CN109948199A - A kind of Topology Optimization Method of shell-interstitital texture - Google Patents
A kind of Topology Optimization Method of shell-interstitital texture Download PDFInfo
- Publication number
- CN109948199A CN109948199A CN201910152297.6A CN201910152297A CN109948199A CN 109948199 A CN109948199 A CN 109948199A CN 201910152297 A CN201910152297 A CN 201910152297A CN 109948199 A CN109948199 A CN 109948199A
- Authority
- CN
- China
- Prior art keywords
- shell
- interstitital texture
- set function
- macrostructure
- situated
- 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.)
- Granted
Links
Landscapes
- Complex Calculations (AREA)
Abstract
The invention belongs to Optimal Structure Designing related fieldss, and specifically disclose a kind of Topology Optimization Method of shell-interstitital texture.Objective function of this method using structural compliance as topological optimization sets outer casing thickness, and initializes macroscopic scale set function and be situated between and see level set function；The sight minor structure that will be situated between is reduced to hyperelement and is assembled into interstitital texture in macro-scale, the macroscopic scale set function of next iteration is obtained after passing through calculating macroscopic view, Jie sees sensitivity and updating design variable and Jie sees level set function and calculates the structural compliance of next iteration, judge whether to meet the condition of convergence, if, optimal shell-interstitital texture is then exported, if otherwise repeating the above steps.The present invention establishes the connection of macrostructure and mesoscopic structure using hyperelement technology, pass through the available optimal filling distribution of the optimization of macro-scale, and shell in homogeneous thickness is automatically derived, while passing through the topology configuration of the available optimal filling porous structure of the optimization of meso-scale.
Description
Technical field
The invention belongs to Optimal Structure Designing related fieldss, excellent more particularly, to a kind of topology of shell-interstitital texture
Change method.
Background technique
Shell-interstitital texture is that a kind of outside is solid shell, and inside is the special construction of porous filling, is widely used in
Material increasing field.Wherein shell suitable for the part for having cooperation to need or is had time pneumatic for keeping the original shape of structure
The structure of mechanical requirements, while internal interstitital texture can also be protected；And internal is the porous weight filled and can reduce structure
Amount, and certain mechanical property is kept, this solid shell combines the structure of porous filling to have preferable anti-flexural property.
Conventional enclosure-interstitital texture designs the method for being based primarily upon empirical formula, in increasing material manufacturing process planning, first
Solid shell is produced, porous filling then is done to the inside of solid shell again, but this manufacturing process is unable to get mechanical property
Optimal shell-the interstitital texture of energy.
The multiple dimensioned Topology Optimization Method rapidly developed in recent years can be designed that optimal macrostructure and microcosmic porous
Structure, although the structure of design still remains two problems close to shell-interstitital texture: on the one hand multiple dimensioned topology is excellent
Change is not accounting for shell macroscopically, and shell is not integrated into process of topology optimization；On the other hand multiple dimensioned topological optimization
Generally carry out the design of porous structure and the Equivalent Calculation of macro property using homogenization method, the hypothesis of homogenization method it
First is that Scale separation, which means that the porous structure of design cannot be guaranteed certain distributed material in real load position, and
And when using a plurality of types of porous structures, good connectivity not can guarantee between porous structure, so that load can not have
Effect transmitting.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of topologys of shell-interstitital texture
Optimization method, wherein by carrying out topology optimization design to shell-interstitital texture from macroscopic view and two scales of sight that are situated between, and using super
Monotechnics establishes the connection of macrostructure and mesoscopic structure, accordingly can easily and accurately obtain optimal shell-interstitital texture.
