CN113392490B - Geometric modeling method for microstructure of carbon nano tube reinforced composite material - Google Patents
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Abstract
The invention discloses a geometric modeling method for a microstructure of a carbon nano tube reinforced composite material. The method mainly comprises the following steps: in the representative volume element, a plurality of random points are generated in a series of local cylindrical coordinate systems, a spline curve is constructed by using the points, the closest distance between the spline curve and the existing spline curve is calculated, and the diameter of the carbon nano tube model is determineddAnd thickness of interphasetTo judge whether to interfere; the spline curve where the interference occurs is geometrically clipped and the non-interference part is preserved. Using spline curve as sweep path, respectively constructing diameters ofdOuter diameter of curved cylinderDAnd inner diameterdThe difference istThe thin-wall cylinder geometric model is used for representing the carbon nano tube and the interface phase thereof. The invention provides a simple, visual and easy-to-realize geometric modeling method based on UG secondary development, curvature change of a carbon nano tube geometric model can be controlled by setting a variable range of a local cylindrical coordinate system, and a foundation is laid for subsequent research on mechanical properties of a carbon nano tube reinforced composite material.
Description
Technical Field
The invention relates to the field of microstructure mechanical analysis of carbon nanotube reinforced composite materials, and discloses a simple and visual geometric modeling method for a microstructure of a carbon nanotube reinforced composite material based on UG/OPEN API programming, so that a working foundation is laid for subsequent microstructure mechanical analysis of materials.
Background
With the rapid update of scientific technology, the material science has also been developed greatly, especially the development of composite materials. Due to the characteristics of small specific gravity, large specific strength, large specific modulus and the like, the composite material is widely applied to various industries of modern production and life. In the composite material, the superiority of the carbon nano tube is particularly outstanding. Carbon nanotubes have excellent mechanical, electrical and thermal properties, such as high elastic modulus, high strength and high toughness, and have a large specific surface area and a low density, and thus are known to be an ideal reinforcing phase for polymer materials. Experiments prove that the rigidity of the composite material can be improved by 36-42% and the strength can be improved by about 25% by adding 1% of the carbon nano tubes into the matrix material.
In the carbon nano tube reinforced composite material, the influence of microstructures such as the size, the purity, the defects, the bending, the interface between the carbon nano tube and a matrix and the like of the carbon nano tube on the mechanical property of the composite material is very obvious. The interface between the carbon nanotube and the matrix has a prominent influence on the mechanical properties of the composite material. Therefore, it is necessary to study the microstructure of the carbon nanotube. In the molecular dynamic method, the motion trail of each atom in the physical system can be calculated through the classical mechanics theory, and then the mechanical property of the physical system is obtained by applying the statistical theory. The motion trail of the atom, particularly the microscopic details related to the atom, can be obtained by the method, but the method has the defects of large calculation scale and limitation to calculation on a small space and time scale. If a finite element simulation method is adopted, the whole continuous solution domain can be dispersed into a combination of a finite number of units, unknown field functions to be solved on the solution domain are expressed in batches by the approximate functions assumed in each unit, and the approximate functions are expressed by numerical interpolation functions of the unknown field functions and derivatives thereof at each node of the units, so that the continuous model can be dispersed into finite element models for calculation.
The first task of using the finite element method is to establish a microscopic model of the carbon nanotube composite material which meets the actual situation, the early research on the carbon nanotubes generally considers that the shape of the carbon nanotubes is regular wave shape, and most researchers use sine functions to simulate the wave shape of the carbon nanotubes. A sinusoidal Fiber is created based on the volume ratio, wavelength and amplitude of each component as published by Mark R. Garnich in 2004, journal of Composite Materials, entitled "finished Element Micromechanix for Stiffness and Strength of wall Fiber Composites". Although this idealized modeling provides a method of studying carbon nanotubes, the reality is that carbon nanotubes are more random and irregular. Also as published in Composites Science and Technology 2014 in Australia, an article entitled "A New method for modifying and modifying the waviness and alignment of carbon nanotubes in Composites" models carbon nanotubes of random waviness, and uses the characteristics of a right circular cone to fit the curvature of the carbon nanotubes, the first point being randomly generated, each point being generated subsequently on the circumference of the base of the right circular cone with the previous point as the apex, and the distance between each point being guaranteed to be greater than a minimum predetermined distance. Although the generalized carbon nano tube with random curvature can be obtained, the process is too complicated, the deflection angle and height of each right circular cone need to be calculated, the workload is large, most importantly, the function of the carbon nano tube interface phase is not considered, and the interface phase plays an important role in actual modeling. Therefore, it is necessary to establish a simple and intuitive microscopic model of the carbon nanotube and its interface phase, which is more suitable for practical situations.
