CN111985127B - Parameterized meshing method of unidirectional composite microscopic finite element model - Google Patents
Parameterized meshing method of unidirectional composite microscopic finite element model Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 31
- 239000002131 composite material Substances 0.000 title claims abstract description 25
- 239000000835 fiber Substances 0.000 claims abstract description 48
- 239000011159 matrix material Substances 0.000 claims abstract description 34
- 238000005192 partition Methods 0.000 claims abstract description 8
- 238000000638 solvent extraction Methods 0.000 claims abstract description 5
- 238000013507 mapping Methods 0.000 claims description 3
- 238000003908 quality control method Methods 0.000 claims description 3
- 238000010408 sweeping Methods 0.000 claims description 3
- 230000000452 restraining effect Effects 0.000 claims description 2
- 238000004458 analytical method Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Abstract
The invention discloses a parameterized meshing method of a unidirectional composite microscopic finite element model, which is characterized by comprising the following steps of: establishing a one-way composite material microscopic geometric model comprising a matrix, an interface layer and fiber monofilaments; dividing the microscopic geometric model into an outer matrix region and an inner square block region; dividing the inner square block area; defining a partitioning parameter expressed in terms of segment numberAs a reference for the mesh division density of the model to control the mesh density of the model as a whole, and the like. The grids divided by the method are regular in shape and close in size, and the accuracy of finite element calculation results can be guaranteed; the orderly change of grids of each region is ensured through the introduced partition constraint, the condition of grid change disorder cannot occur, and the calculation stability can be improved; meanwhile, unified control of the overall grid density of the model is realized by taking a shared dividing parameter as a reference, and the adjustment efficiency of the grid density of the model is high.
Description
Technical Field
The invention belongs to the technical field of composite modeling, and particularly relates to a parameterized grid division method of a unidirectional composite microscopic finite element model.
Background
The mechanical behavior of the composite material is closely related to the microscopic structure of the composite material, so that the research of the influence of the microscopic structure on the mechanical behavior of the composite material has important significance. Because the interior of the composite material is complex in microstructure, the cost of researching the influence of the microstructure on the mechanical behavior of the composite material by a test method is high, the workload is high, and because a test sample with a specific microstructure is difficult to prepare, a comprehensive analysis result cannot be obtained.
In the prior art, the problems are generally solved by a numerical analysis method, firstly, a composite material miniatured finite element model with different structures is established, and then, the relation between the miniatured structure and the mechanical behavior of the miniatured structure can be quickly established by finite element calculation. However, the shape and density of the finite element mesh can have a large impact on the computation results. The influence is larger for the composite material miniscopic model, because the shape and the size of each part in the composite material miniscopic structure have obvious differences, when the composite material miniscopic model is directly subjected to grid division, the density and the shape of grids of different areas are greatly different, the ordered change of the grids of each area is difficult to ensure, and the proper grid size is difficult to select.
Disclosure of Invention
Aiming at the defects of the prior art, the technical aim of the invention is to provide a parameterized grid dividing method which can establish the association of the grid sizes and the shapes of different components in a mesostructure and can avoid calculation errors caused by uncoordinated grid changes so as to ensure the calculation stability and the calculation precision of a composite material mesofinite element model,
the technical scheme provided by the invention is as follows:
the parameterized meshing method of the one-way composite material microscopic finite element model is characterized by comprising the following steps of:
step 1: establishing a one-way composite material microscopic geometric model comprising a matrix, an interface layer and fiber monofilaments;
step 2: dividing the microscopic geometric model established in the step 1 into an external basal body area and an internal square block area, wherein the process is as follows:
on the cross section of the microscopic geometric model, dividing the inner area of the model into a plurality of inner square block areas which are spliced together and have the same size by taking each fiber monofilament as the center of a square unit;
the inner square block area can be divided into a fiber monofilament area, an annular interface layer area and a square matrix area with a round hole in the middle according to the components from inside to outside, and the fiber monofilament area, the annular interface layer area and the square matrix area are concentric, namely, the three areas have center points at the same position;
