A method and system for self-supporting topology design of multi-cell structures driven by geometric feature evolution

Abstract

This invention belongs to the field of material structure topology design technology, and discloses a geometric feature-driven self-supporting topology design method for multi-cell structures. This invention utilizes the base structure method to study the superposition and combination law of base structures within a single cell, and creates a single-cell configuration definition method based on base structures. Combining the traditional density-based topology optimization method, it sets the mapping relationship between the established single-cell configuration and design variables, provides the calculation method for the corresponding stiffness matrix, defines a multi-cell structure optimization model based on the single-cell model, and derives the sensitivity calculation method. Starting from a rod system structure, this invention utilizes the spatial topology of the rod system to design multi-cell structures. Based on the matching relationship between the pose of the rod system and the cantilever constraints of additive manufacturing, it determines the self-supporting forming angle of the manufacturing voxels and the appropriate element search direction, establishing an integrated method for multi-cell structure design and manufacturing based on rod geometric features, thus realizing the self-supporting forming of multi-cell structures.

Description

Technical Field

[0001] This invention belongs to the field of material structure topology design technology, and particularly relates to a geometric feature evolution-driven method and system for self-supporting topology design of multi-cell structures. Background Technology

[0002] The integration of topology optimization and additive manufacturing provides a theoretical approach and implementation method for innovative structural design and the development of high-performance components. Currently, topology optimization design for additive manufacturing mainly considers aspects such as dimensional constraints, overhang constraints, connectivity constraints, and self-support constraints. However, how to optimize material distribution through structural design to achieve self-support during the printing process remains a key focus of research in topology optimization design for additive manufacturing.

[0003] With the development of additive manufacturing technology, advanced unsupported additive manufacturing technologies such as space-suspended 3D printing and MATAERIAL anti-gravity 3D printing have emerged. Currently, topology-optimized structures based on additive manufacturing have been applied in fields such as aviation, aerospace, and medicine, such as the A320 passenger aircraft support structure. However, for multi-scale structures with complex geometric topologies, additional auxiliary supports must be added during the molding process to prevent collapse. However, for the molding of three-dimensional multi-scale structures, these additional auxiliary supports are difficult to remove effectively, and the performance of the manufactured structure often fails to meet design requirements.

[0004] In existing technology design spaces, the extremely high geometric complexity and material distribution freedom of structures make it difficult to match the constraints of material stacking and forming processes in the manufacturing space. This makes it challenging to directly express structures with good mechanical properties, such as closed internal holes and large cantilever structures, without auxiliary support. Considering geometric constraints such as dimensional characteristics and cantilever structures during the structural design process to prevent structural collapse during manufacturing, while ensuring the accurate representation of the structure's design performance in the manufacturing space, and achieving design-as-manufacturing, is a crucial challenge that must be overcome in structural topology optimization design for additive manufacturing.

[0005] Existing technical solutions

[0006] Currently, there has been some research on the design of self-supporting structures in additive manufacturing through topology optimization.

[0007] Reference 1, "Amir E, Amir O. Concurrent high-resolution topology optimization of structures and their supports for additive manufacturing[J]. Structural and Multidisciplinary Optimization, 2021, 63: 2589-2612," investigates the distribution parameters of solid and empty materials, the homogenization interpolation method for octahedral lattices, and the parameters for simultaneous design of solid and empty materials and lattices. Without sacrificing structural mechanical properties, it reduces large cantilever structures with minimal supporting material and establishes a corresponding parallel computation optimization design framework. However, considering the homogenized lattice material formulation, the penalty rules in this method are not gentle enough, thus failing to produce layouts composed of more lattice supports.

[0008] Reference 2, “Reintjes, C., Lorenz, U. Bridging mixed integer linear programming for truss topology optimization and additive manufacturing[J]. Optimization and Engineering, 2021, 22: 849-893,” developed two mixed integer programs to utilize mathematical optimization methods in the context of topology optimization, building upon methods for fitting ground structures. The first mixed integer program focuses on powder-based additive manufacturing, including preprocessing that allows for multi-material topology optimization. The second mixed integer program generates unsupported lattice structures for additive manufacturing processes by considering geometry-based design rules for tilted and unsupported cylinders, as well as assumptions about the position and orientation of parts within the build volume, typically dependent on the support structure. The problem involves strengthening the lattice structure through local thickening, adding beams, or both; however, a suitable heuristic has not yet been developed to generate efficient solutions that address the existence variables defining the beams and solve the remaining linear programming problem, thus the approach is not yet fully developed.

[0009] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0010] The extremely high geometric complexity and high degree of freedom in material distribution of structures in the existing design space are difficult to match the constraints of material stacking and forming processes in the manufacturing space. It is difficult to directly express structures with good mechanical properties, such as closed inner holes and large cantilever structures, without auxiliary support.

[0011] Time and Material Consumption: When printing multi-cell structures using additive manufacturing technology, the diverse spatial orientations of the geometric features within these structures make it difficult to avoid the need for supporting structures during the forming process. To prevent the collapse of multi-scale structures with complex geometric topologies during manufacturing, additional auxiliary supports must be added during the forming process. Printing these auxiliary supports is not only time-consuming but also increases material consumption.

[0012] Impact on structural performance: For the molding of three-dimensional multi-scale structures, the additional auxiliary supports are difficult to remove effectively, and the structural performance after manufacturing often fails to meet the design requirements. Summary of the Invention

[0013] To address the problems of existing technologies, this invention provides a geometric feature evolution-driven method and system for self-supporting topology design of multi-cell structures. Utilizing the base structure method, the superposition and combination laws of base structures within a single cell are studied, and a method for defining single-cell configurations based on base structures is created. Combining traditional density-based topology optimization methods, a mapping relationship between the established single-cell configuration and design variables is established, a method for calculating the corresponding stiffness matrix is ​​given, a multi-cell structure optimization model based on the single-cell model is defined, and a sensitivity calculation method is derived. Simultaneously, the distribution characteristics of the single-cell model in the multi-cell structure are studied, and a method for defining self-supporting manufacturing voxels is established. Furthermore, the evolution law of manufacturing voxel geometric features is discussed in conjunction with the forming direction constraints of additive manufacturing to achieve self-supporting forming of multi-cell structures.

[0014] This invention is implemented as follows: a geometric feature evolution-driven self-supporting topology design method for multi-cell structures includes:

[0015] Step 1: Define the unit cell configuration, select a beam or rod that is easy to directly form to establish the unit cell, and calculate the stiffness matrix of the two-dimensional unit cell;

[0016] Step 2: Construct a unit cell optimization model, calculate the optimized unit cell stiffness matrix, and determine the unit cell design strategy with the internal nodes centered.

[0017] Step 3: Construct an optimization model for the multi-cell vibration reduction structure and derive the sensitivity calculation method;

[0018] Step 4: Construct the manufacturing voxel and define the molding angles of all basic unit cell components in the model;

[0019] Step 5: Provide the search algorithm for voxel construction in unit cell manufacturing. Start the search based on the topological connection relationship of all units so that all basic units can be formed without support.

[0020] Furthermore, the geometric feature evolution-driven multi-cell self-supporting topology design method specifically includes:

[0021] (1) Unit cell configuration for additive manufacturing;

[0022] (2) Construct an optimization model for a multicellular vibration reduction structure;

[0023] (3) Design model post-processing.