To achieve the above object, the invention proposes a kind of Topology Optimization Method of shell-interstitital texture, feature exists
In this method comprises the following steps:
Objective function of the S1 using structural compliance as topological optimization sets outer casing thickness, and initializes macroscopic scale collection letter
Number and the sight level set function that is situated between；
S2 sees level set function according to Jie of current iteration, and the sight minor structure that will be situated between is reduced to hyperelement；
The hyperelement that step S2 is obtained is assembled into an interstitital texture in macro-scale by S3, then to macroscopic scale collection letter
Macrostructure of the number greater than 0 carries out finite element analysis, obtains macroscopical displacement field of current iteration；
S4 according to macroscopical displacement field of the step S3 current iteration obtained, calculate macrostructure flexibility sensitivity information and
The sensitivity information of macrostructure constraint condition, to update macrostructure design variable and obtain macroscopical water of next iteration
Flat set function, and then optimize the distribution of the interstitital texture and obtain shell in homogeneous thickness；
S5 is displaced according to macrostructure hyperelement boundary node, the displacement of inverse hyperelement internal node, and is calculated Jie and seen knot
The sensitivity information of the sensitivity information of structure flexibility, mesoscopic structure constraint condition, so that updating Jie sees interstitital texture design variable
And Jie for obtaining next iteration sees level set function, and then optimizes the topology configuration of the interstitital texture；
S6 calculates the structure of next iteration according to the macroscopic scale set function and the sight level set function that is situated between of next iteration
Flexibility, and judge whether the structural compliance of next iteration meets the condition of convergence, if so, optimal shell-interstitital texture is exported,
If it is not, then repeating step S2~S6 according to the macroscopic scale set function of next iteration and the sight level set function that is situated between.
As it is further preferred that in the step S1 structural compliance expression formula are as follows:
In formula, DMAFor the design domain of macrostructure, ΦMAFor macroscopic scale set function, ΦMELevel set function, u are seen to be situated betweenMA
For macroscopical displacement field, T is the transposition of matrix, kMA(ΦMA,ΦME) be macrostructure in any one unit stiffness matrix, d
ΩMAFor the differential in macrostructure domain.
As it is further preferred that in the step S2 reduce after hyperelement stiffness matrix kIAre as follows:
In formula, KmmFor the stiffness matrix of boundary node, KssFor the stiffness matrix of internal node, KmsFor boundary node and interior
The stiffness matrix of portion's node coupling, KsmThe stiffness matrix coupled for internal node with boundary node.
As it is further preferred that in the step S3 in macrostructure the stiffness matrix of any one unit expression formula
Are as follows:
kMA(ΦMA,ΦME)=kS(H(ΦMA)-H(ΦMA-q))+kIH(ΦMA-q) (3)
In formula, kSFor macroscopical hyperelement stiffness matrix of solid minor structure, q is outer casing thickness, H (ΦMA) it is macroscopic scale
The Heaviside functional form of set function, H (ΦMA- q) be macro-scale under interstitital texture level set function Heaviside letter
Number form formula.
As it is further preferred that interstitital texture is located at the view field that level set function is greater than q in the step S3, outside
Shell is located at view field of the level set function in the section 0~q.
As it is further preferred that in the step S4 macrostructure flexibility expression formula are as follows:
The expression formula of the macrostructure constraint condition are as follows:
In formula, tMAFor the time variable of macro-scale, δ (ΦMA) it is ΦMADirac function, δ (ΦMA- q) it is ΦMA-q
Dirac function, DMAIt is the design domain of macrostructure, DMEFor the design domain of mesoscopic structure, H (ΦME) indicate to be situated between and see level set
The Heaviside functional form of function, d ΩMAFor the differential in macrostructure domain, d ΩMEFor the differential in mesoscopic structure domain, VMEIt indicates
It is situated between and sees the total volume of minor structure unit cell, fMAIndicate macroscopical volume fraction, VMAIndicate the total volume in macrostructure design domain.
