CN105528494B - Lightweight model generation and optimization method based on 3D cellular automata - Google Patents

Lightweight model generation and optimization method based on 3D cellular automata Download PDF

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CN105528494B
CN105528494B CN201511015816.2A CN201511015816A CN105528494B CN 105528494 B CN105528494 B CN 105528494B CN 201511015816 A CN201511015816 A CN 201511015816A CN 105528494 B CN105528494 B CN 105528494B
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李婉婉
邵军强
沈隽晟
姚远
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University of Shanghai for Science and Technology
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Abstract

The light weighed model that the present invention relates to a kind of based on three-dimensional cellular automaton generates and optimization method.Its operating procedure are as follows: firstly, carrying out the division in space using Octree to the grid model of input.Then, it according to the requirement of design, establishes the cellular based on neighborhood information and develops.Secondly, defining relational expression of the cellular automata in conjunction with the finite element analysis based on FEA feedback information based on neighborhood information, the feedback for establishing FEA analysis develops, and generates lightweight structure based on two kinds of evolution rules.A kind of optimisation strategy based on feedback is established, the information of emulation can be fed back into the process of design, the optimization of driving structure changes the macroscopic properties of design object.Finally, carrying out resurfacing and relevant parameter verifying to the light weighed model of generation.Experiments have shown that the invention is adapted to the building of 3D printing light weighed model very much.

Description

Light weighed model based on three-dimensional cellular automaton generates and optimization method
Technical field
The light weighed model that the present invention relates to a kind of based on three-dimensional cellular automaton generates and optimization method, is specifically designed one Kind is changed microcosmic voxel architecture based on three-dimensional cellular automaton and then controls the light weighed model generation of macrostructure, system collection The optimization process that model is acted at finite element analysis realizes the integration of Design and optimization, establishes a kind of based on the light of optimization Quantizing structure design belongs to the research in volume optimization field.
Background technique
3D printing technique presents developing stage at full speed these years recently, its numeral expression can be converted to really by it Personalized designs object, lightweight structure body generation also become research a hot spot, lightweight structure essential requirement Exactly under the premise of not reducing structural behaviour, by the optimization of structure, the application of advanced technique and light material is realized big The performances such as specific surface area, high structural strength, however, the formulation of specific structure can mitigate the weight of itself inside model Amount, realizes the ratio between big specific surface area and higher Strength Mass.Such as the structural form changed inside model uses skin Light-weighted design may be implemented in reticular structure, the inner supporting structures such as axis tree, but to the mechanical property for guaranteeing objective body structure It can need to study.
The realization of the controllable lightweight structure of macroscopic view is one of important research field at this stage, can pass through the microcosmic of structure The different designs target of voxel cell distributed to realize macrostructure, changes the physical aspect of structural body, realizes diversified Design object.It certainly, is to guarantee structural mechanical property, physical property and use for the optimization of the mechanical property of formation structure The effective means of performance.Wang Monan (CN103310072A) devises the biomechanical properties finite element analysis system based on force feedback System, solves the complexity of femur modeling analysis software, improves the efficiency of successful surgery.
Lightweight structure is more complicated to the control process of voxel cell during generation, and parameter is relatively more, raw At structure meet the requirements difficulty.Simultaneously as being limited by current three-dimensional software, surface model is transformed into optimization process There is many information to lose among voxel model, subsequent optimization is caused to be restricted.Secondly, the diversity of cell voids compares Difference, some its pore characters of the lightweight structure obtained by the Boolean calculation being repeated and mechanical performance lack of diversity. Finally, lacking effective self-feedback and self-recision mechanism in the optimization process of lightweight structure, need in model entirety Structure design after can just optimize analysis and assessment, not only increase the cost of modeling, and increase the time.
