CN105701349A - Heterogeneous particle discrete unit rapid linear contact detection method - Google Patents
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Abstract
The invention discloses a heterogeneous particle discrete unit rapid linear contact detection method comprising the following steps: ranking and grouping all particles according to particle sizes and a NBS method; respectively carrying out contact detection between each particle and other particles in each group step by step; finally realizing contact detection between all particles. The advantages are that the NBS method is improved so as to solve the problems that an original method cannot suit a heterogeneous particle system; the heterogeneous particle discrete unit rapid linear contact detection method can ensure detection speed, and thus greatly improving detection accuracy.
Description
Technical field
The invention belongs to discrete element numerical simulation field, be specifically related to a kind of non-uniform granular discrete unit fast linear contact detecting method。
Background technology
Current Calculation Anaysis for Tunnel Structure mainly has three class methods: finite element, discrete element, boundary element。Wherein discrete element is a kind of emerging Calculation Anaysis for Tunnel Structure method, is that a kind of granule discrete bodies proposed first based on molecular dynamics principle by American scholar CundallP.A. professor analyzes method, is the numerical method that solves of a kind of display。Carry out in the process of numerical simulation at application discrete element, using each granule in system as discrete unit founding mathematical models, and it is assigned to shape and physical property to each discrete unit, such as quality, rigidity and damping etc., and derive, according to the interaction between each granule, the state that granular system is overall。Based on this principle, distinct element method has significant advantage in the problem in solving heterogeneous body, discontinuous and large deformation these three。Therefore discrete element numerical simulation has in fields such as ground, mining and metallurgy, agricultural, food, chemical industry, pharmacy and environment and applies widely, for instance the simulation of feed bin discharge process；The simulation of granule mixed process；The stability analysis of rock slope mine；The research etc. of the dynamic process such as earthquake, blast。
Discrete element numerical simulation calculates and mainly includes two parts, and one determines that the contact relation of each granule and other granules, and then determines the interaction between granule；Two be according to granule between Interaction Predicting granule in the state of next period, including position, speed and rotation etc.。Wherein it is determined that namely each granule contacts detection with the contact relation of other granules, being a sufficiently complex process, in conventional method, the detection time presents exponential increase along with the increase of amounts of particles, and can only detect the contact between similar particles。Therefore can the efficiency of contact detecting method and the scope of application directly determine discrete element numerical simulation and be applied on a large scale。
Current contact detecting method includes Binomial model and area search etc.。The efficiency of the NBS method wherein belonging to area search is higher, it is achieved that the detection time is linear with total number of particles, and the multiple that namely time increases is identical with quantity increased times, less simultaneously for taking of internal memory, it is possible to be used for simulating extensive granular system。Specifically it is referred to document MunjizaA, AndrewsKRF.NBScontactdetectionalgorithmforbodiesofsimila rsize [J] .InternationalJournalforNumericalMethodsinEngineering, 1998,43 (1): 131-149.
But this method has a problem in that and is only applicable to the single-size system that size is similar。In uneven grain system, cannot applying of the method。
Summary of the invention
Goal of the invention: for prior art Problems existing, the present invention provides the non-uniform granular discrete unit fast linear contact detecting method that a kind of detection accuracy is high。
Technical scheme: described non-uniform granular discrete unit fast linear contact detecting method, described method step is as follows:
All granules are sorted according to the particle diameter of granule and are divided into n group by step 1 from big to small；
Step 2, carries out contact detection by the granule in the 1st group and the 1st to the granule in n-th group；
Step 3, removes the 1st group of granule from overall, is undertaken contacting by the granule in the granule in the 2nd group and the 2nd to n-th group and detects；
Step 4, removes the 1st group and the 2nd group of granule from overall, is undertaken contacting by the granule in the granule in the 3rd group and the 3rd to n-th group and detects；
Step 5, analogizes according to step 4, the granule group having be carried out detection is removed from overall, carries out the detection of next group granule and remainder particulate, until n-th group granule granule all with n-th group carries out contacting detection。
Specifically, in described step 1, granule is divided into specifically comprising the following steps that of n group by particle diameter according to granule
Step A, the granule set in the 1st group particle diameter as d1, then d1Range for D≤d1< D/ α；
Step B, the granule set in the 2nd group particle diameter as d2, then d2Range for D/ α≤d2<D/α2；
Step C, the granule set in the 3rd group particle diameter as d3, then d3Range for D/ α2≤d3<D/α3；
Step D, the rest may be inferred, if the particle diameter of the granule in n-th group is dn, then dnRange for D/ α(n-1)≤dn；