[0024] Furthermore, the unit cell configuration for additive manufacturing specifically includes:

[0025] In setting the unit cell configuration, considering spatial interference relationships, the following restrictions are imposed on the basic units within the unit cell:

[0026] 1) All nodes within any basic unit of a single cell are adjacent to each other;

[0027] 2) The basic units within a unit cell have independent shape control parameters;

[0028] 3) Basic units within or between units can merge to form more complex geometries;

[0029] The element stiffness matrix K of the bar element e As can be seen from the definition:

[0030] K e =TK′ e T T (1)

[0031] in

[0032] (two-dimensional),

[0033] (3D)

[0034] E is the elastic modulus of the rod material, A and L are the cross-sectional area and length of the rod element, respectively, and α, β, γ are the angles between the local coordinate system and the corresponding axes of the spatial coordinate system of the rod.

[0035] A unit cell consists of shared nodes and unique nodes. Therefore, the stiffness matrix of a defined two-dimensional unit cell can be expressed as:

[0036]

[0037] For two-dimensional unit cells, n = 8; for three-dimensional unit cells, n = 20.

[0038] Then, in order to find the appropriate location for the exclusive node, a unit cell optimization model needs to be constructed;

[0039] In the defined unit cell structure, the stiffness matrix of its unit cell can be rewritten as:

[0040]

[0041] in η i =A i / L i ;

[0042] Since elements with shared nodes are shared with other unit cells, while elements with unique nodes are unique to that unit cell, the unit cell stiffness matrix can be redefined as follows:

[0043]

[0044] Where nn represents the number of shared units in a unit cell, and mm is the total number of units in a unit cell that have unique nodes. In the defined two-dimensional unit cell, mm = 4 and nn = 4; in the three-dimensional unit cell, nn = 12 and mm = 8.

[0045] Combining equations (3) and (4), the unit cell stiffness matrix and coefficient η i The correlation refers to the geometric position of the exclusive node within the unit cell. Therefore, the following model is defined to calculate the appropriate position of the exclusive node.

[0046] find(x,y)

[0047] min K b

[0048] st.0<x<Lx

[0049] 0 < y < Ly

[0050]

[0051] Where (xi,yi) are the coordinates of the four corner points of the unit cell, and Lx and Ly are the length and width dimensions of the unit cell;

[0052] Assuming that the cross-sectional areas of the rod elements that make up the unit cell are the same, solving the above equations shows that for a square unit cell, the stiffness matrix of the unit cell is minimized when the coordinates of the exclusive node are (Lx / 2, Ly / 2).

[0053] For ease of calculation, it is assumed that all the rod elements that make up the unit cell have the same cross-sectional area. In this case, the unit cell stiffness matrix can be written as:

[0054]

[0055] For ease of optimization, the optimization model for a single cell is defined as follows:

[0056]

[0057] Where p is the penalty factor, ρ c This represents the unit cell density.

[0058] Furthermore, the construction of the multicellular vibration reduction structure optimization model specifically includes:

[0059] First, the optimization model is defined as follows:

[0060] Based on the macroscopic structural model of the rod unit cell, the optimization objective is set as minimizing the structural flexibility, and the constraint is that the spatial proportion of the rod is no greater than υ.

[0061] Find: X(ρ)

[0062] min:

[0063] stKU=F

[0064] V≤υ

[0065] 0 < ρ min ≤ρ i,j ≤ρ max i = 1, ..., n i j = 1,...,n j (8)

[0066] Where K, U, and F represent the overall stiffness matrix, displacement field, and external forces of the model, respectively; n i n j ρ represents the total number of unit cells in the x- and y-directions of the design domain, respectively; i,j υ represents the density of the rod unit cell; υ represents the volume constraint of the rod unit cell.

[0067] From equations (4) and (7), it can be seen that the unit cell density is determined by the sum of the cross-sectional area and length of each rod constituting the unit cell, and its mapping can be set as follows:

[0068]

[0069] In the constructed unit cell, the shared unit formed by the shared nodes is shared by multiple unit cells;

[0070] As can be seen from the above unit cell density mapping formula, shared units occupy a certain density proportion in adjacent unit cells. Therefore, to eliminate the redundant calculation of shared units in multiple adjacent unit cells, optimization model 8 can be rewritten as follows:

[0071] Find: X(ρ)

[0072] min:c(ρ)=U T (K1+K2)U

[0073] st(K1+K2)U=F

[0074] V≤υ

[0075] 0 < ρ min ≤ρi,j ≤ρ max i = 1, ..., n i j = 1,...,n j (10)

[0076] Where K1 and K2 are the stiffness matrices corresponding to the shared elements and the independent elements in the unit cell, respectively;

[0077] Then calculate the sensitivity; by differentiating the optimization objective of optimization model 10, we can obtain...

[0078]

[0079] From formula (7), we can see that

[0080]

[0081] Where K b,1 ,K b,2 These are the stiffness matrix components of shared and independent elements in the unit cell stiffness matrix, respectively.

[0082] Since the density of the rod unit cell is continuous, the OC optimization criterion is chosen to update the optimization design variables:

[0083]

[0084] Where ε is the step size, and parameter η = 0.5,

[0085] Furthermore, the post-processing of the design model specifically includes:

[0086] For each basic unit Υ in a unit cell i Add molding information, i.e.

[0087] Υ i :=(P i ,β i (14)

[0088] Where P i Let β be the coordinates of all nodes of this basic unit. i ∈[β i,min ,β i,max ] represents the range of formable overhang angles for this unit in the selected forming direction, β i,min ,β i,max These are the minimum and maximum forming angles, respectively;

[0089] For a two-dimensional model, the minimum and maximum forming angles can be expressed as:

[0090] β i,min :=(β xoy,min ), β i,max:=(β xoy,max );

[0091] For a 3D model, the minimum and maximum forming angles can be expressed as:

[0092] β i,min :=(β xoy,min ,β xoz,min ,β yoz,min ), β i,max :=(β xoy,max ,β xoz,max ,β yoz,max );

[0093] Where β xoy,min β xoy,max β xoz,min β xoz,max β yoz,min β yoz,max In a spatial posture where a self-supporting forming can be achieved under a given forming direction, the minimum and maximum angles between the current basic unit and the XOY, XOZ, and YOZ planes;

[0094] Therefore, the manufacture of voxels can be represented as:

[0095]

[0096] in This is the set of coordinates of all relevant basic unit nodes. The intersection of the range of formable overhang angles of all relevant basic units; from the above definition of manufacturing voxels, we can know the construction principles of manufacturing voxels: 1) All basic units contained in a manufacturing voxel are connected; 2) The formable overhang angle in a manufacturing voxel is the overhang angle that all basic units can be formed without support.

[0097] Then comes the manufacturing of the design model;

[0098] Choose any cell and start the search based on the topological connection relationship of all cells. In addition to ensuring that the characteristics of manufacturing voxel connectivity are met, the self-supporting forming angle of the manufacturing voxel can also be determined based on its forming overhang angle range. Of course, the number of manufacturing voxels constructed will be different depending on the search direction.

[0099] Voxels can be manufactured individually and then assembled into complex topological structures through model assembly; generally, the fewer voxels manufactured, the lower the manufacturing complexity.

