CN105653779B - Manufacturability based on temperature analogy connectivity constrains Topology Optimization Method - Google Patents
Manufacturability based on temperature analogy connectivity constrains Topology Optimization Method Download PDFInfo
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Abstract
The invention discloses a kind of manufacturabilitys based on temperature analogy connectivity to constrain Topology Optimization Method.The purpose of this method is by connectivity constraint present in increasing material manufacturing technique in view of realizing the disposable manufacture of topological optimization structure in topological optimization model.This method virtually adds heat-insulating material by virtually adding high thermal conductivity spontaneous heating material at hole, in structural region, and boundary is set as heat dissipation boundary, the connectivity constraint of structure is equivalent to virtual temperature less than one constant of structure maximum temperature values off field.Due to explicit physical meaning, mathematical expression form is simple for the constraint, and sensitivity information can be asked, and is conducive to solve based on gradient optimal method.The connectivity constraint that structure is considered in topology optimization design can effectively avoid in topological optimum structure the appearance of internal cap holes, using when increasing material manufacturing technique can one-pass molding, avoid secondary operation.
Description
Technical field
The present invention relates in increasing material manufacturing process, it is excellent that topology is constrained using the manufacturability based on temperature analogy connectivity
Change method.It is related to Patent classificating number G06 calculating；It calculates；G06F electricity Digital data processing G06F17/00 is counted especially suitable for spy
Determine digital calculating equipment or data processing equipment or the data processing method G06F17/50 CAD of function.
Background technique
Referring to Fig.1~2, the structure innovations stage such as machinery, aerospace, Conceptual Model Design are occupied more and more important
Status.Structural Topology Optimization technology has become the effective tool of conceptual model innovative design, and the application that succeeds.Due to
Conventional topologies optimize the limitation for not accounting for preparation process, and the structural configuration of acquisition is complicated.Engineer generally requires to tie optimization
Fruit is modified, to meet the requirement of manufacturing process.This process takes time and effort, and extends the structure design cycle；Final structure
Configuration and topological optimization structural configuration have bigger difference.Therefore, the structural Topology Optimization that research considers that manufacturing process requires is set
The theory and method of meter has important theory and application value.
During increasing material manufacturing, powder technology is either sintered using fused glass pellet (FDM) or laser selective
(SLS), removal backing material or the metal powder not melted after structure prints are required, thus requires inside configuration
Closed inner void 1 cannot be contained.For the structure 2 containing inner void, due to not can be removed backing material or not melting
Metal powder, it is often necessary to second-order correction or structural division manufacture, increase the technology difficulty of manufacture significantly, improve into
This.
Therefore connectivity constraint is considered at Structural Topology Optimization Design initial stage, propose a kind of opening up for consideration connectivity constraint
It flutters Optimized model and method for solving has great importance.
Summary of the invention
The it is proposed of the present invention in view of the above problems, and a kind of manufacturability constraint based on temperature analogy connectivity developed
Topology Optimization Method has following steps:
- establish the finite element model of design object and the topological optimization model with design object connectivity constraint；Definition
Load and boundary condition in finite element model；
High thermal conductivity spontaneous heating material is virtually added at-the hole in finite element model, structural region is virtually replaced with
Heat-insulating material, the boundary definition of finite element model are heat dissipation boundary, construct virtual temperature field model；By the connectivity constraint
Be converted to the constraint of virtual temperature field For the temperature maximum in virtual temperature field,For temperature field constant,λ is setting constant, TmaxTemperature when for all material in virtual temperature field model being high thermal conductivity spontaneous heating material
Maximum value.
- the virtual temperature field constraint is obtained using adjoint method solutionSensitivity, which is described
The sensitivity of connectivity constraint in topological optimization model；It chooses gradient optimal method MMA and calculates topological optimization model, obtain manufacture mesh
Target topological optimization result.
As preferred embodiment, the λ is the constant of 1-10.
As preferred embodiment, the topological optimization model are as follows:
subject to Κ(ρe) u=F
0≤ρei≤ 1 for i=1 ..., m
find ρe∈Rm
Wherein ρ is design variable；M is design variable number；F (ρ, u) is objective function；Κ is that finite element model is totally rigid
Spend matrix；F is node equivalent load vectors；U is node global displacement vector；g1For material volume constraint, veFor unit volume, V
For design object total volume, γ is material volume fraction ratio；g2It is listed for connectivity constraint is equivalent, it is real by addition virtual temperature field
It is existing,For temperature maximum in virtual temperature field,For constant.
