A hollow isotropic lattice structure optimization design method

Abstract

The present application belongs to the technical field of hollow lattice structure design, and discloses a hollow isotropic lattice structure optimization design method, which comprises the following steps: constructing a hollow lattice implicit model, obtaining elastic components and volume fractions representing the isotropic characteristics of the hollow lattice based on the implicit model, obtaining a sample database of a limited number of hollow lattices, introducing a proxy model to construct a mechanical property prediction model, and then using an intelligent optimization algorithm to optimize and control the performance, taking the isotropic characteristics as the optimization target, optimizing the hollow lattice structure by adjusting the size control parameters of the implicit modeling, and finally realizing the rapid performance prediction and efficient configuration design of the hollow isotropic lattice structure.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of hollow lattice structure design, and more particularly to a hollow isotropic lattice structure optimization design method. BACKGROUND

[0002] An isotropic lattice structure has the same mechanical response to external loads from any direction in space and does not change with different directions. The isotropic property of the lattice structure makes it have a unique advantage in dealing with uncertain direction statics and dynamics compression or impact, and can be applied to anti-collision / anti-impact structures.

[0003] Isotropic structures have various structural forms, such as truss lattice structures, curved thin shell structures, and plate grid structures, among which truss lattice structures (referred to as lattices or lattice structures) are the most common. Lattice structures have various types and strong designability, and are studied more in the field of isotropic design. The mechanical properties of conventional lattice structures have obvious anisotropy, showing extremely high elastic modulus or extremely high shear modulus, and usually do not have comprehensive characteristics of mechanical properties. Therefore, the isotropic design of truss structures mostly adopts the combined design of anisotropic lattice structures, and the proportion of different types of lattices in the whole structure is adjusted to achieve isotropic properties. Some designs also use hollow design of single-type lattice, and by adjusting the inner and outer diameters of the lattice structure, the isotropic design is achieved under specific rod size parameters. Hollow design only needs one type of lattice structure, has a relatively simple configuration, and has the advantages of high specific surface area and high specific strength / stiffness. However, the parameterized modeling of the hollow lattice structure is difficult, the function-configuration coupling relationship is complex, and the mechanical performance characterization process is tedious and time-consuming. Therefore, the elastic properties of conventional lattice structures are obviously anisotropic, and there is a lack of efficient design, characterization and optimization method for isotropic hollow lattice, and the problem of rapid prediction of isotropic performance and efficient design of hollow lattice structure needs to be solved. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a hollow isotropic lattice structure optimization design method, which can realize the rapid design optimization of the hollow isotropic lattice structure.

[0005] To achieve the above object, according to one aspect of the present application, a hollow isotropic lattice structure optimization design method is provided, which comprises: S1: selecting an arbitrary rod in a lattice structure as an original modeling reference, and extracting geometric coordinate information of all points on a skeleton line of the rod; S2: traversing the points on the skeleton line, obtaining the minimum distance from a point X in the lattice structure geometric space to the points on the skeleton line, in this way, obtaining the minimum distance from all points in the lattice structure space to the points on the skeleton line, and further obtaining an implicit modeling signed distance function of the rod, wherein the implicit modeling signed distance function is a function of a control parameter; S3: rotating and copying the rod to obtain an implicit modeling signed distance function of a derived rod; S4: performing Boolean sum on the implicit modeling signed distance functions of the rod and the derived rod to obtain an implicit modeling signed distance function of the lattice structure; S5: obtaining an implicit modeling signed distance function of a hollow part structure in the manner of steps S1-S4; S6: performing Boolean difference on the signed distance function of the lattice structure and the implicit modeling signed distance function of the hollow part structure to obtain an implicit modeling signed distance function of a hollow lattice structure; S7: obtaining a volume fraction and an isotropic performance of the hollow lattice structure based on the implicit modeling signed distance function of the hollow lattice structure; S8: constructing a relationship proxy model of the control parameter in the hollow lattice structure and the isotropic performance and the volume fraction; S9: taking the rod size control parameter as an optimization variable, and taking the volume fraction and the isotropic performance as optimization objectives, and performing optimization by using an intelligent optimization algorithm to obtain a hollow isotropic lattice structure.

[0006] Preferably, in step S7, obtaining the isotropic performance of the hollow lattice structure specifically comprises: obtaining elastic components in an equivalent elastic matrix of the hollow lattice structure; and obtaining a Zener ratio Z representing the isotropic performance according to the elastic components, specifically according to the following formula:

[0007] Z=2CH 44 / (CH 11 -CH 12 )

[0008] wherein CH 11 , CH 12 and CH 44 are the elastic components in the equivalent elastic matrix.