Disclosure of Invention
In order to provide a simpler, more intuitive and easy-to-realize geometric modeling method for the carbon nano tube reinforced composite material, the invention directly uses UG/OPEN API secondary development knowledge to carry out materialized modeling in UG software.
The invention is realized by the following technical scheme.
A geometric modeling method for a microstructure of a carbon nanotube reinforced composite material comprises the following steps:
1) Generating a cube model (1) of representative volume elements in UG based on UG/OPEN API, with side lengths ofaSpecifying the geometric model diameter of the carbon nanotube asdInterfacial phase thickness oft；
2) In the cube model (1), two sets of random numbers are generated as three-dimensional coordinate values of points by C languageO(x 0 ,y 0 ,z 0 )（2）、A（x t ,y t ,z t ）（3），Connecting two points to form a vectorV(i,j,k) (4) in pointsO(x 0 ,y 0 ,z 0 ) As origin of coordinates, in a vectorV(i,j,k) As a coordinateZAn axis, which constructs a local cylindrical coordinate system (5) and generates a random number R;
3) N random points are generated in the local cylindrical coordinate system (5)ZIn the axial direction, a prescribed length L (L)>20d) The length K = L/n is defined asZRandomly generating one element in e (K/2, 3K/2)ZCoordinate values ofZ 1 And generates 1 set of random numbersr 1 Andθ 1 whereinr 1 ∈（0,R），θ 1 E (0, 360) willZ 1 、r 1 Andθ 1 form a first point in a simultaneous manner (r 1 ,θ 1 ,Z 1 ) (ii) a Then is provided withZ 1 + K/2 as starting point inZ∈（Z 1 +K/2,Z 1 + 3K/2) randomly generating oneZCoordinate values ofZ 2 And generates 1 set of random numbersr 2 Andθ 2 in whichr 2 ∈（0,R），θ 2 E (0, 360), willZ 2 、r 2 And withθ 2 Form a second point in combination (r 2 ,θ 2 ,Z 2 ) (ii) a This operation is repeated until the nth three-dimensional reference point is formed (r n ,θ n ,Z n ) Then according to the conversion relationx i =r i cosθ i +x 0 ，y i =r i sinθ i +y 0 ，z i =Z i +z 0 Will cylindrical coordinate (a), (b)r i ,θ i ,Z i ) Conversion into three-dimensional coordinates (x i ,y i ,z i ) Then will include the origin of the local cylindrical coordinate systemO(x 0 ,y 0 ,z 0 ) (2) sequentially connecting n +1 points inside by using a spline curve (6);
4) And (3) newly building a spline curve (7) again according to the method in the steps 2) and 3), and calculating the minimum distance h (8) between the newly-generated spline curve (7) and the original spline curve (6) and the nearest point A (9) on the newly-built spline curve (7). If the minimum distance (8) h of the two spline curves is larger than or equal to 3D, wherein D = D + t, generating a new spline curve (7) and then performing the step 5); if the minimum distance (8) h of the two spline curves<3D, moving the point A (9) on the newly-built spline curve (7) to two sides by a distance D along the spline curve (7) to obtain a point L by taking the point A (9) as a starting point 1 （10）、R 1 (11) And truncating L 1 (10) And R 1 (11) Two short spline curves (12), (13) are obtained in the middle part, and then the lengths of the two short spline curves are judged firstlyl 1 、l 2 Whether greater than 5D, if the length of the spline curve is shortl 1 、l 2 If the sample size is less than 5D, abandoning the short sample strip curves (12) and (13) and carrying out the step 4) again; if the length of the sample strip curve is shortl 1 、l 2 If the distance is more than 5D, the two short spline curves (12) and (13) are judged to be different from the original curvesIs the smallest distance h between the spline curves (6) 1 、h 1 ' and let the closest point A on the two spline curves 1 、A 1 ', if h 1 Or h 1 ' > equal to or more than 3D, generating a corresponding spline curve and then performing the step 5); if h 1 Or h 1 '<3D, directly discarding;
5) According to
And calculating the volume ratio omega, wherein s is the length of the spline curve, and m is the number of the spline curve. Then the ratio of omega to the desired volume omega is 0 Comparing, if omega is not less than omega 0 Terminating the circulation and outputting all the spline curves; if omega<ω 0 And step 4) is carried out again until omega is more than or equal to omega 0 ；
6) Sweeping all generated spline curves along the spline curves by UG/OPEN API programming, setting the outer diameter of the pipeline as d and the inner diameter as 0, and obtaining a geometric model (14) of the carbon nano tube microstructure;
7) And (3) sweeping the generated geometric models of all the carbon nano tube microstructures along each spline curve by utilizing UG/OPEN API programming, setting the outer diameter of the pipeline as D and the inner diameter as D, and obtaining the geometric model (15) of the interface phase microstructure.
