Rapid modeling method capable of realizing twin crystallization design of lattice structure

Abstract

The invention provides a rapid modeling method capable of realizing twin crystallization design of a lattice structure, and belongs to the technical field of modeling and simulation. According to the method, a lattice unit cell overall interpolation matrix to be mapped is constructed, a twin crystallization target subspace unit cell structure and an overall layout scheme are determined, point cloud data are mapped to a target subspace, finite element entity unit model reconstruction and assembly are carried out, and rapid twin crystallization design of a lattice structure is achieved. According to the rapid modeling method capable of achieving twin crystallization design of the lattice structure, the modeling efficiency can be effectively improved, the design cost is reduced, the method is suitable for twin crystallization design of various lattice structures, rapid modeling can be achieved under the condition of low computing resources, and the modeling efficiency is improved. And the requirements of practical engineering application such as aerospace, automobile manufacturing and biomedicine are met.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation and modeling, and more particularly to a fast modeling method capable of realizing the twinning design of a lattice structure. Background Art

[0002] Due to the limitations of the structural form, the mechanical properties of traditional single-phase lattice structures do not have compatibility characteristics: for example, the overall bearing capacity level of the tensile-dominated lattice structure is relatively high, but its mechanical behavior after yielding is too oscillatory, making this type of structure not conducive to energy absorption and impact load reduction; while the mechanical behavior after yielding of the bending-dominated lattice structure is relatively gentle, which is formally conducive to energy absorption, but under the mass constraint condition, the specific stiffness and overall bearing capacity level of this type of structure are relatively low, and the application scenarios are limited. Therefore, appropriately adjusting the structural form of traditional single-phase lattice structures to enable the lattice structure to simultaneously possess the compatible functions of energy absorption and impact load reduction is of great significance for the practical engineering application of lattice structures.

[0003] Currently, the main structural improvement methods for traditional single-phase lattice structures are as follows: (1) increasing or decreasing the number of rod elements on the basis of the single-cell configuration of the single-phase lattice structure to adjust the local deformation mode of the structure; (2) introducing the gradient concept to make the relative density of the single-phase lattice structure change according to a certain rule; (3) performing topology optimization based on the original geometric shape of the rod elements of the single-phase lattice structure; (4) locally strengthening the nodes or the centers of the rod elements of the single-phase lattice structure; (5) introducing heterogeneous cells and using two or more lattice cells with different mechanical behaviors for hybrid integrated design; (6) performing secondary design on the rod element structure based on the bionic concept, such as changing the traditional solid rod element into a hollow rod element; (7) using machine learning methods to customize the design of lattice structures with specific mechanical behaviors.

[0004] Most of the above design methods are based on experience, requiring a high upfront time cost for iterative design, and there are problems such as difficulties in finite element model modeling and poor predictability of design effects for lattice structures with complex micro-configurations.

[0005] Therefore, developing a modeling method that can quickly realize the twinning design of lattice structures and has compatible mechanical properties is of great practical significance for promoting the application of lattice structures in practical engineering. Summary of the Invention

[0006] The purpose of the present invention is to provide a fast modeling method capable of realizing the twinning design of lattice structures, realizing the twinning design of the octagonal lattice structure by programming the modeling method, and generating a finite element model for actual production and numerical analysis and calculation.

[0007] To achieve the above object, the present invention provides a rapid modeling method capable of realizing the twinning design of a lattice structure, including the following steps:

[0008] Step S1, construct the overall interpolation matrix of the lattice unit cell to be mapped;

[0009] Step S11, construct the CAD solid geometry model of the lattice unit cell to be mapped;

[0010] Step S12, use Hypermesh to perform finite element mesh division on the CAD solid geometry model of the lattice unit cell to be mapped, and place it in an isoparametric coordinate system to generate a finite element model of the lattice unit cell to be mapped containing multiple nodes and elements;

[0011] Step S13, extract the three-dimensional coordinate data of the nodes from the finite element model of the lattice unit cell to be mapped to form the point cloud data of the lattice unit cell to be mapped;

