CN106295062A - In Unidirectional Fiber-reinforced Composite, fiber random distribution generates method - Google Patents
In Unidirectional Fiber-reinforced Composite, fiber random distribution generates method Download PDFInfo
- Publication number
- CN106295062A CN106295062A CN201610712882.3A CN201610712882A CN106295062A CN 106295062 A CN106295062 A CN 106295062A CN 201610712882 A CN201610712882 A CN 201610712882A CN 106295062 A CN106295062 A CN 106295062A
- Authority
- CN
- China
- Prior art keywords
- fiber
- fibre
- generation
- circle
- adjacent
- 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
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
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Reinforced Plastic Materials (AREA)
Abstract
The invention belongs to mechanical engineering technical field, be specifically related to fiber random distribution in Unidirectional Fiber-reinforced Composite and generate method.Comprise the following steps: (S1) generates first fiber on fibre reinforced composites cross section；(S2) generating the adjacent fibre of first fiber, the adjacent fibre of first fiber of definition is second filial generation fiber；(S3) according to the adjacent fibre method of first fiber of generation in step (S2), one by one each fiber in second filial generation fiber is processed, generate adjacent fibre, be defined as third generation fiber；Generate adjacent fibre by generation successively, until to be all within fibre reinforced composites cross-sectional area overseas in the center of circle of fiber of certain generation, terminate this generation process.The present invention can simulate the random character of fiber distribution, and fiber volume fraction can be promoted to more than 70%, realizes less sampling, improve operation efficiency, decrease the time on the premise of not changing fiber random character.
Description
Technical field
The invention belongs to mechanical engineering technical field, be specifically related to fiber random distribution in Unidirectional Fiber-reinforced Composite
Generation method.
Background technology
Fibre reinforced composites (FRP) obtain large-scale application on the equipments such as aircraft, vehicle, naval vessel.But, FRP
Mechanical property affected by production technology and can be presented bigger dispersibility.By the horizontal stroke with sem observation FRP
Cross section, finds that fiber distribution in composite cross-sections is unordered random manner, is illustrated in figure 1 fiber on matrix
Distribution.Fiber random distribution in composite cross-sections can cause its change of local fiber volume ratio on cross section
Change, and the mechanical property of composite has important associating with its fiber volume fraction, thus the random distribution of fiber is likely to
It it is the major reason causing composite materials property dispersibility bigger.
When using traditional Monte Carlo sampling approach to carry out stochastic sampling, sampled point often occurs in a certain set of regions
Poly-situation, for the fiber that simulation generates random distribution, easily occurs that fiber is overlapping, thus causes computational efficiency low
Under.In order to solve this problem, the present invention have employed Latin Hypercube Sampling method during generating random distribution fiber.
Latin Hypercube Sampling method (LHS) is proposed by McKay et al. the earliest, introduces the concept of " layering ", and it makes sampled value whole
While individual sample space random distribution, it is also ensured that do not produce and gather, i.e. there is well covering for whole sample space
Rate.As a example by stochastic variable x is carried out n times sampling, the step of LHS method is:
(1) cumulative distribution of variable x is divided into N number of intervals of equal probability；
(2) i-th interval is sampled according to formula (1), it may be assumed that
Probi=(1/N) ru+(i-1)/N (1)
Wherein, ruFor random number equally distributed on 0 to 1, i=1,2 ..., N；
(3) by ProbiCarry out inverse function conversion, obtain a sample value of x, xi, it may be assumed that
xi=F-1(Probi) (2)
Wherein, F-1Inverse function for the probability density function of x.
If separate random vector group carries out Latin Hypercube Sampling, then can first use said method to often
Individual variable is sampled, and then the sampled value of the sampled value of each variable He its dependent variable is carried out random combine, obtains random
N number of sample value of Vector Groups.