As it is further preferred that the formula that the internal node of inverse hyperelement is displaced in the step S5 are as follows:
The expression formula of the mesoscopic structure flexibility are as follows:
The expression formula of the mesoscopic structure constraint condition are as follows:
In formula, UsFor internal node displacement, FsFor internal node load vectors, UmFor boundary node displacement, tMERuler is seen to be situated between
The time variable of degree, m, n are to handle X in two-dimensional space respectively, be situated between in Y-direction and see the number of minor structure, and i is to be situated between to see in X-direction
The label of minor structure, j are to be situated between to see the label of minor structure, u in Y-directioni,jFor number i, Jie of j sees the motion vector of minor structure, k0
Indicate the stiffness matrix of interstitital texture basis material, d ΩMEIndicate the differential in mesoscopic structure domain, δ (ΦME) it is ΦMEDirac
Function, fMEIt indicates to be situated between and sees volume fraction, VMEIndicate the total volume of mesoscopic structure design domain.
As it is further preferred that the condition of convergence in the step S6 are as follows: the structural compliance of next iteration and it is current repeatedly
The difference of the structural compliance in generation is less than 0.001.
As it is further preferred that the number that the interstitital texture intermediary sees minor structure is preferably 2~10000.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, mainly have below
Technological merit:
1. the present invention carries out topology optimization design to shell-interstitital texture from macroscopic view and two scales of sight that are situated between, using super list
First technology establishes the connection of macrostructure and mesoscopic structure, and the porous interstitital texture of meso-scale can be equivalent in macrostructure
A hyperelement, be distributed by the available optimal filling of optimization of macro-scale, and automatically derive in homogeneous thickness outer
Shell, while by the topology configuration of the available optimal filling porous structure of the optimization of meso-scale, and in optimization process
In the optimization of two scales carry out parallel so that calculating process is more quick and precisely；
2. simultaneously, the present invention considers the influence of shell in optimization process, outer casing thickness value is embedded in Optimized model, and
It is realized with two horizontal planes of a level set function to the description of shell-interstitital texture, so that it is sensitive to simplify topological optimization
The derivation process of degree；
3. seeing sub tie due to being situated between in addition, the present invention sees the stiffness properties of interstitital texture using substructure method come equivalent Jie
Structure and macrostructure have scale associated effect, can guarantee the connectivity between a variety of minor structures, so that the calculating of structural behaviour
It is more accurate.
Detailed description of the invention
Fig. 1 is the flow chart of the Topology Optimization Method of shell-interstitital texture provided by the invention；
Fig. 2 is shell-interstitital texture two-dimensional representation that the present invention constructs；
Fig. 3 is the schematic three dimensional views according to shell in the shell-interstitital texture constructed in the preferred embodiment of the present invention；
Fig. 4 is three according to interstitital texture in the shell-interstitital texture constructed in the preferred embodiment of the present invention and its unit cell
Tie up schematic diagram；
Fig. 5 is according to the shell constructed in the preferred embodiment of the present invention-interstitital texture entirety schematic three dimensional views.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.