[0012] Step S14, extract the coordinates of 8 vertices in the isoparametric space;

[0013] Step S15, obtain the interpolation matrix of all nodes in the finite element model of the lattice unit cell to be mapped according to the Lagrange interpolation method, and construct the overall interpolation matrix of the lattice unit cell to be mapped containing all node interpolation matrices;

[0014] Step S2, determine the single-cell structure and overall layout scheme of the twinning target subspace;

[0015] Step S21, determine the structural parameters of a single unit cell in the twinning lattice structure occupying the twinning target subspace, and construct the vertex coordinate matrix of a single twinning target subspace;

[0016] Step S22, assemble multiple single twinning target subspaces to form a complete overall mapping scheme, that is, construct an overall matrix containing the vertex coordinates of all twinning target subspaces;

[0017] Step S3, map the point cloud data of the lattice unit cell to be mapped obtained in step S1 to the twinning target subspace determined in step S2 through an isoparametric mapping method to obtain the mapped point cloud data;

[0018] Step S4, reconstruct the finite element solid element model based on the mapped point cloud data and complete the integrated assembly of the twinning lattice unit cell.

[0019] Preferably, in step S11, the CAD solid geometry model of the lattice unit cell to be mapped is an octagonal lattice unit cell model, and the relative density of this model is 15%.

[0020] Preferably, in step S12, the finite element mesh is divided into a full hexahedron finite element mesh, and after the mesh division, the model is scaled into the isoparametric space in the isoparametric coordinate system.

[0021] Preferably, in step S15, the interpolation matrix of all nodes in the finite element model of the lattice unit to be mapped is obtained according to the Lagrange interpolation method, and the overall interpolation matrix of the lattice unit to be mapped containing all node interpolation matrices is constructed. The specific operation is as follows:

[0022] Extract the isoparametric coordinates of the m-th node in the finite element model of the lattice unit to be mapped, and substitute them into ξ m , η m , ζ m . Then, substitute the eight vertex coordinates of the isoparametric space into ξ i , η i , ζ i respectively to obtain the interpolation matrix of the m-th node in the lattice unit to be mapped:

[0023]

[0024] N m = [N m1 N m2 N m3 N m4 N m5 N m6 N m7 N m8 ;

[0025] Among them, N mi represents the i-th component of the interpolation matrix of the m-th node; ξ m , η m , ζ m all represent the isoparametric coordinates of the m-th node; ξ i , η i , ζ i all represent the coordinate components of the i-th vertex in the isoparametric space; N m represents the interpolation matrix of the m-th node;

[0026] Solve the interpolation matrix of all nodes in the finite element model of the lattice unit to be mapped one by one and construct the overall interpolation matrix of the lattice unit to be mapped as follows:

[0027]

[0028] Among them, N shape represents the overall interpolation matrix of the lattice unit to be mapped.

[0029] Preferably, in step S21, the structural parameters of the twinning target subspace include the twin boundary angle, the length and height of the unit cell.

[0030] Preferably, in step S21, the vertex coordinate matrix of the nth twinning target subspace is as follows:

[0031]

[0032] where A n represents the vertex coordinate matrix of the nth twinning target subspace; x ni , y ni , z ni represent the coordinate components of the ith vertex in the nth twinning target subspace.

[0033] Preferably, in step S22, the overall matrix containing the vertex coordinates of all twinning target subspaces is as follows:

[0034]

[0035] where A Tnode represents the overall matrix containing the vertex coordinates of n twinning target subspaces.

[0036] Preferably, in step S3, the point cloud data of the lattice unit cell to be mapped obtained in step S1 is mapped to the twinning target subspace determined in step S2 by the isoparametric mapping method to obtain the mapped point cloud data. The specific operations are as follows:

[0037]

[0038] where M represents the mapped point cloud data.

[0039] Preferably, the isoparametric mapping method is an isoparametric transformation, and during the mapping process, the node numbers in the isoparametric space and the twinning target subspace follow the same numbering rule.