[0100] Another objective of this invention is to provide a geometry feature evolution-driven multi-cell structure self-supporting topology design system for implementing the geometry feature evolution-driven multi-cell structure self-supporting topology design method, comprising: a single-cell configuration definition module, a single-cell optimization model construction module, a multi-cell vibration reduction structure optimization model construction module, a manufacturing voxel construction module, and a search algorithm execution module;

[0101] The unit cell configuration definition module is used to select beams and bars that are easy to directly form to establish unit cells and calculate the stiffness matrix of two-dimensional unit cells;

[0102] The unit cell optimization model construction module is used to calculate the optimized unit cell stiffness matrix and determine the design strategy for centering the nodes inside the unit cell.

[0103] The module for constructing a multi-cell vibration reduction structure optimization model is used to derive the sensitivity calculation method and perform multi-cell structure optimization design.

[0104] The manufacturing voxel building module is used to define the molding angles of all basic unit cell components in the model and to achieve unsupported molding of all basic units;

[0105] The search algorithm execution module is used to start the search based on the topological connection relationship of all units to ensure the effective connection and formation of all basic units.

[0106] Furthermore, the unit cell configuration definition module further includes a unit cell stiffness matrix calculation unit, which is responsible for calculating the stiffness matrix of the unit cell based on the physical and geometric parameters of the selected beam, providing basic data for the stability and structural performance evaluation of the unit cell;

[0107] The unit cell optimization model construction module further includes a unit cell internal node position optimization unit. This optimization unit is responsible for determining the optimal position of the internal nodes of the unit cell based on the stiffness matrix and predetermined performance indicators through numerical optimization methods, thereby maximizing the performance of the unit cell structure.

[0108] The multi-cell vibration reduction structure optimization model construction module further includes a vibration reduction performance analysis unit. This analysis unit is responsible for determining the configuration and parameters of each cell in the multi-cell structure based on the constructed multi-cell structure model and external excitation conditions, through sensitivity analysis and optimization algorithms, so as to achieve the best vibration reduction performance of the overall structure.

[0109] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the geometric feature evolution-driven multi-cell self-supporting topology design method.

[0110] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the geometric feature evolution-driven multi-cell self-supporting topology design method.

[0111] Another objective of this invention is to provide an information data processing terminal for implementing the aforementioned geometric feature evolution-driven multi-cell structure self-supporting topology design system.

[0112] Based on the above technical solutions and the technical problems solved, please analyze the advantages and positive effects of the technical solution to be protected by this invention from the following aspects:

[0113] First, this invention uses rods and beams to construct a unit cell, with a node set within the unit cell to give it better mechanical properties. The mechanical properties are further enhanced by the layout of the rod elements within the unit cell. The unit cell structure, composed of simple rods and beams and other basic units, is easy to directly form.

[0114] This invention selects a suitable search direction among the units. Each voxel can be manufactured individually and then assembled into a model to achieve its complex topological structure. Generally, the fewer voxels, the lower the manufacturing complexity. A suitable search direction not only satisfies the connectivity characteristics of the voxels but also determines their self-supporting forming angle based on their forming overhang angle range. The resulting voxel construction scheme has a single forming direction and a small number of voxels, thus reducing manufacturing complexity.

[0115] Therefore, this invention starts with a rod system structure, utilizes the spatial topology of the rod system to design a multi-cell structure, and analyzes the matching relationship between the pose of the rod system and the cantilever constraints of additive manufacturing to establish the evolution of the geometric features of the multi-cell structure rod system under manufacturing constraints. This leads to the establishment of an integrated method for multi-cell structure design and manufacturing based on the rod geometry features. This achieves self-supporting molding of the multi-cell structure, improves material utilization, saves post-processing time and costs, and reduces the risk of structural damage due to the removal of supporting structures.

[0116] Secondly, since rods and beams are easier to form directly, this invention starts from the rod system structure, uses the spatial topology of the rod system to realize the design of the multi-cell structure, and determines the self-supporting forming angle of the manufacturing voxel and the appropriate element search direction based on the matching relationship between the pose of the rod system and the cantilever constraint of additive manufacturing. It establishes an integrated method for multi-cell structure design and manufacturing based on the geometric features of the rod, and realizes the self-supporting forming of the multi-cell structure.

[0117] This invention investigates the coupling relationship between the layout of rod elements within a unit cell and its structural performance, determining a unit cell design strategy with centered nodes and establishing a mapping relationship between the unit cell and density. It also derives a sensitivity calculation method for optimization design variables by combining traditional structural topology optimization methods. Utilizing the spatial pose characteristics of rod elements within the unit cell and considering the cantilever angle constraints during rod element formation, corresponding manufacturing voxels are defined. Through geometric feature evolution such as rod element pose fusion, the construction of manufacturing voxels is achieved. By using manufacturing voxels, unsupported forming of the design model is realized.

[0118] This invention utilizes rod-based basic units to construct an integrated method for the design and manufacturing of multicellular structures. It provides a new approach and method for the organic integration of multicellular structure design and manufacturing.

[0119] Third, the integration of topology optimization and additive manufacturing provides a theoretical approach and implementation method for innovative structural design and the development of high-performance components. However, the extremely high geometric complexity and material distribution freedom of structures in the design space make it difficult to match the constraints of material stacking and forming processes in the manufacturing space, and it is difficult to directly express some structures with good mechanical properties without auxiliary support. Many scholars start from solid structures, simulate the layered superposition of materials in the design domain, ignore the supporting structure, and use solid materials to achieve self-supporting forming of the structure. Therefore, this invention starts from the rod system structure, uses the spatial topology of the rod system to realize the design of multi-cell structures, and analyzes the matching relationship between the pose of the rod system and the cantilever constraints of additive manufacturing to establish the evolution of the geometric features of the multi-cell structure rod system under manufacturing constraints. It establishes an integrated method for multi-cell structure design and manufacturing based on rod geometry features, creating a new method for realizing the self-supporting forming of multi-cell structures. Attached Figure Description

[0120] Figure 1 This is a flowchart of a geometric feature evolution-driven self-supporting topology design method for multi-cell structures provided in an embodiment of the present invention.

[0121] Figure 2 This is a detailed flowchart of the geometric feature evolution-driven self-supporting topology design method for multi-cell structures provided in this embodiment of the invention.

[0122] Figure 3 These are two-dimensional and three-dimensional unit cell diagrams formed by rod elements, provided in embodiments of the present invention.

[0123] Figure 4 These are shared units between cells provided in the embodiments of the present invention: (a) two-dimensional unit cell combination; (b) three-dimensional unit cell combination.

[0124] Figure 5 This is a voxel definition diagram corresponding to the unit cell and its basic unit provided in the embodiments of the present invention.

[0125] Figure 6 This is a voxel construction diagram of a single cell provided in an embodiment of the present invention.

[0126] Figure 7 This is a cantilever beam design domain and unit cell partitioning diagram provided in an embodiment of the present invention.

[0127] Figure 8 This is a diagram showing the optimization results and convergence process provided by the embodiments of the present invention.

[0128] Figure 9 This is a three-dimensional support model diagram provided in an embodiment of the present invention.

[0129] Figure 10 This is an optimized result diagram provided by an embodiment of the present invention.