Further, in the step 1), an origin of an absolute coordinate system is taken as a vertex of the cube, and a cube model (1) of the representative volume element is established by utilizing UG/OPEN API according to two parameters of the vertex coordinate and the side length of the cube.
Further, in the step 2), a point is generated in the cube (1) to construct a local cylindrical coordinate system, and the specific steps are as follows:
2a) Generating two groups of random numbers by a random number generator of C language, and generating three-dimensional coordinate values of points by using the two groups of random numbersO(x 0 ,y 0 ,z 0 )（2）、A（x t ,y t ,z t ）（3）；
2b) To be provided withO(x 0 ,y 0 ,z 0 ) (2) as a starting point,A（x t ,y t ,z t ) (3) connecting two points as end points to form a vectorV(i,j,k)（4）；
2c) To be provided withO(x 0 ,y 0 ,z 0 ) (2) as origin of coordinates, using vectorV(i,j,k) (4) is a coordinateZAnd an axis, constructing a local cylindrical coordinate system (5), and generating a random number R.
Further, in the step 3), n Z values are randomly generated in n intervals, and then n groups of r and r are randomly generatedθN sets of r and theta values are associated with n sets of Z values to form n three-dimensional reference points, then n three-dimensional coordinates are generated according to the conversion relationship, and a spline curve (6) is used to include the point (x) 0 ,y 0 ,z 0 ) And (2) connecting the n +1 points in sequence, wherein the specific steps are as follows:
3a) Generating two random numbers L and n through a random number generator of a C language, wherein K = L/n is defined;
3b) In thatZIn the axial direction, starting from K/2ZRandomly generating a Z value in the epsilon (K/2, 3K/2) and recording the Z valueZ 1 And generating 1 group of random numbers through C languager 1 AndZ 1 will beZ 1 、r 1 Andθ 1 form a first point in a simultaneous manner (r 1 ,θ 1 ,Z 1 ) (ii) a Then is provided withZ 1 + K/2 as starting point inZ∈（Z 1 +K/2,Z 1 + 3K/2) randomly generating oneZValue, is recorded asZ 2 And generating 1 group of random numbers through C languager 2 Andθ 2 will beZ 2 、r 2 Andθ 2 form a second point in combination (r 2 ,θ 2 ,Z 2 ) (ii) a This operation is repeated until the nth three-dimensional reference point is formed（r n ,θ n ,Z n ）；
3c) According to the conversion relationx i =r i cosθ i +x 0 ，y i =r i sinθ i +y 0 ，z i =Z i +z 0 Make the cylinder coordinates (A)r i ,θ i ,Z i ) Conversion to three-dimensional coordinates (x i ,y i ,z i ) Generating n points according to the n three-dimensional coordinate values;
3d) Will include the origin of the local cylindrical coordinate systemO(x 0 , y 0 ,z 0 ) And (2) sequentially connecting n +1 points by using a spline curve (6).
Further, in the step 4), a spline curve (7) is newly built again, whether the spline curve interferes with the original spline curve (6) or not is judged, and if the spline curve does not interfere with the original spline curve, the spline curve (7) is generated; if the spline curves are interfered, the newly generated spline curves (7) are geometrically cut, and non-interference parts are reserved until the length l of the non-interference parts is less than 5D or the distance h between the original spline curves is more than or equal to 3D.
4a) Newly building a spline curve (7) again according to the method of 2) 3);
4b) Judging the distance h (8) between the newly generated spline curve (7) and the original spline curve (6) and the nearest point A (9) on the newly-built spline curve (7);
4c) And judging the size relationship between h and 3D, and determining whether the newly-built spline curve (7) interferes with the original spline curve (6) or not. If the minimum distance (8) h of the two spline curves is larger than or equal to 3D, a new spline curve (7) is generated; if the minimum distance (8) h of the two spline curves<3D, respectively moving the point A (9) on the newly-built spline curve (7) to two sides by a distance D along the spline curve (7) to obtain a point L by taking the point A (9) as a starting point 1 （10）、R 1 (11) And truncate L 1 (10) And R 1 (11) The middle part obtains two short spline curves(12) And (13) judging the length l of the two short spline curves 1 、l 2 If the length of the short sample strip curve is less than 5D, abandoning the short sample strip curves (12) and (13) and carrying out the step 4) again; if the length of the short spline curve is more than 5D, respectively judging the minimum distance h between the two short spline curves (12) and (13) and the original spline curve (6) 1 、h 1 ' and the closest points A on the two spline curves 1 、A 1 ', if h 1 Or h 1 ' ≧ 3D, generating the spline curve and then performing step 5); if h 1 Or h 1 '<3D, then directly discarding.
Further, in the step 5), the volume ratio ω of the carbon nanotubes in the representative volume element to the required volume ratio ω is calculated 0 Comparing, if omega is not less than omega 0 Outputting all spline curves meeting the output condition; if omega<ω 0 Step 4) is performed again.
Further, in the step 6), the pipeline is swept by taking all spline curves reaching the output condition as a sweeping path and taking the outer diameter of the cross section as d and the inner diameter as 0 to obtain a geometric model (14) of the carbon nano tube microstructure.
Further, in the step 7), the generated geometric models of all the carbon nanotube microstructures are subjected to pipeline sweeping by taking the spline curve as a sweeping path, and taking the outer diameter of the cross section as D and the inner diameter as D, so as to generate a geometric model (15) of the interface phase microstructure.
The present invention has several advantages over the prior art.
(1) The invention provides a more generalized geometric modeling method of a carbon nano tube microstructure, and the carbon nano tubes established by the method are arranged randomly and are not limited to regular arrangement.
(2) The method does not need to use a complex abstract mathematical physical model, has simple realization process and lower requirement on readers, and does not need the readers to master complex background knowledge.
(3) The invention can realize the geometric modeling of the microstructures of various carbon nano tubes and interface phases thereof by means of the powerful materialized modeling function of CAD software, and has wide application range.
Drawings
FIG. 1 is a flow chart of a carbon nanotube reinforced composite modeling process.
Fig. 2 is a schematic diagram of spline curve generation using a local cylindrical coordinate system.
Fig. 3 shows two splines that are too close together.
Fig. 4 is a cut spline curve.
Fig. 5 is a schematic view of a geometric model of the microstructure of the carbon nanotube obtained by sweeping according to the cut spline curve.
FIG. 6 is a schematic view of a carbon nanotube and its interface.
FIG. 7 is a schematic diagram of a model of 5% volume carbon nanotubes.
FIG. 8 is a schematic diagram of a 10% volume carbon nanotube model.
Reference numbers and designations in the drawings: 1. RVE volume element, origin of 2 cylindrical coordinate system, and 3 cylindrical coordinate systemZAxial end point, 4, cylindrical coordinate systemZThe method comprises the following steps of shaft, 5, a cylindrical coordinate system, 6, a spline curve, 7, a newly-built spline curve, 8, the minimum distance between the two spline curves, 9, the closest point on the spline curve 7 from the spline curve 6, 10, a cut spline curve endpoint, 11, a cut spline curve endpoint, 12, a cut spline curve, 13, a cut spline curve, 14, a carbon nano tube microstructure geometric model, 15 and an interface phase microstructure geometric model.
Detailed Description
The following will further explain the implementation of the present invention with reference to the attached drawings.
1) Original cube (1) was created using UG/OPEN API programming, setting its side length to 100.0, i.e. a =100.0, vertex coordinates (0.0 ), while specifying carbon nanotube geometric model diameter of 5.0 and interphase thickness of 1.0;
2) Three groups of floating-point random numbers are generated by using a C language random number generator, each group has 2 numbers, and three arrays x [2 ] are respectively endowed]、y[2]、z[2]In the method, two corresponding points are generated by using two groups of x, y and z values to connect the two corresponding pointsPoint construction vectorV(i,j,k) With the point of small value of x as the origin of coordinatesO(x 0 ,y 0 ,z 0 ) By vector ofV(i,j,k) As a coordinateZA shaft, constituting a local cylindrical coordinate system, as shown in fig. 2;
3) Respectively in cylindrical coordinate system by using C language random number generatorZGenerating 5 numbers in 5 intervals of the axis and endowing the numbers to the arrayZ[5]Then, using C language random number generator to generate two groups of floating point type random numbers with the range of (0, R) and (0, 360), and respectively assigning them to the array r [5 ]]、θ[5]In (1), three arrays are combined to form 5 three-dimensional reference points (r i ,θ i ,Z i ) According to the conversion relationx i =r i cosθ i +x 0 ，y i =r i sinθ i +y 0 ，z i =Z i +z 0 Will cylindrical coordinate (a), (b)r i ,θ i ,Z i ) Conversion into three-dimensional coordinates (x i ,y i ,z i ) Then will include the origin of the local cylindrical coordinate systemO(x 0 ,y 0 ,z 0 ) The inner 6 points are connected sequentially by using a spline curve, as shown in FIG. 2;
4) Newly building a spline curve according to the method in the step 2) 3), judging a function of the minimum distance between two objects by utilizing UG/OPEN API secondary development, judging whether the minimum distance h of the two spline curves is greater than 3D, if h is greater than or equal to 3D, generating the newly built spline curve, otherwise, judging whether the length of the newly built spline curve is greater than 5D after geometric cutting processing is carried out on the newly built spline curve, and if the length of the spline curve is greater than 5DlRegeneration is carried out for more than or equal to 5D, as shown in FIG. 3, FIG. 4 and FIG. 5;
5) According to
Calculating the volume ratio omega, and then using C languageProgramming comparison of omega with omega 0 The size of omega is more than or equal to omega 0 Outputting all spline curves, otherwise generating new spline curve again until omega is larger than or equal to omega 0 ；
6) Sweeping along all spline curves by UG/OPEN API programming, setting the outer diameter of the pipeline to be 5.0 and the inner diameter to be 0.0, and obtaining a geometric model of the carbon nano tube microstructure, as shown in FIG. 6;
7) The UG/OPEN API programming was used to sweep along all spline curves, setting the pipe outer diameter to 7.0 and the inner diameter to 5.0, resulting in a geometric model of the interface phase microstructure, as shown in fig. 6.
The present invention is not limited to the above embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts based on the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.
Claims (5)
1. A geometric modeling method for a microstructure of a carbon nano tube reinforced composite material is characterized by comprising the following steps: the method comprises the following steps:
1) Generating a cube model (1) of representative volume elements in UG based on UG/OPEN API with side length ofaSpecifying the carbon nanotube geometric model diameter asdInterfacial phase thickness oft；
2) In the cube model (1), two sets of random numbers are generated as three-dimensional coordinate values of pointsO(x 0 ,y 0 ,z 0 )（2）、A（x t ,y t ,z t ）（3），Connecting two points to form a vectorV(i,j,k) (4); by pointO(x 0 ,y 0 ,z 0 ) As origin of coordinates, in a vectorV(i,j,k) As a coordinateZAn axis, which constructs a local cylindrical coordinate system (5) and generates a random number R;
3) In the local cylindrical coordinate system (5)In generating n random points atZIn the axial direction, a length L is specified, and a length K = L/n is defined inZRandomly generating one element in e (K/2, 3K/2)ZCoordinate values ofZ 1 And generates 1 set of random numbersr 1 And withθ 1 Whereinr 1 ∈（0,R），θ 1 E (0, 360) willZ 1 、r 1 And withθ 1 Form a first point in combination (r 1 ,θ 1 ,Z 1 ) Then is made toZ 1 + K/2 as starting point inZ∈（Z 1 +K/2,Z 1 + 3K/2) randomly generating oneZCoordinate values ofZ 2 And generates 1 set of random numbersr 2 Andθ 2 in whichr 2 ∈（0,R），θ 2 E (0, 360) willZ 2 、r 2 Andθ 2 form a second point in combination (r 2 ,θ 2 ,Z 2 ) (ii) a This operation is repeated until the nth three-dimensional reference point is formed (r n ,θ n ,Z n ) Then according to the conversion relationx i =r i cosθ i +x 0 ，y i =r i sinθ i +y 0 ，z i =Z i +z 0 Make the cylinder coordinates (A)r i ,θ i ,Z i ) Conversion into three-dimensional coordinates (x i ,y i ,z i ) Then will include the origin of the local cylindrical coordinate systemO(x 0 ,y 0 ,z 0 ) (2) sequentially connecting n +1 points inside by using a spline curve (6);
4) Newly building a spline curve (7) again according to the method in the step 2) 3), and calculating the minimum distance h (8) between the newly-generated spline curve (7) and the original spline curve (6) and the nearest point A (9) on the newly-built spline curve (7), if two spline curves exist, selecting a new spline curve (7) and a new spline curve (7) according to the minimum distance h (8) and the nearest point A (9) on the newly-built spline curve (7), and if the two spline curves exist, selecting a new spline curveIf the minimum distance (8) h of the curve is larger than or equal to 3D, and D = D +2t, generating a new spline curve (7) and then performing the step 5); if the minimum distance (8) h of the two spline curves<3D, respectively moving the point A (9) on the newly-built spline curve (7) to two sides by a distance D along the spline curve (7) to obtain a point L by taking the point A (9) as a starting point 1 （10）、R 1 (11) And truncate L 1 (10) And R 1 (11) Two short spline curves (12), (13) are obtained in the middle part, and then the lengths l of the two short spline curves are judged 1 、l 2 Whether it is greater than 5D, if the length l of the sample strip curve is short 1 、l 2 If the sample size is less than 5D, abandoning the short sample strip curves (12) and (13) and carrying out the step 4) again; if the length l of the spline curve is short 1 、l 2 If the distance is more than 5D, respectively judging the minimum distance h between the two short spline curves (12) and (13) and the original spline curve (6) 1 、h 1 ' and the closest points A on the two spline curves 1 、A 1 ', if h 1 Or h 1 ' > equal to or more than 3D, generating a corresponding spline curve and then performing the step 5); if h is 1 Or h 1 '<3D, directly discarding;
5) According to
Calculating a volume ratio omega, wherein s is the length of the spline curve and m is the number of the spline curve, and then comparing omega with the required volume ratio omega 0 Comparing, if omega is not less than omega 0 Terminating the loop, outputting all the spline curves and then performing step 6); if omega<ω 0 And step 4) is carried out again until omega is more than or equal to omega 0 ；
6) Sweeping all generated spline curves along the spline curves by UG/OPEN API programming, setting the outer diameter of the pipeline as d and the inner diameter as 0, and obtaining a geometric model (14) of the carbon nano tube microstructure;
7) And (3) sweeping the generated geometric models of all the carbon nano tube microstructures along each spline curve by UG/OPEN API programming, setting the outer diameter of the pipeline as D and the inner diameter as D, and obtaining the geometric model (15) of the interface phase microstructure.
2. The method of claim 1, wherein the geometric modeling of the microstructure of the carbon nanotube-reinforced composite comprises: in the step 1), a is a real number larger than 0, d is a real number larger than 0 and smaller than a/10, t is a real number larger than 0 and smaller than d/4, in the step 2), the three-dimensional coordinate value range is a real number from 0 to a, R is a real number larger than a/5 and smaller than a/3, in the step 3), L is a real number larger than 0 and smaller than a/2,θis a real number larger than 0 and smaller than 360, in the step 5), omega is 0 Real numbers greater than 0 and less than 1.
3. The method of claim 1, wherein the geometric modeling of the microstructure of the carbon nanotube-reinforced composite material comprises: in the step 3), the step (c) is carried out,r、θandZthe coordinates of the three-dimensional reference points formed in a simultaneous manner are cylindrical coordinates, points cannot be generated in UG by using the cylindrical coordinates, and the required points can be generated only by converting the coordinates into rectangular coordinates according to a coordinate conversion relation.
4. The method of claim 1, wherein the geometric modeling of the microstructure of the carbon nanotube-reinforced composite material comprises: in the step 3), the number n of the random points in the local cylindrical coordinate system is an integer larger than 4 and smaller than 8, and the order of the spline curve is 4.
5. The method of claim 1, wherein the geometric modeling of the microstructure of the carbon nanotube-reinforced composite material comprises: in the step 4), because the newly-built first spline curve has no interference problem, the newly-built first spline curve does not need to be judged whether to interfere with the original spline curve, and whether to interfere with the original spline curve is judged from the second spline curve.
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