matrix areas which are not covered by all inner square block areas, namely outer matrix areas, on the upper side and the lower side of the model;
step 3: and (3) dividing the inner square block area obtained in the step (2), wherein the process is as follows:
3.1 Dividing a square fiber monofilament area in the center of the fiber monofilament area, wherein the square fiber monofilament area is concentric with the square matrix area, but has a relative deflection angle of 45 degrees;
3.2 Dividing the fiber monofilament areas except the square fiber monofilament area into four fan-shaped areas with equal size by using radial lines passing through four corners of the square fiber monofilament area, and setting the radial lines as first dividing lines;
3.3 Along the extending direction of two diagonals of the square matrix area and the extending direction of the transverse central line and the longitudinal central line, the annular interface layer area is divided into eight sections of fan ring areas on average, the square matrix area is divided into eight quadrilateral areas on average, dividing lines between adjacent fan ring areas are set as second dividing lines, dividing lines between adjacent quadrilateral areas pressed in the diagonal direction are set as third dividing lines, and dividing lines pressed in the transverse/longitudinal central line are set as fourth dividing lines;
step 4: defining a partitioning parameter L expressed in terms of the number of segments G_DIV As a benchmark of model mesh division density, to control the overall mesh density of the model;
step 5: for the quadrilateral region, grid quality control is performed by means of restraining the aspect ratio of the unit:
the constraint equation of the grid unit is as follows, assuming that the aspect ratio is smaller than n after the quadrilateral region is divided:
wherein L is 1 ，L 2 ，L 3 And L 4 Respectively the lengths of four sides of the quadrangular region, L 4 Edges, i.e. circular arc edges of quadrangular regions, L 1 The edge is opposite to the arc edge, L 3 The side being the side collinear with the third dividing line, L 4 The side is the side which is collinear with the fourth dividing line; l (L) ConSiC_DIV Represents L 2 And L 3 The number of divisions of the edge;
L 2 ，L 3 ，L 4 and L is equal to 1 The relationship of the other model parameters is as follows:
wherein d f Represents the diameter of the fiber monofilament, t pyc Represents the thickness of the interfacial layer;
step 6: solving the constraint L in step 5 2 And L 3 Edge division number L ConSiC_DIV Is a range of values:
step 7: using the integer closest to the arithmetic average value of the boundary of the value range in the step 6 as L 2 And L 3 The number of divisions of an edge, i.e
Step 8: establishing partition constraint of sector ring areas in the interface layer, and constraining circumferential partition number and L of the sector ring areas 4 The division number of the edges is the same, and the aspect ratio of the constraint fan ring area division unit is 1:1, constraint equation is as follows:
L 6 ＝t pyc
wherein L is 5 Representing the length of the centerline of the sector ring region, L 6 Indicating the width of the sector ring area, L PyC_DIV Represents L 6 Number of divisions of an edge, L 6 The side is the side which is collinear with the second dividing line;
step 9: solving the constraint L in step 8 6 Number of divisions of edge L PyC_DIV ：
Step 10: checking L obtained in step 9 PyC_DIV Whether the result is suitable for meshing or not, the specific rules are as follows: if L PyC_DIV If the calculated result is smaller than 0.5, taking L PyC_DIV =1, if L PyC_DIV If the calculated result of (2) is greater than or equal to 0.5, then for L PyC_DIV Taking outThe constraint equation is as follows:
step 11: the division constraint is carried out on the sector area of the fiber monofilament, and the rule is that: the aspect ratio of the constraining center section unit is 1:1,
wherein L is 7 Indicating the width of the sector-shaped region L 8 Representing the length of the centerline of the sector, L f_DIV Representing a sector area L 7 Number of divisions of an edge, L 7 The edge is the edge which is collinear with the first dividing line;
step 12: solving the constraint equation in step 11 to obtain L 7 Number of divisions of edge L f_DIV ：
Step 13: dividing the grid according to each dividing number obtained in the above steps:
the square matrix area with the round holes in the middle is meshed in a mapping mode, and the fiber monofilament area, the annular interface layer area and the external matrix area are meshed in a sweeping mode.
Preferably, step 13 uses SOLID185 units to build a grid, and the appropriate value of n is 3.
The beneficial effects are that:
1) The grids divided by the method are regular in shape and close in size, and the accuracy of finite element calculation results is guaranteed;
2) The method ensures the ordered change of grids of each region through the introduced partition constraint, does not generate the condition of grid change disorder, and improves the calculation stability;
3) The method of the invention realizes unified control of the overall grid density of the model by taking a shared dividing parameter as a reference, and has high adjustment efficiency of the grid density of the model.