As shown in Figure 1, the present invention provides a kind of Topology Optimization Methods of shell-interstitital texture, which is characterized in that the party
Method includes the following steps:
Objective function of the S1 using structural compliance as topological optimization sets outer casing thickness q, and initializes macroscopic scale collection letter
Number ΦMALevel set function Φ is seen with being situated betweenME, wherein structural compliance J (ΦMA,ΦME) expression formula are as follows:
In formula, DMAFor the design domain of macrostructure, ΦMAFor macroscopic scale set function, ΦMELevel set function, u are seen to be situated betweenMA
For macroscopical displacement field, T is the transposition of matrix, kMA(ΦMA,ΦME) be macrostructure in any one unit stiffness matrix, d
ΩMAFor the differential in macrostructure domain, d ΩMEFor the differential in mesoscopic structure domain；
More specifically, the shell of different-thickness can be obtained, by adjusting the size of q value in order to guarantee q value in whole knot
There is uniform value on structure, introducing reinitializes or level set function is made to have symbolic distance special apart from Regularization Technique
Property；
S2 sees level set function (seeing level set function when first calculating for Jie of initialization) according to Jie of current iteration, will
The sight minor structure that is situated between is reduced to hyperelement, the stiffness matrix k of mesoscopic structure hyperelement after reductionIAre as follows:
In formula, KmmFor the stiffness matrix of boundary node, KssFor the stiffness matrix of internal node, KmsFor boundary node and interior
The stiffness matrix of portion's node coupling, KsmThe stiffness matrix coupled for internal node with boundary node；
The hyperelement that step S2 is obtained is assembled into an interstitital texture in macro-scale by S3, then to macroscopic scale collection letter
Macrostructure of the number greater than 0 carries out finite element analysis, obtains macroscopical displacement field of current iteration, wherein any one in macrostructure
The expression formula of the stiffness matrix of a unit are as follows:
kMA(ΦMA,ΦME)=kS(H(ΦMA)-H(ΦMA-q))+kIH(ΦMA-q) (3)
In formula, kSFor macroscopical hyperelement stiffness matrix of solid minor structure, q is outer casing thickness, H (ΦMA) it is macrostructure
The Heaviside functional form of level set function, H (ΦMA- q) it is interstitital texture level set function under macro-scale
Heaviside functional form；
More specifically, interstitital texture is made of the sight minor structure that is situated between, minor structure topology configuration sees level set function Φ using being situated betweenME
It implicitly describes, the number that interstitital texture intermediary sees minor structure is preferably 2~10000, can define single son in region filling
Structure also can define a plurality of types of minor structures, see Equivalent Calculation, a plurality of types of sons due to carrying out being situated between using subsctructure method
Structure can still keep preferable connectivity after optimization；
It uses the level set function with symbolic distance characteristic to be described in macro-scale, and defines interstitital texture and be located at
Level set is greater than the view field of q, and shell is located at the 0 horizontal view field between q level, less than 0 horizontal view field
For white space, specifically as shown in formula (9):
In formula, x indicates that the space coordinate vector of level set function, t indicate time variable, ΩIIndicate region filling, ΓIIt indicates
The boundary of shell and filling, ΩSIndicate shell domain, ΓSIndicate the boundary of shell and white space, ΩVIndicate white space；
S4 according to macroscopical displacement field of the step S3 current iteration obtained, calculate macrostructure flexibility sensitivity information and
The sensitivity information of macrostructure constraint condition, to update macrostructure design variable and obtain macroscopical water of next iteration
Flat set function, and then optimize the distribution of the interstitital texture and obtain shell in homogeneous thickness, in which:
The expression formula of the macrostructure flexibility are as follows:
The expression formula of the macrostructure constraint condition are as follows:
In formula, tMAFor the time variable of macro-scale, δ (ΦMA) it is ΦMADirac function, δ (ΦMA- q) it is ΦMA-q
Dirac function, DMEFor the design domain of mesoscopic structure, H (ΦME) indicate mesoscopic structure level set function Heaviside letter
Number form formula, d ΩMEFor the differential in mesoscopic structure domain, VMEIt indicates to be situated between and sees the total volume of minor structure unit cell, fMAIndicate macroscopic body integral
Number, VMAIndicate the total volume in macrostructure design domain；
S5 is displaced U according to macrostructure hyperelement boundary nodem, inverse hyperelement internal node displacement Us, it is situated between and sees minor structure
Motion vector ui,jBy UmAnd UsParallel computation raising can be used in composition, and due to the independence between minor structure, when inverse
Then calculating speed calculates the sensitivity information of mesoscopic structure flexibility, the sensitivity information of mesoscopic structure constraint condition, thus more
The new Jie's sight level set function seen interstitital texture design variable and obtain next iteration that is situated between, and then optimize the interstitital texture
Topology configuration, in which:
The formula of the displacement of inverse hyperelement internal node are as follows:
The expression formula of the mesoscopic structure flexibility are as follows:
The expression formula of the mesoscopic structure constraint condition are as follows:
In formula, UsFor internal node displacement, FsFor internal node load vectors, UmFor boundary node displacement, tMERuler is seen to be situated between
The time variable of degree, m, n are to handle X in two-dimensional space respectively, be situated between in Y-direction and see the number of minor structure, and i is to be situated between to see in X-direction
The label of minor structure, j are to be situated between to see the label of minor structure, u in Y-directioni,jFor number i, Jie of j sees the motion vector of minor structure, k0
Indicate the stiffness matrix of interstitital texture basis material, d ΩMEIndicate the differential in mesoscopic structure domain, δ (ΦME) it is ΦMEDirac
Function, fMEIt indicates to be situated between and sees volume fraction, VMEIndicate the total volume of mesoscopic structure design domain；
S6 calculates the structure of next iteration according to the macroscopic scale set function and the sight level set function that is situated between of next iteration
Flexibility, and judge the difference of the structural compliance of next iteration and the structural compliance of current iteration whether less than 0.001, if so,
Optimal shell-interstitital texture is then exported, if it is not, then according to the macroscopic scale set function of next iteration and the sight level set function that is situated between
Repeat step S2~S6.