[0040] Preferably, in step S4, based on the mapped point cloud data, a finite element solid element model is reconstructed. The specific operations are as follows:

[0041] Step S41: Use the Matlab program to batch the nodes in the original lattice unit cell to be mapped into the hexahedron unit node group and establish the node - hexahedron unit data structure;

[0042] Step S42: According to the node and element data structure of the isoparametric space unit cell, sequentially derive the node - hexahedron unit data structure of the twinning target subspace in the twinned lattice structure;

[0043] Step S43: Independently process the node data of the n twinning target subspaces to ensure that the node data of each twinning target subspace is complete and does not interfere with the node data of other twinning target subspaces;

[0044] Step S44: Merge the nodes with the same spatial coordinates to form a twinned lattice structure with completely connected adjacent unit cell nodes;

[0045] ∪(N shape ·A n )=(N shape ·A1)∪(N shape ·A2)∪…∪(N shape ·A n ).

[0046] Therefore, the present invention adopts the above-mentioned fast modeling method capable of realizing the twinning design of the lattice structure, and has the beneficial technical effects: it can quickly model the finite element model of the twinned lattice structure, discretely design the geometric cross-section and mechanical properties of the lattice rod elements at a low cost, and design a twinned octagonal lattice structure that takes into account both energy absorption and impact load reduction based on this method. Description of the Drawings

[0047] Figure 1 Is the projection of the boundary nodes of the unit cell to be mapped;

[0048] Figure 2 Is the overall mapping scheme of the target space: SOCT-Twin2;

[0049] Figure 3 Is the node numbering rule for the isoparametric space and the target subspace;

[0050] Figure 4 Is the reconstruction of the finite element model based on the point cloud data;

[0051] Figure 5 Are the original SOCT structure and the twinned structure SOCT-Twin2;

[0052] Figure 6 Are the mechanical responses of the SOCT and SOCT-Twin2 structures at the load input end and the output end; where, Figure 6 (a) in is the mechanical response of the SOCT structure at the load input end and the output end; Figure 6 (b) in is the mechanical response of the SOCT-Twin2 structure at the load input end and the output end;

[0053] Figure 7 Is an example of the self-similar baseline: the SOCT structure;

[0054] Figure 8 Is the comprehensive comparison of the energy absorption and impact load reduction performances of the two structures. Detailed Embodiments

[0055] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0057] Embodiment 1

[0058] A rapid modeling method for realizing the twinning design of a lattice structure according to the present invention includes the following steps:

[0059] Step S1: Construction of the overall interpolation matrix of the lattice unit cell to be mapped.

[0060] First, use hypermesh to establish a full hexahedron finite element model of the octagonal lattice (SOCT) unit cell to be mapped with a relative density of 15%, and scale the model into the isoparametric space of ξ∈[-1,1], η∈[-1,1], ζ∈[-1,1] in the isoparametric coordinate system. To prevent node escape of the unit cell after isoparametric mapping, project the outermost nodes on the positive and negative directions of the ξ, η, and ζ axes to the plane where the boundary of the isoparametric space is located, as Figure 1 shown.

[0061] Then, construct the overall interpolation matrix of the lattice unit cell to be mapped based on the MATLAB program. Extract the isoparametric coordinates of the m-th node in the finite element model of the lattice unit cell to be mapped, and substitute the isoparametric coordinates into ξ in formula (1) m , η m , ζ m , and then substitute the coordinates of the 8 vertices of the isoparametric space into ξ in formula (1) i , η i , ζ i respectively, and the interpolation matrix of the m-th node in the lattice unit cell to be mapped can be obtained, as formula (2):

[0062]

[0063] N m = [N m1 N m2 N m3 N m4 N m5 N m6 N m7 N m8 (2);

[0064] Solve the interpolation matrix of all nodes in the finite element model of the unit cell to be mapped one by one according to the above method and construct the overall interpolation matrix as follows:

[0065]

[0066] The overall interpolation matrix represents the relative positions of all nodes in the isoparametric space of the cell data model to be mapped. The number of rows of the matrix represents the total number of nodes in the cell data model to be mapped, and each row corresponds to the interpolation matrix of a node.