Drawings
FIG. 1 is a schematic view of a microscopic geometric model of a unidirectional composite of the present invention;
FIG. 2 is a schematic view of region division of a microscopic geometric model in the method of the present invention;
FIG. 3 is a schematic view of the interior square block area of the method of the present invention;
FIG. 4 is a schematic representation of a square matrix region with circular holes in the middle of the method of the invention;
FIG. 5 is a schematic view of the division of the inner square block area in the method of the present invention;
FIG. 6 is a schematic illustration of the division of fiber monofilament areas in the method of the present invention;
FIG. 7 is a schematic illustration of the division of the annular interfacial layer region in the method of the present invention;
FIG. 8 is a schematic illustration of the division of square matrix regions with circular holes in the middle in the method of the invention;
FIG. 9 is a schematic representation of a quadrilateral region in a square base region in the method of the present invention;
FIG. 10 is a schematic view of a sector ring area in the method of the present invention;
FIG. 11 is a schematic representation of square fiber monofilament areas and scalloped areas of a fiber monofilament in a method of the present invention;
FIG. 12 is a grid partitioning result of the method of the present invention;
FIG. 13 is an enlarged view of a portion of the meshing result of the present invention;
the reference numerals are as follows:
1-matrix, 101-outer matrix region, 102-square matrix region, 102 a-third split line, 102 b-fourth split line, 102 c-quadrilateral region, 2-annular interface layer region, 201-sector ring region, 202-second split line, 3-fiber monofilament region, 301-square fiber monofilament region, 302-sector region, 303-first split line, 4-inner square block region.
Detailed Description
In order to clarify the technical scheme and working principle of the present invention, the present invention will be further described with reference to the drawings and the specific embodiments.
A parameterized meshing method of a unidirectional composite microscopic finite element model comprises the following steps:
step 1: a unidirectional composite minigeometric model is built up comprising a matrix 1, an interface layer and fibrous filaments, as shown in fig. 1.
Step 2: the fine-scale geometric model established in the step 1 is divided into an outer basal body area 101 and an inner square block area 4, and the specific process is as follows:
on the cross section of the microscopic geometric model, taking each fiber monofilament (cross section) as the center of a square unit, dividing the inner area of the model into a plurality of inner square block areas 4 which are spliced together and have the same size, as shown in fig. 2;
the inner square block area 4 can be divided into a fiber monofilament area 3, an annular interface layer area 2 and a square matrix area 102 according to the components from inside to outside;
the fiber monofilament area 3 is circular, the annular interface layer area 2 is wrapped on the outer side of the fiber monofilament area 3, and the diameter of the inner ring of the annular interface layer area is equal to the diameter of the fiber monofilament area 3;
the square matrix area 102 is a block with a round hole in the center and a square outline, as shown in fig. 4, the annular interface layer area 2 and the fiber monofilament area 3 are embedded in the round hole in the center, and the diameter of the round hole in the center is equal to the diameter of the outer ring of the annular interface layer area 2;
simultaneously, the fiber monofilament area 3, the annular interface layer area 2 and the square matrix area 102 are concentric, namely, the three areas have the same center point;
the upper and lower sides of the mesoscopic geometric model, i.e. the base areas not covered by all the inner square block areas 4, i.e. the outer base areas 101.
Step 3: the inner square block area 4 obtained in the step 2 is further divided, and the specific process is as follows:
3.1 As shown in fig. 6, a square fiber monofilament area 301 is divided in the center of the fiber monofilament area 3, the square fiber monofilament area 301 being concentric with the square base area 102, but having a relative deflection angle of 45 °;
3.2 Dividing the fiber monofilament areas except the square fiber monofilament area 301 into four equal-sized sector areas 302 by radial lines passing through four corners of the square fiber monofilament area 301, and setting the radial lines as first dividing lines 303;
3.3 As shown in fig. 7 and 8, the annular interface layer region 2 is divided into eight sector ring regions 201 on average, the square base region 102 is divided into eight quadrangle regions 102c on average, the dividing line between adjacent sector ring regions 201 is set as a second dividing line 202, the dividing line between adjacent quadrangle regions 102c pressed in the diagonal direction is set as a third dividing line 102a, and the dividing line pressed in the transverse/longitudinal middle line is set as a fourth dividing line 102b along the directions in which two diagonals of the square base region 102 extend and the directions in which the transverse/longitudinal middle lines extend;
the division result is shown in fig. 5, in which the first division line 303, the fourth division line 102b and the second division line 202 in the horizontal or vertical direction are collinear, and the third division line 102a and the second division line 202 in the obliquely upward or downward direction are collinear.