Further, during the sight minor structure that will be situated between in the step S2 is reduced to hyperelement, a finite element equilibrium equations
(10) form for being written as formula (11) can be separated:
KU=F (10)
In formula, K is stiffness matrix, and U is motion vector, and F is load vectors, and subscript " m " indicates boundary node, subscript " s "
Indicate internal node；
Second row of formula (11) can further be written as following form:
The first row that formula (6) brings formula (11) into is obtained into formula (12):
Formula (12) is rewritable are as follows:
KsubUsub=Fsub (13)
In formula, Ksub、UsubAnd FsubStiffness matrix after respectively indicating reduction, motion vector and load vectors, it may be assumed that
Usub=Um (15)
As shown in Fig. 2, a preferred embodiment according to the invention, which is a hexahedron, long
Width is than being 2:1.2, and four, left side vertex is in freedom degree all constraints in the direction XYZ, i.e. displacement in freedom degree is 0, the right side
Apply the concentrfated load of a F=-1 at center, downward, macroscopic design domain is divided into 20 × 10 × 20 eight sections to loading direction
Point hexahedral element, macroscopical volume fraction are 0.3, outer casing thickness q=1；It is a cube that the design domain of unit cell is filled in the sight that is situated between,
Mesoscopic structure design domain is divided into 14 × 14 × 14 eight node hexahedral elements, and the sight volume fraction that is situated between is 0.8；
Using method provided by the invention carry out topological optimization, obtained after convergence as seen in figures 3-5 in outer casing thickness q
Shell-interstitital texture of best performance in the case where=1, shown in Fig. 3 is 0 < Φ of level set functionMAThe view field of < 1,
That is shell mechanism, shown in Fig. 4 is level set function ΦMAThe view field of > 1, i.e. interstitital texture, partial enlarged view are unit cell
Structural schematic diagram.
