JPH02230379A - Mesh generating system by mapping method - Google Patents

Abstract

PURPOSE:To easily perform an operation and confirmation in the generation of a mesh by providing an on-external side node generating part, an on-side node coordinate transformation part, a mesh generating part, a physical coordinate transformation part, and an input/output part. CONSTITUTION:The on-external side node generating part 1-4 generates an on-external side node based on the instructions of the number of division and the position of division on an external side constituting an external block, and the on-side node coordinate transformation part 1-5 transforms a coordinate in the physical coordinate system of a node on the external side generated by the on-external side node generating part 1-4 to the coordinate in a normal coordinate system. The mesh generating part 1-6 performs the generation of the mesh in the normal coordinate system based on the coordinate in the normal coordinate system of the node on the external side transformed by the on-side node coordinate transformation part 1-5. Furthermore, the physical coordinate transformation part 1-7 converts the mesh in the normal coordinate system generated by the mesh generating part 1-6 to the mesh in a physical coordinate system, and the input/output part 1-10 performs the instruction of the operations for those processings and the confirmation of display, etc. Thereby, the operation for the generation of the mesh for complicated external shape can be simplified, and a human mistake in its operation can be evaded.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a mesh generation method using a mapping method, and in particular to generating a mesh for an external shape on a graph ink display when creating data for an analysis system using a finite element method. Concerning mesh generation method 2 using mapping method (specifying coordinates related to meshes). [Prior Art] Generating a mesh is an important function in creating data for an analysis system using the finite element method, and the generated mesh has a great influence on the performance of the entire analysis system.

There are many methods for generating this mesh, but the mesh generation method using the mapping method is the most common method.

The conventional mesh generation method using this type of mapping method is shown below. I was doing some processing.

First, the model shape (the external shape to be analyzed in the analysis system using the finite element method) is
er Aided Design) system)) into several small areas (if the model shape is a two-dimensional shape, it is a quadrilateral area;
If it is a dimensional shape, it is divided into hexahedral areas (this division is called block division). The small areas divided into blocks in this way (called external blocks) are the units of mesh generation. Note that the external block does not have to be a quadrilateral or hexahedron in the original sense composed of straight lines, but may be a topological quadrilateral or hexahedron (the external block is based on the physical coordinate system (x-y-
z space), and the outline sides that make up the outline block are straight lines. (formed from circular arcs, spline curves, etc.)
．． Next, as data regarding the outline block, the coordinates of each vertex, the coordinates of the intermediate point necessary to approximate each outline edge, and the number of divisions on each outline edge are obtained. Based on these data, each contour side is formed into a linear to cubic curve, and the contour block in the physical coordinate system is transformed into a normal coordinate system (ξ
−η-ζ space. −1≦ξ, η, ζ≦1. Model shape is 2
If the model shape is a dimensional shape, it will be represented by a square in the ξ-η plane, and if the model shape is a three-dimensional shape, it will be represented by a cube in the ξ-l-ζ space.

The normalized external block is divided into equal parts, nodes are set on the external sides, and opposing nodes on opposite sides are connected with straight lines to subdivide into rectangular small areas to generate a mesh. Furthermore, the mesh in the normal coordinate system generated in this way is mapped onto the physical coordinate system to generate a mesh in the physical coordinate system.

By performing the above-mentioned processing (operation) on all external blocks, the generation of all meshes is completed. (Problems to be Solved by the Invention) In the mesoche generation method using the conventional mapping method described above, it is necessary to enter the division on each contour edge constituting the contour block in advance as a parameter from a keyboard, etc. The number of divisions must be set to the same number, so when the number of external blocks increases, the operation (entering the number of divisions, etc.) becomes complicated. It is not easy to check whether the block is set to 0 or not, which makes it easy to make mistakes.Also, since the block can only be divided into equal parts on each side of the block, it is difficult to check whether the block is set to It has the disadvantage that it becomes difficult to take into account the coarse and dense representation of the model shape and to properly set nodes as points of interest during analysis using the finite element method, which poses a practical problem (difficult to put into practical use). In view of the above-mentioned points, it is an object of the present invention to set the number of divisions on each outline side of an outline block interactively while actually checking it on the screen, instead of setting it in advance by inputting parameters from a keyboard or the like. Generate nodes (nodes on the outline side) and generate a mesh (identify the coordinates of the nodes that make up the mensch) using the mapping method based on the nodes.
It is now possible to consider the density of complex model shapes and to place arbitrary nodes according to the user's intentions (node placement that reflects the points of interest during analysis using the finite element method), making operations and confirmation during mesh generation easier. The objective is to provide a mesh generation method using a mapping method that facilitates the [Means for Solving the Problems] The mesh generation method using the mapping method of the present invention is based on instructions such as the number of divisions and division positions on the contour sides constituting the contour block, and generates nodes on the contour sides. A node generation unit, a side-on-side node coordinate conversion unit that converts the coordinates of the node on the outline side generated by the outline-side node generation unit in the physical coordinate system to coordinates in the normal coordinate system, and this side-on-side node coordinate conversion unit. A mesh generation section generates a mesh in the normal coordinate system based on the coordinates in the normal coordinate system of the nodes on the contour side transformed by the section, and a mesh in the normal coordinate system generated by this mesh generation section is converted to physical coordinates. A physical coordinate conversion unit that converts the system into a mesh, and the external edge/node generation unit. The above-mentioned side node coordinate conversion part. It has a human output unit that performs operation instructions and confirmation displays for processing in the mesh generation unit and the physical coordinate conversion unit.

