JP3516129B2 - Analytical mesh density control device - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a CAE system for optimizing and rationalizing design work by numerical simulation using a computer, and particularly for analysis generated from two-dimensional and three-dimensional shape models to be analyzed. The present invention relates to a device for automatically controlling the density of meshes.

[0002]

2. Description of the Related Art There are the following five major conventional mesh density control methods for analysis.

(1) For the Delaunay divided mesh,
Interactively specify the area where you want to roughen the mesh, and specify the number of deleted nodes in the target area. Then, the boundary nodes of the polygonal area after the node deletion are divided into triangle (tetrahedral) groups while ensuring Delaunay division, thereby roughening the elements in the specified area. Regarding this, JP-A-7-219
977.

(2) A triangle whose coarseness and fineness is controlled by connecting the adjacent grid points of the orthogonal mesh used in the difference method based on the input mesh connection condition to make the mesh rough and then inserting the hypotenuse. This is a method of generating a mesh. Regarding this, JP-A-8-29
It is described in Japanese Patent No. 2938.

(3) When creating a coordinate grid in a divided analysis area, the coordinate grid lines displayed on the screen are interactively deleted to roughen the generated mesh, or inserted to make the generated mesh finer. It is a method of controlling the density of the generated mesh by adding a supporting means for This is described in JP-A-4-679.

(4) In a model in which a portion requiring analysis accuracy needs to be moved due to a change in analysis condition, element line segments are divided into halves or returned to the original state so that the mesh density is locally reduced. Is a method of controlling. For this, see ICTAM96 "An Unstructured Adaptiv
e Mesh Navier-Stokes Solution Procedure
for Predicting Confined Explosions "(I.
J. Connell, J. K. Watterson et al.).

(5) When the analytical calculation is performed, the mesh is made coarse by repeating the volume coupling of each contact, and the elements around the contact are finely divided based on the position where the constituent line segment of each contact peripheral element is divided into two. This is a method of controlling mesh density by dividing the mesh. About this, "Commercial C
Analysis and verification using FD code CFX-5 ”Seiichi Kawabe (A
EA Technology Co., Ltd.), CFD software performance comparison, No. 9790 JSME SYMPOSIUM,
p. 109-119, 1997-11.

[0008]

The conventional automatic mesh generation method has the following problems.

The method (1) is a method of interactively specifying the number of nodes to be deleted / inserted from within the specified area, and in order to obtain a desired element size, the resultant mesh is predicted and deleted / inserted. It is necessary to repeat the operation of inputting the number of nodes / positions and confirmation of the generated mesh. It is not possible to directly specify the target element size in the specified area and automatically change the mesh until the average size of the elements in the area reaches the specified value.

The method (2) meets the condition that the system user inputs the vertical and horizontal adjacent grid points of the orthogonal mesh created in the process of inserting the hypotenuse to generate the triangular mesh based on the aspect ratio of the grid spacing. However, it is difficult to apply it to the roughening of the three-dimensional unstructured mesh (tetrahedron) that has already been generated and has irregular arrangement of nodes.

The method (3) is a method of controlling the density of the generated mesh by thinning out and interpolating the orthogonal coordinate grid lines of the coordinate grid created for generating the mesh in the analysis area. It cannot be applied to the case where the number of nodes or the positions of the generated unstructured mesh (triangle and tetrahedron) is directly changed to roughen the generated mesh.

The method (4) is a method of partially making the mesh finer or coarser in accordance with the movement when a portion requiring analysis accuracy moves, such as in the analysis of a phenomenon that changes with time. If you want to roughen the mesh, register the history of dividing the element line segment in half when subdividing, and for the part where you do not need the fine mesh,
It uses the method of merging the halved elements based on the registered information and restoring them. This method requires subdivision history information, and thus requires a large amount of calculation storage capacity when the number of elements increases.

The method (5) has the same purpose as that of (3), and can perform more local processing than (3). But,
The system user directly specifies the area that you want to control the density,
It is difficult to control the mesh density of the target area.

An object of the present invention is to solve the above problems and efficiently generate an analysis mesh for reducing the analysis cost.

