CN105528494B - Light weighed model based on three-dimensional cellular automaton generates and optimization method - Google Patents
Light weighed model based on three-dimensional cellular automaton generates and optimization method Download PDFInfo
- Publication number
- 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
- Authority
- CN
- China
- Prior art keywords
- cellular
- model
- voxel
- neighborhood
- light weighed
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/30—Polynomial surface description
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T19/00—Manipulating 3D models or images for computer graphics
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Computer Graphics (AREA)
- Geometry (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Mathematical Physics (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Algebra (AREA)
- Evolutionary Computation (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
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
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. a kind of light weighed model based on three-dimensional cellular automaton generates and optimization method, it is characterised in that operating procedure is such as
Under:
1) space divides: using Octatree technique, inputs grid model, and carry out space division to the grid model of input；
2) cellular based on three-dimensional cellular automaton neighborhood information develops；
3) feedback based on FEA analysis develops；
4) resurfacing of internal structure resurfacing: is carried out to the lightweight voxel model of generation；
5) verifying of parameter Verification: is carried out to the grid model generated that develops.
2. the light weighed model according to claim 1 based on three-dimensional cellular automaton generates and optimization method, feature
Be: the step 1) space divides: input grid model, and carries out space division to the grid model of input；Using eight forks
Tree method carries out space division to the grid model of input, constructs the bounding box of triangle grid model, adaptive using Octree
Subdivided meshes model after triangle gridding voxelization, determines voxel interior nodes and exterior node, traversal label life based on projection vector method
At hexahedron voxel positional value, and partitioning model be outside, boundary, inside three kinds of situations；Extraction has been labeled model
Boundary and internal information, the voxel difference mark position value for being marked as boundary is 1, i.e. Location=1, and voxel of object is initial
Positional value is 0, i.e. Location=0.
3. the light weighed model according to claim 2 based on three-dimensional cellular automaton generates and optimization method, feature
Be: the step of step 2) is developed based on the cellular of neighborhood information is as follows:
(1) building of cellular models: being based on 6- neighborhood three-dimensional cellular automaton, each voxel be defined as a cellular, uses
Following methods initialization: marking according to initial voxel, is 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 cellular itself
Position；
(2) definition of evolution rule: the state after developing every time due to cellular depends on own situation and surrounding cellular before developing
The case where, it is based on 6- neighborhood three-dimensional cellular automaton, establishes the entirety based on neighborhood information Yu two kinds of evolution rules of external feedback
Functional expression, expression formula are as follows:
F=∫ΩNTGdΩ (3)
T=0,1,2,3 ... ..., t are the time domain for marking voxel,
In formula,Indicate X in the state of t moment；Ω indicates a hexahedral element；N indicates the matrix of secondary basic function；G
Indicate the power that each hexahedral element is subject to；F () indicates the cellular evolution rule based on neighborhood；G () indicates to be based on finite element
The feedback evolution rule of analysis；" " indicates the result of f () and g () interaction；
(3) size of certain center cellular Yu 6- neighborhood cellular positional value the evolution of cellular: is judged according to the positional value that cellular marks
Relationship, 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.
4. the light weighed model according to claim 3 based on three-dimensional cellular automaton generates and optimization method, feature
Be: the step 3) is developed based on the feedback that FEA is analyzed: carrying out stress analysis, above-mentioned association 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 same formula (2)max, and feed back
σmaxInto cellular evolutionary process, if meeting σmax< [σ], and cellular neighborhood is than itself " positional value " big cellular, i.e.,Corresponding cellular, each iteration result are successively removed again according to evolution rule
Finite element analysis will be all carried out, iteration, which develops, is continued until the stress condition σ of local cellularmax> [σ], then in program return
Primary satisfactory iteration result, until all cellulars do not comply withTerminate program, finally,
Generate 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] indicates allowable and answers
Power；Δ σ indicates stress difference threshold value.
5. the light weighed model according to claim 1 based on three-dimensional cellular automaton generates and optimization method, feature
Be: the step 4) resurfacing, traversal extract the equipotential surface of model voxel of object, and the voxel potential function of traversal is used cloth
The operation of your sum is fused into a complicated potential function f (p), that is, indicates that traversal is extracted all three in i to n unit potential function
The equipotential surface constituted when threshold value is C in dimension point set V, shown in following functional expression:
{V(x,y,z)∈V3| f (p)=C }, (6)
I=1,2,3 ... ..., n, i are the number of 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.