In recent years, cellular automata was applied to all be widely used in the fields such as physics, chemistry, military affairs, and obtained Certain achievement, but it is relatively fewer generating structure body Model area research.Cellular automata is a kind of space, time and shape The discrete dynamical system of state, it is made of cellular space, state, neighborhood and regular four major parts.It is each in space A cellular takes limited discrete state, and makees synchronized update according to identical local rule.Cellular automata has component units Simplicity, the locality, the massive parallelism of information processing and complexity, itself flexible of the overall situation that act between unit Property, it is open the features such as be all very beneficial for the modeling process of structure.Wang Zhiyuan (CN103136982A) uses three-dimensional cellular certainly Motivation simulator cooperates the debugging of the program of cellular automata, class is used as religion for studying the rule of three-dimensional cellular automaton Learn the use of device.But it is indefinite for the generation of specific target structure.Currently, the modeling process master of cellular automata If concentrating on the crystallization process of microcosmic crystal, the evolutionary process etc. of traffic flow is relatively fewer for the generation of macrostructure, If holding the essential laws of complicated system evolution well, made effectively according to its flexibility for various concrete conditions Adjustment, so that it may obtain more accurate model structure.
Summary of the invention
It is an object of the invention to be directed to the deficiency of prior art, a kind of lightweight based on three-dimensional cellular automaton is provided Model generates and optimization method, and the data of neighborhood information and finite element analysis feedback based on cellular, which develop, generates lightweight knot Structure, the information of FEA emulation is fed back into the process of design, and the control of the lightweight structure ratio of strength to weight is realized in the optimization of driving structure System not only effectively avoids a large amount of geometrical error of light weighed model generated by Boolean calculation, but also accelerates model Formation speed, construction method is convenient easy to control, mainly microcosmic voxel control on the basis of come change macroscopic view attribute, structure Build the light weighed model of different internal structure.
In order to achieve the above purpose, insight of the invention is that firstly, carrying out the space of grid to the grid model of input It divides.Then, it realizes the cellular evolutionary process based on three-dimensional cellular automaton neighborhood information and is analyzed based on FEA feedback optimized Process.Finally, extracting equipotential surface to the parameterized model of generation and carrying out the resurfacing of internal structure grid model.It will generate Light weighed model carry out relevant parameter verifying.
One, space division is carried out to the grid model of input
The purpose that mesh space divides is to realize the voxelization of triangle grid model, grid model file is inputted, using eight It pitches tree method and space division is carried out to the grid model of input, construct the bounding box of triangle grid model, it is adaptive using Octree Subdivided meshes model is answered, after triangle gridding voxelization, determines that voxel inside/outside node, traversal label generate based on projection vector method Hexahedron voxel positional value, and partitioning model be outside, boundary, inside three kinds of situations.And the body on initialization tag boundary Plain positional value is 1, i.e. Location=1, and voxel of object initial position value is 0, i.e. Location=0.
Two, based on the cellular evolutionary process of three-dimensional cellular automaton neighborhood information
After the voxel of model divides, boundary and the internal information for being labeled model are extracted, is based on V.Neumann type Each voxel is defined as a cellular, the initialization of voxel is carried out, according to initial voxel by 6- neighborhood three-dimensional cellular automaton Label is all cellular labels one " positional value " to determine that it is located at the relative position in entire model.According to certain rule Until all cellular positional values are all labeled, initialization terminates.Then, cellular automata and base based on neighborhood information are defined In the relational expression that the limited of FEA feedback information is combined with analysis, and the evolution of cellular is carried out, the positional value marked according to cellular The size relation of certain center cellular Yu 6- neighborhood cellular positional value is judged, if the member for not having positional value bigger than itself around certain cellular Born of the same parents, then this cellular is removed, and tentatively generates light-weighted voxel model.
Realization of three, based on the FEA feedback optimized process analyzed
Stress analysis is carried out to the cellular models of generation first, is fed back according to the evolutionary process of cellular and finite element analysis Interaction calculates the maximum stress σ that cellular is subject to by FEAmax, and feed back σmaxInto cellular evolutionary process, if full Sufficient σmax< [σ], and cellular neighborhood, not than itself " positional value " big cellular, according to evolution rule, successively removal is corresponding again Cellular, each iteration result will all carry out finite element analysis, and iteration, which develops, is continued until the stress condition σ of local cellularmax> [σ], then program returns to last satisfactory iteration result, terminates journey until all cellulars all optimize analysis Sequence.Finally, generating light weighed model.