Wherein D is the maximum of all grain diameters, and d is the minima of all grain diameters；α=2；N is total group number, n=int [log (D/d)/log α+0.416]+1, if n > 20, takes n=20。
Specifically, described for i-th group of granule and i-th to n-th group granule carry out contact detection, illustrate that its step is as follows:
Step a, with maximum (the D/ α of grain diameter in i-th group(i-1)) for length of side grid division, and granule is mapped on the grid of place；
Step b, travel through all granules, if certain granule belongs to i-th group, then enter step c, otherwise the next granule of traversal；
Step c, the granule traveled through in the periphery grid of this granule, if belonging to certain granule, this granule be more than or equal to i, is then joined in the contact granule array of centrophyten by packet in periphery grid, otherwise next granule in traversal periphery grid, until traversal terminates；
Step d, repetition step b and step c, until all of granule all has carried out contacting detection with the granule in its periphery grid in i-th group。
Specifically, described contact detecting method adopts NBS contact detecting method。
Beneficial effect: compared with prior art, it is an advantage of the current invention that: have employed the detection mode of packet multistep, reduce the gap between size of mesh opening and particle size in detection each time, solve the problem that former method is not applied for uneven grain system, while ensureing detection speed, drastically increase the accuracy of detection。
Accompanying drawing explanation
Fig. 1 is the main flow chart of described a kind of non-uniform granular discrete unit fast linear contact detecting method；
Fig. 2 is the subroutine flow chart of the NBS method adopted in contact detecting method；
Fig. 3 (a) and Fig. 3 (b) is in 2D and 3D situation respectively, the centrophyten required periphery grid considered during detection；
Fig. 4 (a) and Fig. 4 (b) is stress and strain model when the 1st step detection and the detection of the 2nd step under certain 2D example respectively。
Detailed description of the invention
Below in conjunction with the drawings and specific embodiments, it is further elucidated with the present invention。
As Figure 1-4, a kind of non-uniform granular discrete unit fast linear contact detecting method, comprise the steps:
Step 1, according to the particle diameter of granule all granules sorted from big to small and be divided into n group；
Wherein n is total group number, n=int [log (D/d)/log α+0.416]+1, if n > 20, takes n=20；α=2 are class interval, and D is the maximum in all grain diameters, and d is the minima in all grain diameters；
If the particle diameter of the granule in the 1st group is d1, then d1Range for D≤d1< D/ α；
If the particle diameter of the granule in the 2nd group is d2, then d2Range for D/ α≤d2<D/α2；
If the particle diameter of the granule in the 3rd group is d3, then d3Range for D/ α2≤d3<D/α3；
The rest may be inferred, if the particle diameter of the granule in n-th group is dn, then dnRange for D/ α(n-1)≤dn；
According to mentioned above principle, all granules are grouped。
Step 2, by the granule in i-th group and i-th to granule in n-th group carry out contact detection, repeat this step until i is incremented to n from 1；The method of detection is:
(1) with maximum (the D/ α of grain diameter in i-th group(i-1)) for length of side grid division, and granule is mapped on the grid of place；
(2) travel through all granules, if certain granule x belongs to i-th group, then enter next step, otherwise the next granule of traversal；
(3) granule in the periphery grid of x granule is traveled through, if packet belonging to certain granule y (x) is be more than or equal to i in the periphery grid of x, then this granule is joined in the contact granule array of x, otherwise travel through the next granule in the periphery grid of x, until traversal terminates；
(4) (2nd) and (3rd) step is repeated, until all of granule all carries out contacting detection with the granule in its periphery grid in i-th group。
Wherein, in the 2 d case, the periphery grid of centrophyten is such as shown in Fig. 3 (a)；
In the case of 3d, the periphery grid of centrophyten is such as shown in Fig. 3 (b)。
With an instantiation, the present invention is described below:
Assume that certain granular system comprises tri-granules of A, B, C。The particle diameter of each granule respectively 8cm, 4cm and 4cm。
First sort from big to small according to grain diameter and be grouped。
N=int [log (D/d)/log α+0.416]+1=int [log (8/4)/log2+0.416]+1=2
Therefore granule is divided into 2 groups altogether, the particle size range of the 1st group is D≤d1< D/ α, i.e. 8cm≤d1< 4cm, therefore granule A is first group, remaining granule B and granule C is the 2nd group。
Then detection of packets is carried out。
First step detection is the granule of the 1st group and the granule of the 1st to the 2nd group detects。Stress and strain model when Fig. 4 (a) detects for the first step, the length of side of each grid is that D=8cm, A granule belongs to the 1st group, and B, C belong to the 2nd group。In dividing at this, B is arranged in the periphery grid of A, therefore B is placed in the contact granule array of A, calculates subsequently into the next link of discrete element numerical simulation and the contact force of A and B。C is not in the periphery grid of A, therefore C is not placed in the contact granule array of A。
Second step detection is the granule of the 2nd group and the granule of the 2nd group detects。Stress and strain model when Fig. 4 (b) detects for second step, each grid length of side is D/ α1=4cm, the A granule now belonging to the 1st group is got rid of from overall。And under dividing at this, B granule and C granule all do not need in the periphery grid considered the other side, therefore it is not placed in the contact granule array of the other side。Detection terminates。