The impact of composite materials property has been obtained by the technique study fiber distribution using the distribution of analogue simulation fiber
To extensively application, the present invention proposes a kind of fiber random distribution generating algorithm, is named as Latin hypercube random sequence plavini
(Latin Hypercube Sampling based on Random Sequential Expansion, LHS-RSE), it is adopted
By Latin Hypercube Sampling method thus substantially increase random distribution formation efficiency, and simulate the fiber random character of generation
With the fiber distribution data observed, there is good concordance, fiber volume fraction can be simulated and be up to the fiber random distribution of 70%.
This method used time is short, and efficiency is high, and random distribution characteristic is more satisfactory, it is possible to affect for composite cross-sections fiber random distribution
Analysis supports, thus the improvement to process for producing composite material provides scientific guidance.
Summary of the invention
For above-mentioned technical problem, the present invention proposes and generates random distribution fibre on fibre reinforced composites cross section
The method of dimension, concrete technical scheme is as follows:
In a kind of Unidirectional Fiber-reinforced Composite, fiber random distribution generates method, comprises the following steps:
(S1) first fiber is generated: on fibre reinforced composites cross section, choose a rectangular area, described square
The center in shape region and the center superposition of fibre reinforced composites cross section, randomly choose a point (x in rectangular area0,
y0), with (x0,y0) it is the center of circle, determine first fiber, fibre diameter is d μm；
(S2) generate the adjacent fibre of first fiber: define two random vector l and θ, form random vector group l,
θ }, wherein l represents the distance between first fiber and its adjacent fibre center of circle, and θ is that the center of circle of first fiber is fine with neighbouring
The angle of the circle center line connecting of dimension, l and θ obeys and is uniformly distributed, lmin+d≤l≤lmax+ d, 0≤θ≤2 π, lminIt is first fiber
The beeline allowed between adjacent fiber, lmaxBy the maximum allowed between first adjacent fiber of fiber
Distance；
Use Latin Hypercube Sampling (LHS) method, random vector group { l, θ } is extracted N group data, obtains { (li,
θi), i=1,2 ..., N, thus obtain central coordinate of circle the point { (x of N number of fiberi,yi), i=1,2 ..., N, wherein xi=li*
cosθi, yi=li*sinθi；
According to described central coordinate of circle point { (xi,yi), i=1,2 ..., N, successively N root fiber is arranged in first fiber
Around, if certain root fiber and arranged that fiber produces overlap or its center of circle outside rectangular area, then this root fiber is given up；Definition
The adjacent fibre of first fiber is second filial generation fiber；
(S3) according to the adjacent fibre method of first fiber of generation in step (S2), one by one in second filial generation fiber
Each fiber processes, and generates adjacent fibre, is defined as third generation fiber；Adjacent fibre is generated successively by generation, until certain
It is overseas that the center of circle of the fiber of a generation is all within fibre reinforced composites cross-sectional area, terminates this generation process, retains all
Home position fiber in cross section.
Further, described fibre reinforced composites cross section is rectangle, and its length of side size is Lx×Ly, wherein, LxFor
The length of side value in x-axis direction, L in coordinate systemyFor the length of side value in y-axis direction in coordinate system.
Further, the length and width of described rectangular area is the 1/12 of the fibre reinforced composites cross section length of side, i.e. Lx/
12×Ly/12。
Further, described fibre diameter d span is 6 μm～10 μm.
Further, described lminSpan 0～1.5 μm.
Further, described fibre diameter d value is 6.6 μm.
Further, described lminValue is 0, lmaxValue is 1.6 μm.
Above-mentioned span all comprises the endpoint value of interval.
Compared with the existing method simulating fiber random distribution on fibre reinforced composites cross section, this method has
Following remarkable advantage: (1) the inventive method simple and clear, strong operability, can be realized by conventional programming language, such as C language
And Python, it is possible in composite cross-sections fiber random distribution impact analysis.(2) fiber that the present invention proposes
Random distribution generates method can simulate the random character of fiber distribution, and fiber volume fraction can be promoted to more than 70%,
Disclosure satisfy that simulation analysis requirement.(3) present invention is by merging Latin Hypercube Sampling method, is not changing fiber random character
On the premise of realize less sampling, there is higher operation efficiency, reduce and calculate the time used.