[0015]

[Means for Solving the Problems] The above-described object is a display means for displaying on screen a mesh having triangles or tetrahedra as elements, which is generated on a shape model for analysis formed in a computer as a set of numerical data. A means for designating the area of the mesh to be roughened on the shape model displayed on the screen by inputting coordinate values from a mouse or a keyboard, and a target element relating to the size of each element included in the designated area. Means for inputting the dimension, until all the elements in the specified area are equal to or larger than the input target element dimension,
Any one of (2), (1) by matching at least two nodes constituting the element in the designated area to reduce the number of nodes and the number of elements, only the mesh in the designated area is roughened, and the result Means for outputting and displaying on the display means, (2) removing an arbitrary plurality of nodes in the designated area to delete elements in the area, inserting nodes smaller than the number of removed nodes into the area, and then inserting points And connect each area boundary configuration surface to generate a new element, and reduce the number of nodes and the number of elements so that all the newly generated elements in the specified area are equal to or larger than the input target element size, so that only the mesh in the specified area is It is achieved by providing a means for roughening and outputting the result to the display means for display.

The shape of each element after roughening the mesh is judged based on a pre-specified scale, and among the elements generated by roughening the mesh, the judgment result based on the scale is inferior to the initial element shape. If there is, the mesh shape is controlled by changing the combination of the matching nodes, changing the number of nodes and the number of nodes to be removed from the specified area, and changing the position of the newly inserted node, and after roughening the mesh. Also, it is possible to generate a mesh composed only of element shapes that are equal to or better than those before roughening the mesh.

A region where many elements smaller than the target element size input by the system user exist for a portion where the error or gradient of the analysis result obtained from the triangular or tetrahedral mesh generated on the shape model for analysis is small. May be provided, and a means for designating the obtained area as an area for roughening the mesh may be provided.

Instead of designating the range of the region where the mesh is made coarse, the system user designates the region where the fine mesh is generated when generating the mesh on the shape model for analysis, and generates the designated fine mesh. A region other than the region may be designated as a region in which the mesh is automatically roughened.

As a scale for judging the shape of each element, there are, for example, a length aspect ratio and an angle aspect ratio. For these, a reference value (lower limit value) is set in advance, and the reference value is lit. You can determine the superiority or inferiority.

In the present specification, "aspect ratio of length" means the ratio of the minimum line segment length to the maximum line segment length of the target element (minimum line segment length / maximum line segment length), "angle aspect ratio". "
Is the ratio of the minimum angle between two adjacent line segments of the target element in the case of a triangular mesh, and the ratio between the minimum angle of two adjacent planes of the target element and the maximum angle of two adjacent planes of the target element in the case of a tetrahedron. (Both are minimum angle / maximum angle), and the set value range is 0 to 1.0, respectively. The "target element size" is
It is the minimum length of the element edge line that does not depend on the shape.

[0021]

BEST MODE FOR CARRYING OUT THE INVENTION 1. Overall System Configuration and Processing Procedure FIG. 1 is an overall flowchart of the mesh generation method of this embodiment. An embodiment of the present invention will be described with reference to FIG. In this embodiment, a storage means for storing data, a calculation means for performing calculation processing, an input means for inputting data and work instructions, an output means for outputting processing results, and a display means for displaying images and numerical data. It is implemented by an apparatus configured to include. In the present embodiment, the numerical data forming the shape model is input using the keyboard 101b and the mouse 101c, and the shape model is formed in the computer, which is a computer, but it is already input to another computer. Numerical data forming the shape model may be used. In that case, it is desirable that the above device is connected to the computer and configured to perform real-time processing online.

(Procedure 1) A shape model is generated in the device based on the numerical data input by the system user using the keyboard 101b or mouse 101c which is the input device of the device, and is displayed on the display 101a which is the display device. The generated shape model is displayed. The system user uses the keyboard 101b for the created geometric model.
The target element size and the number of line segment divisions are input from (ST1).

(Procedure 2) Based on the data of (Procedure 1), the initial mesh automatically generated by the system and the analysis result are displayed on the display 101a of the input / output device 101 (ST2).

(Procedure 3) In the mesh displayed in (Procedure 2), if a finer mesh than necessary is generated in a portion that does not require high analysis accuracy, the system user may use the keyboard 101b or mouse. A region in which the mesh is to be roughened is designated using 101c (ST3).
The area is specified by specifying the range using coordinate values from the mouse or keyboard, or specifying the element group whose size is to be increased.

