CN111985127A - Parameterized meshing method for one-way composite material mesoscopic finite element model - Google Patents

Parameterized meshing method for one-way composite material mesoscopic finite element model Download PDF

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CN111985127A
CN111985127A CN202010689068.0A CN202010689068A CN111985127A CN 111985127 A CN111985127 A CN 111985127A CN 202010689068 A CN202010689068 A CN 202010689068A CN 111985127 A CN111985127 A CN 111985127A
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CN111985127B (en
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宋迎东
于国强
高希光
贾蕴发
杜金康
董洪年
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Nanjing University of Aeronautics and Astronautics
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    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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Abstract

The invention discloses a parameterized meshing method of a one-way composite microscopic finite element model, which is characterized by comprising the following steps of: establishing a mesoscopic geometric model of the unidirectional composite material comprising the matrix, the interface layer and the fiber monofilaments; dividing the mesoscopic geometric model into an external matrix region and an internal square block region; dividing the internal square block area; defining a partitioning parameter expressed by the number of segment segments
Figure DEST_PATH_IMAGE001
The mesh density of the model as a whole is controlled by using the model mesh division density as a reference. The shape of the grid divided by the method is regular, and the size is close, so that the accuracy of a finite element calculation result can be ensured; by introduction ofThe division constraint ensures the ordered change of the grids in each region, the grid change disorder condition can not occur, and the calculation stability can be improved; meanwhile, unified control of the total grid density of the model is achieved by using a shared division parameter as a reference, and the adjustment efficiency of the grid density of the model is high.

Description

Parameterized meshing method for one-way composite material mesoscopic finite element model
Technical Field
The invention belongs to the technical field of composite material modeling, and particularly relates to a parameterized meshing method of a one-way composite material 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 on the influence of the microscopic structure on the mechanical behavior is of great significance. Due to the fact that the microscopic structure in the composite material is complex, the cost and the workload are high when the microscopic structure is researched by a test method to influence the mechanical behavior of the composite material, and due to the fact that a test sample with a specific microscopic structure 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, a composite material microscopic finite element model with different structures is firstly established, and then the connection between the microscopic structure and the mechanical behavior of the microscopic structure can be quickly established through finite element calculation. However, the shape and density of the finite element mesh have a large influence on the calculation result. The influence is larger for the composite material mesoscopic model because the shapes and sizes of all parts in the composite material mesoscopic structure have obvious differences, when the composite material mesoscopic model is directly subjected to grid division, the density and shape differences of grids in different areas are larger, the ordered change of the grids in 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 purpose of the invention is to provide a parameterized meshing method which can establish the correlation of the sizes and the shapes of different component meshes in a mesoscopic structure and avoid the calculation errors caused by the uncoordinated change of the meshes so as to ensure the calculation stability and the accuracy of a composite mesoscopic finite element model,
the technical scheme provided by the invention is as follows:
a parameterized meshing method for a one-way composite material meso finite element model is characterized by comprising the following steps:
step 1: establishing a mesoscopic geometric model of the unidirectional composite material comprising the matrix, the interface layer and the fiber monofilaments;
step 2: dividing the mesoscopic geometric model established in the step 1 into an external matrix region and an internal square block region, wherein the process is as follows:
on the cross section of the mesoscopic geometric model, each fiber monofilament is taken as the center of a grid unit, and the internal area of the model is divided into a plurality of internal square block areas which are spliced together and have the same size;
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 fiber monofilament area, the annular interface layer area and the square matrix area have the central points at the same positions;
the upper side and the lower side of the model are provided with base body areas which are not covered by all the internal square block areas, namely external base body areas;
and step 3: and (3) segmenting the internal square block area obtained in the step (2), wherein the process is as follows:
