CN105528494A - Three-dimensional cellular automaton based lightweight model and optimizing method - Google Patents
Three-dimensional cellular automaton based lightweight model and optimizing method Download PDFInfo
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Abstract
The invention relates to a three-dimensional cellular automaton based lightweight model and optimizing method, comprising operation steps: firstly, performing space dividing on an input network model with an octree, then according to design demands, establishing neighborhood information based cellular evolution, then, defining the relation that a neighborhood information based cellular automaton combines with FEA feedback information based finite element analysis, establishing FEA analysis feedback evolution, and generating a lightweight structure based on two evolution rules. A feedback based optimizing strategy is established, simulated information can be fed back to a design flow, and a drive structure is optimized to change macro attributes of a design target. Finally, the generated lightweight model is subjected to surface recreating and related parameters verifying, and an experiment proves that the invention is very suitable for establishing a 3D (three-dimensional) printing lightweight model.
Description
Technical field
The present invention relates to a kind of light weighed model based on three-dimensional cellular automaton to generate and optimization method, a kind of light weighed model generation changing microcosmic voxel architecture based on three-dimensional cellular automaton and then control macrostructure of special design, system integration finite element analysis acts on the optimizing process of model, realize the integration of Design and optimization, setting up a kind of lightweight structure design based on optimizing, belonging to the research that volume optimizes field.
Background technology
3D printing technique presents developing stage at full speed these years recently, its numeral expression can be changed into the object of real personalized design by it, the generation of lightweight structure body also becomes a focus of research, lightweight structure essential requirement is exactly under the prerequisite not reducing structural behaviour, by the optimization of structure, advanced technique and the application of light material, realize the performance such as large specific surface area, high structural strength, but, the formulation of the inner ad hoc structure of model can alleviate the weight of self, realizes the ratio of the Strength Mass of large specific surface area and Geng Gao.The structural form such as changing model inside adopts skin reticulate texture, and the inner supporting structures such as axis tree can realize light-weighted design, but to ensureing that the mechanical property of objective body structure needs to study.
The realization of the controlled lightweight structure of macroscopic view is present stage one of important research field, and can be realized the different designs target of macrostructure by the distribution of the microcosmic voxel cell of structure, the physical aspect of change structure body, realizes diversified design object.Certainly, for the optimization of the mechanical property of formation structure, be ensure structural mechanical property, the effective means of physical property and usability.Wang Monan (CN103310072A) devises the biomechanical properties finite element analysing system based on force feedback, solves the complicacy of femur modeling analysis software, improves the efficiency of successful surgery.
Lightweight structure is in the process generated, and to the control procedure more complicated of voxel cell, parameter is relatively many, and the structure of generation meets the demands difficulty.Meanwhile, owing to being subject to the restriction of current three-dimensional software, in optimizing process, surface model is transformed in the middle of voxel model a lot of information dropout, causes follow-up optimization to be restricted.Secondly, the diversity of cell voids is poor, its pore character of lightweight structure that some Boolean calculations passing through repeatedly to carry out obtain and mechanical property lack of diversity.Finally, in the optimizing process of lightweight structure, lack effective self-feedback and self-recision mechanism, need just can be optimized assessment and analysis after the structural design of model entirety, not only increase the cost of modeling, and add the time.
In recent years, cellular automaton was applied in the fields such as physics, chemistry, military affairs and was all widely used, and achieved certain achievement, but relatively less at generating structure body Model area research.Cellular automaton is all discrete power system of a kind of space, time and state, and it is made up of cellular space, state, neighborhood Sum fanction four major parts.Each cellular in space gets limited discrete state, and makes synchronized update according to identical local rule.The features such as cellular automaton has complicacy, the dirigibility of self of locality, the massive parallelism of information processing and the overall situation acted between the simplicity of component units, unit, open are all very beneficial for the modeling process of structure.Wang Zhiyuan (CN103136982A) adopts three-dimensional cellular automaton simulator, and for studying the rule of three-dimensional cellular automaton, coordinate the debugging of the program of cellular automaton, class is used as the use of instructional device.But it is indefinite for the generation of concrete object construction body.At present, the modeling process of cellular automaton mainly concentrates on the crystallization process of the crystal of microcosmic, the evolutionary process etc. of traffic flow, generation for macrostructure is relatively less, if well hold the essential laws of complicated system evolution, dirigibility according to it makes effective adjustment for various concrete condition, just can obtain more accurate model structure.