[0009] Preferably, the equivalent elastic performance is calculated by using a numerical homogenization or energy homogenization method.

[0010] Preferably, step S7 further comprises constructing a hollow lattice structure configuration and a corresponding performance database, and step S9 further comprises training the intelligent optimization algorithm by using the hollow lattice structure configuration and the corresponding performance database.

[0011] Preferably, step S7 specifically comprises the following steps: S71: obtaining a signed distance value matrix of the hollow lattice structure according to the implicit modeling signed distance function of the hollow lattice structure; S72: extracting the signed distance value matrix on the 8 nodes of the octahedral unit C in the discrete space of the hollow lattice structure; S73: encrypting the signed distance value matrix on the 8 nodes of the octahedral unit C to obtain an encrypted signed distance value matrix of the octahedral unit C, and the dimension of the encrypted signed distance value matrix is (N+1)×(N+1)×(N+1); S74: judging the numerical value of the encrypted signed distance value matrix, and counting the number n of numerical values greater than or equal to 0, and then the volume fraction vol C of the octahedral unit C is:

[0012]

[0013] S74: repeating steps S72-S74 to obtain the volume fraction vol(l) of each octahedral unit in the lattice structure, and then obtaining the volume fraction Vol of the entire hollow lattice structure according to the following formula:

[0014]

[0015] Wherein, L is the edge length of the hollow lattice structure.

[0016] Preferably, the shape function is used to interpolate the signed distance value matrix on the 8 nodes of the octahedral unit C to obtain the encrypted signed distance value matrix of the octahedral unit C in step S73.

[0017] Preferably, the linear interpolation method is used to obtain the encrypted signed distance value matrix of the octahedral unit C.

[0018] Preferably, a multi-objective genetic algorithm is used to design the isotropic hollow lattice structure under a specific volume fraction in step S9, and the optimization model is:

[0019]

[0020] Wherein, t1 and t2 are the rod diameter control parameters of the lattice structure, f1 and f2 are the volume fraction and isotropic performance objective functions, Vol is the actual volume fraction of the hollow lattice, μ is the given volume fraction, t min And t max are the minimum and maximum values of the design variables, respectively.

[0021] Overall, compared with the prior art, the hollow isotropic lattice structure optimization design method provided by the present application mainly has the following beneficial effects:

[0022] 1. The present application builds a solid model containing adjustable variables by implicit modeling symbolic distance function, realizes fast modeling, facilitates the generation of different models, significantly improves the model generation efficiency, and the implicit model has smooth geometric boundary, the model can quickly export STL format file, supports subsequent performance simulation verification and preparation.

[0023] 2. The present application builds a relationship proxy model of the control parameters and the isotropic performance and volume fraction, and then obtains the relationship between the model control parameters and the objective function, which is convenient for direct control.

[0024] 3. The present application builds anisotropic performance representation function through elastic component, and the elastic component can be directly obtained through implicit modeling symbolic distance function, realizing indirect representation of anisotropic performance.

[0025] 4. The present application adopts implicit modeling means and equivalent elastic property calculation method, can carry out hollow lattice structure efficient modeling and performance representation, avoids the complex and tedious hollow lattice structure iterative design and calculation process of traditional CAD modeling, finite element performance simulation, elastic performance numerical calculation, etc., and provides a powerful modeling and representation means for isotropic lattice structure optimization.

[0026] 5. The present application can quickly carry out hollow lattice modeling and performance representation, can conveniently build a limited hollow structure database, and further introduces a proxy model to build a multi-parameterized hollow lattice elastic performance prediction model, which can realize efficient and high-precision prediction of the equivalent elastic performance of the hollow lattice, and provides feasibility for rapid design of hollow isotropic lattice structure under any volume fraction.

[0027] 6. The present application introduces the configuration control parameters of the hollow lattice, and carries out isotropic property optimization design of the hollow lattice by means of intelligent optimization algorithm, significantly reduces the isotropic property optimization cost while ensuring the calculation accuracy, obtains the hollow lattice configuration meeting the design requirements, and enriches the content of isotropic lattice structure design method. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 It is a hollow isotropic lattice structure optimization design method of the present application.

[0029] Figure 2 It is a lattice structure cubic space discrete point schematic diagram provided by the present application.

[0030] Figure 3 It is a lattice structure rod skeleton line space discrete point schematic diagram provided by the present application.