3.1) dividing a square fiber monofilament area at the center of the fiber monofilament area, wherein the square fiber monofilament area is concentric with the square matrix area, but the square fiber monofilament area and the square matrix area have a relative deflection angle of 45 degrees;
3.2) dividing the fiber monofilament area except the square fiber monofilament area into four fan-shaped areas with equal size by utilizing 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 substrate area and the extending direction of a transverse center line and a longitudinal center line, equally dividing the annular interface layer area into eight sections of fan-ring areas, equally dividing the square substrate area into eight quadrilateral areas, setting a dividing line between adjacent fan-ring areas as a second dividing line, setting a dividing line between adjacent quadrilateral areas pressed in the diagonal direction as a third dividing line, and setting a dividing line pressed on the transverse/longitudinal center line as a fourth dividing line;
and 4, step 4: defining a partitioning parameter L expressed in the number of segment segmentsG_DIVAs a reference for the model mesh partition density to control the mesh density of the model population;
and 5: and for the quadrilateral area, carrying out grid quality control by restricting the length-width ratio of a unit:
the aspect ratio of the divided quadrilateral area is smaller than n, and the constraint equation of the grid unit is as follows:
Figure BDA0002587616690000031
Figure BDA0002587616690000032
Figure BDA0002587616690000033
Figure BDA0002587616690000034
wherein L is1，L2，L3And L4Respectively the length of four sides of the quadrilateral area, L4The sides being circular-arc sides of quadrilateral areas, L1The edge is opposite to the arc edge, L3The edge being collinear with the third dividing line, L4The edge is the edge collinear with the fourth dividing line; l isConSiC_DIVRepresents L2And L3The number of divisions of an edge;
L2，L3，L4and L1And other model parameters are as follows:
Figure BDA0002587616690000035
Figure BDA0002587616690000036
Figure BDA0002587616690000037
wherein d isfDenotes the diameter of the filament of the fibre, tpycIndicates the thickness of the interfacial layer;
step 6: solving for L constrained in step 52And L3Number of edge divisions LConSiC_DIVThe value range of (A):
Figure BDA0002587616690000041
and 7: taking the integer closest to the arithmetic mean of the boundary of the value range in the step 6 as L2And L3Number of divisions of an edge, i.e.
Figure BDA0002587616690000042
And 8: establishing division constraint of a fan ring area in an interface layer, and constraining the circumferential division number and L of the fan ring area4The division number of the edges is the same, and the length-width ratio of the division unit of the constraint fan ring area is 1: 1, the constraint equation is as follows:
Figure BDA0002587616690000043
Figure BDA0002587616690000044
L6＝tpyc
wherein L is5In the sector of the fan ringLength of wire, L6Width of the sector ring area, LPyC_DIVRepresents L6Number of divisions of an edge, L6The edge is the edge which is collinear with the second dividing line;
and step 9: solving for L constrained in step 86Number of divisions of edge LPyC_DIV：
Figure BDA0002587616690000045
Step 10: checking L obtained in step 9PyC_DIVWhether the result is suitable for grid division or not is determined by the following specific rules: if L isPyC_DIVIf the calculated result of (3) is less than 0.5, then take LPyC_DIVIf L is 1PyC_DIVIf the calculated result of (3) is greater than or equal to 0.5, then L is calculatedPyC_DIVRounding is performed, and the constraint equation is as follows:
Figure BDA0002587616690000046
step 11: the fan-shaped area of the fiber monofilament is divided and restrained according to the following rules: the aspect ratio of the constraint center section unit is 1: 1,
Figure BDA0002587616690000051
Figure BDA0002587616690000052
wherein L is7Indicates the width of the sector area, L8Indicating the length of the line in the sector, Lf_DIVRepresents a sector area L7Number of divisions of an edge, L7The edge is the edge which is collinear with the first dividing line;
step 12: solving the constraint equation in step 11 to obtain L7Number of divisions of edge Lf_DIV：
Figure BDA0002587616690000053
Step 13: dividing grids according to the obtained division numbers:
the square matrix area with the round hole in the middle is divided into grids in a mapping mode, and the fiber monofilament area, the annular interface layer area and the outer matrix area are divided into grids in a sweeping mode.
Preferably, in step 13, the grid is built by using SOLID185 units, and n is suitably 3.
Has the advantages that:
1) the shape of the grid divided by the method is regular, and the size is close, so that the accuracy of a finite element calculation result is ensured;
2) the method ensures the ordered change of the grids in each region through the introduced division constraint, does not generate the condition of grid change disorder, and improves the calculation stability;
3) the method realizes the unified control of the total grid density of the model by using a shared division parameter as a reference, and the adjustment efficiency of the grid density of the model is high.