Accompanying drawing explanation
Fig. 1 fiber volume fraction is the one-way glass fiber resin matrix composite cross-sections scanning electron microscope (SEM) photograph of 54%；
Fig. 2 flow chart of steps of the present invention；
Fig. 3 is fibrogenesis schematic diagram in the present invention；
The random distribution fiber that Fig. 4 the inventive method generates.
Detailed description of the invention
Below in conjunction with the accompanying drawings and specific embodiment, the inventive method is described further.
As in figure 2 it is shown, be flow chart of steps of the present invention.The present embodiment with simulation generate 60% fiber volume fraction fiber with
As a example by machine distribution, the rectangular dimension of composite cross-sections is 200 μ m 50 μm；lminIt is first adjacent fiber of fiber
Between the beeline that allowed, lmaxBy the ultimate range allowed between first adjacent fiber of fiber, embodiment
In, lmin=0, lmax=1.6 μm；Fibre diameter d is 6.6 μm.As it is shown on figure 3, build on fibre reinforced composites cross section
Vertical coordinate system, the lower left corner is zero, and front-right is x-axis forward, and surface is y-axis forward；Specifically comprise the following steps that
S1: generate first fiber, randomly select a bit in rectangular area 16.67 μ m 4.17 μm of the heart in cross-section
As the center of circle of first fiber, coordinate is (91.83,22.70) (unit is μm), and with this point as the center of circle, diameter is 6.6
μm, generates first fiber.As shown in (a) in Fig. 3.
S2: generate the adjacent fibre of first fiber.Defining two random vector l and θ, wherein l represents first fiber
And the distance between its adjacent fibre, θ is that (θ represents two for the angle of the circle center line connecting of the center of circle and the adjacent fibre of first fiber
Circle center line connecting and the angle of x-axis positive direction), l and θ obeys and is uniformly distributed, 6.6 μm≤l≤8.2 μm, 0≤θ≤2 π.In Fig. 3
(b) shown in, figure only gives the schematic diagram of few fibers.
Table 1 uses the value of 20 groups of l and θ that LHS sampling obtains
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| l/μm | 7.362 | 7.068 | 8.013 | 8.071 | 7.785 | 6.781 | 7.221 | 7.487 | 7.619 | 7.419 |
| θ | 1.612 | 0.860 | 1.471 | 5.303 | 3.475 | 4.195 | 2.363 | 2.627 | 6.112 | 5.766 |
| Group | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| l/μm | 7.945 | 7.137 | 6.673 | 6.954 | 8.145 | 7.676 | 6.886 | 7.828 | 6.708 | 7.266 |
| θ | 2.028 | 5.428 | 0.150 | 2.829 | 4.015 | 1.223 | 3.421 | 5.007 | 4.585 | 0.487 |
Use Latin Hypercube Sampling (LHS) method, respectively random vector group { l, θ } is carried out 20 sampling, thus obtains
Central coordinate of circle point { (x to 20 fibersi,yi), i=1,2 ..., 20, wherein xi=l*cos θ, yi=l*sin θ；
20 groups of central coordinate of circle that table 2 is obtained by l and θ
| Group | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| x/μm | 91.53 | 96.44 | 92.63 | 96.32 | 84.47 | 88.47 | 86.69 | 85.31 | 99.33 | 98.27 |
| y/μm | 30.06 | 28.05 | 30.67 | 16.00 | 20.16 | 16.81 | 27.77 | 26.39 | 21.40 | 19.03 |
| Group | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| x/μm | 88.32 | 96.51 | 98.42 | 85.21 | 86.60 | 94.44 | 85.21 | 94.10 | 90.98 | 98.25 |
| y/μm | 29.83 | 17.32 | 23.70 | 24.84 | 16.45 | 29.92 | 20.80 | 15.21 | 16.05 | 26.10 |
Observing according to test of many times, use LHS-RSE method, in S2 walks, N=20 i.e. can ensure that in center fiber week
The fiber enclosing generation reaches saturation (i.e. cannot generate new fiber about again).In this case, necessarily have
The fiber that a part of fiber has existed with other overlaps, and needs to remove the fiber overlapped, such as (c) institute in Fig. 3
Show, figure only gives the schematic diagram of few fibers.The fiber central coordinate of circle obtained after removal is as shown in table 3.