[0031] Figure 4 It is a lattice structure rod skeleton line space discrete point schematic diagram provided by the present application.

[0032] Figure 5 is the schematic diagram of the lattice structure space unit discretization and symbol distance function interpolation refinement provided by embodiment 1 of the present application.

[0033] Figure 6 is the schematic diagram of the hollow BCC lattice generation provided by embodiment 1 of the present application.

[0034] Figure 7 (a) is the hollow BCC lattice elastic performance, volume fraction and double parameter relationship surface based on the Kriging surrogate model t1-t2-CH 11 (b) is the hollow BCC lattice elastic performance, volume fraction and double parameter relationship surface based on the Kriging surrogate model t1-t2-CH 12 (c) is the hollow BCC lattice elastic performance, volume fraction and double parameter relationship surface based on the Kriging surrogate model t1-t2-CH 44 (d) is the hollow BCC lattice elastic performance, volume fraction and double parameter relationship surface based on the Kriging surrogate model t1-t2-Vol.

[0035] Figure 8 is the hollow BCC multi-objective optimization Pareto solution set (volume fraction is 0.2) provided by embodiment 1 of the present application.

[0036] Figure 9 is the isotropic hollow BCC configuration and elastic surface under different volume fractions provided by embodiment 1 of the present application.

[0037] Figure 10 is the schematic diagram of the hollow BCC lattice generation provided by embodiment 2 of the present application,

[0038] Figure 11 (a) is the hollow CC lattice elastic performance, volume fraction and double parameter relationship surface based on the Kriging surrogate model t1-t2-CH 11 (b) is the hollow BCC lattice elastic performance, volume fraction and double parameter relationship surface based on the Kriging surrogate model t1-t2-CH 12 (c) is the hollow CC lattice elastic performance, volume fraction and double parameter relationship surface based on the Kriging surrogate model t1-t2-CH 44 (d) is the hollow CC lattice elastic performance, volume fraction and double parameter relationship surface based on the Kriging surrogate model t1-t2-Vol.

[0039] Figure 12 is the hollow CC multi-objective optimization Pareto solution set (volume fraction is 0.2) provided by embodiment 2 of the present application.

[0040] Figure 13 is the isotropic hollow BCC configuration of different volume fractions and elastic curved surface provided in embodiment 2 of the present application.

[0041] Figure 14 is the multi-order lattice structure of three different spatial orientations, including solid BCC and hollow BCC in spatial direction I, direction II, and direction III model provided in embodiment 3 of the present application.

[0042] Figure 15 is the finite element boundary condition schematic diagram provided in embodiment 3 of the present application.

[0043] Figure 16 is the multi-order lattice finite element simulation deformation cloud chart provided in embodiment 3 of the present application.

[0044] Figure 17 is the multi-order lattice mechanical property result comparison schematic diagram provided in embodiment 3 of the present application. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0046] Embodiment 1

[0047] The present application provides a hollow isotropic lattice structure optimization design method, as shown in Figure 1 , the method mainly includes the following steps S1-S9.

[0048] S1: Select any one rod in the lattice structure as the original modeling reference, and extract the geometric coordinate information of all points on the skeleton line of the rod.

[0049] Establish a spatial coordinate system to obtain the geometric coordinate information of all points in the discrete space of the lattice structure, as shown in Figure 2 , the coordinates of any point are denoted as {x i , y i , z i}, where i=1,...,(L+1) 3 , L is the edge length of the lattice structure, and in this embodiment, L is set to: L=40;

[0050] Based on the spatial geometric symmetry of the lattice structure, any one rod of the lattice structure is taken as the original modeling feature, and the geometric coordinate information of all points (points with integer coordinate values) on the skeleton line of the rod is extracted.j , β j , γ j} as shown in FIG. 1, where i = 1, …, (L + 1), L = 40. Figure 3

[0051] S2: Traverse the points on the skeleton line, obtain the minimum distance from the point X in the lattice structure geometric space to the point on the skeleton line, in this way, obtain the minimum distance from all points in the lattice structure space to the points on the skeleton line, and further obtain the implicit modeling signed distance function of the rod, wherein the implicit modeling signed distance function is a function of the control parameter.

[0052] Calculate the minimum distance from any point {x i , y i , z i} in the space to the point {α j , β j , γ j} on the skeleton line, the mathematical expression is as follows;

[0053]

[0054] Select the minimum distance from any point X in the geometric space to the point on the skeleton line as the implicit modeling signed distance function θ1(x) of the point X, introduce the rod diameter control parameter t for the control of the lattice structure volume fraction, and obtain the implicit modeling signed distance function θ1(x, t) with the control parameter t as the variable.