Summary of the invention
The object of the invention is to the deficiency for prior art, a kind of light weighed model based on three-dimensional cellular automaton is provided to generate and optimization method, lightweight structure is generated based on the neighborhood information of cellular and the data evolves of finite element analysis feedback, the information feed back emulated by FEA is in the flow process of design, the optimization of drives structure, realize the control of the lightweight structure ratio of strength to weight, not only effectively avoid the geometrical error that the light weighed model that generated by Boolean calculation is a large amount of, and accelerate the formation speed of model, construction method is convenient easy to control, on the basis that microcosmic voxel controls, mainly change the attribute of macroscopic view, build the light weighed model of different internal structure.
In order to realize above-mentioned object, design of the present invention is: first, the grid model of input is carried out to the spatial division of grid.Then, realize based on the cellular evolutionary process of three-dimensional cellular automaton neighborhood information and the feedback optimized process based on FEA analysis.Finally, equipotential surface extracted to the parameterized model generated and carry out the resurfacing of inner structure grid model.The light weighed model of generation is carried out correlation parameter checking.
One, spatial division is carried out to the grid model of input
The object that mesh space divides is the voxelization realizing triangle grid model, input grid model file, the grid model of Octatree technique to input is adopted to carry out spatial division, build the bounding box of triangle grid model, utilize Octree self-adapting subdividing grid model, after triangle gridding voxelization, based on projection vector method determination voxel inside/outside node, the positional value of the hexahedron voxel that traversal mark generates, and partitioning model is outside, border, inner three kinds of situations.And the voxel location value on initialization tag border is 1, i.e. Location=1, 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, extract the border and the internal information that have been labeled model, based on V.Neumann type 6-neighborhood three-dimensional cellular automaton, each voxel is defined as a cellular, carry out the initialization of voxel, according to the mark of initial voxel, for all cellulars mark one " positional value " to determine that it is arranged in the relative position of whole model.According to certain rule until all cellular positional values are all labeled, initialization terminates.Then, define the cellular automaton based on neighborhood information and the relational expression combined with analysis based on the limited of FEA feedback information, and carry out the evolution of cellular, the magnitude relationship of certain center cellular and 6-neighborhood cellular positional value is judged according to the positional value of cellular mark, if there is no the cellular that positional value is larger than self around certain cellular, then this cellular is removed, the light-weighted voxel model of preliminary generation.
Three. based on the realization of the feedback optimized process that FEA analyzes
First stress analysis is carried out to the cellular models generated, according to the interaction that evolutionary process and the finite element analysis of cellular are fed back, the maximum stress σ be subject to by FEA calculating cellular
max, and feed back σ
maxto in cellular evolutionary process, if meet σ
max< [σ], and the cellular that cellular neighborhood is not large than self " positional value ", remove corresponding cellular successively again according to evolution rule, each iteration result all will carry out finite element analysis, and iteration develops and continues until the stressing conditions σ of cellular locally
max> [σ], then program returns last satisfactory iteration result, until all cellulars are all optimized analysis terminate program.Finally, light weighed model is generated.
Four. the voxel model of generation is carried out resurfacing
Model application MarchingCube (MC) method extracts surface data information.Due to the cellular models that the model finally generated is hexahedron composition, MC method is adopted the inside of lightweight structure to be carried out to the extraction of equipotential surface, equipotential surface is all set with the point of certain identical value in space, first the unit potential function of each voxel is constructed, traversal extracts the unit potential function of all voxels of whole model inside, and all voxel cell potential functions are fused into a complicated equipotential surface, and then be printable file layout by model conversion.
Five. the light weighed model of generation is carried out correlation parameter checking
Porosity size, optimization efficiency etc. are all the key parameters of lightweight structure performance evaluation, are controlled the mechanical property generating lightweight structure by finite element analysis; The implementation procedure of the lightweight structure of checking design and meet the light weighed model body structure that goal porosity requires, and the determination of optimum evolution number of times under permanent load, the maximum load that under different materials, structure is born.
According to above-mentioned inventive concept, the present invention adopts following technical scheme:
Light weighed model based on three-dimensional cellular automaton generates and an optimization method, it is characterized in that operation steps is as follows: 1) spatial division: input grid model, and carries out spatial division to the grid model of input; 2) cellular based on neighborhood information develops; 3) feedback analyzed based on FEA develops; 4) resurfacing: the resurfacing lightweight voxel model generated being carried out to inner structure; 5) Verification: the grid model generated developing carries out the checking of parameter.