Further, it is solved using adjoint method and show that the virtual temperature field constrainsThe specific mistake of sensitivity
Journey is as follows:
- by constraint functionApproximate continuous
Wherein, N is finite element node number, and pp is approximation parameters, TiFor node temperature value
- use adjoint method to solve the constraint sensitivity, as a result are as follows:
Wherein, KTFor temperature field global stiffness battle array, Q is temperature field load vectors, and adjoint variable λ meets following formula.
As preferred embodiment, the virtual temperature field model includes:
Structural region, design variable ρ=1 in the region are heat-insulating material,
Spontaneous heating material is led for height in perforated, design variable ρ=0 in the region,
Finite element model boundary, for boundary of radiating；
The virtual temperature field model meets temperature control equation,
▽ (k ▽ T)+Q=0
Wherein k is material thermal conductivity coefficient, and T is virtual temperature field, and Q is heat source item.
Further, each unit material properties in definition virtual temperature field model are as follows:
Wherein ε=1e-3 is for avoiding singularity；k0For the highly heat-conductive material coefficient of heat conduction, arbitrary value can use in practice；Q0
For highly heat-conductive material heat source item, boundary condition is T=0 in ΓD, ΓDFor finite element model boundary.
By adopting the above-described technical solution, the manufacturability constraint disclosed by the invention based on temperature analogy connectivity is opened up
Optimization method is flutterred to have the advantages that
1) a kind of new structural connectivity etc. is constructed come the connectivity constraint of description scheme using a kind of virtual temperature field
Imitate description method.
2) mathematic(al) representation that structural connectivity constraint is established using p norm approximate function is constructed and considers that structure connects
The topological optimization model of general character constraint.
3) it is listed using the basis of sensitivity analysis that adjoint method obtains connectivity constraint, to provide theory using gradient optimal method
Basis.Since topological optimization contains a large amount of design variable, which greatly reduces it is only necessary to a finite element analysis
Calculation amount, improves optimization efficiency.
4) control can be carried out to structural connectivity by modifying restriction range, realizes optimal topology knot in conjunction with manufacturing process
Can structure one-pass molding and effective control of one-pass molding time.Manufacturing processing technic is realized in the structural concept design stage
Comprehensive consideration, difficulty of processing, cost and time can be greatly reduced.
Detailed description of the invention
For the clearer technical solution for illustrating the embodiment of the present invention or the prior art, to embodiment or will show below
There is attached drawing needed in technical description to do one simply to introduce, it should be apparent that, the accompanying drawings in the following description is only
Some embodiments of the present invention without creative efforts, may be used also for those of ordinary skill in the art
To obtain other drawings based on these drawings.
Fig. 1 is can be by the one-time formed structural schematic diagram of increases material manufacturing technology in background technique.
Fig. 2 is cannot be by the one-time formed structural schematic diagram of increases material manufacturing technology in background technique.
Fig. 3 is connectivity constraint equivalent schematic of the invention.Wherein 1 is structural region, that is, topological optimization ρ=1, definition
Material is heat-insulating material；2 be perforated, that is, topological optimization ρ=0, and definition material is that height leads spontaneous heating material, and 3 be heat dissipation side
Boundary.
Fig. 4 is the method for the present invention by torsion suspension arm cylinder schematic diagram.
Fig. 5 be the method for the present invention introduce connectivity constraint after it is optimal under different constraint condition by torsion suspension arm cylinder
Topological structure.
It (a) is not consider the optimal topological optimization result of connectivity constraint；
(b) to consider connectivity constraint and taking λ=10 optimal topological optimization result when；
(c) to consider connectivity constraint and taking λ=5 optimal topological optimization result when；
(d) to consider connectivity constraint and taking λ=3 optimal topological optimization result when.
Specific embodiment
To keep the purposes, technical schemes and advantages of the embodiment of the present invention clearer, below with reference to the embodiment of the present invention
In attached drawing, technical solution in the embodiment of the present invention carries out clear and complete description:
As in Figure 3-5: a kind of manufacturability constraint Topology Optimization Method based on temperature analogy connectivity mainly includes
Following steps:
Firstly, such software is more common by finite element software, the behaviour such as foundation of finite element model is can be completed in CAD
Make.It is the definition load and boundary condition of finite element model after the foundation for completing finite element model.
Then it is as follows to establish the topological optimization model with connectivity constraint:
subject to Κ(ρe) u=F
0≤ρei≤ 1 for i=1 ..., m
find ρe∈Rm
Wherein ρ is design variable；M is design variable number；F (ρ, u) is objective function；Κ is that finite element model is totally rigid
Spend matrix；F is node equivalent load vectors；U is node global displacement vector；g1For material volume constraint, veFor unit volume, V
For design object total volume, γ is material volume fraction ratio.
g2For the equivalent column of connectivity constraint, realized by addition virtual temperature field,For temperature in virtual temperature field
Maximum value,For constant.