[0130] Figure 11 This is a structural diagram of a multi-cell self-supporting topology design system driven by geometric feature evolution provided in an embodiment of the present invention.

[0131] Figure 12 This is a schematic diagram of the multi-cell structure of the three-dimensional scaffold provided in the embodiment of the present invention; wherein, (a) is a 1 / 4 design model, and (b) is a shared unit and a unique unit in the design model.

[0132] Figure 13 This is an analysis of the forming support structure for manufacturing voxels provided in an embodiment of the present invention, and a slice result diagram. Detailed Implementation

[0133] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0134] The following are two specific embodiments provided by the geometric feature evolution-driven multi-cell structure self-supporting topology design method according to the present invention:

[0135] Example 1: Lightweight Multicellular Structure Design for Aerospace Components

[0136] Step 1: Define the unit cell configuration

[0137] A lightweight, high-strength beam material, such as aluminum alloy or titanium alloy, is selected to construct the unit cell configuration. A star-shaped unit cell is used as the basic unit because it exhibits good deformation stability under pressure. The stiffness matrix of the two-dimensional star-shaped unit cell is calculated based on the beam's cross-sectional dimensions and length.

[0138] Step 2: Construct a unit cell optimization model

[0139] The stiffness of a star-shaped unit cell was optimized using the finite element method. The optimized unit cell stiffness matrix was obtained by adjusting the cross-sectional dimensions, length, and included angle of the beams. Simultaneously, to ensure the centers of the nodes within the unit cell, a node positioning algorithm was designed to ensure the node positions remain stable during manufacturing.

[0140] Step 3: Construct an optimization model for a multicellular vibration reduction structure

[0141] Considering the vibration effects on aircraft components during high-speed flight, multiple star-shaped unit cells are combined into a multi-cell structure to reduce vibration transmission. Based on the characteristics of vibration transmission and the dynamic model of the multi-cell structure, a sensitivity calculation method is derived to evaluate the impact of different unit cell arrangements on vibration reduction.

[0142] Step 4: Constructing the manufacturing voxel

[0143] To ensure that multicellular structures can be formed without support during additive manufacturing, the forming angle of the basic unit cell components is defined. Fused deposition modeling (FDM) technology is used to design the unit cell components as a stacked structure with a certain tilt angle, so that the supporting forces between adjacent layers cancel each other out.

[0144] Step 5: Provide the search algorithm for voxel construction during single-cell manufacturing.

[0145] Based on the topological connections of all units, a depth-first search (DFS) algorithm was designed to ensure that all basic units can be formed without support during the manufacturing process. Furthermore, considering errors and deformations during manufacturing, the search algorithm was robustly optimized.

[0146] Example 2: Impact-resistant multicellular structure design for automotive components

[0147] Step 1: Define the unit cell configuration

[0148] A high-toughness beam material, such as high-strength steel, is selected to construct the unit cell configuration. A honeycomb unit cell is used as the basic unit because it has good energy absorption capacity under impact. The stiffness matrix of the two-dimensional honeycomb unit cell is calculated based on the beam's cross-sectional dimensions and length.

[0149] Step 2: Construct a unit cell optimization model

[0150] Finite element analysis and multi-objective optimization algorithms were used to jointly optimize the stiffness and energy absorption performance of honeycomb unit cells. The optimized unit cell stiffness matrix and energy absorption performance were obtained by adjusting the cross-sectional dimensions, length, and included angle of the beams. Simultaneously, a node fixing device was designed to ensure the stability of the nodes during the manufacturing process, thereby guaranteeing the centering of the internal nodes.

[0151] Step 3: Construct an optimization model for a multicellular vibration reduction structure

[0152] Considering the impact on automotive components during a collision, multiple honeycomb-shaped unit cells are combined into a multi-cell structure to improve impact resistance. Based on the characteristics of impact transmission and the dynamic model of the multi-cell structure, a sensitivity calculation method is derived to evaluate the impact resistance effect of different unit cell arrangements.

[0153] Step 4: Constructing the manufacturing voxel

[0154] To ensure that multi-cell structures can be formed without support during additive manufacturing, the forming angle of the basic unit cell components is defined. Using laser melting forming (SLM) technology, the unit cell components are designed as a stacked structure with a certain tilt angle, so that the support forces between adjacent layers cancel each other out.

[0155] Step 5: Provide the search algorithm for voxel construction during single-cell manufacturing.

[0156] Based on the topological connections of all units, a breadth-first search (BFS) algorithm was designed to ensure that all basic units can be formed without support during the manufacturing process. Simultaneously, considering the thermal stress and deformation during manufacturing, the search algorithm was optimized for thermal stability.

[0157] These two examples, focusing on lightweighting of aerospace components and impact resistance of automotive components respectively, demonstrate the application of a geometry-driven multi-cell self-supporting topology design method in different fields.

[0158] The geometric feature evolution-driven self-supporting topology design method for multi-cell structures provided by this invention mainly involves defining the single-cell configuration, constructing a single-cell optimization model, constructing a multi-cell vibration reduction structure optimization model, building manufacturing voxels, and achieving unsupported molding of all basic units through a search algorithm. This method has the following core innovations:

[0159] 1. Definition and Optimization of Unit Cell Configuration: Unit cells are established by selecting beams and bars that are easy to directly form, and the stiffness matrix of the two-dimensional unit cell is calculated. Furthermore, by constructing a unit cell optimization model, the optimized unit cell stiffness matrix is ​​calculated, and a unit cell design strategy with centered internal nodes is determined, thus providing a stable foundation for the design of multi-cell structures.

[0160] 2. Construction of the Optimization Model for Multi-cell Vibration-Impairing Structures: This step optimizes the design of multi-cell vibration-impairing structures by deriving sensitivity calculation methods to achieve the best vibration reduction effect. This step is crucial in the design of multi-cell structures, as it directly affects the structure's vibration reduction performance.

[0161] 3. Construction of voxels: By defining the forming angles of all basic unit components in the model and providing a search algorithm for constructing voxels in the unit cell, it is ensured that all basic units can be formed without support. This innovation greatly improves the manufacturing efficiency and feasibility of multicellular structures.

[0162] 4. Unit cell configuration design for additive manufacturing: In the process of setting the unit cell configuration, the basic units within the unit cell are strictly limited to ensure that the basic units within or between units can be integrated to form more complex geometries. At the same time, it is ensured that all nodes within any basic unit within the unit cell are adjacent to each other. This design helps to improve the stability and strength of the structure.

[0163] 5. Post-processing of the design model: By adding molding information to each basic unit in the unit cell and by defining the manufacturing voxel, it is ensured that the basic units contained in the manufacturing voxel are connected, and the formable overhang angle in the manufacturing voxel is the overhang angle that all basic units can be formed without support. This post-processing step further improves the manufacturability of the design model.

[0164] The geometric feature evolution-driven multi-cell structure self-supporting topology design method of the present invention not only innovates in the design and optimization of single-cell configurations, the optimized design of multi-cell vibration reduction structures, the construction of manufacturing voxels, and the post-processing of design models, but also greatly improves the manufacturing efficiency and application range of multi-cell structures through single-cell configuration design for additive manufacturing, providing new ideas and methods for the design and manufacturing of complex structures.

