JPH11110587A - Mesh generation method for numerical analysis - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate a tetrahedral mesh for analysis at a high speed by subdividing only an element whose volume exceeds a target element volume or subdividing only the element, whose aspect ratio is smaller than a target aspect ratio. SOLUTION: In a shape model and target element input part, a shape model generated based on numerical values inputted by a user using a keyboard 101b and a mouse 101c of an input/output device 101 is stored in a data base and displayed on a display 101a. A system user interactively inputs a target element dimension (a standard element dimension, the part and a minimum element dimension at the part in the case of concentrating the mesh at the certain part such as a point, a line segment and a plane, etc., of the shape model and an element dimension change coefficient for indicating through what ratio the size of the mesh is changed from the concentrated part) from the keyboard 101b or the mouse 101c for the prepared shape mode. Thus, a tetrahedral mesh for the analysis is generated at a high speed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a CAE system that optimizes and rationalizes design work by numerical simulation using a computer. In particular, the present invention relates to a method for automatically generating a mesh for numerical analysis from a three-dimensional shape model to be analyzed.

[0002]

2. Description of the Related Art Conventionally, as a method of automatically generating an analysis mesh of a tetrahedron, there is a generation method using Delaunay tetrahedral division. In the analysis mesh generation using the Delaunay tetrahedron division, a node group is arranged in advance in a shape model, nodes arranged in a coarse tetrahedron mesh generated in the shape model are sequentially added, and a tetrahedron including the nodes is added. Analytical mesh data is created by the procedure of exploring elements and performing Delaunay division, and repeating this process by the number of nodes.
The Deloni tetrahedron division is described in “Automatic Division of Three-Dimensional Convex Tetrahedral Finite Elements” by Takeo Taniguchi and Chika Ota, I-16, 432, pp. 137-144, 1991.

In arranging a node group, a plurality of node candidate points are arranged in a grid pattern, and it is determined whether or not the candidate points are used as nodes. At that time, it is necessary to calculate the distance between the candidate point and all the arranged nodes, and the total arrangement time of the node group is proportional to the square of the number of nodes, and it takes time. On the other hand, in the process of searching for a tetrahedral element including a node, it takes time to perform the inside / outside determination process with all the elements.

The following method has been proposed to solve the problem of node group arrangement time. By covering the shape model with a completely enclosing rectangular parallelepiped, dividing it into a number of small rectangular parallelepipeds called buckets, and generating nodes for each bucket,
This is a technique (bucket method) for reducing the number of nodes per bucket and shortening the node group arrangement time. This is described in “Latest Prepost KSWAD Ver. 6.0”, Takashi Chofuku, Computational Engineering Science Vol. 2, No. 1, p. 47-50 1997.

To solve the problem of the search time, the area controlled by the nodes is divided into small cubes called bins, and the order of nodes to be added is determined according to the order given to each bin. A method of saving exploration time (bin sorting method) has also been proposed. For details of this method, see "Automatic Division of Tetrahedral Finite Elements of Three-Dimensional Convex Body" by Takeo Taniguchi and Chika Ota.
No. 32 p. 137-144 1991.

[0006]

Even when the bucket method is used, a new time is required to divide a rectangular parallelepiped completely enclosing the shape model into buckets, and for one bucket, the time for arranging internal nodes is increased. Since is proportional to the square of the number of nodes to be arranged, it takes time to generate an analysis mesh having a large number of nodes.

[0007] Even when the bin sorting method is used,
A new time is required to divide the region controlled by the nodes into bins, and the search time can be reduced using the bin sorting method, but it is necessary to search for tetrahedral elements that include the additional nodes Sex is not lost. For one bin, the search time is proportional to the number of elements, and it takes time to generate an analysis mesh with a large number of elements.

An object of the present invention is to solve the above problems and to provide a mesh generation method for numerical analysis capable of generating a tetrahedral mesh for analysis at high speed.

[0009]

The object of the present invention is to input a target element size and a target element volume of a shape model to be analyzed and an analysis mesh to a computer, and to make a surface of the shape model based on the target element size. A method of generating an analysis mesh by dividing into a rectangular mesh, generating a coarse tetrahedral mesh inside the shape model, arranging the nodes inside the shape model, and subdividing the coarse tetrahedral mesh includes a method of determining the volume of the target element. Means for subdividing only tetrahedral elements larger than volume, means for subdividing only tetrahedral elements whose aspect ratio is smaller than target aspect ratio, Only tetrahedral elements whose maximum volume ratio of adjacent elements is larger than target adjacent volume ratio Can be achieved by a numerical analysis mesh generation method provided with a means for subdividing.

[0010]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is an overall configuration diagram of the present mesh generation device. One embodiment of the mesh generation method of the present invention will be described with reference to FIG.

