JP3763150B2 - Mesh generation method and apparatus - Google Patents

Description

[0001]
[Industrial application fields]
The present invention relates to a method for generating a mesh model used for finite element analysis of a shape to be analyzed, and more particularly to a mesh generation method and apparatus suitable for a model in which members of different materials such as a rotor of a motor are combined.
[0002]
[Prior art]
Conventionally, as a technique for generating mesh data used for finite element analysis from shape data to be analyzed, a shape division rule is applied to the shape model represented by the shape data, and the shape model is divided into a plurality of quadrilaterals or three sides. There is disclosed a technique of dividing a shape into regions (parts), and dividing the inside of the part by giving a mesh size to the boundary line of each part to generate a mesh model (for example, Japanese Patent Laid-Open No. 5-120385). .
[0003]
[Problems to be solved by the invention]
However, in the above prior art, when the mesh size is given to the boundary line of each part to divide the mesh and a mesh model is generated, the accuracy of the analytical solution is ensured, and the data capacity and calculation time are saved. Therefore, the mesh size is changed for each part, and the mesh is divided into coarse and dense meshes. At this time, it is necessary to match the number and position of the nodes on the boundary between adjacent parts, but an analyst inputs the mesh size of each part while matching the part boundary by an interactive format or the like. This mesh creation work, in which the analyst inputs the mesh size, is complicated and results in a reduction in work efficiency, especially in the parts that need to be complicated and dense in consideration of changes in physical quantities. There was a problem of requiring.
In addition, the mesh shape is required to have less distortion in order to avoid a decrease in analysis accuracy, but some analysts may have variations due to the complexity of mesh creation work, which may cause distortion in the mesh model. .
An object of the present invention is to provide a mesh generation apparatus that can reduce a burden on an analyst in mesh creation, improve work efficiency, and obtain a mesh model having a shape with less distortion.
[0004]
[Means for Solving the Problems]
In order to solve the above problem, the present invention provides an outline boundary and a common boundary in a mesh generation method for finite element method analysis in which an analysis target region is divided to form a plurality of parts and the plurality of parts are divided into meshes. When the upper boundary node is initially divided into a rough mesh shape by equally dividing one side of the contour boundary, and the number of nodes on the boundary on the common boundary is different between the adjacent parts, the common of both parts On the boundary, the average value of the number of nodes on the boundary on the boundary is adopted, or the number of nodes on the boundary, whichever is larger or smaller, is adopted, and the line segment of the common boundary is corrected to an equally divided position. A node is generated, a node in the part in which a rectangular mesh mesh is formed in the part is formed in the part, a rectangular element is created using the node in the part, the node on the boundary and its node Close to the part Triangular elements and quadrilateral elements forming a coarse mesh mesh are created by nodes, the quadrilateral elements of the coarse mesh mesh are divided into four, subdivided nodes that divide the triangular elements into three are generated, and the subdivided nodes In this method, the square element and the triangular element are converted into small square elements to form a dense mesh mesh . Further, in a mesh generating apparatus for finite element method analysis comprising means for dividing a region to be analyzed to form a plurality of parts and means for subdividing the divided parts into meshes, the contour boundary and common The boundary node on the boundary is initially divided into a coarse mesh by equally dividing one side of the contour boundary, and when the number of nodes on the boundary on the common boundary is different between the adjacent parts, Adopting the average value of the number of nodes on the boundary on the common boundary, or adopting the number of nodes on the boundary, whichever is larger or smaller, and correcting the boundary to a position where the line segment of the common boundary is equally divided Creates a quadrilateral element using a node generation unit comprising means for generating an upper node, means for generating a node in the part in which a rectangular mesh mesh is formed in the part, and the node in the part You The means and the boundary on the nodes with means and quadrilateral element of the coarse reticulated mesh to create a triangular element and quadrilateral element forming said coarse reticulated mesh by part in nodes near the node 4 is divided, triangular elements An element generation unit comprising means for generating a finely divided node by dividing the square element into three and dividing the square element by the subdivided node and converting the triangular element into a small square element to form a dense mesh mesh It is. In addition, an element shape correction unit that corrects the shape of the small square element by rearranging the subdivision nodes of the small square element is provided.
[0005]
[Action]
By the above means, nodes on the part boundary and inside the part are generated based on data such as part mesh size, coordinate value, or material, and the nodes of the common boundary are matched, and the element generation unit based on the nodes Triangular and quadrilateral elements are created to form a coarse mesh. Next, the triangular element and the quadrilateral element are further divided into small quadrilateral elements to generate subdivided nodes. The subdivided nodes are used to form small quadrilateral elements, and the shape of the small quadrilateral elements is further changed by the element shape correction unit. Since a dense mesh mesh is formed by modification, a highly accurate mesh can be automatically created.
[0006]
【Example】
The present invention will be described below with reference to embodiments shown in the drawings.
FIG. 1 is a block diagram showing an embodiment of the present invention.
In the figure, reference numeral 1 denotes a mesh generation apparatus, which includes a node generation unit 2, an element (mesh) generation unit 3, and an element shape correction unit 4. The input of the mesh generation device 1 is part data created by the part creation device based on the shape data to be analyzed obtained from the shape input device and the mesh size of the part given to the shape data. The part data includes coordinate values indicating a partial area such as a quadrangle, mesh size, and material.