[0165] This invention provides a method for constructing voxels to achieve supportless printing of multicellular structures using additive manufacturing technology. Key innovations include the following steps:

[0166] Using the basis structure method, the superposition and combination rules of basis structures within a single cell were studied, and a method for defining single-cell configurations based on basis structures was created. Combining this with traditional density-based topology optimization methods, a mapping relationship between the established single-cell configuration and design variables was established, and a method for calculating the corresponding stiffness matrix was given. A multi-cell structure optimization model based on the single-cell model was defined, and a sensitivity calculation method was derived. Simultaneously, the distribution characteristics of the single-cell model in multi-cell structures were investigated, and a method for defining self-supporting, formable manufacturing voxels was established.

[0167] like Figure 1 , 2 As shown, the geometric feature evolution-driven self-supporting topology design method for multi-cell structures provided in this embodiment of the invention includes the following steps:

[0168] S101, Define the unit cell configuration, select rods and beams that are easy to form directly to establish the unit cell, and calculate the stiffness matrix of the two-dimensional unit cell; Multi-cell structures usually have complex unit cell configurations and macroscopic structures. In order to form the multi-cell structure under zero-support structural conditions, it is assumed that the unit cell structure is composed of simple rods and beams and other basic units. The stiffness matrix of the two-dimensional unit cell is written through the element stiffness matrix of the rod element and the positional relationship between the rod elements.

[0169] S102, construct a unit cell optimization model, calculate the optimized unit cell stiffness matrix, and determine the unit cell design strategy of centering the nodes inside the unit cell; as can be seen from the definition of a unit cell, the stiffness matrix of the unit cell is related to the geometric position of the exclusive node inside the unit cell. Define the optimization model, calculate the appropriate position of the exclusive node, and determine the unit cell design strategy of centering the nodes inside the unit cell.

[0170] S103. Construct an optimization model for a multi-cell vibration reduction structure and derive a sensitivity calculation method. Based on a macroscopic structural model of a rod-based unit cell, the optimization objective is set to minimize structural flexibility, with the constraint that the spatial proportion of the rods should not exceed the volume constraint of the rod unit cell. The unit cell density is determined by the sum of the cross-sectional area and length of each rod constituting the unit cell. By establishing a unit cell density mapping relationship, the optimization model is derived and constructed.

[0171] S104, construct the manufacturing voxel and define the forming angle of all basic components of the unit cell in the model; since the spatial poses of each basic component that makes up the unit cell are different, additional forming support is inevitably required during its forming process. Considering that the cantilever angle is an important factor affecting the forming of the structure, forming information is added to each basic unit in the unit cell, and the manufacturing voxel is represented by the minimum and maximum forming angles of the two-dimensional and three-dimensional models.

[0172] S105 presents a search algorithm for building voxels using a single cell, which starts the search based on the topological connections of all cells, allowing all basic cells to be formed without support.

[0173] The specific steps are as follows:

[0174] Step 1: Unit cell configuration for additive manufacturing.

[0175] To achieve self-supporting molding of multi-cell structures, this paper introduces a design method for single-cell structures based on rods and beams, which are easier to directly mold. Definition of Single-Cell Configuration: Multi-cell structures typically have complex single-cell configurations and macroscopic structures. To allow multi-cell structures to be molded under zero-support conditions, we assume that the single-cell structure is composed of simple basic units such as rods and beams, such as... Figure 3As shown in the figure. Dots represent unit cell nodes, black line segments between any two nodes represent rod elements, numbers indicate node numbers, oxyz is the local coordinate system, and OXYZ is the global coordinate system. To improve the mechanical properties of the unit cell, a node is placed within the unit cell, and the arrangement of rod elements within the unit cell enhances its mechanical properties.

[0176] In the unit cell defined above, boundary nodes shared with other unit cells are called shared nodes, and nodes inside the unit cell are called unique nodes. For a defined 3D unit cell, nodes located at corners are shared by eight adjacent unit cells, and one node inside the unit cell is unique to that unit cell. If there are nodes within the six boundary planes of the unit cell, these shared nodes are shared by two adjacent unit cells. Among the basic units that make up a unit cell, if a basic unit is entirely composed of shared nodes, we define it as a shared basic unit; if a basic unit contains unique nodes, then that basic unit is a unique basic unit. Therefore, in setting the unit cell configuration, considering spatial interference relationships, the following restrictions are imposed on the basic units within the unit cell:

[0177] 1. Within any basic unit of a single cell, all nodes are pairwise adjacent;

[0178] 2. The basic units within a unit cell have independent shape control parameters;

[0179] 3. Basic units within or between units can merge to form more complex geometries.

[0180] The element stiffness matrix K of the bar element e As can be seen from the definition:

[0181] K e =TK′ e T T (1)

[0182] in

[0183] (two-dimensional),

[0184] (3D)

[0185] E is the elastic modulus of the rod material, A and L are the cross-sectional area and length of the rod element, respectively, and α, β, and γ are the angles between the corresponding axes of the local coordinate system and the spatial coordinate system of the rod.

[0186] A unit cell consists of shared nodes and unique nodes. Therefore, the stiffness matrix of a defined two-dimensional unit cell can be expressed as:

[0187]

[0188] For two-dimensional unit cells, n = 8, and for three-dimensional unit cells, n = 20.

[0189] Then, in order to find the appropriate location for the exclusive node, a unit cell optimization model needs to be constructed.

[0190] In the defined unit cell structure, the stiffness matrix of its unit cell can be rewritten as:

[0191]

[0192] in η i =A i / L i .

[0193] Since elements with shared nodes are shared with other unit cells, while elements with unique nodes are unique to that unit cell, the unit cell stiffness matrix can be redefined as follows:

[0194]

[0195] Where nn represents the number of shared units in a unit cell, and mm is the total number of units in a unit cell that have unique nodes. In the defined two-dimensional unit cell, mm = 4 and nn = 4; in the three-dimensional unit cell, nn = 12 and mm = 8.

[0196] Combining equations (3) and (4), the unit cell stiffness matrix and coefficient η i The correlation is related to the geometric position of the exclusive node within the unit cell. Therefore, we define the following model to calculate the appropriate position of the exclusive node.

[0197]

[0198] Where (xi,yi) are the coordinates of the four corner points of the unit cell, and Lx and Ly are the length and width dimensions of the unit cell.

[0199] Assuming that the cross-sectional areas of the rod elements that make up the unit cell are the same, solving the above equations shows that for a square unit cell, the stiffness matrix of the unit cell is minimized when the coordinates of the exclusive node are (Lx / 2, Ly / 2).

[0200] For ease of calculation, it is assumed that all the rod elements that make up the unit cell have the same cross-sectional area. In this case, the unit cell stiffness matrix can be written as:

[0201]

[0202] For ease of optimization, we define the optimization model for the unit cell as follows:

[0203]

[0204] Where p is the penalty factor, ρ cThis represents the unit cell density.

[0205] Step 2: Construct an optimization model for a multicellular vibration reduction structure

[0206] First, the optimization model is defined as follows:

[0207] Based on the macroscopic structural model of the rod unit cell, the optimization objective is set as minimizing the structural flexibility, with the constraint that the spatial proportion of the rod is no greater than υ.