The voxel model of generation is carried out resurfacing by four,
Model application Marching Cube (MC) method extracts surface data information.Since the model ultimately generated is The cellular models of hexahedron composition, the extraction of equipotential surface is carried out using MC method to the inside of lightweight structure, and equipotential surface is empty Between in all points with some identical value set, construct the unit potential function of each voxel first, traversal extracts entire mould The unit potential function of all voxels inside type, and all voxel cell potential functions are fused into a complicated equipotential surface, It is in turn printable file format by model conversion.
The light weighed model of generation is carried out relevant parameter verifying by five,
Porosity size, optimization efficiency etc. are all the key parameters of lightweight structure performance evaluation, pass through finite element analysis Mechanical property control to lightweight structure is generated；It verifies the realization process of the lightweight structure of design and meets goal porosity It is required that light weighed model body structure and permanent load under optimal evolution number determination, different materials flowering structure bear Maximum load.
Conceive according to above-mentioned invention, the present invention adopts the following technical scheme:
A kind of light weighed model generation and optimization method based on three-dimensional cellular automaton, it is characterised in that operating procedure is such as Under: 1) space divide: input grid model, and carries out space division to the grid model of input；2) based on the member of neighborhood information Born of the same parents develop；3) feedback based on FEA analysis develops；4) internal structure resurfacing: is carried out to the lightweight voxel model of generation Resurfacing；5) verifying of parameter Verification: is carried out to the grid model generated that develops.
The step 1) inputs grid model, and carries out space division to the grid model of input；Using Octatree technique Space division is carried out to the grid model of input, the bounding box of triangle grid model is constructed, utilizes Octree self-adapting subdividing net Lattice model after triangle gridding voxelization, determines voxel inside/outside node, the hexahedron that traversal label generates based on projection vector method The positional value of voxel, and partitioning model is outside, boundary, internal three kinds of situations；Extract the boundary and inside for being labeled model Information, the voxel difference mark position value for being marked as boundary is 1, i.e. Location=1, voxel of object initial position value is 0, Location=0.
The step of step 2) is developed based on the cellular of neighborhood information is as follows:
(1) building of cellular models: it is based on 6- neighborhood three-dimensional cellular automaton, each voxel is defined as a cellular, is adopted It initializes: being marked according to initial voxel using the following method, be all cellular labels one " positional value " to determine that it is located at entire mould Relative position in type；If certain cellular self-position value is 0, and the positional value for having cellular in its 6- neighborhood is not 0, then its position Value becomes the maximum cellular positional value of positional value in 6- neighborhood and adds 1, is expressed as Evolution iteration is successively carried out, until the positional value of all cellulars of structural body is not 0, label terminates；The function of mark position value Formula is as follows:
In formula,Indicate the position of six neighborhoods of T moment cellular；Indicate T+1 moment member The position of born of the same parents itself；
(2) definition of evolution rule: the state after developing every time due to cellular depends on own situation and surrounding before developing The case where cellular, is based on V.Neumann type 6- neighborhood three-dimensional cellular automaton, establishes based on neighborhood information and two kinds of external feedback The whole functional expression of evolution rule, expression formula are as follows:
T=0, the time domain of 1,2,3 ... ... label voxel,
In formula,Indicate X in the state of t moment；Ω indicates a hexahedral element；N indicates the square of secondary basic function Battle array；G indicates the power that each hexahedral element is subject to；F () indicates the cellular evolution rule based on neighborhood；G () indicates to be based on having The feedback evolution rule of finite element analysis；" " indicates the result of f () and g () interaction；
(3) certain center cellular and 6- neighborhood cellular positional value the evolution of cellular: are judged according to the positional value that cellular marks Size relation, if the cellular for not having positional value bigger than itself around certain cellular, i.e., Then this cellular is removed, and mark position is sky, that is, is printed not output state, tentatively generated light-weighted voxel model in this way.