The central coordinate of circle of the second filial generation fiber that table 3 obtains after removing
| Group | 1 | 2 | 3 | 4 | 5 |
| x/μm | 91.53 | 96.32 | 84.47 | 85.31 | 99.33 |
| y/μm | 30.06 | 16.00 | 20.16 | 26.39 | 21.40 |
S3: to second filial generation fiber according to step S2 similar approach, produce the adjacent fibre of second filial generation fiber, the i.e. third generation fine
Dimension, as shown in Fig. 3 (d)；And sequentially generate high for fiber, until the center of circle of the 205th generation fiber is all within 16.67 μ m 4.17
Outside this rectangular area of μm, now method terminates, and retains home position fiber in μ m 4.17 μm of rectangular area 16.67,
The final fiber random distribution effect produced is as shown in Figure 4.
The above is only the preferred embodiment of the present invention, for those skilled in the art,
Without departing from the principles of the invention, it is also possible to make some improvements and modifications, these improvements and modifications also should be regarded as this
Bright protection domain.
Claims (7)
1. in a Unidirectional Fiber-reinforced Composite, fiber random distribution generates method, it is characterised in that comprise the following steps:
(S1) first fiber is generated: on fibre reinforced composites cross section, choose a rectangular area, described rectangle region
The center in territory and the center superposition of fibre reinforced composites cross section, randomly choose a point (x in rectangular area0,y0),
With (x0,y0) it is the center of circle, fibre diameter is d μm, determines first fiber；
(S2) generate the adjacent fibre of first fiber: define two random vector l and θ, wherein l represent first fiber and its
Distance between the adjacent fibre center of circle, θ is the center of circle angle with the circle center line connecting of adjacent fibre of first fiber, l and θ obeys
It is uniformly distributed, lmin+d≤l≤lmax+ d, 0≤θ≤2 π, lminThe shortest by allowed between first adjacent fiber of fiber
Distance, lmaxBy the ultimate range allowed between first adjacent fiber of fiber；
Use Latin Hypercube Sampling (LHS) method, random vector group { l, θ } is extracted N group data, obtains { (li,θi), i=
1,2 ..., N, thus obtain central coordinate of circle the point { (x of N number of fiberi,yi), i=1,2 ..., N, wherein xi=li*cosθi, yi=
li*sinθi；
According to described central coordinate of circle point { (xi,yi), i=1,2 ..., N, successively N root fiber is arranged in first fiber peripheral,
If certain root fiber and arranged that fiber produces overlapping or its center of circle outside rectangular area, then give up this root fiber；Definition first
The adjacent fibre of root fiber is second filial generation fiber；
(S3) according to the adjacent fibre method of first fiber of generation in step (S2), each in second filial generation fiber one by one
Root fiber processes, and generates adjacent fibre, is defined as third generation fiber；Adjacent fibre is generated successively by generation, until certain generation
To be all within fibre reinforced composites cross-sectional area overseas the center of circle of fiber, terminate this generation process, retain all centers of circle
Position fiber in cross section.
2. in a kind of Unidirectional Fiber-reinforced Composite as claimed in claim 1, fiber random distribution generates method, its feature
Being: described fibre reinforced composites cross section is rectangle, its length of side size is Lx×Ly, wherein, LxFor x-axis in coordinate system
The length of side value in direction, LyFor the length of side value in y-axis direction in coordinate system.