[0208]

[0209] Where K, U, and F represent the overall stiffness matrix, displacement field, and external forces of the model, respectively; n i n j ρ represents the total number of unit cells in the x- and y-directions of the design domain, respectively; i,j υ represents the density of the rod unit cell; υ represents the volume constraint of the rod unit cell.

[0210] From equations (4) and (7), it can be seen that the unit cell density is determined by the sum of the cross-sectional area and length of each rod constituting the unit cell, and its mapping can be set as follows:

[0211]

[0212] In the constructed unit cell, the shared unit formed by shared nodes is shared by multiple units cells, such as... Figure 4 Shared units L1 and L2 in (a), Figure 4 In (b), L1, L2, L3 and L4 are all shared by adjacent units.

[0213] As can be seen from the above unit cell density mapping formula, shared units occupy a certain density proportion in adjacent unit cells. Therefore, to eliminate the redundant calculation of shared units in multiple adjacent unit cells, optimization model 8 can be rewritten as follows:

[0214]

[0215] Where K1 and K2 are the stiffness matrices corresponding to the shared elements and the independent elements in the unit cell, respectively.

[0216] Then the sensitivity is calculated. Taking the derivative of the optimization objective of the optimization model (10), we can obtain...

[0217]

[0218] From Formula 7, we can see that

[0219]

[0220] Where K b,1 ,K b,2These are the stiffness matrix components of shared and independent elements in the unit cell stiffness matrix, respectively.

[0221] Since the density of the rod unit cell is continuous, we choose the OC optimization criterion to update the optimization design variables:

[0222]

[0223] Where ε is the step size, and parameter η = 0.5,

[0224] Step 3: Post-processing of the design model

[0225] To design a model that can be formed with minimal support structures, we define a manufacturing voxel. A structure that can be formed without support structures is called a manufacturing voxel. We also define the forming angles of all basic components of the unit cell in the model and use the range of forming angles to achieve supportless forming of the design model.

[0226] First, we construct the manufacturing voxels. Since the spatial poses of the various basic components that make up the unit cell are different, additional forming supports are inevitably required during the forming process. Considering that the cantilever angle is a crucial factor affecting structural forming, we assign a Y-shaped support to each basic unit in the unit cell. i Add molding information, i.e.

[0227] Υ i :=(P i ,β i (14)

[0228] Where P i Let β be the coordinates of all nodes of this basic unit. i ∈[β i,min ,β i,max ] represents the range of formable overhang angles for this unit in the selected forming direction, β i,min ,β i,max These are the minimum and maximum forming angles, respectively.

[0229] For a two-dimensional model, the minimum and maximum forming angles can be expressed as:

[0230] β i,min :=(β xoy,min ), β i,max :=(β xoy,max );

[0231] For a 3D model, the minimum and maximum forming angles can be expressed as:

[0232] β i,min :=(β xoy,min ,β xoz,min ,β yoz,min ), β i,max :=(βxoy,max ,β xoz,max ,β yoz,max );

[0233] Where β xoy,min β xoy,max β xoz,min β xoz,max β yoz,min β yoz,max In a spatial orientation where a self-supporting forming mechanism is given a forming direction, the minimum and maximum included angles between the current basic unit and the XOY, XOZ, and YOZ planes.

[0234] Therefore, the manufacture of voxels can be represented as:

[0235]

[0236] in This is the set of coordinates of all relevant basic unit nodes. The intersection of the range of formable overhang angles of all relevant basic units. Based on the above definition of a manufacturing voxel, the construction principles of a manufacturing voxel are: 1) All basic units contained in a manufacturing voxel are connected; 2) The formable overhang angle in a manufacturing voxel is the overhang angle that all basic units can be formed without support.

[0237] Next is the fabrication of the design model. Taking the defined planar unit cell model as an example, we will demonstrate the voxel construction of this unit cell to achieve its unsupported molding. This planar unit cell contains 4 shared elements and 4 independent elements. Assuming… Figure 5 The vertically upward arrow in the middle indicates the forming direction of the unit cell, and the limit cantilever angle is set to 45°, that is, the structure can achieve self-supporting forming when the angle between the structure and the forming direction is no greater than 45 degrees.

[0238] Arbitrarily select a cell and begin the search based on the topological connections of all cells. Besides ensuring the connectivity of the manufacturing voxel, the self-supporting forming angle of the manufacturing voxel can also be determined based on its forming overhang angle range. Of course, the number of manufacturing voxels constructed will vary depending on the search direction. Figure 6 The figure shows the partitioning results of two different manufacturing voxels within the same unit cell. The arrows in the figure indicate the molding direction, and the angle between the two arrows represents the distribution range of the self-supporting molding direction of the manufacturing voxels. Figure 6 In (a), there are three manufacturing voxels, each of which has its own self-supporting forming angle. For example, the self-supporting forming angle range of manufacturing voxels (L1, L5, L6, L7, L3, L8) is [45°, 90°]. Figure 6 (b) contains two manufacturing voxels: an outer frame (L1, L2, L3, L4) and an inner cross (L5, L6, L7, L8). Each manufacturing voxel has a single self-supporting forming angle.

[0239] exist Figure 6 In the two voxel fabrication schemes shown, each voxel can be manufactured individually and then assembled into a model to achieve its complex topological structure. Generally, the fewer voxels required, the lower the fabrication complexity; therefore, we recommend [the following scheme]. Figure 6 (b) has a single forming direction and a small number of voxels.

[0240] Here, we present the search algorithm for constructing voxels:

[0241] Manufacturing voxel construction algorithm

[0242] Function Ms=getAllMatruaturingModel(model,angle)

[0243] / / model is the set of basic units contained in this model;

[0244] / / angle is the range of formable overhang angles allowed for each basic unit;

[0245] / / Ms is the set of voxels obtained during manufacturing

[0246] for each baseElement in model

[0247] ifβ i ∈[β i,min ,β i,max ]

[0248]

[0249] else new M j

[0250] end

[0251] add M j to Ms

[0252] return Ms

[0253] As a preferred embodiment of the present invention, the geometric feature evolution-driven multi-cell structure self-supporting topology design method includes the following steps: defining a single-cell configuration, constructing a single-cell optimization model, constructing a multi-cell vibration reduction structure optimization model, constructing manufacturing voxels, and achieving unsupported molding of all basic units through a search algorithm to achieve the optimal vibration reduction effect and manufacturing efficiency of the multi-cell structure.

[0254] In the step of defining the unit cell configuration, a beam that is easy to directly form is selected to establish the unit cell, and the stiffness matrix of the two-dimensional unit cell is calculated to provide a stable unit cell configuration as the basis for the design of multi-cell structures.

[0255] In the process of constructing the unit cell optimization model, the structural stiffness of the unit cell is optimized and the internal structural configuration of the unit cell is simplified by calculating the optimized unit cell stiffness matrix and determining the unit cell design strategy with the nodes centered inside the unit cell.

[0256] In the process of constructing the optimization model of the multi-cell vibration reduction structure, a sensitivity calculation method is derived to guide the optimization design of the multi-cell structure and achieve the best vibration reduction effect.

[0257] In the process of constructing manufacturing voxels, the forming angles of all basic components of the unit cell in the model are defined, and a search algorithm is given when constructing unit cell manufacturing voxels to ensure that all basic units can be formed without support, thereby improving the manufacturing efficiency of multi-cell structures.