The step 3) is developed based on the feedback that FEA is analyzed: stress analysis calculating is carried out to the cellular models of generation first, Model is carried out FEA analysis, calculates cellular maximum stress σ by finite element analysis g (F, ∑ Ω) process in above-mentioned cooperating type (2)max, And feed back σmaxInto cellular evolutionary process, if meeting σmax< [σ], and cellular neighborhood is not than itself " positional value " big member Born of the same parentsCorresponding cellular is successively removed again according to evolution rule, and each iteration result is all Finite element analysis will be carried out, iteration, which develops, is continued until the stress condition σ of local cellularmax> [σ], then program returns to upper one Secondary satisfactory iteration result, until all cellulars do not comply withTerminate program, finally, raw At light weighed model.Assuming that [σ]-σmax=Δ σ, if meetingThis cellular is then removed, if Δ σ < 0, Then cellular returns to last time satisfactory result；Relation function formula is as follows:
In formula,Indicate that self-position value is maximum；σmaxIndicate maximum stress suffered by cellular；[σ] expression is permitted Use stress；Δ σ indicates stress difference threshold value.
Step 4) the resurfacing: traversal extracts the equipotential surface of model voxel of object, and the voxel potential function of traversal is adopted It is fused into a complicated potential function f (p) with the operation of boolean sum, that is, it is all in i to n unit potential function to indicate that traversal is extracted Three-dimensional point set V in threshold value equipotential surface for constituting when being C, shown in following functional expression:
{ V (x, y, z) ∈ V3| f (p)=C } (6)
I=1,2,3 ..., the number of n voxel,
In formula, fi(p) potential function of i-th of voxel is indicated, f (p) indicates that the complicated function of fusion, C indicate threshold value.
Step 5) the Verification: Verification is carried out for the light weighed model after developing, passes through finite element analysis Mechanical property control to lightweight structure is generated；It verifies the realization process of the lightweight structure of design and meets goal porosity It is required that light weighed model body structure and permanent load under optimal evolution number determination, different materials flowering structure bear Maximum load.
The present invention compared with prior art, has following obvious prominent substantive distinguishing features and remarkable advantage: first First, grid model space is divided and can be suitble to generate more in the distribution for macroscopically controlling voxel using Octree algorithm Resolution ratio or mixing material model.Secondly, the structural model precision using three-dimensional cellular automaton is high, the time is short, the shape of structure State is easy to control.These structures not only have a lightweight performance, good mechanical property, but also can be to avoid due to a large amount of boolean The a series of error that operation generates.Finally, establishing a kind of whole design and framework based on optimization, FEA can be emulated Information feeds back the optimization of driving structure into the process of design.In the environment of object oriented analysis, lightweight structure is realized Automatic control process from local optimum to global optimization solves cumbersome manually adjust.The light weighed model of generation is answered It uses in existing increasing material manufacturing, saves the time of printing, reduce the consumption of material, saved production cost.
Detailed description of the invention
The present invention is based on the generation of the light weighed model of three-dimensional cellular automaton and the operating procedure processes of optimization method by Fig. 1 Figure.
Fig. 2 grid model preferred embodiment.
Flow chart of the Fig. 3 based on Octree voxelization.
The basic cellular of 6- neighborhood of Fig. 4 three-dimensional cellular automaton.
Fig. 5 is based on Octree and marks cat model inside/outside voxel schematic diagram.
The evolution principle schematic diagram that Fig. 6 light weighed model simplifies.
The light-weighted cellular evolutionary process of Fig. 7 apple, cat, banana, four model realization of bull.
The flow chart that Fig. 8 is combined based on the evolution of cellular automata with FEA analysis feedback.
Fig. 9 generates the general flow schematic diagram of light-weighted cat model.
Figure 10 apple, cat, banana, the porosity of four model of bull and evolution the number of iterations relationship.
Stress envelope when Figure 11 hanging block loads permanent load with spherical model under difference evolution number.
Stress value size when Figure 12 hanging block loads permanent load with spherical model under difference evolution number.