3. in a kind of Unidirectional Fiber-reinforced Composite as claimed in claim 2, fiber random distribution generates method, its feature
It is: the length and width of described rectangular area is the 1/12 of the fibre reinforced composites cross section length of side, i.e. Lx/12×Ly/12。
4. in a kind of Unidirectional Fiber-reinforced Composite as claimed in claim 1, fiber random distribution generates method, its feature
It is: described fibre diameter d span is 6 μm～10 μm.
5. in a kind of Unidirectional Fiber-reinforced Composite as claimed in claim 1, fiber random distribution generates method, its feature
It is: described lminSpan 0～1.5 μm.
6. in a kind of Unidirectional Fiber-reinforced Composite as claimed in claim 1, fiber random distribution generates method, its feature
It is: described fibre diameter d value is 6.6 μm.
7. in a kind of Unidirectional Fiber-reinforced Composite as claimed in claim 1, fiber random distribution generates method, its feature
It is: described lminValue is 0, lmaxValue is 1.6 μm.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610712882.3A CN106295062B (en) | 2016-08-23 | 2016-08-23 | Fiber random distribution generation method in Unidirectional Fiber-reinforced Composite |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610712882.3A CN106295062B (en) | 2016-08-23 | 2016-08-23 | Fiber random distribution generation method in Unidirectional Fiber-reinforced Composite |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106295062A true CN106295062A (en) | 2017-01-04 |
| CN106295062B CN106295062B (en) | 2019-05-14 |
Family
ID=57615908
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610712882.3A Active CN106295062B (en) | 2016-08-23 | 2016-08-23 | Fiber random distribution generation method in Unidirectional Fiber-reinforced Composite |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106295062B (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107256298A (en) * | 2017-06-01 | 2017-10-17 | 上海交通大学 | Unidirectional fibrous composite materials random structure generation method and its system |
| CN108304628A (en) * | 2018-01-18 | 2018-07-20 | 东南大学 | The generation method of unidirectional enhancing composite material representativeness volume elements based on discrete element |
| CN111070720A (en) * | 2019-12-31 | 2020-04-28 | 中国人民解放军国防科技大学 | Fiber position control device and method for fiber reinforced composite material |
| CN112800628A (en) * | 2021-02-25 | 2021-05-14 | 江西省科学院应用物理研究所 | Method for generating unidirectional fiber resin-based composite cross section based on digital image statistical algorithm |
| CN115130320A (en) * | 2022-07-19 | 2022-09-30 | 福州大学 | Space fiber simulation method suitable for fiber reinforced cement-based composite material |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101923590A (en) * | 2010-08-16 | 2010-12-22 | 北京理工大学 | High-efficiency Latin hypercube experimental design method |
| US20120123743A1 (en) * | 2009-05-13 | 2012-05-17 | Airbus Operations, S.L. | Computer-assisted method for optimising surfaces of composite-material structures |
| CN104835194A (en) * | 2015-03-03 | 2015-08-12 | 西北工业大学 | Method for creating three-dimensional microscopic cell model of composite material based on random-sequence growth method |
| CN104834774A (en) * | 2015-04-29 | 2015-08-12 | 西北工业大学 | Comprehensive optimization design method and design platform for stratospheric composite material propeller |
-
2016
- 2016-08-23 CN CN201610712882.3A patent/CN106295062B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20120123743A1 (en) * | 2009-05-13 | 2012-05-17 | Airbus Operations, S.L. | Computer-assisted method for optimising surfaces of composite-material structures |
| CN101923590A (en) * | 2010-08-16 | 2010-12-22 | 北京理工大学 | High-efficiency Latin hypercube experimental design method |
| CN104835194A (en) * | 2015-03-03 | 2015-08-12 | 西北工业大学 | Method for creating three-dimensional microscopic cell model of composite material based on random-sequence growth method |
| CN104834774A (en) * | 2015-04-29 | 2015-08-12 | 西北工业大学 | Comprehensive optimization design method and design platform for stratospheric composite material propeller |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107256298A (en) * | 2017-06-01 | 2017-10-17 | 上海交通大学 | Unidirectional fibrous composite materials random structure generation method and its system |