[0067] Step S2: Determine the single-crystal structure and overall layout scheme of the twinning target subspace.

[0068] Set the overall generation space of the twinning lattice structure to 40mm×40mm×40mm. Subsequently, divide this space into a total of 125 target subspaces with twinning characteristics, such as Figure 2 shown. Each twinning target subspace is the "seat" of the cell after isoparametric transformation in the twinning lattice structure. The geometric characteristics of the twinning target subspace determine the space shape occupied by the cell after performing isoparametric mapping.

[0069] The isoparametric mapping process has strict requirements for the node numbers of the isoparametric space and the twinning target subspace, that is, the 8 space nodes of both must follow the same numbering rule to ensure the accuracy and consistency of the mapping. Here, it is stipulated that in the isoparametric space and the twinning target subspace, the numbering rule and relative positions at the 8 space vertices are as Figure 3 shown. Renumber the space vertices of the 125 target subspaces in the twinning lattice generation area using a program to ensure that the isoparametric mapping program can accurately map the single cell in the isoparametric space to the "relatively distorted" twinning target subspace.

[0070] After completing the renumbering of all the space nodes of the twinning target subspaces, it is necessary to construct the space vertex coordinate matrix of the twinning target subspace

[0071] in the following form:

[0072]

[0073] where, x ni , y ni , z ni represent the coordinate components of the i-th vertex in the n-th twinning target subspace, i = 1, 2,..., 8. A n represents the vertex coordinate matrix of the n-th twinning target subspace. The eight vertex coordinate components in this space are input into formula (4) in sequence according to the Figure 3 numbering order. And so on, a total of 125 subspaces vertex coordinate matrices are constructed, and these matrices are combined into an overall matrix according to formula (5):

[0074]

[0075] Step S3: Map the point cloud data of the lattice unit cell to be mapped obtained in Step S1 to the twinning target subspace determined in Step S2 through the isoparametric mapping method to obtain the mapped point cloud data.

[0076]

[0077] After obtaining the point cloud coordinate matrix M, the discrete geometric data information of the twinned lattice structure has essentially been obtained. For the convenience of subsequent simulation analysis, the finite element model is reconstructed based on the point cloud coordinate matrix of the twinned lattice structure below.

[0078] Step S4: Reconstruction of the finite element model based on the point cloud data

[0079] First, use the Matlab program to batch the nodes in the original lattice unit cell to be mapped into the hexahedron unit node group and establish the data structure of nodes - hexahedron units. As Figure 4 shown, according to the node and element data structure of the isoparametric space unit cell, the data structure of nodes - hexahedron units in the target subspace of the twinned lattice structure is derived in sequence.

[0080] Since the 125 target subspaces are independent of each other, the twinned unit cells generated in the subspaces are not interconnected. There is an adjacent face with exactly the same shape and size between two adjacent target subspaces, and the isoparametric mapping can ensure that the node distributions mapped on this pair of adjacent faces are exactly the same. Therefore, the nodes with the same spatial coordinates can be merged according to formula (7) to form a twinned lattice structure with completely connected nodes of adjacent unit cells.

[0081]

[0082] So far, the finite element modeling process of the twinned lattice structure based on the isoparametric mapping program is completed. The original SOCT structure and the twinned SOCT - Twin2 structure are as Figure 5 shown. All the twinned lattice unit cells in this model have the same mesh division method as the isoparametric space unit cells. All the twinned unit cells are composed of hexahedron units, and the dynamic simulation calculation can be directly performed using LS - DYNA by assigning material properties, boundary conditions, and loading methods.

[0083] Performance evaluation of the "energy absorption - impact load reduction" of the twinned lattice structure.