Figure 13 acrylonitrile-butadiene-styrene copolymer, polylactic acid, three kinds of different materials of steel hanging block model evolution The relationship of the maximum load of number and receiving.
Specific embodiment
Preferred embodiment example of the invention is described with reference to the accompanying drawings as follows:
Embodiment one:
Referring to Fig. 1, a kind of generation of the light weighed model based on three-dimensional cellular automaton and optimization method, it is characterised in that Operating procedure is as follows: 1) space divides.Grid model is inputted, and space division is carried out to the grid model of input.2) based on neighbour The cellular of domain information develops.3) feedback based on FEA analysis develops.4) resurfacing.To the lightweight voxel model of generation into The resurfacing of row internal structure.5) Verification.The verifying of parameter is carried out to the light weighed model generated that develops.
Embodiment two:
The present embodiment is basically the same as the first embodiment, and special feature is as follows:
Step 1) the space divides: to generate the lightweight structure model driven by cellular automata, the present invention is proposed A kind of light weighed model generation and optimization method based on three-dimensional cellular automaton.Environment is developed in Visual Studio 2013 The middle lightweight using C++ language implementation model is realized.The stl triangle grid model preferred embodiment cat (see Fig. 2) of input, Space division is carried out using grid model of the Octatree technique to input, the bounding box of triangle grid model is constructed, utilizes eight forks Self-adapting subdividing grid model is set, after triangle gridding voxelization, voxel inside/outside node, traversal mark are determined based on projection vector method Remember the positional value of the hexahedron voxel generated, and partitioning model is outside, boundary, internal three kinds of situations, flow chart (see Fig. 3), Boundary and the internal information for being labeled model are extracted, the voxel difference mark position value for being marked as boundary is 1, i.e., Location=1, voxel of object initial position value are 0, i.e. Location=0.
The step 2) is developed based on the cellular of neighborhood information: the building for cellular models is based on 6- neighborhood three-dimensional element Cellular automaton, in spatial distribution, each cellular is using up, down, left, right, before and after as neighborhood；Each voxel is defined as one A cellular, shown in six neighborhood cellular model of element (see Fig. 4), model voxelization and then according to formula (1) markup model voxel Positional value, extract inside and the boundary information of model, carry out the division of display model Octree in experiment (see Fig. 5) by taking cat as an example Afterwards inside model, the label on boundary, outside；Pass through formula (2) (3), it may be said that bright cellular evolution rule and base based on neighborhood Interaction between the FEA evolution rule of feedback；We judge certain center cellular and 6- according to the positional value of cellular label The size relation of neighborhood cellular positional value, if the cellular for not having positional value bigger than itself around certain cellular, is expressed asThen this cellular is removed, and mark position is sky, that is, prints not output state, this Sample tentatively generates light-weighted voxel model, realizes and takes out shell lightweight structure；Fig. 6 show simple cellular Evolution plane Schematic diagram successively removes the voxel labeled as 4 and 3 from model center.When Fig. 7 show Octree division 5 times (Level=5) Apple, cat, banana, the model evolution 15 times of bull four part evolution schematic diagram and corresponding sectional view.
The step 3) is developed based on the feedback that FEA is analyzed: we divide the cat mould of 5 times (Level=5) to Octree Type applies constant load F=50N, and the cellular models generated after developing to cellular carry out stress analysis, and cat model is each The stress maximum value that cellular is subject to after secondary FEA analysis is fed back into the evolutionary process of cellular, and the cellular based on neighborhood information develops With the feedback evolution basic procedure (see Fig. 8) of FEA analysis, successively develop according to formula (4) until the stress of all cellulars is all small In the allowable stress value of cast material, finally obtain quality and the optimal cat model of structure (see Fig. 9 f).Lightweight cat The generating process of model (see Fig. 9).
Step 4) the resurfacing: carrying out the resurfacing of internal structure to the lightweight voxel model of generation, uses Marching Cube algorithm extracts the equipotential surface of voxel model in hexahedron；The equipotential surface of unit is connected into the grid of model Surface constructs the body structure of grid model；The data information on surface is extracted, we use formula (5) (6), in the constraint of threshold value C Under, realize the extraction of equipotential surface, and then be printable file format by model conversion.