6. the light weighed model according to claim 1 based on three-dimensional cellular automaton generates and optimization method, feature
It is: the step 5) Verification: Verification is carried out to the light weighed model after evolution, by finite element analysis to generation
The mechanical property of lightweight structure controls；It verifies the realization process of the lightweight structure of design and meets goal porosity requirement
The determination of optimal evolution number under light weighed model body structure and permanent load, the maximum load that different materials flowering structure is born
Lotus.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201511015816.2A CN105528494B (en) | 2015-12-29 | 2015-12-29 | Light weighed model based on three-dimensional cellular automaton generates and optimization method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201511015816.2A CN105528494B (en) | 2015-12-29 | 2015-12-29 | Light weighed model based on three-dimensional cellular automaton generates and optimization method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105528494A CN105528494A (en) | 2016-04-27 |
| CN105528494B true CN105528494B (en) | 2019-02-22 |
Family
ID=55770716
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201511015816.2A Expired - Fee Related CN105528494B (en) | 2015-12-29 | 2015-12-29 | Light weighed model based on three-dimensional cellular automaton generates and optimization method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105528494B (en) |
Families Citing this family (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106408649B (en) * | 2016-08-08 | 2019-06-04 | 上海大学 | A kind of rule-based body structure evolution design method |
| EP3296899A1 (en) * | 2016-09-19 | 2018-03-21 | Biomodex S.A.S. | Method and apparatus for generating a 3d model of an object |
| CN106650124B (en) * | 2016-12-28 | 2020-04-28 | 谢亿民工程科技（常州）有限公司 | Finite element result-based surface lightening method for continuum |
| EP3503040B1 (en) * | 2017-12-24 | 2024-06-05 | Dassault Systèmes | Design of a 3d finite element mesh of a 3d part that comprises a lattice structure |
| CN109334011B (en) * | 2018-11-02 | 2020-05-05 | 珠海赛纳打印科技股份有限公司 | Color 3D printing method, printing device and terminal equipment |
| CN109949267B (en) * | 2019-01-21 | 2021-01-29 | 西安交通大学 | Rapid three-dimensional reconstruction method for multi-material fault data to entity |
| WO2020224634A1 (en) * | 2019-05-09 | 2020-11-12 | 江苏大学 | Subregion hybrid cellular automata method for solving vehicle body thickness optimization |
| CN110298909B (en) * | 2019-06-28 | 2023-04-07 | 北京工业大学 | Three-dimensional cellular automaton-based weathering phenomenon simulation method |
| CN112749502B (en) * | 2021-01-27 | 2022-05-10 | 天津博迈科海洋工程有限公司 | Regional virtual assembly lightweight method for oil-gas platform module |
| CN114781193B (en) * | 2022-06-20 | 2022-09-02 | 苏州培风图南半导体有限公司 | Etching process simulation method and system |
| CN115222898B (en) * | 2022-09-21 | 2022-12-13 | 浙江华东工程数字技术有限公司 | Simplified map model creation method based on oblique photography and voxel modeling technology |
| CN117101438B (en) * | 2023-08-25 | 2024-07-23 | 江苏洁瑞特膜技术有限公司 | Control method and system for PVDF ultrafiltration membrane production based on visible light photocatalyst |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102799717A (en) * | 2012-06-29 | 2012-11-28 | 上海大学 | Sample learning-based porous media modeling method |
| CN104268931A (en) * | 2014-09-11 | 2015-01-07 | 上海大学 | Internal structure controllable assembly method based on network model |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090319453A1 (en) * | 2008-06-24 | 2009-12-24 | Livermore Software Technology Corporation | Sampling Strategy Using Genetic Algorithms in Engineering Design Optimization |
-
2015
- 2015-12-29 CN CN201511015816.2A patent/CN105528494B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102799717A (en) * | 2012-06-29 | 2012-11-28 | 上海大学 | Sample learning-based porous media modeling method |
| CN104268931A (en) * | 2014-09-11 | 2015-01-07 | 上海大学 | Internal structure controllable assembly method based on network model |
Non-Patent Citations (2)
| Title |
|---|
| 《一种基于OpenGL的三维元胞自动机模型》;许林，郭洪民，杨湘杰;《计算机工程与科学》;20051031;第27卷(第10期);第85-89页 |
| 《一种改进的三维元胞自动机模拟铝合金凝固》;许林，郭洪民;《金属铸锻焊技术》;20110331;第40卷(第5期);第1-4,8页 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105528494A (en) | 2016-04-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105528494B (en) | Light weighed model based on three-dimensional cellular automaton generates and optimization method | |
| CN110457982B (en) | Crop disease image identification method based on feature migration learning | |
| Yoo | Porous scaffold design using the distance field and triply periodic minimal surface models | |
| CN109299781A (en) | Distributed deep learning system based on momentum and beta pruning | |
| Kumano et al. | Multidisciplinary design optimization of wing shape for a small jet aircraft using kriging model | |
| CN103593703A (en) | Neural network optimizing system and method based on genetic algorithms | |
| Alejandrino et al. | A machine learning approach of lattice infill pattern for increasing material efficiency in additive manufacturing processes | |
| CN102867101A (en) | Method for determining truss structure parameters | |
| CN106408649B (en) | A kind of rule-based body structure evolution design method | |
| Nagy et al. | Nature-based hybrid computational geometry system for optimizing component structure | |
| Yoo | Advanced projection image generation algorithm for fabrication of a tissue scaffold using volumetric distance field | |
| CN105740968A (en) | Land use space automatic configuration system | |
| CN118133403B (en) | City planning design drawing generation method, device, equipment, medium and product | |
| CN105809286A (en) | Incremental SVR load prediction method based on representative data reconstruction | |
| CN109492522A (en) | Specific objective detection model training program, equipment and computer readable storage medium | |
| CN109502017A (en) | A kind of bionical unmanned plane of topological optimization and its design method | |
| Li et al. | Automated layout design of stiffened container structures based on the morphology of plant ramifications | |
| Yogev et al. | Computational evolutionary embryogeny | |
| Jones | CFD analysis and design optimization of flapping wing flows | |
| Zhang et al. | Function representation based analytic shape hollowing optimization | |
| Klemmt et al. | Discrete vs. Discretized Growth Discretized Fabrication of Geometries Generated with Cellular Growth Simulations | |
| Liu et al. | Realistic view synthesis of a structured traffic environment via adversarial training | |
| CN108733907A (en) | Explore the coupling process of the scale-sensitive of cellular Automation Model | |
| Lang | Simultaneous Structural and Material Optimization | |
| Martínez-Molina et al. | Modeling prey-predator dynamics via particle swarm optimization and cellular automata |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20190222 Termination date: 20211229 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |