CN107918706A - A kind of adaptive concrete carefully sees modeling method - Google Patents
A kind of adaptive concrete carefully sees modeling method Download PDFInfo
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Abstract
The present invention discloses a kind of adaptive concrete and carefully sees modeling method, comprises the following steps：1) circular boundary according to needed for the generation of aggregate grading, convex polygon aggregate is generated in circular boundary, then carries out continuation to its area, is carried out at the same time the intrusion of continuation point and is judged, generates convex polygon aggregate concrete model；2) inner polygon grid transition ring is set inside each convex polygon aggregate, outer polygonal mesh transition ring is set between aggregate mortar interfaces transition band and cement mortar, the polar radius of aggregate is adjusted, obtain aggregate mortar interfaces transition band and inside and outside grid transition ring apex coordinate, according to aggregate size, aggregate mortar interfaces transition tape thickness is set, the size of mesh opening on inside and outside grid transition ring is concurrently set, obtains the concrete multiphase meso-mechanical model of mesh adaption.This method can realize the random generation launched with adaptive mesh of aggregate in meso-mechanical model, ensure to improve computational efficiency while different zones computational accuracy in model.
Description
Technical field
The present invention relates to a kind of thin sight modeling technique, and in particular to a kind of adaptive concrete carefully sees modeling method, belongs to
In the meso-level simulation technical field that concrete damage destroys.
Background technology
With the development of computer technology, the method for numerical simulation of microscopic parameter is widely used in concrete damage destruction
Analysis.Wherein, the foundation of meso-mechanical model is an important part.In face of the internal structure of concrete complexity, rationally
Thin modeling pattern of seeing be to analyze the key that concrete damage destroys.The raising of model fine degree means with actual conditions more
Adjunction is near, but also improves calculation scale, thereby produce how balance model become more meticulous degree and calculation scale the problem of.
If considering the actual geometric format of aggregate-mortar interface intermediate zone (ITZ), calculation scale will be due to the reduction of unit size and big
Width increases, if make certain hypothesis to ITZ thickness and reduce calculation scale, and and the actual certain deviation of generation.
The content of the invention
Goal of the invention：A kind of adaptive concrete is provided for deficiency, the present invention existing for existing thin sight modeling method
It is thin to see modeling method, the random meso-mechanical model of polygonal aggregate concrete of mesh adaption can be established by this method, to coagulation
Native damage and failure carries out efficiently and accurate batch is simulated.
Technical solution：A kind of adaptive concrete of the present invention carefully sees modeling method, comprises the following steps：
1) circular boundary according to needed for the generation of aggregate grading, generates convex polygon aggregate, so in circular boundary
Continuation is carried out to its area afterwards, the intrusion of continuation point is carried out at the same time and judges, generate convex polygon aggregate concrete model；
2) inner polygon grid transition ring, aggregate-mortar interface intermediate zone and water are set inside each convex polygon aggregate
Outer polygonal mesh transition ring is set between cement mortar, the polar radius of convex polygon aggregate is adjusted, obtains aggregate-mortar
Interfaces transition band and inside and outside polygonal mesh transition ring apex coordinate, aggregate-mortar interface intermediate zone is set according to aggregate size
Thickness, concurrently sets the size of mesh opening on inside and outside polygonal mesh transition ring, and the concrete multiphase for obtaining mesh adaption is carefully seen
Model.
Above-mentioned steps 1) in, the generation method of convex polygon aggregate is：Taken at random on circular boundary and be used as polygon
First vertex of aggregate, and the 2 to n-th apex coordinate is sequentially generated according to polar angle and polar radius, according to aggregate vertex
Genesis sequence carries out convexity judgement, each aggregate vertex is met Convex Conditions.
Wherein, the method for convexity judgement is：By the directed area on 3 aggregate vertex being newly generated it is positive and negative realize it is convex
Property condition judgement, when directed area is positive number, illustrate form directed area triangle the 3rd order point be convexity point,
When all aggregate vertex can ensure after judging polygon as convex polygon when, aggregate generation finish.