[Effect]

In the mesh generation method using the mapping method of the present invention, the edge-on-the-edge node generation unit generates nodes on the edge of the edge based on instructions such as the number of divisions and division positions on the edge of the edge constituting the outer block, and coordinates the nodes on the edge. The conversion unit converts the coordinates in the physical coordinate system of the nodes on the contour side generated by the node generation unit on the contour side into the coordinates in the normal coordinate system, and the mesh generation unit converts the coordinates of the node on the contour side generated by the node generation unit on the contour side into the coordinates in the normal coordinate system, and the mesh generation unit converts the coordinates of the node on the contour side generated by the node generation unit on the contour side into coordinates in the normal coordinate system. Generates a mesh in the normal coordinate system based on the coordinates of the nodes on the sides in the normal coordinate system, and the physical coordinate conversion section converts the mesh in the normal coordinate system generated by the mesh generation section to a mesh in the physical coordinate system. The input/output part is the node generation part on the outline side. Provides operational instructions and confirmation displays for processing in the edge-on-node coordinate conversion unit, mesh generation unit, and physical coordinate conversion unit. [Example] Next, the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of an embodiment of the mesh generation method using the mapping method of the present invention.

The mesh generation method using the mapping method of this embodiment consists of a contour side node generation unit 1-4 that generates nodes (nodes on the contour side) on the contour sides constituting the contour proc. Side-on-side node coordinate conversion unit 1- that converts the coordinates of the node in the physical coordinate system (physical coordinates) to the coordinates in the normal coordinate system (normal coordinates)
5, a mesh generation unit 1-6 that calculates the normal coordinates of the constituent nodes of each mesh based on the normal coordinates of the nodes on the contour sides (generates a mesh in the normal coordinate system), and a mesh generation unit 1
A physical coordinate conversion unit 1-7 that converts the mesh in the normal coordinate system generated by -6 to a mesh in the physical coordinate system (converts the normal coordinates of the constituent nodes of the mesh into physical coordinates), and It is configured to include an input/output section 1-10 that performs operation instructions, confirmation displays, etc.

The human output unit 1-10 executes processing in the same way as the keyboard 1-2 using a keyboard 1-2 for inputting processing execution instructions (commands), a method for generating nodes on the outline side, parameter values, etc., and an attached stylus pen. Tablet 1-3 for manually giving instructions on how to generate nodes on the contour sides, etc., and the model shape. It is configured to include a graphic display 1-4 for displaying the contour sides and nodes on the contour sides, and displaying the generated meshes.

FIG. 2 shows conversion information (mapping relationship information; vertices and intermediate points for specifying external edges; It is a figure which shows an example of the conversion information regarding (there exist two intermediate points in order to approximate an outline side by a linear to cubic curve).

The vertices of any external shape (3D shape) on the physical coordinate system (
Let the physical coordinates of 1) to (8) and intermediate points (9) to (32) be (xi, yi, zi) (+=1 to 32), and the vertex (
If the normal coordinates of 1) to (8) and intermediate points (9) to (32) are (ξi.ηi, ζi), the relationship between them is as shown in the equation in FIG.

Here, if the external shape on the physical coordinate system is a two-dimensional shape, only vertices (1) to (4) and intermediate points (9) to (16) are used, and ζ = -1 is fixed. The information shown in FIG. 2 is used.

Next, the operation of the mesh generation system using the mapping method of this embodiment configured as described above will be explained.

The node generation unit 1-4 on the contour side sets the designation of the contour side on which the node on the contour side is to be generated, the generation method of the node on the contour side, parameter values, etc. from the human output unit l-10.
Based on the settings, nodes on the outer edges are generated and displayed on the graph ink display l-1.

The methods of generating nodes on the contour sides include dividing the contour sides equally and generating them by dividing the contour sides in equal proportions. There are two methods: one is to generate by dividing the outline edges arithmetic, the other is to generate by specifying all the division ratios of the outline edges.Additionally, some of these methods can be combined to create a grid between the nodes on the outline edges that have already been generated. Furthermore, nodes on the contour sides can also be generated. This makes it possible to generate nodes on the contour sides at arbitrary intervals. The side node coordinate conversion unit 1-5 converts the physical coordinates of the nodes on the contour sides of the contour sides constituting the contour block for each contour block into a normal coordinate system (conversion is performed using the information shown in FIG. 2). (At this time, mapping relationships related to nodes on the outline sides are created), and the number of divisions, division positions, etc. are determined as data necessary for mesh generation, and are delivered to the mesh generation unit 1-6. The mesh generation unit 1-6 connects opposite sides of the nodes on the outer side with straight lines in the normal coordinate system, and subdivides the block into small regions having the same shape as the outer block (this small region corresponds to the mesh). , a mesh is generated by finding the normal coordinates of nodes, which are grid points, generated by this subdivision (the mesh is expressed by the nodes, which are grid points that make up the mesh). The physical coordinate conversion unit 1-7 converts the normal coordinates of the constituent nodes of the mesh generated by the mesh generation unit 1-6 into physical coordinates using the mapping relationship created by the side-on-node coordinate conversion unit 1-5 ( The mapped mesh in the physical coordinate system is displayed on the graphic display 1-1 in the input/output unit l-10 for the convenience of the user. Next, in addition to FIGS. 1 and 2, we will explain the specific operations of the mesh generation method using the mapping method of this embodiment.
This will be explained with reference to the figures. Here, mesh generation for a model shape 3-1 having a two-dimensional shape (including a curved surface in a three-dimensional space) as shown in FIG. 3 will be explained.

It is assumed that the model shape 3-1 is divided into two topological quadrilateral outline blocks B1 and B2. The external block B1 is composed of external sides LL, L5, L6, and L7. The external block B2 has an external side L2
, L3. It is composed of L4 and L7. Each outer side Ll-L7 has vertices P1 to P6 and intermediate points MPI to
It is expressed as a linear to cubic curve approximated by MP14. Based on the input from the input/output section 1-10, the node generation section 1-4 generates nodes on the contour side on all of the contour sides Ll-L7 (the display on the graphic display 1-1 does not proceed). Keyboard 1-2 and tablet while
l-3 provides input for generating nodes on the contour sides). In this case, the manner in which the nodes on the contour sides are generated includes the fourth
There are combinations of equal division, equal difference division, and equal division as shown in the figure (not limited to the number of divisions shown in Figure 4). Here, the outer shape side L2. For L3, L4, and L7, nodes on the outer edges are generated with equal division (the outer edges L2, L3, L4, and L7 are specified by the tablet console 1-3, and the keyboard 1-2 indicates that they are equally divided). and the number of divisions are input). Regarding the outline sides L5 and L6,
Nodes on the contour sides are generated by the arithmetic division (the tablet notebook 13 specifies the contour sides L5 and L6, and the keyboard 1-2 inputs the fact that it is an arithmetic division, the number of divisions, the initial value, and the arithmetic value). ). For the outer side L1, nodes on the outer side are generated by a combination of equal divisions (Tableno}1-3 creates the nodes on the outer side LL
is instructed, and the keyboard l-2 is used to equally divide the object into three equal parts to generate nodes on the outer side, and further, between each two points of the generated nodes on the outer side are equally divided into two or three equal parts. )
.

Through the above processing, nodes on the outline sides are generated on all the outline sides L1 to L7 (this state (model shape 3-
The state in which nodes on the contour sides are added to 1) can be easily confirmed on the graphic display l-1).