(Procedure 4) A menu for inputting the lower limit target element size for determining the minimum size of the element in the area where the mesh is roughened is displayed on the display 101a,
The system user uses the keyboard 101 of the input / output device 101.
Using b or the mouse 101c, the threshold value regarding the generated element is interactively input and changed (ST4). FIG. 2 shows an example of a screen for interactive input. The threshold setting items are
Aspect ratio of length and angle of each element (3
a) and the target element size (3b), etc. (FIG. 3). Further, in the screen display example of FIG. 2, when the button 2a is turned ON and the area is designated, the mesh coarsening process is executed for the inside of the designated area, and when the button 2a is turned OFF and the area is designated, the designated area is specified. The mesh coarsening process is executed for the outside.

(Procedure 5) The method described in Chapter 2 is repeated until all the elements in the designated area or the designated shape in (Procedure 3) above the target element dimensions input and stored in (Procedure 4). The mesh is regenerated by and the result of roughening the elements in the specified area or in the specified shape is displayed (ST
5).

When the mesh is further roughened after the above procedure is completed, the procedure returns to (Procedure 3).

When the above procedure is incorporated into an analysis program, an area for roughening the mesh is searched according to the gradient and error of the analysis result obtained from the initial mesh generated in (Procedure 1), and the procedure of (Procedure 4) and (Procedure 5) Execute the process.

2. Basic algorithm for roughening mesh The present invention is based on a method for partially roughening a mesh by reducing the number of element constituent nodes included in a mesh generated in an arbitrary region to reduce the number of elements in the region. There is. There are two methods for reducing the number of nodes in the area. Both are executed in the procedure 5 by the computing means. Each method will be described. When searching a region in which the mesh is to be roughened according to the gradient or error of the analysis result obtained from the initial mesh generated in (procedure 1), this operation is also executed in the procedure 5 by the calculating means.

2.1 Node-Coupling Coarse Mesh Generation Algorithm This method is a line segment composed of two nodes by matching the coordinate values of two nodes forming one arbitrary element to form one node. To reduce the number of peripheral elements sharing the line segment. FIG. 4 is a flowchart of the method, and FIG. 5 is a two-dimensional triangular mesh.
The following shows how the element shape changes when one arbitrary node is connected. FIG. 5A shows the initial mesh shape, and FIG. 5B shows the mesh shape after the node connection.

The area specified in Chapter 1 (Procedure 2) (see FIG. 5)
The flow of nodal connection will be described for one nodal point (5a1) in the (a) overall shape.

(Join procedure 1) Target node (5a) to be joined
1) is determined, a flag indicating that the data has been processed as a connection target node is set in the data of the node, and all the elements (triangles) including the node (5a1) are searched (inside the thick line 5b in FIG. 5),
It is registered as an element group M (target element group) related to the combination (ST1 to ST2). As a general rule, the joint target node is a point completely inside the previously specified area.

(Joining procedure 2) The nodes included in the target element group M are searched in order, and the point having the shortest distance to the node (5a1) to be joined is one as the node to be joined (in this case, 5a).
2) A flag indicating that the node has been selected and processed as the node to be joined is set in the data of the node (5a2) (ST
3). The reason why the point having the shortest distance from the connecting node (5a1) is selected is to reduce the distortion of the resulting mesh. You may make it search for the node contained in a target element group in order from the element whose length of either side is less than the target element dimension input previously.

(Joining procedure 3) The coordinate values of the node 5a1 and the node 5a2 are matched. The position to be matched is determined to be the position of 5a2 when the node 5a2 is a node on the area boundary, and the position where the line segments 5a1 and 5a2 are internally divided (intermediate point as an initial value) otherwise (ST4).

(Joining procedure 4) Among the target element group M (elements within the thick line 5b), the element (shaded element in FIG. 5 (a)) including both the joint node 5a1 and the jointed node 5a2 is the same as the above ( A line segment that is degenerate when the nodes 5a1 and 5a2 are joined in the joining procedure 3) is shared. Since the area (volume) of these elements becomes 0 due to the node connection, they are not registered when the elements are regenerated. An element including either the node 5a1 or the node 5a2 updates the coordinate value of the corresponding node for each element to the combined position (ST5 to ST6). At this time, if the node to be combined is on the area boundary, all the elements including the node are searched, and the position of the node that is the movement target is updated for them.

(Joining procedure 5) The volume and aspect ratio of each element of the newly generated element group (inside the thick line 5c of FIG. 5B) are obtained. As a result, the distortion is large (the aspect ratio is input first and is smaller than the specified aspect ratio)
If the element is included, an unchecked node in the target element group (a node for which joining procedures 3 to 5 have not been executed)
Whether or not there is a node to be combined is determined by the presence or absence of a node for which the flag is not set. If there is a node for which the target node to be joined is not flagged, the procedure returns to (joining procedure 2) and another node is selected again as a joined node (ST7 to ST
9), the process after (combining procedure 3) is repeated. If the aspect ratio of the newly generated element group is larger than the specified aspect ratio, the procedure proceeds to the combining procedure 7.