To convex polygon aggregate area carry out continuation method be：The apex coordinate of each polygonal aggregate is turned by polar coordinates
Cartesian coordinate is changed to, the polygon length of side is calculated respectively and is stored in array, then obtain length of side value maximum in array
aiai-1；Again using longest edge to take continuation point P on the circumference of diameter at random, its coordinate parameters is as follows：
In formula：aiai-1For the continuation side length of side, η is (0,1) interior uniformly distributed function, and γ is the random number in (0,2 π).
When carrying out area continuation to convex polygon aggregate, the triangle that continuation point both sides adjacent with extending side are formed need to be ensured
Directed area S is both greater than zero；So as to ensure that continuation point is convexity point.
To ensure that continuation point does not invade other aggregates, the distance between continuation point and aggregate center of circle are limited in corresponding aggregate pair
Answer grading maximum particle diameter rmaxWithin the scope of.
Judge that the method whether continuation point P invades other aggregates is：When whether the continuation point P for judging aggregate B invades aggregate A
When, inverse time needle sort is pressed on the vertex of aggregate A, calculates directed area S respectivelynPn+1Positive and negative (n=1,2,3), work as SnPn+1Value
When all to bear, illustrate inside P points intrusion aggregate A, work as SnPn+1Value it is positive and negative not for the moment, illustrate two aggregate of A, B mutually from.
Above-mentioned steps 2) in, by convex polygon aggregate apex coordinate (ρi, θi) obtain aggregate-mortar interface intermediate zone vertex
Coordinate and inside and outside polygonal mesh transition ring apex coordinate parameter expression：
In formula, αiFor aggregate-mortar interface transition tape thickness or inside and outside polygonal mesh transition ring thickness.Aggregate-mortar
Interfaces transition tape thickness is 0.02mm to 0.05mm with aggregate size linear change；Inside and outside polygonal mesh transition ring thickness point
0.7 times and 1.2 times of aggregate size is not arranged to；Size of mesh opening and transition circumference on inside and outside polygonal mesh transition ring
It is directly proportional.
Further, the size of mesh opening L on inside and outside polygonal mesh transition ring is determined by following formula：
In formula, A is corresponding inside and outside grid transition ring girth, and B is aggregate-mortar interface intermediate zone girth, I for aggregate-
The size of mesh opening of mortar interface intermediate zone, the value of I are equal to or slightly less than the thickness of aggregate-mortar interface intermediate zone.
Beneficial effect：Compared with prior art, the advantage of the invention is that：The present invention is in finite element simulation, coagulation
On the basis of soil material, damage mechanics theory, computational efficiency and precision have been taken into account, integrated polygonal aggregate has been devised and mixes
Solidifying soil random fine sees model modelling approach, and this method considers the actual (real) thickness of ITZ and its change with aggregate size, utilizes this
Method can realize that the random of aggregate in meso-mechanical model is launched and the generation of adaptive mesh, so as to ensure in model not same district
Computational efficiency is improved while the computational accuracy of domain；This method, which can be established, is more in line with actual efficient computation model, also for batch
Numerical quantity simulation is provided convenience, and the concrete meso-mechanical model established by this method is very suitable for concrete damage destruction
Simulation.
Brief description of the drawings
Fig. 1 is a kind of modeling procedure of adaptive concrete meso-mechanical model of the present invention；
Fig. 2 is the random generation of circular aggregate and launches flow chart；
Fig. 3 judges schematic diagram for polygon Convex Conditions；
Fig. 4 is convex polygon aggregate area continuation schematic diagram；
Fig. 5 judges schematic diagram for the intrusion of convex polygon aggregate, in figure, two aggregate of A, B phase from；
Fig. 6 is the random product process figure of convex polygon aggregate concrete model；
Fig. 7 is the convex polygon aggregate concrete model schematic generated in embodiment；
Fig. 8 is that the inner ＆ outer polygon grid transition ring of convex polygon aggregate sets schematic diagram；
Fig. 9 (a) is the concrete finite element model finally established in embodiment, and Fig. 9 (b) is single convex polygon in Fig. 9 (a)
The mesh generation schematic diagram of the ITZ of shape aggregate and inside and outside grid transition ring.
Embodiment
Technical scheme is described further with specific embodiment below in conjunction with the accompanying drawings.
A kind of adaptive concrete of the present invention carefully sees modeling method, is carried out on the basis of polygonal aggregate generation
ITZ areas are established to be set with adaptive mesh, by setting polygonal mesh transition ring automatically around polygonal aggregate, in ITZ
Grid intermediate zone is formed between cement mortar and aggregate, adaptive grid transition is formed, allows ITZ by actual geometric format
Build among meso-mechanical model, be difficult to ensure to count at the same time so as to solve original polygonal aggregate concrete and carefully see in modeling technique
The problem of calculating efficiency and computational accuracy.
Such as Fig. 1, a kind of adaptive concrete of the invention is carefully seen modeling method and is comprised the following steps：
1) circular boundary according to needed for the generation of aggregate grading, utilizes the polar coordinates (r on polygonal aggregate vertexi, θi)
The position on aggregate vertex is determined in circular boundary, it is met Convex Conditions, then continuation is carried out to polygonal aggregate, while into
Row intrusion judges；
2) aggregate polar radius is adjusted, obtains ITZ and inside and outside grid transition ring apex coordinate, set according to aggregate size
ITZ thickness is put, concurrently sets the mesh-density on inside and outside grid transition ring, the concrete multiphase for obtaining mesh adaption carefully sees mould
Type.
Embodiment
Step 1)：
(a) model boundary coordinate is determined, it is assumed that be (xl, yl), (xr, yr).Calculate section endoparticle particle diameter D and be less than sieve aperture D0
In the range of probability Pc(D ＜ D0)：
In formula, PkFor the percentage of the total volume of aggregate volume in concrete sample.
Calculate the particles of aggregates number of each particle diameter, such as following formula：
Wherein, niFor the granule number in a certain particle size range；Ai, A be respectively aggregate area and area of section, for diameter
For the circular aggregate of D, its area is：A=π D2/4。
(b) the aggregate size r in the range of each grading is generated at randomi。
(c) the aggregate grain in aggregate Geometric center coordinates (x, y) and corresponding particle size range is generated in the range of model boundary
Footpath ri, its relation such as following formula：
Distances of the wherein u between aggregate and border.So ensure that any circle of generation will not be with test specimen border
Intersecting, two circular phases are from judging need to only to make to be more than the sum of radius of circle with a distance between two centers of circle：
V is the minimum range between two circles in formula.
The random generation of circular aggregate and dispensing flow chart such as Fig. 2.
(d) first vertex (r, θ) as polygonal aggregate is taken in the step (c) on the circumference of generation at random, its
Coordinate parameters are as follows：
λ is the random number in (0,1) in formula.2nd to n-th apex coordinate (ri, θi) value mode it is as follows：
To avoid the generation of needle-shaped aggregate, the value range of polar angle and polar radius is set：rbFor (0,0.5r0)、θbForIn the range of random number.
(e) such as Fig. 3, generating a little in the case of 1,2, meeting polygon Convex Conditions to ensure to put 3, by Δ 123
The positive negative judgement of directed area S realize, SΔ123Calculating formula it is as follows：
Work as SΔ123For positive number when, the 3rd point 3 in the downside of 1,2 line extended lines, figure3Point, is " convexity point "；Work as SΔ123
When being zero, on extended line, 3 in figure2Point；Work as SΔ123For negative when, 3 points on the upside of extended line, be " concavity point ".When the 3rd point
For " convexity point " when, preserve data, continue generation the 4th point；It is direct with the 3rd point using " method of substitution " during if " concavity point "
Substitute at the 2nd point, this increases not only aggregate area and also improve sequential operation efficiency.
Follow-up aggregate vertex generating algorithm is similar to the 3rd point.When each apex coordinate can ensure that polygon is convex
During polygon, data are stored, and are sequentially connected with each vertex generation convex polygon aggregate.Since the convex polygon of generation is located at phase
Inside circular aggregate, so the problem of convex polygon aggregate generated will not produce juxtaposition herein.This algorithm is easy,
And the generation of lopsided aggregate is avoided, greatly improve computational efficiency.
(f) apex coordinate is converted into cartesian coordinate by polar coordinates, and calculates the polygon length of side respectively and be stored in
Array, calculation formula are：Then length of side value a maximum in array is obtainediai-1.With most
For long side to take continuation point P at random on the circumference of diameter, coordinate parameters are as follows：
In formula：aiai-1For the continuation side length of side, η is (0,1) interior uniformly distributed function, and γ is the random number in (0,2 π).Bone
Expect that the shape after continuation is as shown in Figure 4.
(g) during area continuation is carried out, to ensure that continuation point P is convexity point, point P need to be ensured with extending side adjacent two
Side ai-1ai、ai+1ai+2The triangle directed area S of composition is both greater than zero.To ensure that continuation point P does not invade other aggregates, limit
The distance between continuation point and the aggregate center of circle match somebody with somebody maximum particle diameter r in B aggregates respective stagesmaxWithin the scope of.The method of judgement is：
Inverse time needle sort is pressed on the vertex of aggregate A, calculates directed area S respectivelynPn+1Positive and negative (n=1,2,3), when all for it is negative when, P
Inside point intrusion aggregate A, work as SnPn+1Value it is positive and negative not for the moment, two aggregate of A, B is mutually from such as Fig. 5.
Flow such as Fig. 6 that above-mentioned convex polygon aggregate concrete model generates at random, generates polygon inside rounded aggregate
Aggregate vertex polar coordinates, since the aggregate of generation is due to being inside the circular aggregate of random distribution, so what is generated at this time is convex
Aggregate overlap problem is not present in polygonal aggregate, avoids taking computing resource.The convex polygon aggregate concrete model of generation shows
It is intended to such as Fig. 7.
Step 2)：
Inner polygon grid transition ring 2, aggregate-mortar interface intermediate zone 3 and water are set inside each convex polygon aggregate 1
Outer polygonal mesh transition ring 4 is set between cement mortar 5, such as Fig. 8.
(h) by convex polygon aggregate apex coordinate (ρi, θi) obtain interfacial transition zone vertex and inside and outside polygonal mesh mistake
Area's apex coordinate parameter is crossed, expression formula is：
α in formulaiFor ITZ or inside and outside polygonal mesh transition region thickness.Wherein, ITZ thickness linearly becomes with aggregate size
Change, from 0.02mm to 0.05mm.Inside and outside polygonal mesh transition ring thickness is respectively set to 0.7 times and 1.2 of aggregate size
Times, it is distributed with forming rational grid.
(i) ITZ, grid transition region and aggregate girth are calculated respectively, the relation between each layer size of mesh opening is：
L is the size of mesh opening on inside and outside grid transition ring in formula, and A is corresponding inside and outside grid transition ring girth, and B is
ITZ girths, I are the size of mesh opening of ITZ, and the value of I is equal to or slightly less than ITZ thickness.
(j) establish concrete using integrated modelling program and carefully see finite element model, such as Fig. 9 (a)~9 (b).
Claims (10)
1. a kind of adaptive concrete carefully sees modeling method, it is characterised in that includes the following steps：
1) circular boundary according to needed for the generation of aggregate grading, generates convex polygon aggregate in circular boundary, then right
Its area carries out continuation, is carried out at the same time the intrusion of continuation point and judges, generates convex polygon aggregate concrete model；
2) inner polygon grid transition ring, aggregate-mortar interface intermediate zone and cement bonded sand are set inside each convex polygon aggregate
Outer polygonal mesh transition ring is set between slurry, the polar radius of convex polygon aggregate is adjusted, obtains aggregate-mortar interface
Intermediate zone and inside and outside polygonal mesh transition ring apex coordinate, aggregate-mortar interface transition tape thickness is set according to aggregate size
Degree, concurrently sets the size of mesh opening on inside and outside polygonal mesh transition ring, the concrete multiphase for obtaining mesh adaption carefully sees mould
Type.
2. adaptive concrete according to claim 1 carefully sees modeling method, it is characterised in that described in step 1)
The generation method of convex polygon aggregate is：Take first vertex as polygonal aggregate at random on circular boundary, and according to
The 2 to n-th apex coordinate is sequentially generated according to polar angle and polar radius, convexity judgement is carried out according to the genesis sequence on aggregate vertex,
Each aggregate vertex is set to meet Convex Conditions.
