JPH05298409A - Mash generating method - Google Patents

Abstract

PURPOSE:To uniformize plural rectangles by generating plural rectangles whose number of nodal points is four by repeating specified processing about two polygons generated by dividing. and averaging the nodal points positioned inside the boundary line of an area. CONSTITUTION:The nodal point (j) other than the nodal point (i) is selected from among the nodal points 1, 2, ...(N-1), N and is initialized. Then, angles alpha1, alpha2, beta1, beta2 determined by the modal point (j) and the nodal point (i) are found, and simultaneously, the sums of squares of the deviations of four angles are determined. Then, the nodal point (i) whose sum of square of the deviation is minimum is found (this is expressed as nodal point K). Next, the polygon is divided into two parts by connecting the nodal point (i) and the nodal point K, and the polygons 601, 602 are generated. In this case, if the number of nodal points is not four, the processing is repeated, and the polygon 601 or the polygon 602 is divided further, and on the other hand, if the number of the nodal points is four, the processing is shifted to the next processing. Through such a processs, a mesh divdied area is divided into the rectangles and the like whose number of the nodal points is four, and plural rectangles and the like are generated.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a mesh forming method for forming a quadrilateral mesh necessary for numerical analysis.

[0002]

2. Description of the Related Art In performing numerical analysis such as finite element method, finite volume method, boundary element method, etc., a quadrilateral mesh is better than a triangular mesh in that the analysis time is short and a highly accurate solution can be obtained. It is known that it is advantageous to use.

Conventionally, many methods for dividing an arbitrary region to generate a triangular mesh have been devised, but there is no suitable method for generating a quadrilateral mesh, and two triangular meshes are combined two by one. The current situation was to generate a quadrilateral mesh.

[0004]

However, there is a drawback that a large amount of time is required to correct the mesh because the mesh is distorted and the size is not uniform, and the triangular mesh may be mixed. It was

The present invention was created under the background described above, and an object of the present invention is to provide a mesh forming method capable of forming a square mesh having a small distortion and a uniform size.

[0006]

In order to achieve this object, a mesh forming method according to the present invention has nodes 1, 2, ... N (N) on a boundary line of an arbitrary region to be divided into meshes.
Is generated), a polygon is generated by connecting adjacent nodes to each other, the node i having the largest interior angle of the polygon is found among all the nodes, and the nodes other than the node i are connected to the node j.
And the nodes adjacent to the node i are the nodes (i-1),
(I + 1), nodes adjacent to the node j are nodes (j-1),
The angle formed by connecting the node (j-1), the node j, and the node i is α1, the angle formed by connecting the node (j + 1), the node j, and the node i is α2, and the node (i-
1), the angle formed by connecting the node i and the node j is β1, and the angle formed by connecting the node (i + 1), the node i and the node j is β2.
, The deviation square sums of the angles α1, α2, β1, β2 are calculated for all the nodes j other than the node i, and the node k for which the calculated deviation square sum is the minimum is calculated.
The polygon is divided into two by connecting the node i and the node k,
After that, the above processing is repeated for the two divided polygons to generate a plurality of quadrilaterals having 4 nodes, and the nodes inside the boundary line of an arbitrary area are averaged to obtain a plurality of quadrangles. The quadrangles were made uniform.

[0007]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A method of an embodiment of the present invention will be described below with reference to the drawings. The method described here is incorporated in a part of the software of the numerical analysis computer, so that the quadrilateral mesh necessary for performing the numerical analysis is automatically created by the processing procedure shown in FIG. Is becoming

First, a plurality of nodes are generated on the boundary line of an arbitrary analysis area to be divided into meshes. The analysis area here is shown as a mesh division area 201 as shown in FIG. 2, and its boundary line is shown as a boundary 202. The nodes on the boundary 202 are shown as nodes 1, 2, ... (N-1), N as shown in FIG.

That is, when the user sets the mesh division area 201, the length of the boundary 202 is determined. Divide the length of this boundary 202 by the size of the mesh size specified by the user,
As a result, the number of nodes N is obtained. However, since the number of nodes N must be an even number in order to generate a quadrilateral mesh, when the number of nodes N is an odd number, it is increased or decreased to be adjusted. Then, the boundary 202 is divided by an even number N, and thereby nodes 1, 2, ... (N-1), N are generated.
The nodes 1, 2, ..., I, (N-1), N are arranged in this order in the counterclockwise direction as shown in FIG. 3 (step 1).

Next, as shown in FIG. 4, a polygon 401 is generated by connecting adjacent nodes. A line element connecting the node 1 and the node 2 is represented as a line element 1, and other line elements are also represented as shown in the figure. And N
A node i corresponding to the vertex having the maximum interior angle of the polygon 401 surrounded by the line elements is obtained (step 2).

Here, as shown in FIG. 5, nodes 1, 2, ...
, (N-1), and N except the node i are represented as the node j as a representative. Further, nodes adjacent to the node i are represented as nodes (i-1) and (i + 1), while nodes adjacent to the node j are represented as nodes (j-1) and (j + 1). Further, the angle formed by connecting the node (j−1), the node j, and the node i is α1, the node (j + 1), the node j, and the node i.
The angle formed by connecting the points is α2, node (i-1), node i,
It is assumed that the angle formed by connecting the node j is β1, and the angle formed by connecting the node (i + 1), the node i, and the node j is β2.

After that, the number of nodes of the polygon 401 is 4 or 6
To see if. If this is not the case, the number of nodes of the polygon 401 is 8 or more. In this case, therefore, the two nodes required to divide the polygon 401 into two are obtained in the next step 3. The processing when the number of nodes of the polygon 401 is 4 or 6 will be described later.

First, nodes 1, 2, ..., (N-1), N
The node j other than the node i is arbitrarily selected from among the above, and is initialized. Then, an angle α1 determined by the node j and the node i,
In addition to obtaining α2, β1 and β2, the sum of squared deviations of the four angles is obtained. After that, the setting of the node j is changed to another node one after another, and the sum of squared deviations is calculated each time in the same manner as above. In this way, the sum of squared deviations of the angles α1, α2, β1, and β2 for all the nodes j other than the node i is sequentially obtained. Then, a node i having the smallest sum of squared deviations (this is represented as a node k) is obtained (step 3).

Next, as shown in FIG. 6, node i and node k
Polygon 401 is divided into two by connecting and
Generate 601 and 602 (the boundary 202 (of the polygons 601 and 602
(See FIG. 2) The number of nodes above is represented as s [= (N−2) / 2]).

First, since the size of the mesh size to be finally obtained has already been specified, the number of nodes to be added on the boundary line connecting the node i and the node k in consideration of this specified value. Find m. However, as in the case of step 1, since the number of nodes s + n must be an even number, when the number of nodes s + n is an odd number, it is increased or decreased to be adjusted. Then, the boundary line connecting the node i and the node k is divided by the number of m to generate nodes N + 1 ... N + m. As a result, the polygon 401 is divided into two by the polygons 601 and 602. A line element connecting the node N and the node N + 1 is defined as a line element N + 1, and other line elements are also represented as shown in the figure (step 4).

After that, whether or not the number of nodes of the polygon 601 and the polygon 602 is 4 is checked. As a result, if the number of nodes of the polygon is not 4, the processes of steps 3 and 4 are repeated. , While further dividing polygon 601 or polygon 602,
If the number of nodes of the polygon is 4, the process proceeds to step 6 described later. Through this process, the mesh division area 20
1 is divided into squares and the like with four nodes to generate a plurality of squares and the like.

However, when a hexagon with 6 nodes is generated in the process of dividing the mesh division area 201,
The following processing is performed.

On the boundary line of the polygon 700 shown in FIG. 7, nodes 701, 702, 703, 704, 705 and 706 are arranged in this order. First, find the node with the largest interior angle of polygon 700. Here, the node with the largest interior angle is the node 701.
And After that, the node having the second largest interior angle of the polygon 700 is obtained. If the node 704 is the second largest, then FIG.
As shown in, the polygon 700 is divided into two by the nodes 701 and 704. When the nodes 703 and 705 are the second largest, a new node is provided in the polygon 700 as shown in FIG. 9, and the polygon 700 is divided into three. If the node 702 or 706 is the second largest, the polygon 700 is divided into four as shown in FIG. 10 (step 5).