Step 4: defining a partitioning parameter L expressed in terms of the number of segments G_DIV As a benchmark of model mesh division density, to control the overall mesh density of the model;
step 5: for the quadrangular region 102c divided by the inner square block region 4, since its shape is largely changed, mesh quality control is performed by constraining the aspect ratio of the cells:
in this embodiment, the SOLID185 units are used to build the grid, so in this embodiment, the aspect ratio of the area unit is constrained to be not greater than 3, and the constraint equation is as follows:
wherein L is 1 ，L 2 ，L 3 And L 4 Respectively represent the lengths of four sides of the quadrangular region 102c, as shown in FIG. 9, L 4 The sides are circular arc sides of the quadrangular region 102c, L 1 The edge is opposite to the arc edge, L 3 The side is the side collinear with the third parting line 102a, L 4 The side is a side collinear with the fourth split line 102b; l (L) ConSiC_DIV Represents L 2 Edge and L 3 The number of segment divisions of the edge;
L 2 ，L 3 ，L 4 and L is equal to 1 The relationship of the other model parameters is as follows:
wherein d f Represents the diameter of the fiber monofilament, t pyc Represents the thickness of the interfacial layer;
in the present embodiment L 1 ＝4.5μm，d f ＝7μm，t pyc ＝0.551μm。
Step 6: solving the constraint L in step 5 2 Edge and L 3 Edge division number L ConSiC_DIV Is a range of values:
step 7: using the integer closest to the arithmetic average value of the boundary of the value range in the step 6 as L 2 And L 3 The number of divisions of an edge, i.e
Step 8: establishing partition constraint of sector ring region 201 in interface layer, and constraining circumferential partition number and L 4 The division number of the sides is the same, and the aspect ratio of the division units of the constraint fan ring area 201 is 1:1, constraint equation is as follows:
L 6 ＝t pyc
wherein L is 5 Indicating the length of the centerline in sector ring region 201, L 6 Indicating the width of the sector ring region 201, L PyC_DIV Represents L 6 The number of divisions of the edge;
as shown in FIG. 10, the L 6 The side is the side collinear with the second dividing line 202, the center line is the broken line in fig. 10, the center line is an arc concentric with the inner and outer edges of the sector ring region 201, and the starting points of both ends are L 6 The midpoint of the edge.
Step 9: solving the constraint L in step 8 6 Number of divisions of edge L PyC_DIV ：
Step 10: checking L obtained in step 9 PyC_DIV Whether the result is suitable for meshing or not, the specific rules are as follows: if L PyC_DIV If the calculated result is smaller than 0.5, taking L PyC_DIV =1, if L PyC_DIV If the calculated result of (2) is greater than or equal to 0.5, then for L PyC_DIV Rounding is performed and constraint equations are as follows:
step 11: the division constraint is applied to the fan-shaped region 302 of the fiber filaments with the rule: the aspect ratio of the constraining center section unit is 1:1, a step of;
wherein L is 7 Indicating the width of the scalloped region 302, L 8 Representing the length of the centerline of the sector, L f_DIV Representing a sector area (302) L 7 The number of divisions of the edge;
as shown in FIG. 11, the L 7 The side, i.e. the side collinear with the first parting line 303, L 8 The center line is the broken line in the figure, and is an arc concentric with the outer edge of the sector area 302, and the starting points at both ends fall at L 7 At the midpoint of the edge.
Step 12: solving the constraint equation in step 11 to obtain L 7 Number of divisions of edge L f_DIV ：
Step 13: dividing the grid according to each dividing number obtained in the above steps:
the square matrix region 102 with circular holes in the middle is meshed in a mapping manner, and the fiber monofilament region 3, the annular interface layer region 2 and the outer matrix region 101 are meshed in a sweeping manner.
In the present embodiment, L G_DIV The meshing result is shown in fig. 12, the enlarged partial area is shown in fig. 13, and the mesh shape rule obtained by the method of the present invention can be seen.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the foregoing embodiments, which have been described in the foregoing embodiments and description merely illustrates the principles of the invention, and various changes and modifications may be made therein without departing from the spirit and scope of the invention, the scope of which is defined in the appended claims, specification and their equivalents.