Described step 1) input grid model, and spatial division is carried out to the grid model of input; The grid model of Octatree technique to input is adopted to carry out spatial division, build the bounding box of triangle grid model, utilize Octree self-adapting subdividing grid model, after triangle gridding voxelization, based on projection vector method determination voxel inside/outside node, the positional value of the hexahedron voxel that traversal mark generates, and partitioning model is outside, border, inner three kinds of situations; Extract and be labeled border and the internal information of model, the voxel being marked as border respectively mark position value is 1, i.e. Location=1, voxel of object initial position value is 0, Location=0.
Described step 2) step that develops based on the cellular of neighborhood information is as follows:
(1) structure of cellular models: based on 6-neighborhood three-dimensional cellular automaton, each voxel is defined as a cellular, adopt following methods initialization: according to initial voxel mark, for all cellulars mark one " positional value " to determine that it is arranged in the relative position of whole model; If certain cellular self-position value is 0, and have the positional value of cellular not to be 0 in its 6-neighborhood, then the cellular positional value that its positional value becomes positional value in 6-neighborhood maximum adds 1, is expressed as
carry out evolution iteration successively, until the positional value of all cellulars of structure is not 0, mark terminates; The functional expression of mark position value is as follows:
In formula,
represent the position of six neighborhoods of T moment cellular;
represent the position of T+1 moment cellular itself;
(2) definition of evolution rule: due to the state after cellular develops at every turn depend on develop before the situation of own situation and surrounding cellular, based on V.Neumann type 6-neighborhood three-dimensional cellular automaton, set up the overall functional expression based on neighborhood information and external feedback two kinds of evolution rules, its expression formula is as follows:
T=0,1,2,3 ... the time numbering of mark voxel,
In formula,
represent the state of X in t; Ω represents a hexahedral element; N represents the matrix of secondary base function; G represents the power that each hexahedral element is subject to; F () represents the cellular evolution rule based on neighborhood; G () represents the feedback evolution rule based on finite element analysis; " " represents f () and the interactional result of g ();
(3) evolution of cellular: the magnitude relationship judging certain center cellular and 6-neighborhood cellular positional value according to the positional value of cellular mark, if there is no the cellular that positional value is larger than self around certain cellular, namely
then this cellular is removed, and mark position is empty, namely prints not output state, the light-weighted voxel model of so preliminary generation.
Described step 3) based on FEA analyze feedback develop: first to generate cellular models carry out stress analysis calculating, finite element analysis g (F in above-mentioned cooperating type (2), ∑ Ω) process, model is carried out FEA analysis, calculates cellular maximum stress σ
max, and feed back σ
maxto in cellular evolutionary process, if meet σ
max< [σ], and the cellular that cellular neighborhood is not large than self " positional value "
remove corresponding cellular successively again according to evolution rule, each iteration result all will carry out finite element analysis, and iteration develops and continues until the stressing conditions σ of cellular locally
max> [σ], then program returns last satisfactory iteration result, until all cellulars all do not meet
end program, finally, generates light weighed model.Suppose [σ]-σ
max=Δ σ, if meet
then remove this cellular, if Δ σ < 0, then cellular returns satisfactory result last time; Relation function formula is as follows:
In formula,
represent that self-position value is maximum; σ
maxrepresent the maximum stress suffered by cellular; [σ] represents permissible stress; Δ σ represents stress difference threshold value.
Described step 4) resurfacing: the equipotential surface of traversal extraction model voxel of object, the computing of boolean sum the voxel potential function of traversal is adopted to be fused into a complicated potential function f (p), namely represent that traversal extracts the equipotential surface formed when threshold value is C in three-dimensional point set V all in i to n unit potential function, shown in following functional expression:
{V(x，y，z)∈V
3|f(p)＝C}(6)
I=1,2,3 ..., the number of n voxel,
In formula, f
ip () represents the potential function of i-th voxel, f (p) represents the complicated function merged, and C represents threshold value.
Described step 5) Verification: Verification is carried out for the light weighed model after developing, by finite element analysis, the mechanical property generating lightweight structure is controlled; The implementation procedure of the lightweight structure of checking design and meet the light weighed model body structure that goal porosity requires, and the determination of optimum evolution number of times under permanent load, the maximum load that under different materials, structure is born.