[0055] S3: Rotate the rod to obtain the implicit modeling signed distance function of the derived rod;

[0056] According to the geometric symmetry of the lattice structure, rotate it to obtain the signed distance function θ k (x, t) of the remaining rods of the lattice structure, where k = 1, 2, 3, 4.

[0057] S4: Perform Boolean sum on the implicit modeling signed distance functions of the rod and the derived rod to obtain the implicit modeling signed distance function of the lattice structure.

[0058] Perform Boolean sum operation on the implicit modeling signed distance functions θ k (x, t) of different rods of the lattice structure, obtain the complete implicit modeling signed distance function of the lattice structure, as shown in FIG. 2, and the mathematical expression of the sum Boolean operation is as follows: Figure 4

[0059] θ(X, t) = max(θ1(X, t), θ2(X, t), …, θ r (X, t))

[0060] ​​Wherein, r represents the number of lattice structure rods, according to the implicit modeling expression, the implicit model of the solid lattice structure is constructed, and the mathematical expression is as follows:

[0061]

[0062] S5: Obtain the implicit modeling symbolic distance function of the hollow part structure in the manner of steps S1-S4.

[0063] The hollow lattice is a hollow structure with a certain wall thickness, and the implicit models a and b of the solid lattice structure with different volume fractions are constructed, and the symbolic distance function θ a (X, t1), θ b (X, t2) are subjected to Boolean difference operation to obtain the symbolic distance function of the hollow lattice implicit model As Figure 6 shown, the mathematical expression of the Boolean difference operation is as follows:

[0064]

[0065] In this embodiment, a=1, b=2, the implicit function of the large volume fraction BCC lattice structure is The implicit function of the small volume fraction BCC lattice structure is The t1 and t2 are rod diameter control parameters of the lattice structure, and the value of t1 is greater than t2.

[0066] S6: The symbolic distance function of the lattice structure and the implicit modeling symbolic distance function of the hollow part structure are subjected to Boolean difference operation to obtain the implicit modeling symbolic distance function of the hollow lattice structure.

[0067] The implicit modeling symbolic distance function Φ(x) of the hollow lattice structure is:

[0068]

[0069] The hollow lattice is obtained by subtracting the small volume fraction lattice from the large volume fraction lattice, and the hollow structure with a certain wall thickness is obtained, the volume fraction of the hollow lattice is obtained by the implicit model to obtain the unit density matrix, and the volume fraction (Volume, Vol) of the hollow lattice is further calculated.

[0070] S7: Obtain the volume fraction and isotropic performance of the hollow lattice structure based on the implicit modeling symbolic distance function of the hollow lattice structure.

[0071] Specifically includes the following steps:

[0072] S71: Obtain the symbolic distance value numerical matrix of the hollow lattice structure according to the implicit modeling symbolic distance function of the hollow lattice structure;

[0073] According to the implicit modeling signed distance function, a signed distance value numerical matrix PHI of the hollow lattice structure is obtained, and the dimension of the matrix PHI is: (L+1)×(L+1)×(L+1).

[0074] S72: extracting a numerical matrix of signed distance values ​​on eight nodes of the octahedral unit C in the discrete space of the hollow lattice structure.

[0075] Extract the signed distance value matrix of the eight nodes of any octahedral unit C from the lattice structure discrete space. The mathematical expression of the extraction process is as follows:

[0076] PHI C =S C PHI

[0077] Among them, S C For numerical selection matrix, PHI C is the signed distance function numerical matrix on the 8 nodes of the octahedral unit C, expressed as follows: PHI C =[Phi_1 Phi_2 Phi_3…Phi_8].

[0078] S73: Encrypt the signed distance value numerical matrix on the 8 nodes of the octahedral unit C to obtain the encrypted signed distance value numerical matrix of the octahedral unit C. The dimension of the encrypted signed distance value numerical matrix is ​​(N+1)×(N+1)×(N+1).

[0079] In a further preferred solution, the shape function N(x) is used to interpolate the signed distance value matrix on the 8 nodes of the octahedral unit C to obtain the encrypted signed distance value matrix Phi of the octahedral unit C. Further preferably, the linear interpolation method is used to obtain the encrypted signed distance value matrix of the octahedral unit C, such as Figure 5 shown.