[0258] By designing unit cell configurations for additive manufacturing, spatial interference relationships are considered, the layout of basic units within a unit cell is restricted, and basic units within or between units are allowed to merge to form more complex geometries, thereby improving the stability and strength of the structure.

[0259] The technical effects of the present invention will be further described below with reference to specific implementation examples.

[0260] 1. Optimization Design of Two-Dimensional Cantilever Beam Structure

[0261] like Figure 7 In the cantilever beam structure shown, the design domain is a×b=2×1, fixed on the left side, and a downward force F=1 is applied at the upper right corner of the design domain. Within the design domain, the number of unit cells is set to n1×n2=20×10, and the sensitivity filtering radius is set to 2.1 times the side length of the unit cell.

[0262] The optimization results and convergence process are as follows: Figure 8 As shown. To ensure the mechanical properties and manufacturability of the rod basic elements within the unit cell, the minimum relative density of the unit cell was set to 0.05 and the maximum relative density was set to 0.4 during the optimization process.

[0263] 2. Three-dimensional support frame structure design

[0264] Using the proposed method, a three-dimensional model with its four corners fixed at the bottom is designed, such as... Figure 9As shown, the design domain is D = 1m × 0.5m × 1m, and a concentrated downward force F = 1N is applied to the top center of the design domain. The volume constraint of the model is set to 0.2. The internal configuration of the 3D scaffold is designed using the constructed unit cells. The diameter Φ of the rods in the unit cell is controlled by the unit cell density, and the diameters of shared and exclusive units within the unit cell are set to be equal. The design domain unit cells are divided into n1 × n2 × n3 = 6 × 3 × 6, and the sensitivity filtering radius is set to 1.1 times the side length of the unit cell.

[0265] Optimization results are as follows Figure 10 As shown in (a), its convergence process is as follows: Figure 10 As shown in (b), during the optimization process, we set symmetric constraints, and the optimized structure has a distinct spatial topological configuration.

[0266] like Figure 11 As shown in the embodiment of the present invention, the geometric feature evolution-driven multi-cell structure self-supporting topology design method for multi-cell structures provides a geometric feature evolution-driven multi-cell structure self-supporting topology design system, which includes: a single-cell configuration definition module, a single-cell optimization model construction module, a multi-cell vibration reduction structure optimization model construction module, a manufacturing voxel construction module, and a search algorithm execution module.

[0267] The unit cell configuration definition module is used to select beams and bars that are easy to directly form to establish unit cells and calculate the stiffness matrix of two-dimensional unit cells;

[0268] The unit cell optimization model construction module is used to calculate the optimized unit cell stiffness matrix and determine the design strategy for centering the nodes inside the unit cell.

[0269] The module for constructing a multi-cell vibration reduction structure optimization model is used to derive the sensitivity calculation method and perform multi-cell structure optimization design.

[0270] The manufacturing voxel building module is used to define the molding angles of all basic unit cell components in the model and to achieve unsupported molding of all basic units;

[0271] The search algorithm execution module is used to start the search based on the topological connection relationship of all units to ensure the effective connection and formation of all basic units.

[0272] The unit cell configuration definition module further includes a unit cell stiffness matrix calculation unit, which is responsible for calculating the stiffness matrix of the unit cell based on the physical and geometric parameters of the selected beam, providing basic data for the stability and structural performance evaluation of the unit cell.

[0273] The unit cell optimization model construction module further includes a unit cell internal node position optimization unit. This optimization unit is responsible for determining the optimal position of the internal nodes of the unit cell based on the stiffness matrix and predetermined performance indicators through numerical optimization methods, thereby maximizing the performance of the unit cell structure.

[0274] The multi-cell vibration reduction structure optimization model construction module further includes a vibration reduction performance analysis unit. This analysis unit is responsible for determining the configuration and parameters of each cell in the multi-cell structure based on the constructed multi-cell structure model and external excitation conditions, through sensitivity analysis and optimization algorithms, so as to achieve the best vibration reduction performance of the overall structure.

[0275] Since poles and beams are easier to form directly, this invention starts from the pole system structure, uses the spatial topology of the pole system to realize the design of multi-cell structures, and determines the self-supporting forming angle of the manufacturing voxel and the appropriate element search direction based on the matching relationship between the pole system pose and the additive manufacturing cantilever constraint. It establishes an integrated method for multi-cell structure design and manufacturing based on the pole geometry features, realizing the self-supporting forming of multi-cell structures.

[0276] In the three-dimensional support frame structure design of Example 2, to facilitate the identification of manufacturing voxels for the three-dimensional support model, the cell was divided into n1×n2×n3=4×2×4 to obtain an optimized configuration before analyzing its manufacturing voxel construction. Due to the symmetry of the design results, a 1 / 4 model was selected for analysis, such as... Figure 12 As shown in (a).

[0277] Figure 11 The 3D scaffold is composed of a multicellular structure. The constructed voxels are imported into melt-forming additive manufacturing slicing software to analyze the forming support structure of the voxels. The slicing results are as follows: Figure 13 As shown in the slicing results, the constructed voxel can complete the fabrication of the entire model without the need for a supporting structure during the forming process. This result verifies the effectiveness of the present invention in achieving self-supporting molding of multicellular structures. Figure 12 Results of voxel layering.

[0278] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0279] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A geometric feature evolution-driven method for designing self-supporting topology for multi-cell structures, characterized in that, include: Step 1: Set the unit cell configuration, select a beam or rod that is easy to form directly to establish the unit cell, and calculate the stiffness matrix of the two-dimensional unit cell; Step 2: Construct a unit cell optimization model, calculate the optimized unit cell stiffness matrix, and determine the unit cell design strategy with the internal nodes centered. Step 3: Construct an optimization model for the multi-cell vibration reduction structure and derive the sensitivity calculation method; Step 4: Construct the manufacturing voxel and define the forming angles of all basic unit cell components in the model; Step 5: Provide the search algorithm for voxel construction during unit cell manufacturing. Start the search based on the topological connection relationship of all units so that all basic units can be formed without support. In setting the unit cell configuration, considering spatial interference relationships, the following restrictions are imposed on the basic units within the unit cell: 1) All nodes within any basic unit of a single cell are adjacent to each other; 2) The basic units within a unit cell have independent shape control parameters; 3) Basic units within or between units can merge to form more complex geometries; The element stiffness matrix K of the bar element e As can be seen from the definition: K e =TK' e T T , (1) in For a two-dimensional unit cell For a three-dimensional unit cell E is the elastic modulus of the rod material, A and L are the cross-sectional area and length of the rod element, respectively, and α, β, γ are the angles between the local coordinate system and the corresponding axes of the spatial coordinate system of the rod. A unit cell consists of shared nodes and unique nodes, and the stiffness matrix of the unit cell is: among them or i =A i / L i ; For two-dimensional unit cells, n = 8; for three-dimensional unit cells, n = 20. In the defined unit cell, elements consisting of shared nodes are shared with other unit cells, while elements containing unique nodes are unique to that unit cell. Therefore, the unit cell stiffness matrix can be redefined as: Where nn represents the number of shared units in a unit cell, and mm is the total number of units in a unit cell that have unique nodes. In the defined two-dimensional unit cell, mm = 4 and nn = 4; in the three-dimensional unit cell, nn = 12 and mm = 8. Define the following model to calculate the appropriate location for the exclusive node. find (x,y) my K b st.0<x<Lx 0 < y < Ly Where (xi,yi) are the coordinates of the four corner points of the unit cell, and Lx and Ly are the length and width dimensions of the unit cell; Assuming that the cross-sectional areas of the rod elements that make up the unit cell are the same, solving the above equations shows that for a square unit cell, the stiffness matrix of the unit cell is minimized when the coordinates of the exclusive node are (Lx / 2, Ly / 2). At this point, the unit cell stiffness matrix can be written as: For ease of optimization, the optimization model for a single cell is defined as follows: Where p is the penalty factor, ρ c This represents the unit cell density.