The node generation unit 2 includes a part boundary node generation unit 21 that generates nodes on the part boundary, and an intra-part node generation unit 22 that generates nodes arranged in a grid within the part.
The element generation unit 3 includes a quadrilateral element creation unit 31 based on nodes inside the part, a triangle / quadrature element creation unit 32 based on the nodes on the part boundary and the nodes inside the part that are close thereto, and a small quadrilateral element by subdivision of the elements. It is comprised from the conversion part 33. FIG.
[0007]
Here, a method of forming a mesh based on the shape of the analysis target region shown in FIG. 2 will be described.
FIG. 2 includes three parts 51, 52, and 53 made of two materials A and B. Each part has a boundary 6 with the outside world, and the boundary 6 has no relation to other parts and forms a contour. It consists of a common boundary 62, 63, which is a boundary between the contour boundary 61 and adjacent parts. That is, part 51 and part 52 have a common boundary 62 that is a boundary between adjacent parts, and part 52 and part 53 show an example of the shape of the analysis target region having a common boundary 63.
In the part boundary upper node generation unit 21, as shown in FIGS. 3A, 3 </ b> B, and 3 </ b> C, the boundary upper node 71 on the contour boundary 61 and the common boundaries 62 and 63 is set to, for example, 1 of the contour boundary 61. An initial division is made into a coarse mesh by dividing the sides equally. When the number of nodes 71 on the common boundary is different between adjacent parts, as shown in FIG. 4, for example, the average value of the number of nodes on the common boundary of both parts is adopted, whichever is greater or smaller By adopting the number of nodes, a modified node is provided at the position where the line segment of the common boundary is equally divided and shared.
That is, since the numbers of nodes of the initial common boundary 62 of the parts 51 and 52 are 3 and 6, respectively, the number of nodes of the common boundary 62 after matching is 4. Further, since the number of nodes at the initial common boundary 63 of parts 52 and 53 is 6 and 7, the number of nodes at the common boundary 63 after matching is set to 6.
As shown in FIG. 4, the intra-part node creation unit 22 generates a intra-part node 72 in which a square mesh mesh is formed in the parts 51 and 52 using the mapping function.
The quadrangular element creation unit 31 of the element generation unit 3 creates the quadrangular element 81 using the part internal node 72 generated by the part internal node generation unit 22.
Further, the triangle / quadrangle element creation unit 32 uses the upper boundary node 71 generated by the upper part boundary node generation unit 21 and the inner node 72 near the node to form a triangular element 82 that forms a coarse mesh. And the square element 83 is created.
Similarly, the quadrilateral element 81, the triangular element 82, and the quadrilateral element 83 are created for the other parts to form a coarse mesh.
The rectangular element conversion unit 33 generates the subdivided nodes 9 in which the quadrilateral element 81 and the quadrilateral element 83 created as described above are divided into four, and the triangular element 82 is divided into three, and as shown in FIG. The subdivided nodes 9 are converted from the quadrilateral elements 81 and 83 and the triangular element 82 to the small quadrilateral element 91 to form a dense mesh mesh.
[0008]
As a result, a dense mesh mesh of small square elements 91 is generated in the parts 51, 52, and 53.
Thereafter, if the above is repeated for all the parts, a dense mesh-like mesh composed of small square elements 91 in the entire analysis region is generated.
The element shape correction unit 4 uses, for example, a shape correction method such as a Laplacian method for the shape of the small square element 91 created as described above, and the nodes 71 and 72 relating to elements with large distortion so as not to have an extremely large area change. 9 is rearranged and corrected to a dense mesh mesh as shown in FIG.
Here, since the parts 51 and 52 are made of the same material, the upper boundary node 71 on the common boundary 62 only needs to be inside the parts 51 and 52. In this case, the upper boundary node 71 on the common boundary 62 is an element. The shape correcting unit 4 recognizes the node as a distorted element, and moves so that the area of the element adjacent to the node 71 on the boundary and the adjacent node changes gradually.
As described above, a mesh with high analysis accuracy is obtained, and the completed mesh is sent to a mesh display device for display or stored in a mesh database.
[0009]
【The invention's effect】
As described above, according to the present invention, data such as part mesh size, coordinate value or material is stored in the shape input device, and the data is input to the mesh generation device via the part creation device, Nodes on and within the part boundary are generated, the nodes on the common boundary are aligned, the element generation unit divides them into small square elements based on the nodes, and the element shape correction unit corrects the element shape Therefore, it is possible to automatically create a highly accurate mesh, and there is an effect that the mesh creation time can be greatly reduced and the analysis time can be shortened.
[Brief description of the drawings]
FIG. 1 is a block diagram showing an embodiment of the present invention.
FIG. 2 is a plan view showing the shape of a region to be analyzed according to an embodiment of the present invention.
FIG. 3 is a plan view showing a part of an analysis target area according to the embodiment of the present invention.
FIG. 4 is a plan view showing a state in which a part of an analysis target area according to an embodiment of the present invention is divided into a triangular element and a quadrangular element.
FIG. 5 is a plan view showing a state in which a part of an analysis target area according to an embodiment of the present invention is divided into small square elements.
FIG. 6 is a plan view showing a state where a small square element of a part of an analysis target area according to an embodiment of the present invention is corrected.
[Explanation of symbols]
1 mesh generation device, 2 node generation unit, 21 part boundary upper node generation unit, 22 part internal node generation unit, 3 element generation unit, 31 quadrilateral element creation unit, 32 triangle / quadrature element creation unit, 33 conversion to quadrilateral element Part, 4 element shape correction part, 51, 52, 53 part, 61 contour boundary, 62, 63 common boundary, 71 boundary upper node, 72 part inner node, 81 square element, 82 triangular element, 83 square element, 91 small square element