(Joining procedure 6) Even if all the nodes are checked in the above-mentioned (joining procedure 5), if a large distortion element remains, mesh coarsening using that node (in this case, node 5a1) is not executed. In (ST10), the process proceeds to ST13.

(Join procedure 7) Register newly created element attributes and adjacency relationships (ST11 to ST12). At this time, the state of each element adjacent to the element group (element group within the thick line 5c) is also updated (because the condition of which element is adjacent is changed).

The above procedure (combining procedure 1) to (combining procedure 5) is repeated until there is no element whose size in the designated area is equal to or smaller than the target element size registered in Chapter 1 (procedure 3).
Alternatively, the elements are partially roughened by sequentially performing processing on arbitrary nodes in the region until all the nodes of the region are checked.

FIG. 6 shows an example in which a plurality of nodes are sequentially connected to the same area as in FIG. 5 to make the elements in the area coarse.

In each step of FIG. 6, the shaded element group is the same connection-related element group as the element group M in the thick line 5b of FIG. The state in which the node 6a1 in FIG. 6A is connected to the node 6a2 is shown in FIG. 6B and the node 6b in FIG. 6B.
6 shows the state in which 1 is connected to the node 6b2, and the state in which the node 6c1 in FIG. 6 (c) is connected to the node 6c2 is FIG.
(D) of FIG. 6 and (e) of FIG. 6, which is the final result, is a state in which the node 6d1 of FIG. In the initial state of FIG. 6A, the designated region is composed of 24 elements, whereas in the final result of FIG. 6E, the designated region is reduced to 16 elements, and the mesh in the region is coarse. The processing for roughening the mesh shown in FIG. 6 is also all automatically executed by the arithmetic means according to the procedure shown in FIG.

2.2 Node Deletion / Insertion Type Mesh Generation Algorithm This method removes an arbitrary number (n) of nodes, deletes the element group sharing each removed node, and deletes n elements in the space after deletion. This is a method of reducing the number of elements by inserting the following nodes, connecting the inserted nodes and each line segment (plane) forming the spatial boundary, and regenerating a new element group. FIG. 7 shows a flow chart of the present method, and FIG. 8 shows how the element shape changes when a two-dimensional triangular mesh is targeted and one node is inserted after one arbitrary node is deleted to regenerate the element.

The flow of node deletion / insertion will be described for the area (entire shape in FIG. 8A) designated in Chapter 1 (Procedure 2).

(Delete / insert procedure 1) Node to be deleted (8a
1) and (8a2) are selected, a flag indicating that the node has been processed as a deletion target node is set, and nodes (8a1) and (8a) are set.
All elements including 2) are searched (inside of thick line 8b in FIG. 8) and registered as an element group related to element regeneration (ST1 to ST.
3). In principle, the nodes to be deleted are completely inside the region, and any two points are selected from the node pairs directly connected to each other by line segments.

(Deletion / insertion procedure 2) All the nodes to be deleted in (deletion / insertion procedure 1) and all elements (shaded triangles in FIG. 6A) included in the target element group Delete (ST4). Deletion in this case means deleting the record of the target element from the element information registration table in which the element information is registered, and the coordinate values of the boundary constituent nodes of the element group within the thick line 8b are changed. Instead, the polygonal shape as shown in FIG.

(Delete / Insert Procedure 3) The positions of the nodes to be inserted inside the polygon generated in (Delete / Insert Procedure 2) are set (ST5). In the case of the example in FIG. 8, since the number of deleted nodes is two, 2-1 = 1 node positions are set. The insertion point position is within the range enclosed by the deleted nodal coordinate values (in the case of two points, on the line segment), and the area of all regenerated elements is 0.
The position will be larger. FIG. 9 shows an example in which the element area becomes negative. FIG. 9 shows a case where a new node is to be inserted on the line segments 9a and 9b in the element group including the deletion target points 9a and 9b. If the new node is set to the position of 9c, the elements 9a,
The areas of 9c and 9e (shaded elements) become negative. In this case, the node 9c is determined to be the position between the point 9d and the point 9a, which is the intersection of the line segments 9a and 9b and the extended line of the points 9e and 9f.