1. Shape Model, Target Element Input Unit In the shape model, target element input unit, a shape model generated based on numerical values input by the user using the keyboard 101b or mouse 101c of the input / output device 101 is stored in a database and displayed on the display 101a. To be displayed. When the system user wants to concentrate target element dimensions (standard element dimensions and mesh on a point, line segment, surface, or the like in the shape model) from the keyboard 101b or the mouse 101c, the system user inputs the target element dimensions. The element size change coefficient that indicates how much the part, the minimum element size at that part, and the mesh size are changed from the concentrated part)
Can be entered interactively.

FIG. 2 is an example of an input screen for standard element dimensions. In this example, with respect to the shape model shown in FIG. 4A, the standard element size is 10, the mesh is concentrated on the point 2a on the shape model, the minimum element size at that time is 1, and the element size change coefficient is 1 .3 and generate a mesh (ST
1).

2. Element Subdivision Reference Input The element subdivision reference input allows the user to select a subdivision criterion for the element, such as a target element volume or target aspect ratio or target adjacent volume ratio. FIG. 3 is an example of an input screen for the element subdivision criterion. A subdivision criterion to be used is selected as in 3a, and a subdivision reference value is input to 3b. In addition, when the target element volume is used as the subdivision reference and the target element volume is determined from the surface triangular mesh, 3c is selected (ST2).

3.3 Triangular Mesh Generation Unit The triangular mesh generation unit generates a triangular mesh on the surface of the shape model using, for example, the front method or the Deloni triangulation method based on the input target element dimensions. . FIG.
(B) is a triangular mesh generated on the surface of the shape model of FIG. 4 (a) (ST3).

4. Initial tetrahedral mesh generator The initial tetrahedral mesh generator generates a rough tetrahedral mesh (initial tetrahedral mesh) inside the shape model based on the surface triangle mesh of the shape model. The initial tetrahedral mesh is generated in the following procedure. First, a tetrahedron including a shape model is created. FIG. 4C shows FIG.
It is an example of a tetrahedron including the shape model of (a).

Next, nodes constituting a triangular mesh on the model surface are sequentially arranged, and, for example, Delaunay tetrahedron division is performed to generate a rough tetrahedral mesh. Finally, elements existing outside the shape model are removed (ST4).

5.4 Tetrahedral Mesh Subdivision Unit The tetrahedral mesh subdivision unit subdivides the initial tetrahedral mesh according to the subdivision standard input by the user to generate an analysis mesh. FIG. 5 shows an algorithm of tetrahedral mesh subdivision when a target volume is selected as a subdivision criterion.

First, an element subdivision criterion (a target element volume, a target aspect ratio, a target adjacent volume) selected by a user in an element subdivision criterion input unit is applied to an element existing inside the model.
, The user input values at the element subdivision reference input unit are set for all the elements. However, when determining the target element volume from the surface triangular mesh, the target element volume is determined for each element according to the following method (ST7).

There are two types of tetrahedrons existing inside the shape model: a tetrahedron in which at least one of the four surfaces constituting the tetrahedron is a surface triangular mesh, and a tetrahedron not including the surface triangular mesh. Classify into.

A method for determining a target element volume of a tetrahedron in which at least one of the four surfaces constituting the tetrahedron is a surface triangular mesh will be described. First, the total number of triangular surfaces and the total area of triangular surfaces are determined, and the average area is calculated. Next, the positive 3 of the same area as the average area
The length of one side of the polygon is determined, and the volume of a regular tetrahedron having this side as one side is determined. The volume of this tetrahedron is defined as the target 4
This is the target element volume of the face.

An example in which this method is applied to the tetrahedral element 6a in FIG. 6 will be described. In this example, one surface is a surface triangular mesh, and the lengths of three sides of the triangular mesh are 3, 4, and 5, respectively. Therefore, the length of one side of the regular triangle having the same area as the triangle is about 3.87, and the volume of the regular tetrahedron having this side as one side is about 6.83.
Becomes Therefore, 6.83 is set as the target element volume of the tetrahedral element 6a.

A method for determining a target element volume of a tetrahedral element not including a surface triangular mesh will be described. Among the tetrahedral elements that are in contact with the target tetrahedral element, the number of elements for which the target element volume is set and the sum of the target element volumes of the elements for which the target element volume is set are calculated, and the average target element volume is obtained. Is calculated, and this is set as the target element volume of the target tetrahedral element.

An example in which this method is applied to the tetrahedral element shown in FIG. 7 will be described. In this example, the target element volume of the tetrahedral element 7a is determined. Tetrahedral elements 7b, 7c, 7 contacting by face
Of d and 7e, the tetrahedral elements for which the target element volume is set are two elements 7c and 7d, and are 5 and 10, respectively. Therefore, the average value of the target element volumes of the two elements is 7.5, which is the target element volume of the tetrahedron 7a.

According to this determination method, a tetrahedral element including a surface triangular mesh having a large area has a surface 3 having a small area.
A target element volume larger than a tetrahedral element including a rectangular mesh can be set. In addition, for a tetrahedral element that does not include the surface triangle, a target element volume can be set according to the area change of the surface triangle mesh.

The volume of all tetrahedral elements is determined (ST
8).

When there is an element whose volume exceeds the target element volume, an internal node is arranged at the center of gravity of the element, and the mesh is subdivided (Deloni tetrahedron division) (ST9,
ST10, ST11).

Each of the four generated by the Delaunay tetrahedral division
A target element volume is set for the face element. According to the element subdivision criterion (target element volume, target aspect ratio, target adjacent volume) selected by the user in the element subdivision criterion input unit, a user input value in the element subdivision criterion input unit is set for all elements. . However, when the target element volume is automatically determined from the surface triangular mesh, the target volume of each element is set according to the following method (ST12).

First, the average value of the target element volumes of the element group removed by Delaunay division is set as the target element volume of each newly generated element. Next, among the elements that are in contact with the target tetrahedral element on the surface, elements other than the newly generated element are searched. Then, the target element volume of the target element is changed to the average of the target element volume and the target element volume of the retrieved element. If there is no element other than the newly generated element among the elements that are in contact with the target tetrahedral element on the surface, the element is not changed.

An example in which this method is applied will be described with reference to FIG. Consider a case where a node occurs at the center of gravity of the tetrahedral element 8a2 shown in FIG. By the Delaunay division, the two tetrahedral elements 8a1 and 8a2 are removed, and FIG.
It is assumed that six tetrahedral elements 8b1 to 8b6 shown in (b) are newly generated. At this time, the target element volumes of the newly generated six elements are replaced with the removed elements 8a1 and 8a2.
The average value of the target element volume of is set to 10. Further, FIG.
As shown in the figure, with respect to the tetrahedral element 8b1, of the tetrahedral elements that are in contact with each other,
c1 is searched, and the average value 10.5 of the target element volumes of 8b1 and 8c1 is set as the target element volume of element 8b1. Element 8b
The target element volumes of 2 to 8b6 are obtained in the same procedure.

The volume of each tetrahedral element generated by Delaunay division is determined (ST13).

This processing is repeated until there is no element whose volume is larger than the target element volume (ST5).

By setting the target element volume for each element and arranging the internal nodes at the center of gravity only for the elements whose volume exceeds the target element volume, the arrangement of the internal nodes and the elements including the nodes Exploration in a short time. Therefore, a large-scale analysis mesh having a large number of elements and nodes can be generated at high speed.

1.6 Analysis Mesh Output Unit The analysis mesh output unit displays the generated analysis mesh on the display 101b. FIG. 4D shows FIG.
4A is a tetrahedral mesh generated inside the shape model of FIG. In order to make the display easier to understand, several elements near the boundary of the shape model are selected and displayed (ST6).

Similarly, when the target aspect ratio is selected as the subdivision criterion, only nodes having an aspect ratio smaller than the target aspect ratio have internal nodes located at their centroids, and the mesh is repeatedly subdivided for analysis. Generate a mesh. In addition, when the target adjacent volume ratio is selected, only nodes whose maximum volume ratio of the adjacent elements is larger than the target volume ratio have internal nodes located at the center of gravity, and by repeating subdivision of the mesh, high speed is achieved. An analysis mesh can be generated.

[0035]

According to the present invention, only the element whose volume exceeds the target element volume is subdivided, or only the element whose aspect ratio is smaller than the target aspect ratio is subdivided, or the maximum volume ratio of adjacent elements is obtained. Generates an analysis mesh by subdividing only elements larger than the target volume ratio, so there is no need to search for tetrahedral elements that include the nodes to be arranged. The time required for node placement can be kept proportional to the number of nodes. Therefore, a tetrahedral mesh for analysis can be generated at high speed.

[Brief description of the drawings]

FIG. 1 is a system configuration diagram of a mesh generation method according to an embodiment of the present invention.

FIG. 2 is a diagram showing an example of a target element dimension input screen of FIG. 1;

FIG. 3 is a diagram showing an example of an input screen of an element subdivision criterion in FIG. 2;

FIG. 4 is a diagram illustrating a process of generating a mesh.

FIG. 5 is a flowchart showing an algorithm for subdividing elements.

FIG. 6 is a diagram showing an example of determining a target element volume of a tetrahedral element from the area of a triangular mesh.

FIG. 7 is a diagram illustrating an example of determining a target element volume of a tetrahedral element from a target element volume of an element in contact with a surface.

FIG. 8 is a diagram showing an example of determining a target element volume of a tetrahedral element generated by Delaunay division.

[Explanation of symbols]

101: input / output device, 101a: display, 101
b ... keyboard, 101c ... mouse.

Continued on the front page (72) Inventor Chie Takizawa 502 Kandamachi, Tsuchiura-shi, Ibaraki Pref.

Claims (1)

[Claims] 1. A shape model to be analyzed and a target element size and a target element volume of an analysis mesh are input to a computer, and the surface of the shape model is divided into a triangular mesh based on the target element size. A coarse tetrahedral mesh is generated inside, and nodes are arranged inside the shape model.
In a method of generating an analysis mesh by subdividing a tetrahedral mesh, a tetrahedral mesh is generated inside the shape model by subdividing only tetrahedral elements whose volume is larger than the target element volume. To generate meshes for numerical analysis.