It chooses differentValue can obtain different topological optimization results.
Generally before solving topological optimization model, first calculating virtual temperature field model in all material be high thermal conductivity from
When exothermic material, temperature maximum Tmax, then enable
Wherein λ generally takes the constant less than 10, greater than 1.
Then in order to solve connectivity constraint g2, high thermal conductivity spontaneous heating material is virtually added at the hole in finite element model
Structural region is virtually replaced with heat-insulating material by material, and at hole and the boundary definition of structural region is heat dissipation boundary, and building is virtual
Models for temperature field.
Virtual temperature field consists of three parts:
Structural region (1) the i.e. region of design variable ρ=1 indicates all virtually to replace with heat-insulating material in the region；
Perforated (2) the i.e. region of design variable ρ=0, all virtually replacing with height leads spontaneous heating material in the region；
Structure boundary (3), or perhaps the outer boundary of finite element model are defined as heat dissipation boundary in the present invention.
Meet temperature control equation
▽ (k ▽ T)+Q=0 (2)
Wherein k is material thermal conductivity coefficient, and T is virtual temperature field, and Q is heat source item.To be easy to use finite element method meter
Temperature field equation is calculated, each unit material properties are defined are as follows:
Wherein ε=1e-3 is for avoiding singularity；k0For the highly heat-conductive material coefficient of heat conduction, arbitrary value can use in practice；Q0
For highly heat-conductive material heat source item, arbitrary value can use in practice.
Boundary condition is
T=0 in ΓD (4)
Wherein ΓDFor finite element model outer boundary.
In order to solve connectivity constraint function g2Sensitivity information, by constraint functionApproximate continuous
Wherein, N is finite element node number, and pp is approximation parameters, TiFor node temperature value.
Solving the constraint sensitivity based on adjoint method is
Wherein, KTFor temperature field global stiffness battle array, Q is temperature field load vectors, and adjoint variable λ meets
Then the gradient optimal method MMA that topological optimization model brings selection into calculates topological optimization model, and system can be obtained
Make the topological optimization result of target.
Embodiment
Referring to Fig. 4~5, the present invention is illustrated for by torsion suspension arm cylinder by three-dimensional.Three-dimensional cantilever cylinder having a size of long 60mm,
Diameter of section 20mm.Complete fixed on the left of cantilever beam, right side is by torque.The cantilever beam structure is designed, so that its rigidity is maximum, body point
Than being 40%, both ends are can not finite element model.Specific step is as follows for method:
(a) CAD the and CAE model of initial configuration is established, the boundary conditions such as load, constraint are applied.Model is loaded
For right end section torque, boundary condition is that left side is fixed entirely.
(b) determine structure can finite element model and can not finite element model.One layer unit of model left and right ends portion
For can not finite element model, interlude be can finite element model.
(c) topological optimization model is established are as follows:
subject to Κ(ρe) u=F
0≤ρei≤ 1 for i=1 ..., m
find ρe∈Rm
Wherein ρ is design variable；M is design variable number；f(ρe, u) and it is objective function；Κ is that finite element model is overall
Stiffness matrix；F is node equivalent load vectors；U is node global displacement vector；g1For material volume constraint, veFor cell cube
Product, V are design object total volume, and γ is material volume fraction ratio；g2It is listed for connectivity constraint is equivalent, by adding virtual temperature field
It realizes,For temperature maximum in virtual temperature field,For constant.It calculates when all material is high thermal conductivity spontaneous heating material and ties
The temperature field maximum of T of structuremax, enableWherein λ takes 10,5,3 respectively in this example, as a result as shown in Figure 5 respectively.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
Anyone skilled in the art in the technical scope disclosed by the present invention, according to the technique and scheme of the present invention and its
Inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (4)
1. a kind of manufacturability based on temperature analogy connectivity constrains Topology Optimization Method, it is characterised in that have following step
It is rapid:
Establish the finite element model of design object and the topological optimization model with design object connectivity constraint；Define finite element
Load and boundary condition in model；
The topological optimization model are as follows:
subject to K(ρe) u=F
0≤ρe≤ 1 for e=1 ..., m
find ρe∈Rm
Wherein ρ is design variable；M is design variable number；F (ρ, u) is objective function；K is finite element model global stiffness square
Battle array；F is node equivalent load vectors；U is node global displacement vector；g1For material volume constraint, veFor unit volume, V is to set
Target population product is counted, γ is material volume fraction ratio；g2It lists for connectivity constraint is equivalent, is realized by addition virtual temperature field,
For temperature maximum in virtual temperature field,For constant；
High thermal conductivity spontaneous heating material is virtually added at hole in finite element model, and structural region is virtually replaced with into heat insulating material
Material, the boundary definition of finite element model are heat dissipation boundary, construct virtual temperature field model；The connectivity constraint is converted to
The constraint of virtual temperature field For the temperature maximum in virtual temperature field,For temperature field constant,λ is setting constant, TmaxTemperature is most when for all material in virtual temperature field model being high thermal conductivity spontaneous heating material
Big value；
It is solved using adjoint method and obtains the virtual temperature field constraintSensitivity, which is that the topology is excellent
Change the sensitivity of connectivity constraint in model；It chooses gradient optimal method and calculates topological optimization model, obtain the topology of manufacturing objective
Optimum results；
It is solved using adjoint method and obtains the virtual temperature field constraintSensitivity detailed process is as follows:
By constraint functionApproximate continuous,
Wherein, N is finite element node number, and pp is approximation parameters, TiFor node temperature value；
The constraint sensitivity is solved using adjoint method, as a result are as follows:
Wherein, KTFor temperature field global stiffness battle array, Q is temperature field load vectors, and adjoint variable Λ meets following formula:
2. the manufacturability according to claim 1 based on temperature analogy connectivity constrains Topology Optimization Method, feature
Also reside in the constant that the λ is 1-10.