[0080] The mathematical expression of linear interpolation is as follows:

[0081] Phi=N(x)PHI C =N(x)S C PHI

[0082] The shape function N(x) is defined as follows:

[0083]

[0084] Expand it to:

[0085]

[0086] Among them, X, Y, and Z are the coordinates of the local coordinate system.

[0087] S74: Determine the numerical value of the encrypted symbol distance value matrix, and count the number of values greater than or equal to 0, n, then the volume fraction vol_C of the octahedral unit C is:

[0088]

[0089] S74: Repeat steps S72-S74 to obtain the volume fraction vol(l) of each octahedral unit in the lattice structure, and then obtain the volume fraction Vol of the entire hollow lattice structure according to the following formula:

[0090]

[0091] where L is the side length of the hollow lattice structure.

[0092] In a further preferred aspect, obtaining the isotropic property of the hollow lattice structure specifically comprises:

[0093] Step 1: Obtain the elastic components in the equivalent elastic matrix of the hollow lattice structure; preferably, numerical homogenization or energy homogenization method is used to calculate the equivalent elastic property.

[0094] Step 2: Obtain the Zener ratio Z representing the isotropic property according to the elastic components, and the specific formula is:

[0095] z = 2CH 44 / (CH 11 - CH 12 )

[0096] where CH 11 , CH 12 and CH 44 are the elastic components in the equivalent elastic matrix. The isotropy of the structure is represented by the Zener ratio, and the closer the Zener ratio value is to 1, the closer the mechanical properties are to isotropy.

[0097] For an orthotropic lattice structure, the elastic matrix is:

[0098]

[0099] Further, the elastic components exist CH 11 = CH 22 = CH 33 , CH 12 = CH 21 = CH 13 = CH 31 = CH 23 = CH 32 , CH 44 = CH s5 = CH66 The relationship between CH 11 , CH 12 and CH 44 .

[0100] S8: Construct a relationship agent model between the regulation parameters in the hollow lattice structure and the isotropic performance and the volume fraction.

[0101] S9: Take the rod size regulation parameters as the optimization variables, and take the volume fraction and the isotropic performance as the optimization objectives, and use an intelligent optimization algorithm to obtain the hollow isotropic lattice structure.

[0102] In a further preferred scheme, step S7 further comprises constructing a hollow lattice structure configuration and a corresponding performance database, and step S9 further comprises training the intelligent optimization algorithm using the hollow lattice structure configuration and the corresponding performance database.

[0103] In a further preferred scheme, the finite hollow lattice database is built by pre-computing the volume fraction and the elastic performance under the corresponding volume fraction of a finite number of hollow lattices, the finite number of hollow lattices are obtained by regulating the rod size regulation parameters t1 and t2 in the modeling, the hollow lattices are hollow lattices with a certain wall thickness having different external dimensions and different internal dimensions, thereby obtaining a certain number of hollow lattice configurations and performance databases as a sample library for subsequent efficient and high-precision prediction models.

[0104] In a further preferred scheme, the body-centered cubic hollow lattice used in the present example has an external dimension of 40x40x40, and the rod size regulation parameter varies in the range of 5.46<t2<t1<10.64. By equidistant sampling, 154 data points are obtained, i.e., the equivalent elastic performance and the volume fraction of 154 lattice structures are calculated.

[0105] The mechanical property prediction model is constructed based on the finite hollow lattice database, and a Kriging agent model is introduced. The sample points in the finite hollow lattice database are used as learning data to construct efficient and high-precision prediction models of the rod size regulation parameters t1 and t2 and the elastic performance of the hollow lattice, the rod size regulation parameters t1 and t2 and the volume fraction of the hollow lattice, and the relationship agent models of t1-t2-CH 11 , t1-t2-CH 12 , t1-t2-CH 44 , and t1-t2-Vol are constructed, as shown in FIG. 8. Figure 7

[0106] ​In a further preferred solution, the isotropic hollow lattice structure at a specific volume fraction is designed in step S9 by using a multi-objective genetic algorithm, the multi-objective genetic algorithm taking the rod size control parameters t1 and t2 as optimization variables, taking the volume fraction and isotropic performance as double optimization objectives, and realizing the isotropic hollow lattice design at a specific volume fraction, and the optimization model is:

[0107]

[0108] wherein t1 and t2 are the rod diameter control parameters of the lattice structure, f1 and f2 are the volume fraction and isotropic performance objective functions, Vol is the actual volume fraction of the hollow lattice, μ is the given volume fraction, t min and t max are the minimum value and maximum value of the design variable, respectively.

[0109] In this embodiment, the parameters in the multi-objective genetic algorithm are set as follows: the initial population number is 30, the genetic iteration step number is 150, the chromosome crossover probability is 0.85, the mutation probability is 0.1, the predicted volume fraction and isotropic performance error are simultaneously less than 0.001 to end the iteration, and the volume fraction is preset to be 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7.

[0110] Further, the multi-objective genetic algorithm will obtain a Pareto solution set, as shown in FIG. 4 (Pareto solution set of volume fraction 0.2), the horizontal axis is the volume fraction error, and the vertical coordinate is the Zener ratio error, and after optimization, the double objective errors are both less than 0.001, and it can be considered that the solutions in the Pareto solution set are all optimal solutions. Figure 8

[0111] Further, according to the obtained approximate isotropic hollow BCC related control parameters at different volume fractions (the structure size is 40×40×40), the actual volume fraction and elastic performance of the hollow lattice are calculated according to the predicted related control parameters, wherein Vol represents the actual isotropic hollow lattice volume fraction, t1 is the large volume fraction solid lattice diameter control parameter, t2 is the small volume fraction solid lattice diameter control parameter, Z is the Zener ratio, T end is the iteration end time, T 1st is the first time when a feasible solution appears, and N 1st is the iteration number when the first feasible solution appears:

[0112] Vol=0.1997, t1=8.385, t2=6.406, Z=0.9976, T end =63.4 seconds, T 1st =2.5 seconds;

[0113] ​Vol = 0.3002, t1 = 8.737, t2 = 5.234, Z = 0.9993, T end = 66.4 seconds, T 1st = 3.1 seconds;

[0114] Vol = 0.3992, t1 = 9.088, t2 = 5.027, Z = 1.0012, T end = 62.4 seconds, T 1st = 10.8 seconds;

[0115] Vol = 0.4983, t1 = 9.485, t2 = 4.320, Z = 1.0015, T end = 67.2 seconds, T 1st = 19.9 seconds;

[0116] Vol = 0.6017, t1 = 9.955, t2 = 3.558, Z = 1.0031, T end = 59.4 seconds, T 1st = 14.7 seconds;

[0117] Vol = 0.6998, t1 = 10.412, t2 = 2.857, Z = 0.9999, T end = 58.4 seconds, T 1st = 11.2 seconds.

[0118] Further, the isotropic hollow BCC configuration and elastic surface at different volume fractions are plotted, as shown in Figure 9 As shown, the elastic surface is close to a spherical shape, indicating that the isotropic property is good.

[0119] Example 2

[0120] The present embodiment takes a common cylindrical cube (CC) as the research object, and further illustrates and verifies the applicability and superiority of the present application. The hollow lattice modeling of the CC is shown in Figure 10 The specific hollow lattice implicit modeling and equivalent elastic property calculation, finite hollow lattice database construction, mechanical property prediction model construction, isotropic elastic property optimization, and the like, are similar to those of Example 1, and are not repeated here.

[0121] Further, in the present example, the CC hollow lattice has an outer size of 40x40x40, and the rod size control parameter changes in the range of 6.5<t2<t1<16.33. By equidistant sampling, 208 effective data points are obtained, i.e., the equivalent elastic properties of 208 lattice structures and the volume fraction are calculated.

[0122] Further, the t1-t2-CH11 , t1-t2-CH 12 , t1-t2-CH 44 , t1-t2-Vol relationship agent model, as shown in Figure 11

[0123] Further, the multi-objective genetic algorithm will obtain the Pareto solution set, as shown in Figure 12 the volume fraction is 0.2, the horizontal axis is the volume fraction error, and the vertical coordinate is the Zener ratio error. After optimization, the double-objective error is less than 0.001, and it can be considered that the solutions in the Pareto solution set are all optimal solutions.

[0124] Further, the obtained approximate isotropic hollow CC related control parameters under different volume fractions are as follows (the structure size is 40x40x40), and the actual volume fraction and elastic properties of the hollow lattice are calculated according to the predicted related control parameters, wherein Vol represents the actual isotropic hollow lattice volume fraction, t1 is the large volume fraction solid lattice diameter control parameter, t2 is the small volume fraction solid lattice diameter control parameter, Z is the Zener ratio, T end is the iteration end time, T 1st is the first time when a feasible solution appears, and N 1st is the first time when a feasible solution appears:

[0125] Vol = 0.2061, t1 = 10.946, t2 = 7.687, Z = 0.9532, T end = 51.10 seconds, T 1st = 3.9 seconds;