Step 5) the Verification: the verifying of parameter is carried out to the light weighed model generated that develops, first verifies that light weight Change the change of structure porosity size, apple shown in Fig. 7, cat, banana, bull porosity are tested, as a result (see figure 10): in curve as can be seen that when the number of iterations progressively increases to 10 times or so, the porosity value of model has progressivelyed reach receipts It holds back, apple porosity is 73.92% at this time, and cat porosity is 63.12%, and banana voidage is 51.24%, bull porosity It is 57.61%.The effect that the lightweight of the parameter display model is realized；Figure 11 shows verifying model hanging block and ball material is When acrylonitrile-butadiene-styrene copolymer respectively by constant load 50N and 85N when the optimal number that develops, from Figure 12 In it can be seen that hanging block allowable stress requirement under, when developing 8 times, by maximum stress be 12.33Mpa, realize structure It is optimal；Ball is the light-weighted structure that 23.71Mpa is optimal by maximum stress when developing 3 times；Figure 13 is shown pair In acrylonitrile-butadiene-styrene copolymer, polylactic acid, three kinds of different materials of steel suspension block models with evolution number Change, the maximum load that corresponding model is born changes correspondingly.
The lightweight structure of generation is printed on the FDM printer of FORTUS 360mc, materials'use acrylic nitrile-butadiene Diene-styrol copolymer, yield strength 24.3N/mm2.And with other methods realize identical lightweight structure into The comparison of row time, intensity and quality.And the test of pressure bearing is carried out on general testing machine.Weigh print structure body Weight is simultaneously compared with the structural model of the realization of other methods at this stage, and then the dependable with function of verification method.

Claims (6)

1.一种基于三维元胞自动机的轻量化模型生成及优化方法，其特征在于操作步骤如下：1. a light-weight model generation and optimization method based on three-dimensional cellular automata, is characterized in that operating steps are as follows: 1)空间划分：采用八叉树方法，输入网格模型，并对输入的网格模型进行空间划分；1) Space division: The octree method is used to input the grid model, and the space is divided for the input grid model; 2)基于三维元胞自动机邻域信息的元胞演化；2) Cellular evolution based on the neighborhood information of 3D cellular automata; 3)基于FEA分析的反馈演化；3) Feedback evolution based on FEA analysis; 4)表面重建：对生成的轻量化体素模型进行内部结构的表面重建；4) Surface reconstruction: the surface reconstruction of the internal structure of the generated lightweight voxel model; 5)参数验证：对演化生成的网格模型进行参数的验证。5) Parameter verification: verify the parameters of the grid model generated by evolution. 2.根据权利要求1所述的基于三维元胞自动机的轻量化模型生成及优化方法，其特征在于：所述步骤1)空间划分：输入网格模型，并对输入的网格模型进行空间划分；采用八叉树方法对输入的网格模型进行空间划分，构建三角网格模型的包围盒，利用八叉树自适应细分网格模型，三角网格体素化后，基于投影向量法确定体素内节点和外节点，遍历标记生成的六面体体素的位置值，且划分模型为外部、边界、内部三种情况；提取已被标记模型的边界和内部信息，被标记为边界的体素分别标记位置值为1，即Location＝1，内部体素初始位置值为0，即Location＝0。2. The light-weight model generation and optimization method based on three-dimensional cellular automata according to claim 1, characterized in that: described step 1) space division: input grid model, and spatially carry out the input grid model Division; the octree method is used to divide the input mesh model in space, the bounding box of the triangular mesh model is constructed, and the octree is used to adaptively subdivide the mesh model. After the triangular mesh is voxelized, it is based on the projection vector method. Determine the inner node and outer node of the voxel, traverse the position value of the hexahedral voxel generated by the mark, and divide the model into three cases: external, boundary, and internal; extract the boundary and internal information of the marked model, and the volume marked as the boundary The pixel is marked with a position value of 1, that is, Location=1, and the initial position value of an internal voxel is 0, that is, Location=0. 