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 diagram of the subdivision geometric model region division in the method of the present invention;
FIG. 3 is a schematic view of the internal square block area of the process of the present invention;
FIG. 4 is a schematic illustration of a square substrate area with a circular hole in the middle according to the method of the present invention;
FIG. 5 is a schematic diagram of the division of the internal square block area in the method of the present invention;
FIG. 6 is a schematic illustration of the division of the filament regions of the fibers in the process of the present invention;
FIG. 7 is a schematic illustration of the division of the annular interface layer region in the method of the present invention;
FIG. 8 is a schematic illustration of the division of a square matrix area with a circular hole in the middle according to the method of the present invention;
FIG. 9 is a schematic illustration of a quadrilateral area in a square substrate area in the process of the present invention;
FIG. 10 is a schematic view of the sector ring area of the process of the present invention;
FIG. 11 is a schematic representation of the square fiber filament area and the fan-shaped area of the fiber filaments in the process of the present invention;
FIG. 12 is a result of the meshing of the method of the present invention;
FIG. 13 is a partial enlarged view of the result of the meshing of the present invention;
the reference numbers are as follows:
1-matrix, 101-outer matrix region, 102-square matrix region, 102 a-third division line, 102 b-fourth division line, 102 c-quadrilateral region, 2-annular interface layer region, 201-fan ring region, 202-second division line, 3-fiber monofilament region, 301-square fiber monofilament region, 302-fan region, 303-first division line, 4-inner square bulk region.
Detailed Description
To clarify the technical solution and working principle of the present invention, the present invention will be further described with reference to the accompanying drawings and specific embodiments.
A parameterized meshing method of a unidirectional composite material mesoscopic finite element model comprises the following steps:
step 1: a macroscopic geometric model of a unidirectional composite comprising matrix 1, interfacial layers and fiber filaments was created as shown in fig. 1.
Step 2: dividing the mesoscopic geometric model established in the step 1 into an external matrix region 101 and an internal square block region 4, wherein the specific process is as follows:
on the cross section of the mesoscopic geometric model, taking (the cross section of) each fiber monofilament as the center of a square unit, dividing the internal area of the model into a plurality of internal 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 from inside to outside according to the components;
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 that of the fiber monofilament area 3;
the square substrate region 102 is a block with a round hole at the center and a square outline, as shown in fig. 4, the annular interface layer region 2 and the fiber monofilament region 3 are embedded in the round hole at the center, and the diameter of the round hole at the center is equal to the diameter of the outer ring of the annular interface layer region 2;
meanwhile, 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 central point;
the upper and lower sides of the mesoscopic geometric model, i.e. the substrate areas not covered by all inner square block areas 4, i.e. the outer substrate areas 101.
And step 3: further dividing the internal square block area 4 obtained in the step 2, wherein 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 area except the square fiber monofilament area 301 into four fan-shaped areas 302 with equal size by using 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 equally divided into eight sector ring regions 201 along the directions in which the two diagonals of the square base region 102 extend and the directions in which the transverse center line and the longitudinal center line extend, the square base region 102 is equally divided into eight quadrilateral regions 102c, the dividing line between the adjacent sector ring regions 201 is set as a second dividing line 202, the dividing line between the adjacent quadrilateral regions 102c pressed in the diagonal direction is set as a third dividing line 102a, and the dividing line pressed in the transverse/longitudinal center line is set as a fourth dividing line 102 b;
the division result is shown in fig. 5, in which the first division line 303, the fourth division line 102b are collinear with the second division line 202 in the horizontal or vertical direction, and the third division line 102a is collinear with the second division line 202 in the oblique upper or oblique lower direction.
And 4, step 4: defining a partitioning parameter L expressed in the number of segment segmentsG_DIVAs a reference for the model mesh partition density to control the mesh density of the model population;
and 5: for the quadrilateral region 102c divided by the internal square block region 4, the grid quality control is performed by restricting the length-width ratio of the unit due to the large shape change:
in this embodiment, the grid is built by using SOLID185 cells, so in this embodiment, the aspect ratio of the region cell is constrained to be not greater than 3, and the constraint equation is as follows:
Figure BDA0002587616690000081
Figure BDA0002587616690000082
Figure BDA0002587616690000083
Figure BDA0002587616690000091
wherein L is1，L2，L3And L4Respectively, the lengths of four sides of the quadrangular region 102c, L shown in FIG. 94The side is a circular arc side of the quadrangular region 102c, L1The edge is opposite to the arc edge, L3The side is a side collinear with the third dividing line 102a, L4The side is a side collinear with the fourth dividing line 102 b; l isConSiC_DIVRepresents L2Edge and L3The number of edge segment divisions;
L2，L3，L4and L1And other model parameters are as follows:
Figure BDA0002587616690000092
Figure BDA0002587616690000093
Figure BDA0002587616690000094
wherein d isfDenotes the diameter of the filament of the fibre, tpycIndicates the thickness of the interfacial layer;
in this embodiment L1＝4.5μm，df＝7μm，tpyc＝0.551μm。
Step 6: solving for L constrained in step 52Edge and L3Number of edge divisions LConSiC_DIVThe value range of (A):
Figure BDA0002587616690000095
and 7: taking the integer closest to the arithmetic mean of the boundary of the value range in the step 6 as L2And L3Number of divisions of an edge, i.e.
