure BCCZ;

[0058] Figure 6a This is a schematic diagram illustrating the replacement of the BCC lattice structure with the P-BCC lattice structure.

[0059] Figure 6b This is a schematic diagram illustrating the replacement of the BCC lattice structure with the C-BCC lattice structure.

[0060] Figure 7a This is a schematic diagram illustrating the design of the P-BCC lattice structure to the P-BCCXY lattice structure.

[0061] Figure 7b This is a schematic diagram illustrating the design of the C-BCC lattice structure to the C-BCCXY lattice structure.

[0062] Figure 8a This is a schematic diagram illustrating the design of the P-BCCXY lattice structure to the P-BCCXYZ lattice structure.

[0063] Figure 8b This is a schematic diagram illustrating the design of the C-BCCXY lattice structure to the C-BCCXYZ lattice structure.

[0064] Figure 9 A comparison of stress-strain curves for BCC, P-BCC, and C-BCC lattice structures with the Z-direction as the compression direction;

[0065] Figure 10 A comparison of stress-strain curves for BCC, P-BCCXY, and C-BCCXY lattice structures with the Z-direction as the compression direction.

[0066] Figure 11 A comparison of stress-strain curves for BCCZ, P-BCCXYZ, and C-BCCXYZ lattice structures with the Z-direction as the compression direction. Detailed Implementation

[0067] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention; various substitutions are permitted within the scope of protection of the present invention without departing from its design concept.

[0068] Down Figure 1 This invention discloses a method for modeling lattice structures under tensile and compressive loads, which includes the following steps:

[0069] S1. Define the original solid unit cell as a cube with a side length of 6mm, and use Solidworks 3D modeling software to create the original unit cell model and save it in .sat format.

[0070] S2. Generative topology optimization with stress constraints is performed on the original solid unit cell. The mathematical model is expressed as follows:

[0071]

[0072] In the formula, t is the element topology design variable vector, N represents the number of element topology design variables, M is the total mass of the solid unit cell, and f m (t i ) is the unit quality filtering function. For the inherent mass of the element, σ ih Let f be the Von Mises stress of element i under operating condition h. σ (t i ) represents the allowable stress filtering function for the element. The constraint stress is H, which represents the total number of working conditions.

[0073] Among them, f m (t i ) and f σ (t i The filtering function is in exponential form, i.e.:

[0074] f m (t i )=t i α

[0075] f σ (t i )=t i γ

[0076] In the formula, α and γ are constants, determined by the structure itself.

[0077] Generative topology optimization specifically includes the following steps:

[0078] S21. Import the original solid unit cell model into generative structural lightweight design software. Whether the lattice structure can meet service characteristics largely depends on the base material, and lightweight requirements and machinability must be comprehensively considered. The base material selected here is additively manufactured aluminum alloy AlSi10Mg with a density ρ. s 2.7×10 -6 kg / mm 3 Elastic modulus E s The strength is 68 GPa, Poisson's ratio μ is 0.3, and the yield strength σ is... S The pressure is 165 MPa.

[0079] S22. Determine the applicable working condition h for the lattice unit cell, and apply the load and constraints. For example... Figure 2a As shown, under a triaxial uniform tensile load, the force at each loading position has equal components in the X, Y, and Z directions. The loading positions of the original cube unit cell are at the eight vertices, and the tensile force at each loading position has 5N components in the X, Y, and Z directions. The translational degrees of freedom of the center of mass of the original cube unit cell in the X, Y, and Z directions are constrained.

[0080] like Figure 2b As shown, under unidirectional dominant tensile load conditions, the tensile force at each loading position has equal components in the X and Y directions, while the component in the Z direction is greater than that in the X and Y directions. The loading positions of the original cube unit cell are at its eight vertices. The tensile force at each loading position has a component of 5N in the X and Y directions, and a component greater than 5N in the Z direction. The translational degrees of freedom of the centroid of the original cube unit cell in the X, Y, and Z directions are constrained. This invention analyzes the influence of different unidirectional dominant load magnitudes on the optimization results of the lattice structure by setting unidirectional dominant load gradients, i.e., the component force along the Z direction is 10N, 15N, 20N, and 25N respectively.