Claims (3)

In the mesh generation method for the finite element method analysis that divides the analysis target region to form a plurality of parts and divides the plurality of parts into meshes,
The boundary nodes on the boundary and the common boundary are initially divided into coarse meshes by equally dividing one side of the boundary,
When the number of nodes on the boundary on the common boundary is different between the adjacent parts, the average value of the number of nodes on the boundary on the common boundary of the two parts is adopted, or the boundary that is either larger or smaller Adopting the number of upper nodes, generating the upper boundary node modified to the position where the common boundary line segment is equally divided,
Generating a node in the part in which a rectangular mesh mesh having a rectangular shape is formed in the part;
Create a square element using the nodes in the part,
Create triangular and quadrilateral elements that form a coarse mesh mesh with the nodes on the boundary and the nodes in the part close to the nodes;
A quadrilateral element of the coarse mesh mesh is divided into four, and a subdivided node that divides the triangular element into three is generated;
A mesh generation method comprising: converting the quadrilateral element or the triangular element into a small quadrilateral element by the subdividing nodes to form a dense mesh mesh . In a mesh generation apparatus for finite element information analysis comprising means for dividing a region to be analyzed to form a plurality of parts and means for subdividing the divided parts into meshes,
When the boundary boundary and the boundary boundary node on the common boundary are initially divided into a coarse mesh shape by equally dividing one side of the boundary boundary, the number of nodes on the boundary on the common boundary is different between the adjacent parts, The average value of the number of nodes on the boundary on the common boundary of both parts is adopted, or the number of nodes on the boundary, whichever is greater or smaller, is adopted, and the line segment of the common boundary is equally divided. A node generator comprising: means for generating the corrected node on the boundary; and means for generating a node in the part in which a square-shaped coarse mesh mesh is formed in the part ;
Means for creating a quadrilateral element using the nodes in the part, means for creating a triangular element and a quadrilateral element that form a coarse mesh-like mesh by the nodes on the boundary and the nodes in the part close to the node, and the coarse mesh A quadrilateral element of the mesh mesh is divided into four, and a subdivided node that divides the triangular element into three is generated, and the subdivided node converts the quadrilateral element and the triangular element into a small quadrilateral element to form a dense mesh mesh. mesh generation apparatus characterized by comprising a further comprising element generator and means.   The mesh generation device according to claim 2, further comprising an element shape correcting unit that rearranges the subdivided nodes of the small square element to correct the shape of the small square element.

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