The present invention provides a kind of Topology Optimization Method of shell-interstitital texture, is the design method of a kind of system, needs simultaneously
Consider shell and its thickness, filling unit cell configuration, cannot macroscopical load and boundary condition to macroscopical shell and be situated between and see interstitital texture
The key factors such as influence, the design method based on emulation, test and experience cannot achieve or cost of implementation is excessively high, and can not look for
To optimization design scheme.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (9)
1. a kind of Topology Optimization Method of shell-interstitital texture, which is characterized in that this method comprises the following steps:
Objective function of the S1 using structural compliance as topological optimization, set outer casing thickness, and initialize macroscopic scale set function and
It is situated between and sees level set function；
S2 sees level set function according to Jie of current iteration, and the sight minor structure that will be situated between is reduced to hyperelement；
The hyperelement that step S2 is obtained is assembled into an interstitital texture in macro-scale by S3, then big to macroscopic scale set function
Macrostructure in 0 carries out finite element analysis, obtains macroscopical displacement field of current iteration；
S4 calculates the sensitivity information and macroscopic view of macrostructure flexibility according to macroscopical displacement field of the step S3 current iteration obtained
The sensitivity information of structure constraint, to update macrostructure design variable and obtain the macroscopic scale collection of next iteration
Function, and then optimize the distribution of the interstitital texture and obtain shell in homogeneous thickness；
S5 is displaced according to macrostructure hyperelement boundary node, the displacement of inverse hyperelement internal node, and it is soft to calculate mesoscopic structure
The sensitivity information of the sensitivity information of degree, mesoscopic structure constraint condition is seen interstitital texture design variable and is obtained to update Jie
Jie for obtaining next iteration sees level set function, and then optimizes the topology configuration of the interstitital texture；
S6 calculates the structural compliance of next iteration according to the macroscopic scale set function and the sight level set function that is situated between of next iteration,
And judge whether the structural compliance of next iteration meets the condition of convergence, if so, optimal shell-interstitital texture is exported, if it is not,
Step S2~S6 is then repeated according to the macroscopic scale set function of next iteration and the sight level set function that is situated between.
2. the Topology Optimization Method of shell-interstitital texture as described in claim 1, which is characterized in that tied in the step S1
The expression formula of structure flexibility are as follows:
In formula, DMAFor the design domain of macrostructure, ΦMAFor macroscopic scale set function, ΦMELevel set function, u are seen to be situated betweenMAIt is macro
Displacement field is seen, T is the transposition of matrix, kMA(ΦMA,ΦME) be macrostructure in any one unit stiffness matrix, d ΩMAFor
The differential in macrostructure domain.
3. the Topology Optimization Method of shell-interstitital texture as claimed in claim 1 or 2, which is characterized in that in the step S2
The stiffness matrix k of hyperelement after reductionIAre as follows:
In formula, KmmFor the stiffness matrix of boundary node, KssFor the stiffness matrix of internal node, KmsFor boundary node and internal section
The stiffness matrix of point coupling, KsmThe stiffness matrix coupled for internal node with boundary node.
4. the Topology Optimization Method of shell-interstitital texture as claimed in any one of claims 1 to 3, which is characterized in that the step
In rapid S3 in macrostructure the stiffness matrix of any one unit expression formula are as follows:
kMA(ΦMA,ΦME)=kS(H(ΦMA)-H(ΦMA-q))+kIH(ΦMA-q) (3)
In formula, kSFor macroscopical hyperelement stiffness matrix of solid minor structure, q is outer casing thickness, H (ΦMA) it is macroscopic scale collection letter
Several Heaviside functional forms, H (ΦMA- q) be macro-scale under interstitital texture level set function Heaviside function shape
Formula.
5. such as the Topology Optimization Method of the described in any item shell-interstitital textures of Claims 1 to 4, which is characterized in that the step
Interstitital texture is located at the view field that level set function is greater than q in rapid S3, and shell is located at level set function in the section 0~q
View field.
6. the Topology Optimization Method of shell-interstitital texture as claimed in any one of claims 1 to 5, which is characterized in that the step
The expression formula of macrostructure flexibility in rapid S4 are as follows:
The expression formula of the macrostructure constraint condition are as follows:
In formula, tMAFor the time variable of macro-scale, δ (ΦMA) it is ΦMADirac function, δ (ΦMA- q) it is ΦMADi of-q
Clarke function, DMAIt is the design domain of macrostructure, DMEFor the design domain of mesoscopic structure, H (ΦME) indicate to be situated between and see level set function
Heaviside functional form, d ΩMAFor the differential in macrostructure domain, d ΩMEFor the differential in mesoscopic structure domain, VMEIt indicates to be situated between and see
The total volume of minor structure unit cell, fMAIndicate macroscopical volume fraction, VMAIndicate the total volume in macrostructure design domain.