| CN108304628A (en) * | 2018-01-18 | 2018-07-20 | 东南大学 | The generation method of unidirectional enhancing composite material representativeness volume elements based on discrete element |
| CN108304628B (en) * | 2018-01-18 | 2019-02-05 | 东南大学 | The generation method of unidirectional enhancing composite material representativeness volume elements based on discrete element |
| CN111070720A (en) * | 2019-12-31 | 2020-04-28 | 中国人民解放军国防科技大学 | Fiber position control device and method for fiber reinforced composite material |
| CN112800628A (en) * | 2021-02-25 | 2021-05-14 | 江西省科学院应用物理研究所 | Method for generating unidirectional fiber resin-based composite cross section based on digital image statistical algorithm |
| CN112800628B (en) * | 2021-02-25 | 2023-04-04 | 江西省科学院应用物理研究所 | Method for generating unidirectional fiber resin-based composite cross section based on digital image statistical algorithm |
| CN115130320A (en) * | 2022-07-19 | 2022-09-30 | 福州大学 | Space fiber simulation method suitable for fiber reinforced cement-based composite material |
| CN115130320B (en) * | 2022-07-19 | 2024-06-04 | 福州大学 | Space fiber simulation method suitable for fiber reinforced cement-based composite material |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106295062B (en) | 2019-05-14 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106295062A (en) | In Unidirectional Fiber-reinforced Composite, fiber random distribution generates method | |
| CN104715117B (en) | A kind of method based on BIM positioning continuous box girder prestress pipes | |
| CN110162856B (en) | Intelligent beam stirrup generation method based on dynamo | |
| CN109190167B (en) | Transverse microstructure generation method of unidirectional long fiber reinforced composite material | |
| CN117150858B (en) | Crack-containing continuous fiber reinforced resin matrix composite three-dimensional finite element modeling method | |
| CN108549748A (en) | The modeling method of surface of concrete structure single line shape reinforcing bar based on CATIA | |
| CN104331271A (en) | Parallel computing method and system for CFD (Computational Fluid Dynamics) | |
| CN107256298A (en) | Unidirectional fibrous composite materials random structure generation method and its system | |
| CN112182933A (en) | Modeling and optimal design method of variable-rigidity composite material cylindrical shell | |
| CN112069562B (en) | Zero-collision rapid arrangement method for three-way hoop reinforcement cage structure in rectangular component | |
| CN111898295A (en) | Finite element modeling method of variable-rigidity composite laminated plate | |
| CN103353830A (en) | Three-dimensional (3D) printing method based on three-dimensional braiding | |
| CN105046632A (en) | Space-time efficient binary image binary logic operation method | |
| CN205799931U (en) | A kind of carbon fiber rod skeleton of 7 degree of freedom carbon fiber rod structural composite material | |
| KR101251445B1 (en) | Apparatus and Method of automatically extracting sweep/extrude/revolve feature shape from atypical digital data | |
| CN104835194B (en) | Based on the microcosmic micro-cell model creation method of random sequence growth method composite three dimensional | |
| CN116702182A (en) | Unstructured full quadrilateral mesh coordinated multi-stage encryption method based on template method | |
| CN116525039A (en) | Efficient composite random fiber generation method suitable for wide volume fraction range | |
| CN109344424A (en) | Winding tension applying method in a kind of composite element finite element analysis model | |
| CN106776844A (en) | A kind of simulation field of force boundling binding method of complex node connection figure | |
| CN105022896A (en) | Method and device for APDL modelling based on dynamic numbering | |
| CN107239586A (en) | The domain decomposition parallel method effective to unconditionally stable FDTD method | |
| Frangos et al. | A Bio-Informed Topology Optimization Algorithm Based on Leaf Venation Structures | |
| Mazzucato | Additive manufacturing through micro direct laser metal deposition technology: influence of the material and process parameters on the product quality | |
| Chen et al. | Improvement of Traditional Village Protection Infrastructure Management System |
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 |