3.根据权利要求2所述的基于三维元胞自动机的轻量化模型生成及优化方法，其特征在于：所述步骤2)基于邻域信息的元胞演化的步骤如下：3. The light-weight model generation and optimization method based on three-dimensional cellular automata according to claim 2, is characterized in that: the step of described step 2) cell evolution based on neighborhood information is as follows: (1)元胞模型的构建：基于6-邻域三维元胞自动机，将每个体素定义为一个元胞，采用以下方法初始化：按照初始体素标记，为所有元胞标记一个“位置值”以确定其位于整个模型中的相对位置；若某元胞自身位置值为0，且其6-邻域中有元胞的位置值不为0，则其位置值变为6-邻域中位置值最大的元胞位置值加1，表示为 依次进行演化迭代，直到结构体所有元胞的位置值都不为0，标记结束；标记位置值的函数式如下：(1) Construction of the cellular model: Based on the 6-neighborhood 3D cellular automaton, each voxel is defined as a cell, and initialized by the following method: Mark all cells with a "position value" according to the initial voxel labeling " to determine its relative position in the entire model; if a cell's own position value is 0, and the position value of a cell in its 6-neighborhood is not 0, its position value becomes 6-neighborhood. The position value of the cell with the largest position value is incremented by 1, which is expressed as The evolution iteration is performed in turn until the position value of all cells in the structure is not 0, and the mark ends; the function formula of the mark position value is as follows: 式中，表示T时刻元胞的六个邻域的位置；表示T+1时刻元胞本身的位置；In the formula, Represents the positions of the six neighborhoods of the cell at time T; Represents the position of the cell itself at time T+1; (2)演化规则的定义：由于元胞每次演化后的状态取决于演化前自身情况与周围元胞的情况，基于6-邻域三维元胞自动机，建立基于邻域信息与外部反馈两种演化规则的整体函数式，其表达式如下：(2) Definition of evolution rules: Since the state of a cell after each evolution depends on its own conditions and the conditions of surrounding cells before evolution, based on the 6-neighborhood three-dimensional cellular automaton, two methods based on neighborhood information and external feedback are established. The overall functional formula of an evolutionary rule, its expression is as follows: F＝∫ΩNTGdΩ (3)F=∫ Ω N T Gd Ω (3) t＝0，1，2，3，……，t为标记体素的时间编号，t=0, 1, 2, 3, ..., t is the time number of the marked voxel, 式中，表示X在t时刻的状态；Ω表示一个六面体单元；N表示二次基函数的矩阵；G表示每一个六面体单元受到的力；f()表示基于邻域的元胞演化规则；g()表示基于有限元分析的反馈演化规则；“·”表示f()和g()相互作用的结果；In the formula, Represents the state of X at time t; Ω represents a hexahedral unit; N represents the matrix of quadratic basis functions; G represents the force on each hexahedral unit; f() represents the neighborhood-based cell evolution rule; g() represents Feedback evolution rule based on finite element analysis; "·" indicates the result of interaction between f() and g(); (3)元胞的演化：根据元胞标记的位置值判断某中心元胞与6-邻域元胞位置值的大小关系，若某元胞周围没有位置值比自身大的元胞，即则这个元胞被去除，标记位置为空，即打印不输出状态，这样初步生成轻量化的体素模型。(3) Evolution of the cell: According to the position value of the cell label, the size relationship between a central cell and the position value of the 6-neighbor cell is judged. If there is no cell with a position value larger than itself around a cell, that is Then this cell is removed, and the marked position is empty, that is, the printing does not output the state, so that a lightweight voxel model is initially generated. 4.