7. the Topology Optimization Method of shell-interstitital texture as described in any one of claims 1 to 6, which is characterized in that the step
The formula of the internal node displacement of inverse hyperelement in rapid S5 are as follows:
The expression formula of the mesoscopic structure flexibility are as follows:
The expression formula of the mesoscopic structure constraint condition are as follows:
In formula, UsFor internal node displacement, FsFor internal node load vectors, UmFor boundary node displacement, tMEFor meso-scale
Time variable, m, n are to handle X in two-dimensional space respectively, be situated between in Y-direction and see the number of minor structure, and i is to be situated between to see son knot in X-direction
The label of structure, j are to be situated between to see the label of minor structure, u in Y-directioni,jFor number i, Jie of j sees the motion vector of minor structure, k0It indicates
The stiffness matrix of interstitital texture basis material, d ΩMEIndicate the differential in mesoscopic structure domain, δ (ΦME) it is ΦMEDirac function,
fMEIt indicates to be situated between and sees volume fraction, VMEIndicate the total volume of mesoscopic structure design domain.
8. the Topology Optimization Method of shell-interstitital texture as described in any one of claims 1 to 7, which is characterized in that the step
The condition of convergence in rapid S6 are as follows: the difference of the structural compliance of the structural compliance and current iteration of next iteration is less than 0.001.
9. the Topology Optimization Method of shell-interstitital texture as described in any one of claims 1 to 8, which is characterized in that described to fill out
Filling structure intermediary to see the number of minor structure is preferably 2~10000.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910152297.6A CN109948199B (en) | 2019-02-28 | 2019-02-28 | Topology optimization method of shell-filling structure |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910152297.6A CN109948199B (en) | 2019-02-28 | 2019-02-28 | Topology optimization method of shell-filling structure |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109948199A true CN109948199A (en) | 2019-06-28 |
| CN109948199B CN109948199B (en) | 2020-11-24 |
Family
ID=67007070
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910152297.6A Active CN109948199B (en) | 2019-02-28 | 2019-02-28 | Topology optimization method of shell-filling structure |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109948199B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111460622A (en) * | 2020-03-06 | 2020-07-28 | 华中科技大学 | Multi-component layout topology optimization method based on parameterized color level set |
| CN116432330A (en) * | 2022-12-23 | 2023-07-14 | 华中科技大学 | Multi-scale shell design method and equipment filled with functionally gradient auxetic metamaterial |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100076732A1 (en) * | 2008-09-23 | 2010-03-25 | Sangpil Yoon | Meshfree Algorithm for Level Set Evolution |
| CN107025340A (en) * | 2017-03-30 | 2017-08-08 | 华中科技大学 | A kind of self-supporting network structure method of topological optimization design suitable for increasing material manufacturing |
| CN107766629A (en) * | 2017-10-09 | 2018-03-06 | 吉利汽车研究院（宁波）有限公司 | A kind of nonmetallic reinforcement structure design method of automobile body |
| CN108647405A (en) * | 2018-04-24 | 2018-10-12 | 华中科技大学 | The minor structure interpolation model modeling method of multi-layer lattice structure topology optimization design |
| CN109271693A (en) * | 2018-09-05 | 2019-01-25 | 上海理工大学 | The multiple dimensioned design method of bi-material layers free damping layer structure |
| CN109325256A (en) * | 2018-08-16 | 2019-02-12 | 上海宇航系统工程研究所 | One second level connect segment construction design method of offset placed load boosting uniform force |
-
2019
- 2019-02-28 CN CN201910152297.6A patent/CN109948199B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100076732A1 (en) * | 2008-09-23 | 2010-03-25 | Sangpil Yoon | Meshfree Algorithm for Level Set Evolution |