[0126] Vol = 0.3045, t1 = 11.992, t2 = 7.1662, Z = 0.9759, T end = 67.2 seconds, T 1st = 3.5 seconds;

[0127] Vol = 0.4046, t1 = 13.077, t2 = 6.643, Z = 0.9885, T end = 56.3 seconds, T 1st = 5.7 seconds;

[0128] Vol = 0.5034, t1 = 14.130, t2 = 6015, Z = 0.9955, T end = 51.14 seconds, T 1st = 13.4 seconds;

[0129] Vol = 0.6026, t1 = 15.261, t2 = 5.351, Z = 1.0021, T end = 49.9 seconds, T​1st = 12.3 seconds;

[0130] Vol = 0.7013, t1 = 16.412, t2 = 5.553, Z = 0.9999, T end = 62.4 seconds, T 1st = 11.8 seconds.

[0131] Further, the isotropic hollow CC configuration at different volume fractions and elastic curved surfaces close to spherical shape are drawn, which shows that the isotropic property is better, as shown in Figure 13 .

[0132] The microstructure obtained in Example 1 and Example 2 is a hollow structure at a typical volume fraction, and it can be found that the volume fraction and Zener ratio values are very close to the ideal values, and the errors are less than 1%, which can be considered that the present application can effectively realize the design of hollow isotropic lattice structure at a given volume fraction. In addition, it should be pointed out that the time for carrying out the calculation of the volume fraction of the hollow lattice and the homogenization elastic property is about 25 seconds, and the optimization requires hundreds or even thousands of calculations, and the time for directly using the intelligent optimization algorithm for isotropic optimization design is more than 2 hours, and the time for obtaining the isotropic configuration design of the present application is not more than 20 seconds. Therefore, it can be considered that the present application can greatly reduce the optimization design time of the isotropic lattice structure, and the efficiency is significantly improved.

[0133] Example 3

[0134] The present embodiment example takes the conventional solid BCC and the isotropic hollow BCC lattice provided by the present application as the research object, and illustrates the mechanical performance advantage of the isotropic hollow lattice provided by the present application in any spatial direction through the finite element simulation means.

[0135] Further, the solid BCC and the isotropic hollow BCC with a volume fraction of 0.3 are respectively constructed into 10x10x10 multi-order lattices, and 6x6x6 order lattices at three different spatial positions are cut according to the specified direction, which are direction I, direction II and direction III, as shown in Figure 14 .

[0136] Further, in the finite element analysis, the given outer size of the lattice structure is L = 240mm, and the material is structural steel: the density is 7850kg / m 3 , the elastic modulus is 2x10 5 MPa, and the Poisson's ratio is 0.3.

[0137] Further, Figure 15 the boundary conditions of the lattice structure in the finite element analysis are shown, the upper plane of the lattice structure is applied with a forced displacement μ = 2.4mm vertically downward, and the lower surface of the lattice structure is fixedly constrained.

[0138] Further, finite element simulation analysis is carried out on the 6 lattice structures according to the given boundary conditions, and the counterforce values of the lower plane of the lattice structure after compression are recorded respectively, and the deformation cloud diagram of the lattice structure is drawn.

[0139] Further, finite element simulation analysis is carried out on the 6 lattice structures according to the given boundary conditions, and the counterforce values of the lower plane of the lattice structure after compression are recorded respectively, and the deformation cloud diagram of the lattice structure is drawn.

[0140] Further, Figure 16 The deformation cloud diagram of the 6 lattice structures is shown, and the deformation modes of the three different spatial positions of the conventional solid BCC lattice structure are quite different, and the model in direction III has obvious lateral deformation. The isotropic hollow BCC lattice designed by the application has basically the same deformation mode in three different spatial positions, and the deformation is stable during vertical compression, and no lateral deformation occurs.

[0141] Further, according to the counterforce values of the lower plane of the lattice structure after compression, a counterforce comparison column chart is drawn, as shown in Figure 17 It can be found that the conventional solid BCC lattice structure in different spatial positions presents significant mechanical property difference, and the mechanical property in direction II is more than twice that in direction I and direction III. The counterforce values of the isotropic hollow BCC lattice designed by the application in three different spatial positions are close, with an error of about 10%, which exhibits the advantages of stable mechanical property. The present example further illustrates the effectiveness of the design method and the correctness of the designed configuration.

[0142] In summary, the hollow isotropic lattice structure optimization design method provided by the application can solve the problems of rapid prediction and efficient design of the isotropic performance of the hollow lattice structure, and exhibits good applicability and superiority, and provides a new idea for the design of the isotropic lattice structure.