Figure BDA0002587616690000096
And 8: establishing division constraint of the fan ring area 201 in the boundary layer, and constraining the circumferential division number and L of the boundary layer4The division number of the sides is the same, and the length-width ratio of the division unit of the constraint fan ring area 201 is 1: 1, the constraint equation is as follows:
Figure BDA0002587616690000101
Figure BDA0002587616690000102
L6＝tpyc
wherein L is5Indicates the length of the centerline, L, of the sector ring area 2016Indicates the width, L, of the sector ring area 201PyC_DIVRepresents L6The number of divisions of an edge;
as shown in FIG. 10, the L6The side is collinear with the second dividing line 202, and the center line is dotted line in fig. 10, the center line is a circular arc line concentric with the inner and outer edges of the fan ring area 201, and the starting point of the two ends is L6The midpoint of the edge.
And step 9: solving for L constrained in step 86Number of divisions of edge LPyC_DIV：
Figure BDA0002587616690000103
Step 10: checking L obtained in step 9PyC_DIVWhether the result is suitable for grid division or not is determined by the following specific rules: if L isPyC_DIVIf the calculated result of (3) is less than 0.5, then take LPyC_DIVIf L is 1PyC_DIVIf the calculated result of (3) is greater than or equal to 0.5, then L is calculatedPyC_DIVRounding is performed, and the constraint equation is as follows:
Figure BDA0002587616690000104
step 11: the fan-shaped area 302 of the fiber monofilament is subject to a partitioning constraint with the following rules: the aspect ratio of the constraint center section unit is 1: 1;
Figure BDA0002587616690000105
Figure BDA0002587616690000111
wherein L is7Indicates the width, L, of the sector area 3028Indicating the length of the line in the sector, Lf_DIVRepresents a sector area (302) L7The number of divisions of an edge;
as shown in FIG. 11, the L7The edge being collinear with the first dividing line 303, L8The center line, i.e., the dotted line in the figure, is a circular arc line concentric with the outer edge of the sector area 302, and the starting points at both ends fall on L7At the midpoint of the edge.
Step 12: solving the constraint equation in step 11 to obtain L7Number of divisions of edge Lf_DIV：
Figure BDA0002587616690000112
Step 13: dividing grids according to the obtained division numbers:
the square matrix area 102 with the circular 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.
In this embodiment, LG_DIVAs shown in fig. 12, the result of the mesh division is shown in fig. 18, and the enlarged view of the partial area is shown in fig. 13, it can be seen that the mesh shape obtained by the method of the present invention is regular.
The foregoing shows and describes the general principles, essential 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 embodiments described above, which are described in the foregoing description only for the purpose of illustrating the principles of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the appended claims, specification, and equivalents thereof.