根据权利要求3所述的基于三维元胞自动机的轻量化模型生成及优化方法，其特征在于：所述步骤3)基于FEA分析的反馈演化：首先对生成的元胞模型进行应力分析，上述协同式(2)中有限元分析g(F，∑Ω)过程，将模型进行FEA分析，计算元胞最大应力σmax，并反馈σmax到元胞演化过程中，如果满足σmax＜[σ]，且元胞邻域没有比自身“位置值”大的元胞，即根据演化规则再依次去除相应的元胞，每次迭代结果都将进行有限元分析，迭代演化继续直到局部的元胞的受力情况σmax＞[σ]，则程序返回上一次符合要求的迭代结果，直到所有的元胞都不符合结束程序，最后，生成轻量化模型；假设[σ]-σmax＝Δσ,若符合则去除此元胞，若Δσ<0,则元胞返回上次符合要求的结果；关系函数式如下：4. The light-weight model generation and optimization method based on three-dimensional cellular automata according to claim 3, characterized in that: described step 3) feedback evolution based on FEA analysis: first, stress analysis is performed on the generated cellular model , the finite element analysis g(F, ∑Ω) process in the above synergistic formula (2), the model is subjected to FEA analysis, the maximum stress σ max of the cell is calculated, and σ max is fed back to the cell evolution process, if σ max < [σ], and there is no cell whose neighborhood is larger than its own "position value", i.e. According to the evolution rules, the corresponding cells are removed in turn, and the results of each iteration will be subjected to finite element analysis. The iterative evolution continues until the stress condition of the local cells is σ max > [σ], then the program returns to the last iteration that meets the requirements As a result, until all cells do not fit End the program, and finally, generate a lightweight model; assuming [σ]-σ max = Δσ, if the Then remove this cell, if Δσ<0, the cell returns the result that met the requirements last time; the relational function is as follows: 式中，表示自身位置值最大；σmax表示元胞所受的最大应力；[σ]表示许用应力；Δσ表示应力差阈值。In the formula, Represents the maximum value of its own position; σ max represents the maximum stress on the cell; [σ] represents the allowable stress; Δσ represents the stress difference threshold. 5.根据权利要求1所述的基于三维元胞自动机的轻量化模型生成及优化方法，其特征在于：所述步骤4)表面重建，遍历提取模型内部体素的等势面，将遍历的体素势函数采用布尔和的运算融合成一个复杂的势函数f(p)，即表示遍历提取i至n个单元势函数中所有的三维点集V中阈值为C时构成的等势面，如下函数式所示：5. The light-weight model generation and optimization method based on three-dimensional cellular automata according to claim 1, characterized in that: said step 4) surface reconstruction, traversing the equipotential surfaces of the voxels inside the extracted model, and traversing the traversed The voxel potential function is merged into a complex potential function f(p) by the operation of Boolean sum, which means that the equipotential surface formed by traversing and extracting all the three-dimensional point sets V in the i to n unit potential functions when the threshold value is C, The following functional formula is shown: {V(x,y,z)∈V3|f(p)＝C}，(6){V(x,y,z)∈V 3 |f(p)=C}, (6) i＝1，2，3，……，n，i为体素的个数，i=1, 2, 3, ..., n, i is the number of voxels, 式中，fi(p)表示第i个体素的势函数，f(p)表示融合的复杂函数，C表示阈值。In the formula, f i (p) represents the potential function of the ith voxel, f(p) represents the complex function of fusion, and C represents the threshold. 6.根据权利要求1所述的基于三维元胞自动机的轻量化模型生成及优化方法，其特征在于：所述步骤5)参数验证：对演化后的轻量化模型进行参数验证，通过有限元分析对生成轻量化结构的力学性能控制；验证设计的轻量化结构的实现过程和满足目标孔隙率要求的轻量化模型体结构，以及恒定载荷下最优演化次数的确定，不同材料下结构承受的最大载荷。6. The light-weight model generation and optimization method based on three-dimensional cellular automata according to claim 1, characterized in that: said step 5) parameter verification: parameter verification is performed on the evolved lightweight model, and the finite element method is used to verify the parameters. Analyze the mechanical properties control of the generated lightweight structure; verify the realization process of the designed lightweight structure and the lightweight model body structure that meets the target porosity requirements, as well as the determination of the optimal evolution times under constant load. Maximum load.
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