2. The geometric feature evolution-driven self-supporting topology design method for multi-cell structures as described in claim 1, characterized in that, The construction of the multicellular vibration reduction structure optimization model specifically includes: First, define the optimization model: Based on the macroscopic structural model of the rod unit cell, the optimization objective is set as minimizing the structural flexibility, and the constraint is that the spatial proportion of the rod is no greater than υ. Find: X(ρ) min: stKU=F V≤υ 0:ρ min ≤ρ i,j ≤ρ max ,i=1,...,n i ;j=1,...,n j , (8) Where K, U, and F represent the overall stiffness matrix, displacement field, and external forces of the model, respectively; n i n j ρ represents the total number of unit cells in the x- and y-directions of the design domain, respectively; i,j υ represents the density of the rod unit cell; υ represents the volume constraint of the rod unit cell. The unit cell density is determined by the sum of the cross-sectional areas and lengths of the individual rods that make up the unit cell, and its mapping can be set as follows: In the constructed unit cell, the shared unit formed by the shared nodes is shared by multiple unit cells; As can be seen from the above unit cell density mapping formula, the shared unit occupies a certain density proportion in each adjacent unit cell. Therefore, in order to eliminate the repeated calculation of the shared unit in multiple adjacent unit cells, the optimization model (8) can be rewritten as follows: Find: X(ρ) min:c(ρ)=U T (K1+K2)U st(K1+K2)U=F V≤υ 0:ρ min ≤ρ i,j ≤ρ max ,i=1,...,n i ;j=1,...,n j , (10) Where K1 and K2 are the stiffness matrices corresponding to the shared elements and the independent elements in the unit cell, respectively; Then calculate the sensitivity; by differentiating the optimization objective of the optimization model (10), we can obtain... From formula (7), we can see that Where K b,1 ,K b,2 These are the stiffness matrix components of shared and independent elements in the unit cell stiffness matrix, respectively. Since the density of the rod unit cell is continuous, the OC optimization criterion is chosen to update the optimization design variables: Where ε is the step size, and parameter η = 0.5, 3. The geometric feature evolution-driven self-supporting topology design method for multi-cell structures as described in claim 1, characterized in that, Step four specifically includes: For each basic unit γ in a unit cell i Add forming information, i.e. c i :=(P i ,b i ) (14) Where P i Let β be the coordinates of all nodes of this basic unit. i ∈[β i,min ,β i,max ] represents the range of formable overhang angles for this unit in the selected forming direction, β i,min ,β i,max These are the minimum and maximum forming angles, respectively; For a two-dimensional model, the minimum and maximum forming angles are expressed as: β i,min :＝(β xoy,min )，β i,max :＝(β xoy,max )； For a 3D model, the minimum and maximum forming angles are expressed as: β i,min :＝(β xoy,min ,β xoz,min ,β yoz,min )，β i,max :＝(β xoy,max ,β xoz,max ,β yoz,max )； Where β xoy,min β xoy,max β xoz,min β xoz,max β yoz,min β yoz,max In a spatial posture where a self-supporting forming can be achieved under a given forming direction, the minimum and maximum angles between the current basic unit and the XOY, XOZ, and YOZ planes; Therefore, the manufacturing of voxels is represented as: in This is the set of coordinates of all relevant basic unit nodes. The intersection of the range of formable overhang angles of all relevant basic units; from the above definition of manufacturing voxels, we can know the construction principles of manufacturing voxels: 1) All basic units contained in the manufacturing voxel are connected; 2) The formable overhang angle in the manufacturing voxel is the overhang angle that all basic units can be formed without support. Step five specifically includes: Choose any cell and start the search based on the topological connection relationship of all cells. On the basis of ensuring the connectivity of the manufacturing voxel, determine the self-supporting forming angle of the manufacturing voxel according to its forming overhang angle range. The number of manufacturing voxels constructed will be different depending on the search direction. After each voxel is manufactured, its complex topological structure is achieved through model assembly; generally, the fewer voxels manufactured, the lower the manufacturing complexity.

4. A geometry feature evolution-driven self-supporting topology design system for multi-cell structures, implementing the geometry feature evolution-driven self-supporting topology design method for multi-cell structures as described in any one of claims 1 to 3, characterized in that, include: The module includes a single-cell configuration setting module, a single-cell optimization model construction module, a multi-cell vibration reduction structure optimization model construction module, a manufacturing voxel construction module, and a search algorithm execution module. The unit cell configuration setting module is used to select beams and bars that are easy to form directly to establish unit cells and calculate the stiffness matrix of the two-dimensional unit cells; The unit cell optimization model construction module is used to calculate the optimized unit cell stiffness matrix and determine the design strategy for centering the nodes inside the unit cell. The module for constructing a multi-cell vibration reduction structure optimization model is used to derive the sensitivity calculation method and perform multi-cell structure optimization design. The manufacturing voxel building block is used to define the forming angles of all basic unit cell components in the model and to achieve unsupported forming of all basic units; The search algorithm execution module is used to start the search based on the topological connections of all units to ensure the effective connection and formation of all basic units.

5. The geometric feature evolution-driven self-supporting topology design system for multi-cell structures as described in claim 4, characterized in that, The unit cell configuration setting module further includes a unit cell stiffness matrix calculation unit, which is responsible for calculating the stiffness matrix of the unit cell based on the physical and geometric parameters of the selected beam, providing basic data for the stability and structural performance evaluation of the unit cell. The unit cell optimization model construction module further includes a unit cell internal node position optimization unit. This optimization unit is responsible for determining the optimal position of the internal nodes of the unit cell based on the stiffness matrix and predetermined performance indicators through numerical optimization methods, thereby maximizing the performance of the unit cell structure. The multi-cell vibration reduction structure optimization model construction module further includes a vibration reduction performance analysis unit. This analysis unit is responsible for determining the configuration and parameters of each cell in the multi-cell structure based on the constructed multi-cell structure model and external excitation conditions, through sensitivity analysis and optimization algorithms, so as to achieve the best vibration reduction performance of the overall structure.

6. A computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the geometric feature evolution-driven self-supporting topology design method for multi-cell structures as described in any one of claims 1 to 3.

7. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the geometric feature evolution-driven self-supporting topology design method for multi-cell structures as described in any one of claims 1 to 3.

8. An information data processing terminal, the information data processing terminal being used to implement the geometric feature evolution-driven multi-cell structure self-supporting topology design system as described in any one of claims 4 to 5.

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