The present invention compared with prior art, there is following apparent outstanding substantive distinguishing features and remarkable advantage: first, Octree algorithm is adopted to carry out dividing can, in the distribution macroscopically controlling voxel, be applicable to generating multiresolution or composite material model grid model space.Secondly, utilize the structural model precision of three-dimensional cellular automaton high, the time is short, and the form of structure is easy to control.These structures not only have lightweight performance, good mechanical property, but also can avoid a series of error because a large amount of Boolean calculations produces.Finally, establish a kind of whole design and framework based on optimizing, can by the information feed back of FEA emulation in the flow process of design, the optimization of drives structure.In the environment of object oriented analysis, realize the automatic control process of lightweight structure from local optimum to global optimization, solve loaded down with trivial details manual adjustments.The light weighed model of generation is applied in the manufacture of existing increasing material, saves the time of printing, decrease the consumption of material, saved production cost.
Accompanying drawing explanation
Fig. 1 the present invention is based on the generation of the light weighed model of three-dimensional cellular automaton and the operation steps process flow diagram of optimization method.
Fig. 2 grid model preferred embodiment.
Fig. 3 is based on the process flow diagram of Octree voxelization.
The basic cellular of 6-neighborhood of Fig. 4 three-dimensional cellular automaton.
Fig. 5 is based on Octree mark cat model inside/outside voxel schematic diagram.
The evolution principle schematic diagram that Fig. 6 light weighed model simplifies.
Fig. 7 apple, cat, banana, bull four-model realize light-weighted cellular evolutionary process.
Fig. 8 analyzes based on the evolution of cellular automaton and FEA the process flow diagram feeding back and combine.
Fig. 9 generates the general flow schematic diagram of light-weighted cat model.
The porosity of Figure 10 apple, cat, banana, bull four-model and the relation of evolution iterations.
Stress envelope when Figure 11 hanging block and spherical model loading permanent load under different evolution number of times.
Stress value size when Figure 12 hanging block and spherical model loading permanent load under different evolution number of times.
The hanging block model evolution number of times of Figure 13 acrylonitrile-butadiene-styrene copolymer, PLA, steel three kinds of different materials and the relation of the maximum load of bearing.
Embodiment
Preferred embodiment example of the present invention, is described with reference to the accompanying drawings as follows:
Embodiment one:
See Fig. 1, a kind of generation of the light weighed model based on three-dimensional cellular automaton and optimization method, is characterized in that operation steps is as follows: 1) spatial division.Input grid model, and spatial division is carried out to the grid model of input.2) cellular based on neighborhood information develops.3) feedback analyzed based on FEA develops.4) resurfacing.The lightweight voxel model generated is carried out to the resurfacing of inner structure.5) Verification.The light weighed model generated developing carries out the checking of parameter.
Embodiment two:
The present embodiment is substantially identical with embodiment one, and special feature is as follows:
Described step 1) spatial division: for generating the lightweight structure model driven by cellular automaton, the present invention proposes a kind of light weighed model based on three-dimensional cellular automaton and generates and optimization method.In VisualStudio2013 development environment, use the lightweight of C Plus Plus implementation model to realize.Stl triangle grid model preferred embodiment cat (see Fig. 2) of input, the grid model of Octatree technique to input is adopted to carry out spatial division, build the bounding box of triangle grid model, utilize Octree self-adapting subdividing grid model, after triangle gridding voxelization, based on projection vector method determination voxel inside/outside node, the positional value of the hexahedron voxel that traversal mark generates, and partitioning model is outside, border, inner three kinds of situations, process flow diagram (see Fig. 3), extract the border and the internal information that have been labeled model, the voxel being marked as border respectively mark position value is 1, i.e. Location=1, voxel of object initial position value is 0, i.e. Location=0.