[0081] S23. Set the loading and constraint locations as non-design spaces. These non-design spaces will be frozen during optimization, and the material will not be removed. The geometry of the non-design spaces largely determines the minimum geometric features of the lattice structure; therefore, the minimum forming size of additive manufacturing must be considered when determining the dimensions of the non-design spaces. Here, the eight loading locations 1 and one constraint location 2 in the original cubic unit cell model are set as non-design spaces. The minimum rod diameter for rod-shaped structures formed by laser selective melting should not be less than 0.5 mm; therefore, each non-design space is a cube with a side length of 0.5 mm.

[0082] S24. Determine the constraint stress values ​​for generative topology optimization. Generative topology optimization elements are set, including support density level and complexity, and iterative model calculations are performed. Constraint stress can be determined based on the stress level of the original components for which lightweight design is required, or based on the properties of the selected parent material. In practical applications, we want the lattice structure to be in the elastic stage; therefore, the stress in the lattice structure must not exceed the yield limit, otherwise plastic deformation will occur. Under triaxial uniform tensile loading, constraint stress gradients are set using the ratio of the yield strength of AlSi10Mg (165 MPa) to safety factors (1.5, 3, 6, 12), corresponding to the constraint stresses... The effects of different constraint stresses on the optimization results of the lattice structure were analyzed at 110 MPa, 55 MPa, 27 MPa, and 13.75 MPa, respectively. Under uniaxial dominant tensile load conditions, the constraint stress was set based on the ratio of the yield strength of AlSi10Mg to the safety factor of 3. That is, 55 MPa.

[0083] In generative design systems, the support density levels—sparse, medium, and dense—determine the stiffness of the topology optimization results to a certain extent. Complexity refers to the amount of computer memory used during generative design analysis; it needs to be set appropriately based on the computer's performance and the support density of the model. Generally, the denser the supports, the more computational memory is required, and the more complex the optimized model structure. Considering computer processing power, a medium support density and a complexity of 8 are uniformly chosen for generative topology optimization schemes.

[0084] Figure 3 This describes the topology optimization process under triaxial uniform stress with a constraint stress of 110 MPa. It can be seen that as the number of iterations increases, the mass of the lattice structure decreases, and the overall stress level gradually approaches the constraint value.

[0085] Table 1 shows the optimization results of the lattice structure under different constraint stresses when subjected to triaxial uniform force. It can be seen that, under the same constraints and loading conditions, the constraint stress affects both the lightweighting of the model and the topological configuration of the lattice structure. The larger the constraint stress value in the generative design, the smaller the mass of the topology optimization model, i.e., the higher the lightweighting level. Under the same constraints and loading conditions, the lattice structure is an FCC structure when the constraint stress is 13.75 MPa and 27 MPa, and a BCC structure when the constraint stress is 55 MPa and 110 MPa. Since the laser selective melting process inevitably results in a long horizontal overhang structure in FCCs, it will not be discussed further.

[0086] Table 1

[0087]

[0088] Table 2 shows the impact of different magnitudes of unidirectional dominant force on the optimization results of the lattice structure under unidirectional dominant force. It can be seen that the topology optimization result under unidirectional dominant force is a BCCZ structure with added reinforcing struts in the dominant force direction to improve the load-bearing capacity in the Z direction. As the force in the Z direction increases, the struts in the Z direction become thicker and gradually shift outwards, and the mass of the lattice structure gradually increases to withstand greater loads. This also illustrates the importance of the Z-direction struts when bearing unidirectional forces.

[0089] Table 2

[0090]

[0091] S3. Reconstruct the lattice structure obtained by generative topology optimization. Model reconstruction methods include skeleton model-based reconstruction, surface model-based reconstruction, and volume-invariant principle-based reconstruction. Skeleton model-based reconstruction is fast and efficient, and the parameters of the resulting rod-shaped lattice structure are easy to adjust, and its mechanical properties are easy to control.

[0092] Model reconstruction specifically includes the following steps:

[0093] S31. Based on the topology optimization model, extract the skeleton lines. The generative topology optimization results show that the lattice structure skeleton features obtained under both loading conditions are obvious, facilitating skeleton line extraction. (See also...) Figure 4a When subjected to uniform force in three directions, the skeleton lines connect from the center of mass 3 of the cube to vertices 4-11, which is the skeleton line of a traditional BCC lattice structure; see reference. Figure 4b When the force is unidirectional, skeleton lines 48, 59, 610 and 711 are added parallel to the direction of the dominant force, which are the skeleton lines of the traditional BCCZ lattice structure.