Next, based on the instruction of the external block B1 by the tablet 1-3 in the input/output unit 1-10, the vertices PIP2, P5 and P6 and intermediate points MPI, MP2 and MP9-MP14 locus 4
l! (physical coordinates) and the node array formed by the nodes on the contour sides of the contour sides Ll and L5 to L7 that constitute the contour block B1 are Nodal coordinate conversion unit 1-
It is retrieved by 5. The side node coordinate conversion unit 1-5 first calculates the sum of the distances of the node arrays of each outline side L1 and L5 to L7 (PI, P between each vertex).
2, the distance between P5 and P6) is set to 2, the start point of the node array is -1, and the end point is +1, and the physical coordinate system is converted to the normal coordinate system. As a result, the coordinate transformation of the nodes on the contour sides of the contour block B1 from the physical coordinate system to the normal coordinate system as shown in FIG. 5 is performed.

In the mesh generation unit 1-6, the nodes on opposite sides of the outline are connected by straight lines based on the nodes on the outline side that have been converted to the normal coordinate system (see the right diagram in Figure 5). Subdivision is performed into small areas of the same shape (quadrilateral) as the external block (the small area subdivided in this way is a mesh, and the grid points at this time become nodes), and the constituent nodes of each mesh are The coordinates (normal coordinates) of are found. In the physical coordinate conversion section 1-7, the mesh is generated by the mesh generation section 1-6 based on the conversion information between the physical coordinate system and the regular coordinate system regarding the external block Bl (information as shown in FIG. 2!!!). The normal coordinates of the constituent nodes of the mesh on the normal coordinate system are converted to physical coordinates, and a mesh in the physical coordinate system as shown in the left diagram of FIG. Graphic display 1-1 inside
(displayed on the screen and hit by users).

If the mesh in the physical coordinate system of the external block B1 displayed on the graphic display 1-1 is confirmed as described above and there is no problem, the external block B2 is designated by the tablet 1-3 and the external form described above is specified. A mesh is generated in the same way as the process for block Bl. As a result, mesh generation for all external blocks (outline blocks B1 and B2) is completed, and as a result, the model shape 3-2 after mesh generation in Fig. 3 is completed.
is obtained. Note that when the model shape is a three-dimensional shape, the model shape is treated as a set of external shapes (curved surfaces) of the two-dimensional shape, and a mesh, which is a small area of a hexahedron, is generated by repeating the above process. ．． [Effects of the Invention] As explained above, the present invention includes a node generation unit on an outline side, a node coordinate conversion unit on an edge, and a mesh generation unit. By providing a physical coordinate conversion unit and an input/output unit, operations for generating meshes for complex external shapes are simplified, reducing human errors in the operations, and reducing the user's thinking when generating meshes. Arbitrary node placement suitable for the process (intention) and analysis content of the finite element analysis system can be made for two-dimensional and three-dimensional external shapes (it also makes it easy to change the mesh generation mode). effective.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the configuration of an embodiment of the present invention, FIG. 2 is a diagram showing an example of conversion information (mapping-related information) between a physical coordinate system and a normal coordinate system, and FIG. Figure 1 shows an example of a model shape in which a mesh is generated using the mesh generation method using the mapping method. FIG. 5 is a diagram showing an example of how sides are divided; FIG. 5 is a diagram showing an example of how to transform between the physical coordinate system and the normal coordinate system regarding the external block in mesh generation method 2 using the mapping method shown in FIG. It is. In the figure, 1-1...Graphic display, 1-2...
Keyboard, 1-3...Table left, 1-4...Outline edge node generation unit, 1-5...Edge edge node coordinate conversion unit, 1-6...Methoche generation unit, 1-7. ...Physical coordinate conversion section, 1-lO...Input/output section, 3-1...Model shape, 3-2...Model shape after mesh generation. Fig.3

Claims (1)

[Scope of Claims] A contour side on-edge node generation section that generates nodes on the contour edge based on instructions such as the number of divisions and division positions on the contour side constituting the contour block; The side-side node coordinate conversion unit converts the coordinates of the nodes on the contour sides in the physical coordinate system into the coordinates in the normal coordinate system, and the normal coordinate system of the nodes on the contour sides converted by this side-side node coordinate conversion unit. a mesh generation unit that generates a mesh in a normal coordinate system based on the coordinates of the mesh, and a physical coordinate conversion unit that converts the mesh in the normal coordinate system generated by the mesh generation unit to a mesh in the physical coordinate system; Based on a mapping method characterized by having an input/output section that performs operation instructions and confirmation display for processing in the contour side node generation section, the side node coordinate conversion section, the mesh generation section, and the physical coordinate conversion section. Mesh generation method.