Claims (3)

1. A parameterized meshing method for a one-way composite material meso finite element model is characterized by comprising the following steps:
step 1: establishing a mesoscopic geometric model of the unidirectional composite material comprising the matrix (1), the interface layer and the fiber monofilaments;
step 2: dividing the mesoscopic geometric model established in the step 1 into an external matrix region (101) and an internal square block region (4), wherein the process is as follows:
on the cross section of the mesoscopic geometric model, each fiber monofilament is taken as the center of a grid unit, and the internal area of the model is divided into a plurality of internal square block areas (4) which are spliced together and have the same size;
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 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 fiber monofilament area, the annular interface layer area and the square matrix area have the central points at the same positions;
the upper side and the lower side of the model, and the base area which is not covered by all the inner square block areas (4), namely an outer base area (101);
and step 3: -segmenting said internal square block area (4) obtained in step 2 by:
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 area except the square fiber monofilament area (301) into four fan-shaped areas (302) with equal size by utilizing 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) the annular interface layer area (2) is evenly divided into eight fan-ring areas (201) along the extending directions of two diagonals of the square base area (102) and the extending directions of a transverse middle line and a longitudinal middle line, the square base area (102) is evenly divided into eight quadrilateral areas (102c), a dividing line between the adjacent fan-ring areas (201) is set as a second dividing line (202), a dividing line between the adjacent quadrilateral areas (102c) pressed in the diagonal direction is a third dividing line (102a), and a dividing line pressed in the transverse/longitudinal middle line is set as a fourth dividing line (102 b);
and 4, step 4: defining a partitioning parameter L expressed in the number of segment segmentsG_DIVAs a reference for the model mesh partition density to control the mesh density of the model population;
and 5: for the quadrilateral area (102c), the grid quality control is carried out by restricting the length-width ratio of the unit:
assuming that the aspect ratio of the quadrilateral area (102c) is smaller than n after division, the constraint equation of the grid unit is as follows,
Figure FDA0002587616680000021
Figure FDA0002587616680000022
Figure FDA0002587616680000023
Figure FDA0002587616680000024
wherein L is1，L2，L3And L4Length L of four sides of the quadrangular region (102c), respectively4The side is a circular arc side L of the quadrangular region 102c1The edge is opposite to the arc edge, L3The side is a side collinear with the third dividing line (102a), L4The edge is an edge collinear with the fourth dividing line (102 b); l isConSiC_DIVRepresents L2And L3The number of divisions of an edge;
L2，L3，L4and L1And other model parameters are as follows:
Figure FDA0002587616680000025
Figure FDA0002587616680000031
Figure FDA0002587616680000032
wherein d isfDenotes the diameter of the filament of the fibre, tpycIndicates the thickness of the interfacial layer;
step 6: solving for L constrained in step 52And L3Number of edge divisions LConSiC_DIVThe value range of (A):
Figure FDA0002587616680000033
and 7: taking the integer closest to the arithmetic mean of the boundary of the value range in the step 6 as L2And L3Number of divisions of an edge, i.e.
Figure FDA0002587616680000034
And 8: establishing a partition constraint of a sector ring area (201) in the boundary layer, and constraining the number of circumferential partitions and L thereof4The division number of the sides is the same, and the length-width ratio of the division unit of the constraint fan ring area (201) is 1: 1, the constraint equation is as follows:
Figure FDA0002587616680000035
Figure FDA0002587616680000036
L6＝tpyc
wherein L is5Denotes the length of the center line of the fan ring area (201), L6Indicates the width, L, of the fan-ring area (201)PyC_DIVRepresents L6Number of divisions of an edge, L6The side is the side which is collinear with the second dividing line (202);
and step 9: solving for L constrained in step 86Number of divisions of edge LPyC_DIV：
Figure FDA0002587616680000037
Step 10: checking L obtained in step 9PyC_DIVWhether the result is suitable for grid division or not is determined by the following specific rules: if L isPyC_DIVIf the calculated result of (3) is less than 0.5, then take LPyC_DIVIf L is 1PyC_DIVIf the calculated result of (3) is greater than or equal to 0.5, then L is calculatedPyC_DIVRounding is performed, and the constraint equation is as follows:
Figure FDA0002587616680000041
step 11: the fan-shaped area (302) of the fiber monofilament is subjected to division constraint according to the following rules: the aspect ratio of the constraint center section unit is 1: 1,
Figure FDA0002587616680000042
Figure FDA0002587616680000043
wherein L is7Indicates the width, L, of the sector area (302)8Indicating the length of the line in the sector, Lf_DIVRepresents a sector area (302) L7Number of divisions of an edge, L7The edge is the edge which is collinear with the first dividing line (303);
step 12: solving the constraint equation in step 11 to obtain L7Number of divisions of edge Lf_DIV：
Figure FDA0002587616680000044
Step 13: dividing grids according to the obtained division numbers:
the square matrix area (102) with the round hole in the middle is divided into grids in a mapping mode, and the fiber monofilament area (3), the annular interface layer area (2) and the outer matrix area (101) are divided into grids in a sweeping mode.
2. The parameterized meshing method for the uni-directional composite material meso finite element model as claimed in claim 1, wherein step 13 uses SOLID185 units to build the mesh.
3. The parametric meshing method for the unidirectional composite microscopic finite element model as claimed in claim 2, wherein n is 3.
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