[0084] This patent uses polylactic acid (PLA) as the matrix material to conduct high-speed impact simulation of a single-phase octagonal lattice structure SOCT with a relative density of 15% and a twinned octagonal lattice structure SOCT-Twin2. The simulation condition is uniaxial loading, and the loading speed is 30 m / s. The mechanical responses at the load input and output ends of the SOCT and SOCT-Twin2 structures are compared horizontally to evaluate the influence of the twinning design on the structural energy absorption and impact load reduction performance.

[0085] In this embodiment, the stress-strain curve at the load input end is used to calculate the energy absorption of the structure, as Figure 6 shown.

[0086] The stress-strain curve at the load output end is used to evaluate the impact reduction effect of the structure, and the method is as follows:

[0087] (a) Based on the stress-strain curve at the structure output end, draw a self-similar baseline as Figure 7 shown.

[0088] (b) By subtracting the stress-strain curves at the load output ends of the two structures from the self-similar baseline respectively, the stress oscillation curves are obtained;

[0089] (c) Calculate the area under the stress oscillation curve, and normalize it with the total energy absorption of the structure to obtain the normalized discrete area.

[0090] After that, the impact reduction performance of the structure at the load output end can be measured by this scalar of the normalized discrete area. The smaller the normalized discrete area, the better the impact reduction effect of the structure.

[0091] Figure 8 It shows that the twinning design method can design a high-performance lattice structure that takes into account both energy absorption and target protection. The twinning design (SOCT-Twin2) of the SOCT structure reduces the stress oscillation at the output end of the original structure by 69.20%, and the energy absorption only loses 2.68%. The twinning advantage is relatively significant.

[0092] It should be noted that the content not elaborated in detail in this invention is all prior art and is well-known to those skilled in the art.

[0093] Therefore, this invention adopts the above-mentioned rapid modeling method that can realize the twinning design of the lattice structure, realizes the twinning design of the octagonal lattice structure by programming the modeling method, and generates a finite element model for actual production and numerical analysis and calculation.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A rapid modeling method capable of realizing the twinning design of a dot matrix structure, characterized in that It includes the following steps: Step S1: Construct the overall interpolation matrix of the lattice unit cell to be mapped; Step S11: Construct the CAD solid geometry model of the lattice unit cell to be mapped; Step S12: Use Hypermesh to perform finite element mesh division on the CAD solid geometry model of the lattice unit cell to be mapped, and place it in the isoparametric coordinate system to generate a finite element model of the lattice unit cell to be mapped containing multiple nodes and elements; Step S13: Extract the three-dimensional coordinate data of the nodes from the finite element model of the lattice unit cell to be mapped to form the point cloud data of the lattice unit cell to be mapped; Step S14: Extract the coordinates of the 8 vertices in the isoparametric space; Step S15: Obtain the interpolation matrix of all nodes in the finite element model of the lattice unit cell to be mapped according to the Lagrange interpolation method, and construct the overall interpolation matrix of the lattice unit cell to be mapped containing all node interpolation matrices; Step S2: Determine the structure and overall layout scheme of the twinned target subspace unit cell; Step S21: Determine the structural parameters of a single unit cell in the twinned lattice structure occupying the twinned target subspace, and construct the vertex coordinate matrix of a single twinned target subspace; Step S22: Assemble multiple single twinned target subspaces to form a complete overall mapping scheme, that is, construct an overall matrix containing the vertex coordinates of all twinned target subspaces; Step S3: Map the point cloud data of the lattice unit cell to be mapped obtained in Step S1 to the twinned target subspace determined in Step S2 through the isoparametric mapping method to obtain the mapped point cloud data; Step S4: Reconstruct the finite element solid element model based on the mapped point cloud data and complete the integrated assembly of the twinned lattice unit cell.

2. A rapid modeling method for realizing the twinning design of a dot matrix structure according to claim 1, characterized in that In Step S11, the CAD solid geometry model of the lattice unit cell to be mapped is an octagonal lattice unit cell model, and the relative density of this model is 15%.

3. A rapid modeling method capable of realizing the twinning design of a dot matrix structure according to claim 1, characterized in that In Step S12, the finite element mesh division is a full hexahedron finite element mesh division, and after the mesh division, the model is scaled into the isoparametric space under the isoparametric coordinate system.