Final result is the granule B contact granule being detected as granule A, and is placed into the contact granule array of granule A, and namely the next link subsequently into discrete element numerical simulation calculates the contact force between contact granule。
Analyze it appeared that, if do not carry out packet multistep detection according to original method, under the stress and strain model of Fig. 4 (a), the 1st group is detected with all granules in the 2nd group, so granule B will be located in the granule C periphery grid considered, granule B is detected as and contacts with granule C。And it practice, granule B and granule C distance is relatively big, not in contact with。
If so according to original method, when solving the problem of non-uniform granular system, it will much similar error detection phenomenon occur, namely two actual ranges granule farther out is detected as contact。The accuracy causing contact detection is substantially reduced by this, and the whole efficiency of numerical simulation reduces。
And in the method, adopt the mode of packet multistep detection, first larger-size granule A and granule B, C are detected, then granule A is removed from overall, by grid reodering, then carry out the detection of granule B and granule C。Now stress and strain model is relatively thin, and granule B is not in the periphery grid of granule C, and error detection is excluded。
Analyze it is found that in the packet multistep detection mode that this method adopts, the particle size of the size of each step stress and strain model and institute's detection group is closer to。Therefore, the relative position of granule place grid can comparatively objectively reflect the relative position that granule is actual, and the probability that namely granule in periphery grid contacts with granule in central gridding improves greatly。Therefore relative to original method, present method solves original method and be not applied for the problem of uneven grain system, while ensure that detection speed, greatly improve the accuracy of detection。
Claims (4)
1. a non-uniform granular discrete unit fast linear contact detecting method, it is characterised in that: described method step is as follows:
All granules are sorted according to the particle diameter of granule and are divided into n group by step 1 from big to small；
Step 2, carries out contact detection by the granule in the 1st group and the 1st to the granule in n-th group；
Step 3, removes the 1st group of granule from overall, is undertaken contacting by the granule in the granule in the 2nd group and the 2nd to n-th group and detects；
Step 4, removes the 1st group and the 2nd group of granule from overall, is undertaken contacting by the granule in the granule in the 3rd group and the 3rd to n-th group and detects；
Step 5, analogizes according to step 4, the granule group having be carried out detection is removed from overall, carries out the detection of next group granule and remainder particulate, until n-th group granule granule all with n-th group carries out contacting detection。
2. non-uniform granular discrete unit fast linear contact detecting method according to claim 1, it is characterised in that: in described step 1, granule is divided into specifically comprising the following steps that of n group by the particle diameter according to granule
Step A, the granule set in the 1st group particle diameter as d1, then d1Range for D≤d1< D/ α；
Step B, the granule set in the 2nd group particle diameter as d2, then d2Range for D/ α≤d2<D/α2；
Step C, the granule set in the 3rd group particle diameter as d3, then d3Range for D/ α2≤d3<D/α3；
Step D, the rest may be inferred, if the particle diameter of the granule in n-th group is dn, then dnRange for D/ α(n-1)≤dn；
Wherein D is the maximum of all grain diameters, and d is the minima of all grain diameters；α=2；N is total group number, n=int [log (D/d)/log α+0.416]+1, if n > 20, takes n=20。
3. non-uniform granular discrete unit fast linear contact detecting method according to claim 1, it is characterised in that: described for i-th group of granule and i-th to n-th group granule carry out contact detection, illustrate that its step is as follows:
Step a, with maximum (the D/ α of grain diameter in i-th group(i-1)) for length of side grid division, and granule is mapped on the grid of place；
Step b, travel through all granules, if certain granule belongs to i-th group, then enter step c, otherwise the next granule of traversal；
Step c, the granule traveled through in the periphery grid of this granule, if belonging to certain granule, this granule be more than or equal to i, is then joined in the contact granule array of centrophyten by packet in periphery grid, otherwise next granule in traversal periphery grid, until traversal terminates；
Step d, repetition step b and step c, until all of granule all has carried out contacting detection with the granule in its periphery grid in i-th group。
4. non-uniform granular discrete unit fast linear contact detecting method according to claim 1, it is characterised in that: described contact detecting method adopts NBS contact detecting method。
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| CN109284537A (en) * | 2018-08-24 | 2019-01-29 | 河海大学 | A kind of any sphering convex polygon discrete element method of deformable two dimension |
| CN112116611A (en) * | 2020-09-02 | 2020-12-22 | 吉林大学 | Spine segmentation and character recognition system and method |
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| CN112116611A (en) * | 2020-09-02 | 2020-12-22 | 吉林大学 | Spine segmentation and character recognition system and method |
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