3. adaptive concrete according to claim 2 carefully sees modeling method, it is characterised in that what the convexity judged
Method is：The positive and negative judgement for realizing Convex Conditions by the directed area on 3 aggregate vertex being newly generated, works as directed area
For positive number when, illustrate form directed area triangle the 3rd order point be convexity point, when all aggregate vertex after judgement all
When can to ensure polygon be convex polygon, aggregate generation finishes.
4. adaptive concrete according to claim 1 carefully sees modeling method, it is characterised in that described in step 1)
To convex polygon aggregate area carry out continuation method be：The apex coordinate of each polygonal aggregate is converted into flute card by polar coordinates
That coordinate, calculates the polygon length of side and is stored in array, then obtain length of side value a maximum in array respectivelyiai-1；Again with
For longest edge to take continuation point P at random on the circumference of diameter, its coordinate parameters is as follows：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mi>x</mi>
<mo>=</mo>
<mn>0.5</mn>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
<mo>+</mo>
<mn>0.5</mn>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<msub>
<mi>a</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mi>&eta;</mi>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mo>(</mo>
<mi>&gamma;</mi>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>y</mi>
<mo>=</mo>
<mn>0.5</mn>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>y</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
<mo>+</mo>
<mn>0.5</mn>
<msub>
<mi>a</mi>
<mi>i</mi>
</msub>
<msub>
<mi>a</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mi>&eta;</mi>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mo>(</mo>
<mi>&gamma;</mi>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula：aiai-1For the continuation side length of side, η is (0,1) interior uniformly distributed function, and γ is the random number in (0,2 π).
5. adaptive concrete according to claim 4 carefully sees modeling method, it is characterised in that to described convex polygon
When shape aggregate carries out area continuation, it is ensured that the triangle directed area S that continuation point both sides adjacent with extending side are formed is both greater than zero.
6. adaptive concrete according to claim 4 carefully sees modeling method, it is characterised in that to the convex polygon
When aggregate carries out area continuation, limit the distance between continuation point and aggregate center of circle and match somebody with somebody maximum particle diameter in corresponding aggregate respective stages
rmaxWithin the scope of.
7. adaptive concrete according to claim 4 carefully sees modeling method, it is characterised in that in step 1), judges
The method whether continuation point P invades other aggregates is：When whether the continuation point P for judging aggregate B invades aggregate A, by aggregate A's
Inverse time needle sort is pressed on vertex, calculates directed area S respectivelynPn+1Positive and negative, n=1,2,3, work as SnPn+1Value all for it is negative when, explanation
Inside P points intrusion aggregate A, work as SnPn+1Value it is positive and negative not for the moment, illustrate two aggregate of A, B mutually from.
8. adaptive concrete according to claim 1 carefully sees modeling method, it is characterised in that in step 2), by institute
State convex polygon aggregate apex coordinate (ρi, θi) obtain aggregate-mortar interface intermediate zone apex coordinate and inside and outside polygon latticed
Lattice transition ring apex coordinate parameter expression：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>&rho;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>&rho;</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mover>
<mi>&theta;</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, αiFor aggregate-mortar interface transition tape thickness or inside and outside polygonal mesh transition ring thickness.
9. adaptive concrete according to claim 8 carefully sees modeling method, it is characterised in that the aggregate-mortar
Interfaces transition tape thickness is 0.02mm to 0.05mm with aggregate size linear change；Inside and outside polygonal mesh transition ring thickness point
0.7 times and 1.2 times of aggregate size is not arranged to；Size of mesh opening and transition ring on the inside and outside polygonal mesh transition ring
Girth is directly proportional.
10. adaptive concrete according to claim 1 carefully sees modeling method, it is characterised in that described inside and outside polygon
Size of mesh opening L on shape grid transition ring is determined by following formula：
<mrow>
<mi>L</mi>
<mo>=</mo>
<mfrac>
<mi>A</mi>
<mi>B</mi>
</mfrac>
<mo>*</mo>
<mi>I</mi>
</mrow>
In formula, A is corresponding inside and outside grid transition ring girth, and B is aggregate-mortar interface intermediate zone girth, and I is aggregate-mortar
The size of mesh opening of interfaces transition band, the value of I are equal to or slightly less than the thickness of aggregate-mortar interface intermediate zone.
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