Described step 2) develop based on the cellular of neighborhood information: for the structure of cellular models, based on 6-neighborhood three-dimensional cellular automaton, in space distribution, each cellular take up, down, left, right, before and after as neighborhood; Each voxel is defined as a cellular, shown in six neighborhood cellular model of elements (see Fig. 4), after model voxelization, again according to the positional value of formula (1) markup model voxel, the inside of extraction model and boundary information, carry out display model Octree for cat (see Fig. 5) in experiment and divide rear model inside, border, outside mark; By formula (2) (3), the interaction between the cellular evolution rule based on neighborhood and the FEA evolution rule based on feedback can be described; We judge the magnitude relationship of certain center cellular and 6-neighborhood cellular positional value according to the positional value of cellular mark, if do not have the cellular that positional value is larger than self around certain cellular, are expressed as
then this cellular is removed, and mark position is empty, namely prints not output state, the light-weighted voxel model of so preliminary generation, realizes taking out shell lightweight structure; Figure 6 shows that simple cellular Evolution floor map, remove the voxel being labeled as 4 and 3 from model center successively.The part evolution schematic diagram of apple when Figure 7 shows that Octree divides 5 times (Level=5), cat, banana, bull four model evolutions 15 times and corresponding sectional view.
Described step 3) based on FEA analyze feedback develop: we apply constant load F=50N to the cat model that Octree divides 5 times (Level=5), the cellular models generated after developing to cellular carries out stress analysis, the stress maximal value that cellular after the FEA analysis each time of cat model is subject to is fed back in the evolutionary process of cellular, based on the feedback evolution basic procedure (see Fig. 8) that cellular develops and FEA analyzes of neighborhood information, according to formula (4) develop successively until the stress of all cellulars be all less than cast material permissible stress value, finally obtain the cat model (see Fig. 9 f) of quality and structure optimum.The generative process (see Fig. 9) of lightweight cat model.
Described step 4) resurfacing: the resurfacing lightweight voxel model generated being carried out to inner structure, adopts MarchingCube algorithm to extract the equipotential surface of voxel model in hexahedron; The equipotential surface of unit is connected into the surface mesh of model, build the body structure of grid model; Extract the data message on surface, we adopt formula (5) (6), under the constraint of threshold value C, realize the extraction of equipotential surface, and then are printable file layout by model conversion.
Described step 5) Verification: the light weighed model generated developing carries out the checking of parameter, first the change of lightweight structure porosity size is verified, apple shown in Fig. 7, cat, banana, bull porosity are tested, result (see Figure 10): can find out in curve, when iterations is increased to about 10 times gradually, the porosity value of model reaches convergence gradually, now apple porosity is 73.92%, cat porosity is 63.12%, banana voidage is 51.24%, and bull porosity is 57.61%.The effect of the lightweight realization of this parameter display model; Figure 11 shows the optimum number of times developed when being subject to constant load 50N and 85N respectively when verification model hanging block and ball material are acrylonitrile-butadiene-styrene copolymer, as can be seen from Figure 12 hanging block is under permissible stress requires, develop 8 times time, being subject to maximum stress is 12.33Mpa, realizes structure optimum; Ball is subject to maximum stress when evolution 3 times be the light-weighted structure that 23.71Mpa reaches optimum; Figure 13 shows hanging block model for acrylonitrile-butadiene-styrene copolymer, PLA, steel three kinds of different materials along with the change of evolution number of times, and the maximum load that corresponding model is born changes thereupon.
The lightweight structure generated prints on the FDM printer of FORTUS360mc, and materials'use acrylonitrile-butadiene-styrene copolymer, its yield strength is 24.3N/mm
2.And realize with additive method the comparison that identical lightweight structure carries out time, intensity and quality.And on general testing machine, carry out the test of pressure bearing.Weigh the weight of print structure body and contrast with the structural model that present stage additive method realizes, and then the dependable with function of verification method.
Claims (6)
1. the light weighed model based on three-dimensional cellular automaton generates and an optimization method, it is characterized in that operation steps is as follows: 1) spatial division: input grid model, and carries out spatial division to the grid model of input; 2) cellular based on neighborhood information develops; 3) feedback analyzed based on FEA develops; 4) resurfacing: the resurfacing lightweight voxel model generated being carried out to inner structure; 5) Verification: the grid model generated developing carries out the checking of parameter.
2. the light weighed model based on three-dimensional cellular automaton according to claim 1 generates and optimization method, it is characterized in that: described step 1) spatial division: input grid model, and spatial division is carried out to the grid model of input; The grid model of Octatree technique to input is adopted to carry out spatial division, build the bounding box of triangle grid model, utilize Octree self-adapting subdividing grid model, after triangle gridding voxelization, based on projection vector method determination voxel inside/outside node, the positional value of the hexahedron voxel that traversal mark generates, and partitioning model is outside, border, inner three kinds of situations; Extract and be labeled border and the internal information of model, the voxel being marked as border respectively mark position value is 1, i.e. Location=1, voxel of object initial position value is 0, Location=0.