If the mesh division area 201 is divided into a plurality of squares as shown in FIG. 11 through the above process, then
The nodes inside the boundary 202 are averaged, so that a plurality of squares are made uniform. For example, the mesh division area 20
The node coordinates on the boundary 202 at 1 are Xi (i = 1 to 1
2), set the coordinates of the nodes inside the boundary 202 to xi (i = 1
˜5), xi is expressed by the relational expression of Formula 1.

[0020]

X1 = (X12 + X2 + x3) / 3 x2 = (X10 + X12 + x3 + x8) / 4 x3 = (x1 + x2 + x4 + x5) / 4 x4 = (x3 + X2 + X4 + X6) / 4 x5 = (X6 + X8 + x3) / 3

By rearranging the relational expression of the equation 1, a simultaneous linear equation regarding x1 is obtained, which is expressed by the equation of the equation 2.

[0022]

[Equation 2]

By solving the equation 2, the node coordinates xi (i = 1 to 5) in the mesh division area 201 shown in FIG. 12 are obtained, and the node coordinates Xi on the boundary 202 in the mesh division area 201 are obtained.
It is an averaged value based on (i = 1 to 12). As a result, the plurality of quadrangles that divide the mesh division area 201 are made uniform (step 6).

With this, the mesh division area 201 is divided, a desired quadrilateral mesh is created, and this processing ends. After that, the following processing for performing numerical analysis using this mesh is performed.

In the above-described method of the embodiment, in addition to the merits described later, since the hexagon obtained in the process of dividing the mesh division area 201 is also dealt with, the distortion of the mesh as a whole can be reduced. There is an advantage. There is also an advantage that a mesh of a desired size can be generated.

[0026]

As described above, according to the mesh forming method of the present invention, it is possible to automatically form a square mesh having a small distortion and a uniform size. Therefore, unlike the conventional method, there is an advantage that the numerical analysis can be smoothly performed without the labor and time for modifying the mesh.

[Brief description of drawings]

FIG. 1 is a diagram for explaining an embodiment method and is a flowchart showing a processing procedure for creating a mesh.

FIG. 2 is an explanatory diagram showing mesh division areas.

FIG. 3 is an explanatory diagram showing a plurality of nodes generated on a boundary of a mesh division area.

FIG. 4 is an explanatory diagram showing a polygon generated by connecting adjacent nodes.

FIG. 5 is a diagram for explaining a process of obtaining a node required to divide a polygon into two parts.

FIG. 6 is a diagram for explaining a process of dividing a polygon into two polygons.

FIG. 7 is a diagram showing a polygon with 6 nodes.

FIG. 8 is a diagram for explaining a process of dividing a 6-node polygon into two 4-node polygons.

FIG. 9 is a diagram for explaining a process of dividing a 6-node polygon into three 4-node polygons.

FIG. 10 is a diagram for explaining a process of dividing a 6-node polygon into four 4-node polygons.

FIG. 11 is a diagram showing a state in which a mesh division area is divided into squares.

FIG. 12 is a diagram for explaining a process of averaging the nodes in the mesh division region.

[Explanation of symbols]

 201 mesh division area 202 boundary 401 polygon

Claims (1)

[Claims] 1. A method for creating a quadrilateral mesh necessary for performing numerical analysis, wherein first, nodes 1, 2, ... N (N is an even number) on a boundary line of an arbitrary region to be divided into meshes. Is generated, a polygon is generated by connecting adjacent nodes, the node i having the largest interior angle of the polygon is found among all the nodes, and the nodes other than the node i are represented as the node j. The nodes adjacent to i are represented as nodes (i-1) and (i + 1), and the nodes adjacent to node j are represented as nodes (j-1) and (j + 1), respectively, and node (j-1), node j, and node The angle formed by connecting i is α
1, an angle formed by connecting the node (j + 1), the node j, and the node i is α2, an angle formed by connecting the node (i-1), the node i, and the node j is β1, a node (i + 1), the node i, When the angle formed by connecting the nodes j is represented as β2, angles α1, α2, β for all nodes j other than the node i
The deviation sum of squares of 1 and β2 is calculated respectively, the k node having the minimum calculated deviation sum of squares is calculated, and the polygon is divided into two by connecting the node i and the k, and then divided. By repeating the above process for two polygons, a plurality of quadrangles with 4 nodes are generated, and the quadrangle is uniformized by averaging the nodes inside the boundary line of any area. A mesh creation method characterized by