(Deletion / insertion procedure 4) The new insertion node (8c) is sequentially connected to each line segment forming the polygonal boundary (boundary indicated by the thick line 8d) in FIG. Is generated (ST6).

(Deletion / insertion procedure 5) The volume and aspect ratio of each element in the newly generated element group are obtained. As a result, if an element with an aspect ratio less than the threshold value specified in Chapter 1 (Procedure 4) has been generated, or if an element with a volume of 0 has been generated, the insertion node position within the movable range Change and return to (Deletion / insertion procedure 4) (ST
7-ST8). Here, when three or more nodes are deleted from the area, if only one point is inserted and a negative element is generated at any position of the insertion point, connection with the insertion point results in a negative element. Do not execute the process for the node on the boundary line segment where the element of is generated. As a result, when a polygonal area of a quadrangle or more remains, one more point is additionally inserted into the polygonal area, and the procedure returns to (deletion / insertion procedure 3). At this time,
The number of points to be inserted is up to the number of deleted points minus 1 (ST9).

(Delete / Insert Procedure 6) If the node position could not be changed in the above (Delete / Insert Procedure 5), the number of deleted nodes is incremented by one and the procedure returns to (Delete / Insert Procedure 1). The procedure up to the insertion procedure 4) is repeated (ST10).

(Deletion / insertion procedure 7) When an element whose aspect ratio is more than a specified threshold value and whose volume is all positive is created in the target area, newly created element attributes and adjacency relations are registered. . At this time, the state of each element adjacent to the regenerated mesh (element group within the thick line 8d) of FIG. 8D is also updated (ST11 to ST12).

By following the above-described (deletion / insertion procedure 1) to (deletion / insertion procedure 7), if the element size in the designated area is equal to or smaller than the target element dimension registered in Chapter 1 (procedure 3), The element is partially roughened by running sequentially through any of the nodes in the region until it is exhausted.
FIG. 10 shows an example of repeating the deletion / insertion of nodes in the same area as in FIG. 8 to roughen the elements in the area.

In each step of FIG. 10, the shaded element group is the regeneration target element group. After deleting the nodes 10a1 and 10a2 of FIG. 10A, the node 10b is inserted into the midpoint of the line segment connecting the two nodes to regenerate the element, and the state of FIG. The nodes 10c1 and 10c2 in (b) are selected as deletion targets, the element group including the two nodes is shaded, and the regeneration target element group is displayed (c) in FIG. 10 and (c) in FIG. ) Node 10c1 and node 1
After deleting 0c2, the node 10
The state in which d is inserted and the element is regenerated is (d) of FIG.
1E, the node 10e1 and the node 10e2 in FIG. 10D are selected as deletion targets, and the element group including the two nodes is shaded to display the regeneration target element group.
In FIG. 10 (f), which is the final result, after deleting the node 10e1 and the node 10e2 of (e) of 0, the node 10f is inserted into the midpoint of the line segment connecting the two nodes, and the element is regenerated. is there. In the initial state (a) of FIG. 10, the designated area (inside the thick line frame) is composed of 24 elements, whereas in the final result (f) of FIG. It's getting rough.

By any of the methods described in Chapter 2, the magnitude of the distortion of the newly created element is determined.
If the newly generated element includes an element with large distortion, the position of the joint node or the insertion node after joining is moved to near the center of gravity of the target element group to correct the distortion. As a value for determining the degree of distortion, for example, the aspect ratio (aspect ratio of length, aspect ratio of angle) of each element is used.

When the method of the present invention is applied to a three-dimensional model, the triangle in the explanation in Chapter 2 is replaced with a tetrahedron and the boundary line segment is replaced with a boundary surface. Figure 3 shows the method in section 2.1.
Any one node (11
An example of partial change in the element connection state when a) is connected to the node (11b) is shown. Before connecting the nodes ((a) of FIG. 11), the part composed of four elements is connected after the nodes connecting (see FIG. 1).
In 1 (b), the number is reduced to 2 elements.

[0055]

EFFECTS OF THE INVENTION In the meshes generated in the two-dimensional and three-dimensional shape models to be analyzed, the mesh of the portion that is less important in terms of analysis accuracy is roughened to reduce the total number of elements, thereby shortening the analysis calculation time. And it is possible to subdivide the mesh of a portion that requires analysis accuracy without increasing the total number of meshes, and it is possible to efficiently generate a mesh for accurate analysis.