[0094] S32. Assign cross-sectional features to the skeleton lines to obtain the reconstructed model of the rod-shaped lattice structure. Cross-sectional shapes include, but are not limited to, circles and polygons; cross-sectional dimensions can be uniform or have varying gradients. See also... Figure 5a By assigning a uniform circular cross-section to the skeleton lines of the BCC lattice structure, a rod-shaped BCC lattice structure is obtained, with the inclined rod 12 having a cross-sectional diameter of 0.8 mm; see reference. Figure 5b By assigning a uniform circular cross section to the skeleton line of the BCCZ lattice structure, a rod-shaped BCCZ lattice structure is obtained. The diameter of the cross section of the inclined rod 12 is 0.8 mm, and the diameter of the cross section of the rod 13 in the Z direction is 0.6 mm.

[0095] S4. Evaluate the manufacturability of the lattice structure in conjunction with the characteristics of additive manufacturing processes. In the reconstructed BCC and BCCZ lattice structures, the angle between the tilted rod 12 and the horizontal plane is less than 40°. When the powder layer thickness of the laser selective melting process is 0.03 mm, the area overlap ratio R between the nth and (n+1)th layers is... AIf the accuracy is less than 95%, the stepped effect on the surface of the formed rod will be very obvious, so the rod structure needs further improvement.

[0096] S5. Perform derivative designs on the reconstructed lattice structure to improve its manufacturability and load-bearing capacity.

[0097] S51. The rod 12 of the reconstructed lattice structure is replaced using derivative methods. (See attached document) Figure 6a By incorporating the parallel diagonals of deep-sea glass sponges into the rod replacement process, the body diagonal rod 12 of the BCC is replaced with a set of parallel rods 14, resulting in a derived parallel body-centered cubic lattice structure (P-BCC); see reference Figure 6b By replacing the body diagonal member 12 of BCC with a set of intersecting members 15, a derived design of intersecting body-centered cubic lattice structure (C-BCC) is obtained.

[0098] Furthermore, the rods 14 of P-BCC and C-BCC are respectively connected to the edges of the outer envelope cube of the lattice structure. The side length of the cube is one. A shape factor a is introduced to represent the position of the rod connection point from the vertex of the outer envelope cube. The shape factor a of both P-BCC and C-BCC lattice structures is 1 / 4.

[0099] Furthermore, compared to BCC, the number of members in the derived designs P-BCC and C-BCC increases several times. In order not to change the overall mass of the lattice structure, the cross-sectional diameter of member 14 in P-BCC and member 15 in C-BCC is reduced accordingly to 0.6mm.

[0100] Furthermore, the angle between rods 14 and 15 and the horizontal plane is increased (greater than 40°) after the derivative design, and the material distribution in the load-bearing direction is increased, which can improve the quality of additive manufacturing and enhance the load-bearing capacity in the Z direction.

[0101] S52. Add connecting members to enhance the connectivity of the members. See also Figure 7a By adding a horizontal short rod 16 to improve the connectivity between the free members of the P-BCC lattice structure, the stiffness and strength of the lattice structure are increased, resulting in the P-BCCXY lattice structure. The horizontal short rod 16 has a cross-sectional diameter of 0.6 mm. (See reference...) Figure 7b By adding short rod 17 to improve the connectivity between the free members of the C-BCC lattice structure, the stiffness and strength of the lattice structure are increased, resulting in a C-BCCXY lattice structure. The short rod 17 has a cross-sectional diameter of 0.6 mm. (See reference...) Figure 8a Add a member 18 parallel to the dominant force direction Z to connect the corresponding nodes of P-BCCXY, thereby enhancing the load-bearing capacity in the dominant force direction, resulting in the P-BCCXYZ lattice structure. The cross-sectional diameter of member 18 is 0.6 mm. (See reference...) Figure 8b Add a member 19 parallel to the dominant force direction Z to connect the corresponding nodes of C-BCCXY to enhance the bearing capacity in the dominant force direction, thus obtaining the C-BCCXYZ lattice structure. The cross-sectional diameter of member 19 is 0.6mm.