4. A rapid modeling method for realizing the twinning design of a dot matrix structure according to claim 1, characterized in that In Step S15, according to the Lagrange interpolation method, obtain the interpolation matrix of all nodes in the finite element model of the lattice unit cell to be mapped, and construct the overall interpolation matrix of the lattice unit cell to be mapped containing all node interpolation matrices. The specific operation is as follows: Extract the isoparametric coordinates of the \(m\)-th node in the finite element model of the lattice unit cell to be mapped, and substitute them into \(\xi\) m , \(\eta\) m , \(\zeta\) m . Then, substitute the coordinates of the 8 vertices in the isoparametric space into \(\xi\) i , \(\eta\) i , \(\zeta\) i to obtain the interpolation matrix of the \(m\)-th node in the lattice unit cell to be mapped: N m = [N m1 N m2 N m3 N m4 N m5 N m6 N m7 N m8 ; Among them, N mi represents the i-th component of the interpolation matrix of the m-th node; ξ m , η m , ζ m all represent the isoparametric coordinates of the m-th node; ξ i , η i , ζ i all represent the coordinate components of the i-th vertex in the isoparametric space; N m represents the interpolation matrix of the m-th node; Solve the interpolation matrix of all nodes in the finite element model of the lattice unit cell to be mapped one by one and construct the overall interpolation matrix of the lattice unit cell to be mapped as follows: Among them, N shape represents the overall interpolation matrix of the lattice unit cell to be mapped.

5. A rapid modeling method for realizing the twinning design of a dot matrix structure according to claim 4, characterized in that In Step S21, the structural parameters of the twinned target subspace include the twin boundary angle, the length and height of the unit cell.

6. A rapid modeling method for realizing the twinning design of a dot matrix structure according to claim 4, characterized in that In Step S21, the vertex coordinate matrix of the nth twinned target subspace is as follows: Among them, A n represents the vertex coordinate matrix of the nth twinning target subspace; x ni , y ni , z ni represent the coordinate components of the ith vertex in the nth twinning target subspace.

7. A rapid modeling method for realizing the twinning design of a dot matrix structure according to claim 6, characterized in that In Step S22, the overall matrix containing the vertex coordinates of all twinned target subspaces is as follows: Among them, A Tnode represents the overall matrix containing the vertex coordinates of n twinned target subspaces.

8. A rapid modeling method for realizing the twinning design of a dot matrix structure according to claim 7, characterized in that In Step S3, map the point cloud data of the lattice unit cell to be mapped obtained in Step S1 to the twinned target subspace determined in Step S2 through the isoparametric mapping method to obtain the mapped point cloud data. The specific operation is as follows: Among them, M represents the mapped point cloud data.

9. A rapid modeling method for realizing the twinning design of a dot matrix structure according to claim 8, characterized in that The isoparametric mapping method is an isoparametric transformation, and during the mapping process, the node numbers in the isoparametric space and the twinned target subspace follow the same numbering rule.

10. A rapid modeling method for realizing the twinning design of a dot matrix structure according to claim 9, characterized in that, In step S4, based on the mapped point cloud data, a finite element solid element model reconstruction is performed, and the specific operations are as follows: Step S41: Use the Matlab program to batch code all the nodes in the original lattice unit cell to be mapped into the hexahedron unit node group, and establish the node-hexahedron unit data structure; Step S42: According to the node and element data structure of the isoparametric space unit cell, sequentially derive the node-hexahedron unit data structure of the twinned target subspace in the twinned lattice structure; Step S43: Independently process the node data of n twinned target subspaces to ensure that the node data of each twinned target subspace is complete and does not mix with the node data of other twinned target subspaces; Step S44: Merge the nodes with the same spatial coordinates to form a twinned lattice structure with completely connected adjacent unit cell nodes; ∪(N shape ·A n ) = (N shape ·A1) ∪ (N shape ·A2) ∪ … ∪ (N shape ·A n )。

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