[Brief description of drawings]

FIG. 1 is an overall flow chart of a mesh density control method for carrying out the present invention.

FIG. 2 is a screen display example of a target element size menu in the embodiment shown in FIG.

FIG. 3 is a menu for setting element target element dimensions and a result display method in the embodiment shown in FIG.

FIG. 4 is a flowchart of a method for roughening a mesh by node connection in the embodiment shown in FIG.

5 is an example of a change in the triangular mesh shape in which one-node connection is executed according to the procedure of FIG.

6 is an example of a mesh shape change when the node connection in FIG. 5 is repeated four times.

FIG. 7 is a flowchart of a method for roughening a mesh by deleting / inserting nodes in the embodiment shown in FIG.

8 is an example of a change in the triangular mesh shape in which node deletion / insertion is executed according to the flow of FIG.

FIG. 9 is an example in which an element having a negative area is generated depending on the position of an insertion node.

10 is an example of mesh shape change when the node connection in FIG. 8 is repeated three times.

11 is a flow chart of FIG. 7 in which one-node connection is executed 4
It is an example of a change in the shape of a face piece mesh.

[Explanation of symbols]

2a button 3a Aspect ratio 3b Target element size 101a display 101b keyboard 101c mouse

Front page continuation (72) Ichiro Nishigaki Ichiro Nishigaki 502 Jinrachi-cho, Tsuchiura-shi, Ibaraki, Ltd. Inside the Mechanical Research Laboratory, Hitachi, Ltd. (56) Reference JP 6-259404 (JP, A) JP 7-219977 (JP , A) (58) Fields investigated (Int.Cl. ⁷ , DB name) G06F 17/50 612

Claims (6)

(57) [Claims] 1. Display means for displaying on a screen a mesh having triangles or tetrahedra as elements, which is generated on a shape model for analysis formed in a computer as a set of numerical data, and the shape model displayed on the screen. For the upper mesh, a means to specify the area to roughen the mesh,
Means for inputting the target element size of each element included in the specified area to the computer, and at least two nodes constituting the element in the specified area until all the elements in the specified area are equal to or larger than the target element size. And the number of elements and the number of elements are reduced to roughen the mesh in the designated area, and the result is output to the display unit to be displayed and displayed. 2. The analysis mesh density control device according to claim 1, wherein the shape of each element after roughening the mesh is determined based on a prespecified scale.
When there is an element whose judgment result based on the scale is inferior to the initial element shape in the elements generated by roughening the mesh, the generated mesh shape is controlled by changing the combination of the matching nodes, And a means for generating a mesh consisting only of element shapes that are equal to or better than those before roughening the mesh. 3. Display means for displaying a mesh having triangles or tetrahedra as elements on a shape model for analysis formed in a computer as a set of numerical data, and a shape model displayed on the screen. For the upper mesh, a means to specify the area to roughen the mesh,
Means for inputting the target element size of each element included in the specified area into the computer, and removing any plural nodes in the specified area until all the elements in the specified area are equal to or larger than the target element size. Operation to delete elements in the region,
By reducing the number of nodes and the number of elements by repeating the operation of inserting fewer nodes than the number of removed nodes into the area, and the operation of connecting the insertion point and each area boundary line segment or face to generate elements. And a means for displaying the result by displaying the result on the display means. 4. The analysis mesh density control device according to claim 3, wherein the shape of each element after the mesh is roughened is determined based on a prespecified scale.
If there is an element whose judgment result based on the scale is inferior to the initial element shape among the elements generated by roughening the mesh, the nodes to be removed from the specified area, the number of nodes to be changed, and the positions of newly inserted nodes And a means for controlling the generated mesh shape to generate a mesh consisting only of element shapes that are equal to or better than those before roughening the mesh even after roughening the mesh. The analysis mesh density control device. 5. The analysis mesh density control device according to claim 1, wherein an error or a gradient of an analysis result obtained from a triangle or tetrahedral mesh generated on a shape model for analysis is small. A mesh for analysis characterized by including means for searching a region where many elements smaller than the target element size input by the system user exist for the part and specifying the range of the obtained region as a region for roughening the mesh. Density control device. 6. The analysis mesh coarse / dense control device according to claim 1, wherein a mesh is generated on a shape model for analysis, instead of means for designating a range of a region in which the mesh is to be roughened. 2. An analysis mesh coarse / fine control device, characterized in that it further comprises means for designating a range other than a region for which a system user has designated generation of a fine mesh as a region for roughening the mesh.