[0143] Those skilled in the art will readily understand that the above description is only a preferred embodiment of the application and is not intended to limit the application, and any modification, equivalent replacement and improvement made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A method for optimizing the design of a hollow isotropic lattice structure, characterized in that: The method comprises: S1: Select any rod in the lattice structure as the original modeling reference, and extract the geometric coordinate information of all points on the skeleton line of the rod; S2: Traverse the points on the skeleton line and obtain the minimum distance from point X in the lattice structure geometric space to the points on the skeleton line. In this way, the minimum distance from all points in the lattice structure space to the points on the skeleton line is obtained, and then the implicit modeling signed distance function of the rod is obtained, where the implicit modeling signed distance function is a function of the control parameters; S3: rotating and copying the member to obtain an implicit modeling signed distance function of the derived member; S4: performing Boolean summation on the implicit modeling signed distance functions of the member and the derived member to obtain the implicit modeling signed distance function of the lattice structure; S5: Obtaining an implicit modeling signed distance function of the hollow part structure using the method in steps S1 to S4; S6: performing Boolean difference between the signed distance function of the lattice structure and the implicit modeling signed distance function of the hollow part structure to obtain the implicit modeling signed distance function of the hollow lattice structure; S7: Obtaining the volume fraction and isotropic properties of the hollow lattice structure based on an implicit modeling signed distance function of the hollow lattice structure; S8: Construct a proxy model for the relationship between the control parameters and the isotropic properties and volume fraction in the hollow lattice structure; S9: Taking the rod size control parameters as optimization variables, and the volume fraction and isotropic performance as optimization targets, an intelligent optimization algorithm is used to optimize and obtain a hollow isotropic lattice structure.

2. The method according to claim 1, characterized in that In step S7, obtaining the isotropic properties of the hollow lattice structure specifically includes: Obtaining elastic components in an equivalent elastic matrix of the hollow lattice structure; The Zener ratio Z, which characterizes the isotropic performance, is obtained based on the elastic component. The specific formula is: Z=2CH 44 / (CH 11 -CH 12 ) Among them, CH 11 、CH 12 With CH 44 is the elastic component in the equivalent elastic matrix.

3. The method according to claim 2, characterized in that The equivalent elastic properties are calculated using numerical homogenization or energy homogenization methods.

4. The method according to claim 1, wherein Step S7 also includes constructing a hollow lattice structure configuration and a corresponding performance database, and step S9 also includes training an intelligent optimization algorithm using the hollow lattice structure configuration and the corresponding performance database.

5. The method according to claim 1, wherein Step S7 specifically includes the following steps: S71: obtaining a signed distance value matrix of the hollow lattice structure according to an implicit modeling signed distance function of the hollow lattice structure; S72: extracting a numerical matrix of signed distance values ​​on eight nodes of the octahedral unit C in the discrete space of the hollow lattice structure; S73: Encrypting the signed distance value numerical matrix on the eight nodes of the octahedral unit C to obtain an encrypted signed distance value numerical matrix of the octahedral unit C, wherein the dimension of the encrypted signed distance value numerical matrix is ​​(N+1)×(N+1)×(N+1); S74: Determine the value of the encrypted signed distance value matrix, and count the number n of values ​​greater than or equal to 0. The volume fraction vol_C of the octahedral unit C is: S74: Repeat steps S72 to S74 to obtain the volume fraction vol(l) of each octahedral unit in the lattice structure, and then obtain the volume fraction Vol of the entire hollow lattice structure according to the following formula: Wherein, L is the side length of the hollow lattice structure.

6. The method according to claim 5, characterized in that In step S73 , the shape function is used to interpolate the signed distance value numerical matrix on the eight nodes of the octahedral unit C to obtain the encrypted signed distance value numerical matrix of the octahedral unit C.

7. The method according to claim 6, characterized in that The encrypted signed distance value matrix of octahedral unit C is obtained by linear interpolation method.

8. The method according to claim 1, characterized in that In step S9, a multi-objective genetic algorithm is used to design the isotropic hollow lattice structure at a specific volume fraction, and the optimization model is: Among them, t1 and t2 are the rod diameter control parameters of the lattice structure, f1 and f2 are the volume fraction and isotropic performance objective functions, Vol is the actual volume fraction of the hollow lattice, μ is the given volume fraction, t min and t max are the minimum and maximum values ​​of the design variables, respectively.

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