[0102] Based on the above design, lattice structure samples were prepared, and the lattice structures were experimentally verified. A laser selective melting process was used to prepare lattice structures with AlSi10Mg as the parent material, including eight lattice structures: BCC, BCCZ, P-BCC, C-BCC, P-BCCXY, C-BCCXY, P-BCCXYZ, and C-BCCXYZ. The prepared lattice samples had a unit cell side length of 6 mm, with 5×5×5 unit cells arranged in the X, Y, and Z directions. The overall size of the lattice structure samples was 30 mm × 30 mm × 30 mm. Three samples of each lattice structure were printed for repeated experiments. Quasi-static compressive mechanical property tests were performed along the Z direction on an electronic universal testing machine to obtain the compressive stress-strain curves of the lattice structures, as shown below. Figure 9-11 As shown, the stress-strain curves of all lattice structures exhibit a consistent trend, namely, they can be divided into four stages: elastic deformation stage, plastic yielding stage, stress fluctuation stage, and densification stage. The elastic modulus and yield strength of each lattice structure are obtained from the stress-strain curves, and the corresponding specific stiffness and specific strength are calculated. Table 3 shows the mechanical properties of each lattice structure.

[0103] Table 3

[0104]

[0105]

[0106] As shown in Table 3, compared to the BCC lattice structure, the elastic modulus and yield strength of C-BCC and P-BCC are both more than 30% higher. The addition of horizontal short bars to C-BCCXY and P-BCCXY increases both elastic modulus and yield strength, indicating that the horizontal short bars increase the connectivity between the lattice structure members, thus resulting in greater load-bearing capacity. Considering mass, the specific stiffness of C-BCCXY decreases by 16.43% and the specific strength decreases by 5.10% compared to C-BCC, while the specific stiffness of P-BCCXY increases by 18.44% and the specific strength increases by 5.52% compared to P-BCC, indicating that the mechanical properties of the lattice structure are affected by both mass and topology. The addition of Z-direction struts to P-BCCXYZ and C-BCCXYZ significantly improves both strength and stiffness. Among all lattice structures, P-BCCXYZ has an absolute advantage with a specific stiffness of 1313.71 MPa and a specific strength of 39.95 MPa, exhibiting the best load-bearing capacity.

[0107] In summary, the present invention provides a method for modeling lattice structures under tensile and compressive load conditions, which can realize the design of lattice structures under tensile and compressive load conditions based on actual usage functions. The derived lattice structures exhibit greater specific strength and specific stiffness compared to the BCC and BCCZ lattice structures that are directly reconstructed from the topology optimization results. Among them, the PBCCXYZ lattice structure demonstrates the best load-bearing capacity and is expected to be directly applied to components used under tensile and compressive load conditions, such as satellite supports, bearing supports, and flanges.

[0108] Finally, it should be noted that the above embodiments are for illustration only and not for limiting the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention without departing from the spirit and scope of the present invention. Any modifications or partial substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for modeling lattice structures under tensile and compressive loading conditions, characterized by, It comprises the following steps: S1, using CAD software to design the original entity cell, the geometric structure of the original entity cell includes triangular prism, quadrangular prism and rhombic dodecahedron, the shape parameters of the original entity cell include edge length size and angle size; S2, performing generative topology optimization on the original entity cell with stress as the constraint, the mathematical model of the generative topology optimization with stress as the constraint is represented as: where t is the unit topology design variable vector, N represents the number of unit topology design variables, M is the total mass of the solid unit, f m (t i ) is the unit mass filter function, is the unit inherent mass, σ ih is the Von Mises stress of the unit i at the working condition h, f σ (t i ) is the unit stress filter function, is the constraint stress, and H is the total number of working conditions. where f m (t i ) and f σ (t i ) are filter functions in exponential form, i.e.: f m (t i )=t i α f σ (t i )=t i γ In the formula, α and γ are constants; S21, importing the original entity cell into the generative topology optimization system, and defining the material properties; S22, determining the applicable working condition h of the lattice cell, and applying the load and constraint conditions; S23, setting the loading and constraint positions as non-design space; S24, determining the constraint stress value of the generative topology optimization Setting generative topology optimization elements, including support density levels and complexity, performing model iteration operations; S3, using the methods including reconstruction based on skeleton line, reconstruction based on curved surface model and reconstruction based on volume invariance principle to reconstruct the lattice structure obtained by the generative topology optimization; S31, extracting the skeleton line based on the topology optimization model; S32, giving the skeleton line a cross-sectional feature to obtain a rod-shaped lattice structure reconstruction model, the cross-sectional shape includes a circle and a polygon, and the cross-sectional size includes a uniform cross-sectional size and a variable gradient cross-sectional size; S4, determining the manufacturability of the lattice structure; When the additive manufacturing is used to form a rod-shaped lattice structure with a circular cross-section, the area overlap ratio R A is introduced for the introduction of the n-th layer and the n+1-th layer slices A is greater than 95%, wherein: where β is the inclination angle of the rod, d is the diameter of the rod, t s is the slice layer thickness, A(β, d, t s ) is the overlapping area of the nth slice layer and the (n+1)th slice layer. where A(β, d, t) is a function of β, d and t s s and t​ S5, performing derivative design on the reconstructed lattice structure; S51, performing rod element derivative replacement; S52, adding connecting rods to enhance the connectivity between free rods, and establishing a lattice structure model for tension and compression load conditions.