Claims (3)
1. The parameterized meshing method of the one-way composite material microscopic finite element model is characterized by comprising the following steps of:
step 1: establishing a one-way composite material microscopic geometric model comprising a matrix (1), an interface layer and fiber monofilaments;
step 2: dividing the microscopic geometric model established in the step 1 into an outer matrix area (101) and an inner square block area (4), wherein the process is as follows:
on the cross section of the microscopic geometric model, dividing the inner area of the model into a plurality of inner square block areas (4) which are spliced together and have the same size by taking each fiber monofilament as the center of a square unit;
the inner square block area (4) can be divided into a fiber monofilament area (3), an annular interface layer area (2) and a square matrix area (102) with a round hole in the middle according to the components from inside to outside, and the fiber monofilament area (3), the annular interface layer area (2) and the square matrix area (102) are concentric, namely, the three areas have center points at the same position;
the upper side and the lower side of the model are provided with matrix areas which are not covered by all the inner square block areas (4), namely outer matrix areas (101);
step 3: dividing the inner square block area (4) obtained in the step 2, wherein the process is as follows:
3.1 Dividing a square fiber monofilament area (301) in the center of the fiber monofilament area (3), wherein the square fiber monofilament area (301) is concentric with the square matrix area (102) but has a relative deflection angle of 45 degrees;
3.2 Dividing the fiber monofilament areas except the square fiber monofilament area (301) into four equal-sized sector areas (302) by radial lines passing through four corners of the square fiber monofilament area (301), and setting the radial lines as first dividing lines (303);
3.3 Along the extending direction of two diagonals of the square matrix area (102) and the extending direction of a transverse midline and a longitudinal midline, the annular interface layer area (2) is divided into eight sections of sector ring areas (201) on average, the square matrix area (102) is divided into eight sections of quadrilateral areas (102 c) on average, the dividing line between the adjacent sector ring areas (201) is set as a second dividing line (202), the dividing line between the adjacent quadrilateral areas (102 c) pressed in the diagonal direction is set as a third dividing line (102 a), and the dividing line pressed in the transverse/longitudinal midline is set as a fourth dividing line (102 b);
step 4: defining a partitioning parameter L expressed in terms of the number of segments G_DIV As a benchmark of model mesh division density, to control the overall mesh density of the model;
step 5: for the square area (102 c), grid quality control is performed by means of restraining the aspect ratio of the unit:
assuming that the aspect ratio is smaller than n after division of the quadrangular region (102 c), the constraint equation of the mesh unit is as follows,
wherein L is 1 ，L 2 ，L 3 And L 4 The lengths of four sides of the quadrangular region (102 c), L 4 Sides, i.e. circular arc sides, L of the quadrangular region (102 c) 1 The edge is opposite to the arc edge, L 3 The side is a side collinear with the third dividing line (102 a), L 4 The side is a side collinear with the fourth dividing line (102 b); l (L) ConSiC_DIV Represents L 2 And L 3 The number of divisions of the edge;
L 2 ，L 3 ，L 4 and L is equal to 1 The relationship of the other model parameters is as follows:
wherein d f Represents the diameter of the fiber monofilament, t pyc Represents the thickness of the interfacial layer;
step 6: solving the constraint L in step 5 2 And L 3 Edge division number L ConSiC_DIV Is a range of values:
step 7: using the integer closest to the arithmetic average value of the boundary of the value range in the step 6 as L 2 And L 3 The number of divisions of an edge, i.e
Step 8: establishing partition constraint of sector ring region (201) in interface layer, and constraining circumferential partition number and L 4 The number of division of the sides is the same, and the aspect ratio of the division units of the constraint fan ring area (201) is 1:1, constraint equation is as follows:
L 6 ＝t pyc
wherein L is 5 Representing the length of the centerline of the sector ring region (201), L 6 Represents the width of the sector ring area (201), L PyC_DIV Represents L 6 Number of divisions of an edge, L 6 The edge is the edge which is collinear with the second parting line (202);
step 9: solving the constraint L in step 8 6 Number of divisions of edge L PyC_DIV ：
Step 10: checking L obtained in step 9 PyC_DIV Whether the result is suitable for a gridThe specific rules are as follows: if L PyC_DIV If the calculated result is smaller than 0.5, taking L PyC_DIV =1, if L PyC_DIV If the calculated result of (2) is greater than or equal to 0.5, then for L PyC_DIV Rounding is performed and constraint equations are as follows:
step 11: the division constraint is applied to the sector (302) of the fiber filaments, with the rule: the aspect ratio of the constraining center section unit is 1:1,
wherein L is 7 Represents the width of the sector (302), L 8 Representing the length of the centerline of the sector, L f_DIV Representing a sector area (302) L 7 Number of divisions of an edge, L 7 The side is the side which is collinear with the first dividing line (303);
step 12: solving the constraint equation in step 11 to obtain L 7 Number of divisions of edge L f_DIV ：
Step 13: dividing the grid according to each dividing number obtained in the above steps:
the square matrix area (102) with round holes in the middle is meshed in a mapping mode, and the fiber monofilament area (3), the annular interface layer area (2) and the outer matrix area (101) are meshed in a sweeping mode.
2. The parameterized meshing of a one-way composite microscopic finite element model of claim 1, wherein step 13 uses SOLID185 elements to build the mesh.
3. The parameterized meshing method of a unidirectional composite microscopic finite element model of claim 2, wherein n has a value of 3.
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| 纤维尺寸随机引起的复合材料性能分散性研究;高希光, 宋迎东, 孙志刚;材料科学与工程学报;20050620(03);全文 * |
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