3. the light weighed model based on three-dimensional cellular automaton according to claim 1 generates and optimization method, it is characterized in that: described step 2) step that develops based on the cellular of neighborhood information is as follows:
(1) structure of cellular models: based on 6-neighborhood three-dimensional cellular automaton, each voxel is defined as a cellular, adopt following methods initialization: according to initial voxel mark, for all cellulars mark one " positional value " to determine that it is arranged in the relative position of whole model; If certain cellular self-position value is 0, and have the positional value of cellular not to be 0 in its 6-neighborhood, then the cellular positional value that its positional value becomes positional value in 6-neighborhood maximum adds 1, is expressed as
carry out evolution iteration successively, until the positional value of all cellulars of structure is not 0, mark terminates; The functional expression of mark position value is as follows:
In formula,
represent the position of six neighborhoods of T moment cellular;
represent the position of T+1 moment cellular itself;
(2) definition of evolution rule: due to the state after cellular develops at every turn depend on develop before the situation of own situation and surrounding cellular, based on 6-neighborhood three-dimensional cellular automaton, set up the overall functional expression based on neighborhood information and external feedback two kinds of evolution rules, its expression formula is as follows:
F＝∫
ΩN
TGd
Ω(3)
T=0,1,2,3 ... the time numbering of mark voxel,
In formula,
represent the state of X in t; Ω represents a hexahedral element; N represents the matrix of secondary base function; G represents the power that each hexahedral element is subject to; F () represents the cellular evolution rule based on neighborhood; G () represents the feedback evolution rule based on finite element analysis; " " represents f () and the interactional result of g ();
(3) evolution of cellular: the magnitude relationship judging certain center cellular and 6-neighborhood cellular positional value according to the positional value of cellular mark, if there is no the cellular that positional value is larger than self around certain cellular, namely
then this cellular is removed, and mark position is empty, namely prints not output state, the light-weighted voxel model of so preliminary generation.
4. the light weighed model based on three-dimensional cellular automaton according to claim 1 generates and optimization method, it is characterized in that: described step 3) based on FEA analyze feedback develop: first to generate cellular models carry out stress analysis, finite element analysis g (F in above-mentioned cooperating type (2), ∑ Ω) process, model is carried out FEA analysis, calculates cellular maximum stress σ
max, and feed back σ
maxto in cellular evolutionary process, if meet σ
max< [σ], and the cellular that cellular neighborhood is not large than self " positional value "
remove corresponding cellular successively again according to evolution rule, each iteration result all will carry out finite element analysis, and iteration develops and continues until the stressing conditions σ of cellular locally
max> [σ], then program returns last satisfactory iteration result, until all cellulars all do not meet
end program, finally, generates light weighed model; Suppose [σ]-σ
max=Δ σ, if meet
then remove this cellular, if Δ σ < 0, then cellular returns satisfactory result last time; Relation function formula is as follows:
In formula,
represent that self-position value is maximum; σ
maxrepresent the maximum stress suffered by cellular; [σ] represents permissible stress; Δ σ represents stress difference threshold value.
5. the light weighed model based on three-dimensional cellular automaton according to claim 1 generates and optimization method, it is characterized in that: described step 4) resurfacing, the equipotential surface of traversal extraction model voxel of object, the computing of boolean sum the voxel potential function of traversal is adopted to be fused into a complicated potential function f (p), namely represent that traversal extracts the equipotential surface formed when threshold value is C in three-dimensional point set V all in i to n unit potential function, shown in following functional expression:
{V(x，y，z)∈V
3|f(p)＝C}，(6)
I=1,2,3 ..., the number of n voxel,
In formula, f
ip () represents the potential function of i-th voxel, f (p) represents the complicated function merged, and C represents threshold value.
6. the light weighed model based on three-dimensional cellular automaton according to claim 1 generates and optimization method, it is characterized in that: described step 5) Verification: Verification is carried out to the light weighed model after developing, by finite element analysis, the mechanical property generating lightweight structure is controlled; The implementation procedure of the lightweight structure of checking design and meet the light weighed model body structure that goal porosity requires, and the determination of optimum evolution number of times under permanent load, the maximum load that under different materials, structure is born.
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