2. The method for modeling lattice structures under tensile and compressive loading conditions according to claim 1, wherein, The material properties in step S21 include density p s , modulus of elasticity E s , Poisson's ratio μ and yield strength σ S .

3. The method for modeling lattice structures under tensile and compressive loading conditions according to claim 1, wherein, In step S22, the applicable working conditions of the lattice cell include multi-directional uniform tension and single-directional dominant tension, the loading position is the vertex of the original entity cell, and the constraint position is the cell centroid; under the multi-directional uniform tension load condition, the constraint stress gradient is set, and the influence of different constraint stress values on the optimization results of the lattice structure is analyzed; under the single-directional dominant tension load condition, the single-directional dominant load gradient is set, and the influence of different single-directional dominant load sizes on the optimization results of the lattice structure is analyzed.

4. The method for modeling lattice structures under tensile and compressive loading conditions according to claim 1, wherein, In step S5, parallel diagonal lines and cross diagonal lines are introduced into rod element derivative design, and the connectivity between free rods of the lattice structure is increased by adding horizontal short rods and rods parallel to the bearing direction.

5. The method for modeling lattice structures under tensile and compressive loading conditions according to claim 1, wherein, It also includes an experimental verification step for verifying the performance characteristics of the lattice structure before and after optimization, and the verification parameters of the experimental verification step include: Specific stiffness: wherein E is the elastic modulus of the lattice structure, is the relative density of the lattice structure; Specific strength: where σ' s the yield strength of the lattice structure; Energy Absorption: Wherein, ε0 is the energy absorption cutoff strain; Specific energy absorption: wherein p s is the density of the matrix material of the dot matrix structure.

6. A BCC derived lattice structure obtained from the method for modeling lattice structures under tensile and compressive loading conditions according to one of claims 1 to 5, characterized in that, It includes parallel body-centered cubic lattice structure P-BCC and cross body-centered cubic lattice structure C-BCC; The body diagonal direction of the parallel body-centered cubic lattice structure P-BCC is a group of parallel rods; the body diagonal direction of the cross body-centered cubic lattice structure C-BCC is a group of intersecting rods.

7. A BCC derived lattice structure obtained from the method for modeling lattice structures under tensile and compressive loading conditions according to one of claims 1 to 5, characterized in that, It includes P-BCCXY and C-BCCXY lattice structures; the P-BCCXY and C-BCCXY lattice structures respectively add horizontal short rods through connecting free nodes on the basis of the P-BCC and C-BCC lattice structures.

8. A BCCZ derived lattice structure obtained from the method for modeling a lattice structure under tensile and compressive load conditions according to one of claims 1 to 5, characterized in that, The P-BCCXYZ and C-BCCXYZ lattice structures are added with a bar member parallel to the main stress direction Z on the basis of the P-BCCXY and C-BCCXY lattice structures respectively. The P-BCCXYZ and C-BCCXYZ lattice structures are added with a bar member parallel to the main stress direction Z on the basis of the P-BCCXY and C-BCCXY lattice structures respectively.

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