3. the manufacturability according to claim 1 based on temperature analogy connectivity constrains Topology Optimization Method, feature
Also residing in the virtual temperature field model includes:
Structural region, design variable ρ=1 in the region are heat-insulating material；
Perforated, design variable ρ=0 in the region are high thermal conductivity spontaneous heating material,
Finite element model boundary, for boundary of radiating；
The virtual temperature field model meets temperature control equation,
▽ (k ▽ T)+Q=0
Wherein k is material thermal conductivity coefficient, and T is virtual temperature field, and Q is heat source item.
4. the manufacturability according to claim 3 based on temperature analogy connectivity constrains Topology Optimization Method, feature
It also resides in and defines each unit material properties in virtual temperature field model are as follows:
Wherein ε=1e-3 is for avoiding singularity；k0For the highly heat-conductive material coefficient of heat conduction, arbitrary value can use in practice；Q0For height
Heat Conduction Material heat source item, boundary condition are T=0 in ΓD, ΓDFor finite element model boundary.
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| CN107025340B (en) * | 2017-03-30 | 2017-11-24 | 华中科技大学 | A kind of self-supporting network structure method of topological optimization design suitable for increasing material manufacturing |
| CN107887669B (en) * | 2017-11-07 | 2019-08-13 | 大连理工大学 | A kind of heat dissipation metal power battery pack construction design method and battery pack |
| CN108490024B (en) * | 2018-03-28 | 2021-02-19 | 大连理工大学 | Method for measuring heterogeneous content of limited-thickness material based on virtual heat source principle |
| CN109063291B (en) * | 2018-07-20 | 2021-07-13 | 西安交通大学 | Intelligent topological optimization design method for cooling channel structure of electromechanical equipment |
| CN109657378B (en) * | 2018-12-25 | 2020-09-18 | 山东大学 | Heterogeneous hierarchical structure topology optimization method containing variable-size unit cells |
| CN110414127B (en) * | 2019-07-26 | 2022-12-06 | 东北大学 | Support volume constraint topological optimization method for additive manufacturing |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102789533A (en) * | 2012-07-31 | 2012-11-21 | 西北工业大学 | Structure topology optimization design sensitivity filtering method based on density threshold value |
| KR20150142241A (en) * | 2014-06-11 | 2015-12-22 | 한양대학교 산학협력단 | Method for topology optimization design considering fatigue life of structure and record media recorded program for implement thereof |
-
2015
- 2015-12-28 CN CN201511008080.6A patent/CN105653779B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102789533A (en) * | 2012-07-31 | 2012-11-21 | 西北工业大学 | Structure topology optimization design sensitivity filtering method based on density threshold value |
| KR20150142241A (en) * | 2014-06-11 | 2015-12-22 | 한양대학교 산학협력단 | Method for topology optimization design considering fatigue life of structure and record media recorded program for implement thereof |
Non-Patent Citations (3)
| Title |
|---|
| An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures;Shutian LIU等;《Frontiers of Mechanical Engineering》;20150630;第10卷(第2期);第126-137页，图8-13 |
| MULTIPLE-MATERIAL TOPOLOGY OPTIMIZATION OF COMPLIANT MECHANISMS CREATED VIA POLYJET 3D PRINTING;Nicholas A. Meisel等;《Journal of Manufacturing Science and Engineering》;20141231;第136卷(第6期);全文 |
| 基于制造工艺约束的悬架控制臂拓扑优化;时培成等;《机械设计》;20131031;第30卷(第10期);全文 |
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