| CN107025340A (en) * | 2017-03-30 | 2017-08-08 | 华中科技大学 | A kind of self-supporting network structure method of topological optimization design suitable for increasing material manufacturing |
| CN107766629A (en) * | 2017-10-09 | 2018-03-06 | 吉利汽车研究院（宁波）有限公司 | A kind of nonmetallic reinforcement structure design method of automobile body |
| CN108647405A (en) * | 2018-04-24 | 2018-10-12 | 华中科技大学 | The minor structure interpolation model modeling method of multi-layer lattice structure topology optimization design |
| CN109325256A (en) * | 2018-08-16 | 2019-02-12 | 上海宇航系统工程研究所 | One second level connect segment construction design method of offset placed load boosting uniform force |
| CN109271693A (en) * | 2018-09-05 | 2019-01-25 | 上海理工大学 | The multiple dimensioned design method of bi-material layers free damping layer structure |
Non-Patent Citations (3)
| Title |
|---|
| JUNJIAN FU等: "Design of shell-infill structures by a multiscale level set topology optimization method", 《COMPUTERS AND STRUCTURES》 * |
| 张卫红等: "多孔材料/结构尺度关联的一体化拓扑优化技术", 《力学学报》 * |
| 牛飞: "结构拓扑优化设计若干问题的建模、求解及解读", 《中国博士学位论文全文数据库 基础科学辑》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111460622A (en) * | 2020-03-06 | 2020-07-28 | 华中科技大学 | Multi-component layout topology optimization method based on parameterized color level set |
| CN116432330A (en) * | 2022-12-23 | 2023-07-14 | 华中科技大学 | Multi-scale shell design method and equipment filled with functionally gradient auxetic metamaterial |
| CN116432330B (en) * | 2022-12-23 | 2024-03-19 | 华中科技大学 | Multi-scale shell design method and equipment filled with functionally gradient auxetic metamaterial |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109948199B (en) | 2020-11-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Long et al. | A meshless local Petrov-Galerkin method for solving the bending problem of a thin plate | |
| CN107491599B (en) | Heterogeneous material compliant mechanism Topology Optimization Method under a kind of stress constraint | |
| CN105302974A (en) | Real-time cutting simulation method of flexible object on the basis of finite element and time-variant modal analysis | |
| Feng et al. | Validation of the 3D AMR SIP–CESE solar wind model for four Carrington rotations | |
| CN105096326B (en) | A kind of Laplce using Moving Least scratches figure matrix method | |
| Buchert et al. | Regional averaging and scaling in relativistic cosmology | |
| CN109948199A (en) | A kind of Topology Optimization Method of shell-interstitital texture | |
| CN110570486B (en) | Under-sampling nuclear magnetic resonance image reconstruction method based on deep learning | |
| CN103699714B (en) | A kind of flexible article real-time cutting simulation method coupled based on finite element and mesh free | |
| CN107391855A (en) | A kind of material structure integration construction method towards a variety of microstructures | |
| CN107515982A (en) | A kind of contact analysis method in three-dimensional mechanical finite element modal analysis | |
| CN110659727A (en) | Sketch-based image generation method | |
| CN106062786A (en) | Computing system for training neural networks | |
| CN114662172B (en) | Neural network-based dynamic simulation method for clothing fabric | |
| CN112765856B (en) | Mixed level set method for topological optimization of functionally graded porous structure | |
| CN105635963A (en) | Multi-agent distributed cooperative location method | |
| CN109146001A (en) | Multi-angle of view ISAR image interfusion method | |
| Fan et al. | S–R decomposition based numerical manifold method | |
| CN109241562A (en) | Fine structure material elastic property measuring method based on multi-level finite element modeling method | |
| CN106446432A (en) | Optimal transportation meshless method for solving large deformation of material | |
| CN103378888B (en) | Down beam shaping method and equipment | |
| CN110298922A (en) | A kind of three-dimensional model simplifying method, device and equipment | |
| CN110210151A (en) | Lattice structure based on B-spline parameterizes implicit modeling and optimization method | |
| CN105591876B (en) | A kind of mapping method of virtual network | |
| CN111680361B (en) | Airship scaling model design method based on similarity theory |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |