JP3545896B2 - Analysis mesh generator - Google Patents

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an apparatus for generating mesh data necessary for finite element analysis in a numerical analysis simulation of a structure or the like, and in particular, a hexahedral mesh and a tetrahedral mesh are mixed when analyzing a structure having a complicated shape. The present invention relates to an analysis mesh generation device for generating mesh data.
[0002]
[Prior art]
For example, when the strength of a structure is calculated by a finite element method using a computer, the analysis is performed by expressing a three-dimensional region to be analyzed as a collection of hexahedral or tetrahedral finite elements. The vertices of the finite element are connected to points called nodes, and adjacent elements are connected via the nodes. A collection of elements and nodes is called a mesh, and data representing this mesh is called mesh data. The mesh generation includes a method of generating a hexahedral mesh suitable for handling a simple shape and a method of generating a tetrahedral mesh suitable for generating a mesh in a region having a complicated shape. Conventionally, mesh generation has been performed using only one of a generation method using a hexahedral mesh and a tetrahedral mesh. In other words, if the accuracy of the analysis is prioritized, a hexahedral mesh must be used even if a great deal of effort is spent, and a tetrahedral mesh must be used to automatically generate the mesh even at the expense of the analysis accuracy. Was.
[0003]
If mesh generation can be performed in a state where hexahedral meshes and tetrahedral meshes are mixed, mesh data with high analysis accuracy can be generated with a small amount of labor. To realize this, there is a "method and apparatus for creating a mesh for analysis" disclosed in Japanese Patent Application Laid-Open No. 8-16629. In the mesh creation method shown here, after dividing the whole into a plurality of partial regions, a hexahedral mesh is created for each partial region, and a tetrahedral mesh is created for a portion where the hexahedral mesh could not be created. Then, in a region where the hexahedral mesh and the tetrahedral mesh are adjacent to each other, two tetrahedral meshes facing each other along one diagonal line of the hexahedral mesh are arranged on the surface of the hexahedral mesh.
[0004]
In addition, a quadratic hexahedral mesh and a quadratic tetrahedral mesh (each having a node at the center of the mesh ridge line) are used and are connected to the hexahedral mesh and shared with any side of the hexahedral mesh. There is a method of using MPC (Multi-Point Constraints: restricting the operation of one node by the operation of another node) to constrain the nodes on the sides of the tetrahedral mesh not to be used. Regarding this technique, Donald
"The Combination of Hexahedral and Tetrahedral Meshing Algorithm," by Dewhirst, Sledhar Vangavolu, and Harley Watrick.
[0005]
[Problems to be solved by the invention]
However, in the conventional technology for generating a mesh in a state where the hexahedral mesh and the tetrahedral mesh are mixed, the side of the tetrahedral mesh that is on the joint surface with the hexahedral mesh and is not shared with any side of the hexahedral mesh (Free edge) exists. For this reason, when analyzing, there is a problem that a gap or mesh interference occurs on the joint surface. Further, as described above, in the method of constraining the free side using MPC, the constraint on the displacement of the slave node is obtained by approximating the displacement of the master node group using the shape function, thereby increasing the amount of calculation. Further, depending on the degree of deformation of the mesh, there is a possibility that an unnecessary constraint is applied to the joint, and the analysis result may be inaccurate.
[0006]
An object of the present invention is to join a hexahedral mesh and a tetrahedral mesh without forming free sides by using a tetragonal pyramid-shaped mesh at a joint between the hexahedral mesh and the tetrahedral mesh without increasing the calculation amount. An object of the present invention is to provide an analysis mesh generation device capable of improving accuracy.
[0007]
[Means for Solving the Problems]
The present invention is an analysis mesh generation device that generates mesh data for finite element analysis based on a model of a three-dimensional geometric shape to be analyzed, wherein input means for inputting data related to the model, and A shape model creating means to be created, an area setting means for designating an area for generating a hexahedral mesh, a hexahedral mesh generating means for generating a hexahedral mesh, and a hexahedral mesh adjacent to the tetrahedral area are searched. A quadrangular pyramid mesh generating unit that arranges a quadrangular pyramid mesh on the surface of the quadrangular pyramid mesh; and a tetrahedral mesh generating unit that generates a tetrahedral mesh in an area that is in contact with the quadrangular pyramid mesh. Based on the dimensions of the tetragonal pyramid mesh and the generated hexahedral mesh, the positions of the vertices shared by the four triangular faces are determined. The position of the vertex is generated based on the nodes of the corresponding hexahedral mesh, the coordinates of the center of gravity of the bottom surface and the top surface of the hexahedral mesh, the height of the hexahedral mesh, and the position of the quadrangular pyramid mesh. Disclosed is an analysis mesh generation device that is calculated based on height.
[0008]
Further, the present invention is an analysis mesh generating apparatus for generating mesh data for finite element analysis based on a model of a three-dimensional geometric shape to be analyzed, wherein input means for inputting data related to the model, , A region setting unit for designating a region for generating a hexahedral mesh, a hexahedral mesh generating unit for generating a hexahedral mesh, and a hexahedral mesh adjacent to the tetrahedral region. A quadrangular pyramid mesh generating unit that arranges a quadrangular pyramid mesh on the surface of the hexahedral mesh; and a tetrahedral mesh generating unit that generates a tetrahedral mesh in an area in contact with the quadrangular pyramid mesh;
The quadrangular pyramid mesh generating means generates the quadrangular pyramid mesh such that all the identification numbers of the nodes belonging to one surface of the hexahedron have the same value and have the same topological structure as the hexahedral mesh. A mesh generation device for analysis characterized by the above is disclosed.
[0010]
BEST MODE FOR CARRYING OUT THE INVENTION
An embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a block diagram showing a schematic configuration of an analysis mesh generation device according to the present invention. The analysis mesh generation device according to the present invention is mainly configured by the analysis processor 1 and includes a shape model input unit 11 and an automatic mesh generation unit 12. A model database 2 is connected to the analysis processor 1. The model database 2 includes shape model data 21 for storing a shape model and a mesh model 22 for storing a mesh model. The model database 2 provides data to the analysis processor 1 and stores the data. The shape model data 21 is connected to the shape model input unit 11, and the mesh model 22 is connected to the automatic mesh generation unit 12. Further, the shape input / display device 3 is connected to the shape model input unit 11. A keyboard 4 and a mouse 5 for inputting a shape model are connected to the shape input / display device 3. A CRT as a display is installed on the front of the shape input / display device body.
The above-mentioned shape model input unit 11 performs processing while interactively creating a shape model to be analyzed, setting a hexahedral mesh area, setting the number of mesh divisions, setting a standard mesh size, and the like. Further, the automatic mesh generation unit 12 automatically and continuously executes processes such as hexahedral mesh generation, quadrangular pyramid mesh generation for hexahedron / 4-tetrahedral mesh joining, and tetrahedral mesh generation. Hereinafter, these operations will be described.
[0011]
FIG. 2 is a flowchart showing a mesh generation process by the analysis processor 1.
First, the operator operates the keyboard 4 and the mouse 5 attached to the shape input / display device 3 to input a shape model to be analyzed (step S201), and creates a shape model (step S202). Then, an area for generating a hexahedral mesh is designated, and the number of divisions of the hexahedral mesh generation area and standard mesh dimension values are set (steps S203, S204, S205). The processing of steps S203 to S205 described above is processing executed by the shape model input unit 11. Here, the designation of the hexahedral mesh area is performed in consideration of the following points. That is, the hexahedral mesh is generally used when regularity is required for the node coordinate values when evaluating the analysis result. In an analysis including a contact problem, there is a case where a hexahedral mesh is arranged at the contact portion to improve the convergence of the analysis. However, since it is difficult to automatically divide the entire complex shape model by the hexahedral mesh, such a portion is left as a region for generating a tetrahedral mesh highly adaptable to the complex shape model, and the hexahedral mesh is left. It is not a mesh area.
[0012]
The following processing is executed by the automatic mesh generation unit 12. The first is hexahedral mesh generation. (Step S206). The partial region for generating the hexahedral mesh is one of a plurality of partial regions constituting the shape model, and has a hexahedral shape having six quadrilateral faces with boundaries. However, since the quadrilateral surface of the boundary may be a curved surface, the partial region for generating the hexahedral mesh is not necessarily a rectangular parallelepiped. An internal grid is generated by using the mapping method in the partial region where the quadrilateral surface of the boundary is a curved surface. In this mapping method, a partial area for generating a hexahedral mesh is regarded as a rectangular parallelepiped, and meshes are generated on the surface and inside of the rectangular parallelepiped based on information such as the number of mesh divisions input by a user, and then the original is formed using a shape function. This is a method of mapping a mesh onto a shape, and is generally used in generating a hexahedral mesh. If there are a plurality of hexahedral mesh regions, a hexahedral mesh generation process is performed on all of them.
[0013]
When the hexahedral mesh generation is completed, the remaining area is divided into meshes by the tetrahedron. However, if the tetrahedral mesh is directly pasted on the hexahedral mesh as described above, mesh mismatch occurs. In other words, since the hexahedral mesh and the tetrahedral mesh have different surface shapes (one is a quadrangle and the other is a triangle), the consistency of nodes and elements is maintained, and there is little problem in analysis. It is desirable to connect by a method. In order to satisfy this problem, in the present invention, a quadrangular pyramid mesh is sandwiched only between the hexahedral mesh region and the tetrahedral mesh region (step S207), and the joining of the two types of meshes is realized while maintaining the consistency of the nodes. ing. By making this quadrangular pyramid mesh the same topological structure as the hexahedral mesh (generated by degenerating one face of the hexahedral mesh into one point), even when an analysis program that does not support the quadrangular pyramid mesh is used. Analysis becomes possible. The degeneracy mentioned here is a process in which the identification numbers of the nodes belonging to one surface of the hexahedron are all set to the same value, and apparently a quadrangular pyramid-shaped mesh is formed.
When generating the tetrahedral mesh, first, a hexahedral mesh region having a joint surface is searched, that is, a hexahedral mesh region adjacent to the tetrahedral mesh region is searched, and a tetrahedral mesh having the joint surface portion as a bottom surface is searched. Generate The coordinate values of the vertices facing the bottom surface of the quadrangular pyramid mesh are determined based on geometric information such as the node coordinate values of the hexahedral mesh and the standard mesh dimension values.
[0014]
When the generation of the quadrangular pyramid mesh for the necessary part is completed, a tetrahedral mesh is generated. (Step S208). As a method of generating a tetrahedral mesh, a triangular mesh at a boundary surface excluding a junction between the tetrahedral mesh region and the hexahedral mesh is generated, and the tetrahedral mesh is sequentially generated while generating nodes toward the inside of the region. The advancing front method or the like to be generated is used. At this time, the mesh size follows the standard mesh size (average size of the generated mesh) set in the shape model input unit. In addition, a quadrangular pyramid mesh is previously arranged at a joint with the hexahedral mesh region, and since all the boundaries are triangular, a triangular mesh is not generated in this portion.
[0015]
Note that, in terms of graphic processing, when a hexahedron and a tetrahedron are joined, any one of a four-sided pyramid, a three-sided prism, and a three-dimensional object having both a four-sided surface and a three-sided surface on its surface is used. Two types of meshes can be joined by joining a square face to a hexahedron and joining one of the triangle faces to a tetrahedron. However, such a method requires a great deal of time for automatic processing because of a large amount of calculation. On the other hand, according to the above-described embodiment, as an integrated process of automatically generating a mesh in which a hexahedral mesh and a tetrahedral mesh are mixed, a hexahedral mesh as an intermediate product is always generated after the hexahedral mesh is generated. Since the mesh is regularly arranged on the surface of the hexahedral mesh, the amount of calculation can be reduced and automatic processing becomes easy.
[0016]
Hereinafter, of the above-described processes, the features of the present invention will be described in more detail.
FIG. 3 is a diagram illustrating a quadrangular pyramid-shaped mesh generated by degenerating a hexahedral mesh. The structures of the data representation 301 on the computer and the data representation 302 of the quadrangular pyramid mesh in handling the hexahedral mesh are common to the hexahedral mesh and the quadrangular pyramid mesh. 1 "to" 8 "). In the case of the quadrangular pyramid mesh, the node identification numbers are duplicated in columns “1”, “2”, “3”, and “4” (for columns “1” to “4”, node identification numbers “1” at four nodes) Are duplicated). As described above, although the mesh is apparently a tetragonal pyramid, the same structure as that of the hexahedral mesh is used by using a mesh having the same phase as the hexahedral mesh (both are composed of 8 columns). The analysis calculation of the quadrangular pyramid mesh can be performed by the means described above. In other words, generally, the element types that can be handled by the finite element analysis program are a hexahedral mesh and a tetrahedral mesh. However, since they can be processed as a hexahedral mesh while using a tetragonal pyramid mesh, the conventional finite element analysis program can be changed without any change. Can be used.
[0017]
FIG. 4 shows the node identification numbers and data representations of the mesh when there is also a node at the center of the side of the mesh. The node identification numbers "9" to "20" of the data representation 401 representing the hexahedron are the mesh representations. It corresponds to a node at the center of the side (this is called a secondary element). The data representation 402 representing the quadrangular pyramid mesh generated by degenerating this has the same column configuration, and the identification numbers of the nodes degenerated to one point are all degenerated to “1”. As described above, in the tetragonal pyramid mesh generation processing, when the hexahedral mesh to which the hexahedron mesh is connected is the type (primary element with hexahedron) shown in FIG. In the case of the quadrilateral element type hexahedral mesh as shown in FIG. 4, a quadrilateral pyramid mesh of the quadratic element type is generated for connection.
[0018]
FIG. 5 shows an example of a shape model to be subjected to finite element analysis, and a process of generating a mesh model in which a hexahedral mesh and a tetrahedral mesh are mixed using this shape model will be described. Portions 501 and 502 shown by hatching in FIG. 5 are regions where a hexahedral mesh is generated. These regions are defined by intentionally dividing the model to be analyzed. In this example, a portion where upper and lower structures are in contact with each other is considered to be an important region for analysis, and a hexahedral mesh region is arranged in this portion. . The remaining blank portions 503 and 504 are regions for generating a tetrahedral mesh. It should be noted that since the area where the hexahedral mesh is generated is subjected to meshing by the mapping method, the area itself is also a hexahedron, but the shape of the area where the tetrahedral mesh is generated is arbitrary. this is,
It is related to the good regularity of the hexahedral mesh and the high applicability to the complex shape of the tetrahedral mesh. By making use of the advantages of each mesh, it is possible to increase the efficiency of mesh generation. I have.
[0019]
FIG. 6 is a diagram in which the number of mesh divisions is set for each side of the hexahedral mesh regions 501 and 502 in FIG. 5 and a hexahedral mesh is generated using a mapping method. The number of mesh divisions is set by interactively instructing a ridge line in the vertical, horizontal, and height directions of the hexahedral mesh generation area in the shape model input unit 11 and inputting an integer value representing the number of divisions into the ridge line. In this example, the region 501 in FIG. 5 is represented by a mesh of (length, width, height) = (3, 3, 5), and the region 502 in FIG. 5 is represented by a mesh of (3, 3, 3). Is shown. In this example, the intervals between the nodes of the mesh are uniform in each region. However, if the mesh division ratio is input as the mesh division information in addition to the number of mesh divisions, the mesh can be locally concentrated. Since the algorithm of the mapping method itself is known, the description is omitted here. The hatched portions 601 and 602 in FIG. 6 are hexahedral meshes adjacent to the tetrahedral mesh region among the hexahedral meshes generated as described above. The hexahedral meshes 601 and 602 can be easily extracted by searching for a shared surface between the regions based on the boundary expression structure of each region of the shape model (such as the identification number of a surface group constituting the region).
[0020]
FIG. 7 is an explanatory diagram showing a method of determining the coordinates of the vertices (nodes facing the bottom surface) of the quadrangular pyramid mesh. In FIG. 7, symbols N1 to N8 are nodes of the hexahedral mesh, symbol Np is the center of gravity of the surface <N1, N2, N3, N4>, and symbol Nq is the center of gravity of the surface <N5, N6, N7, N8>. It is. Also, let the coordinate value of the center of gravity Np be (Xp, Yp, Zp) and the coordinate value of the center of gravity Nq be (Xq, Yq, Zq). Further, the distance between the nodes N1 and N2 is D1, the distance between the nodes N2 and N3 is D2, the distance between the nodes N3 and N4 is D3, the distance between the nodes N4 and N1 is D4, and the average of D1 and D3 is Dd. , D2 and D4 as Dw, and the distance between the centers of gravity Np and Nq as Dh. Here, Dd, Dw, and Dh generally correspond to the width, depth, and height of the hexahedral mesh. When the standard mesh size is MS, the height Ht of the quadrangular pyramid mesh is expressed by the following equation based on the MS and the above defined values.
(Equation 1)
Ht = min (Dd / 2, Dw / 2, Dh / 2, MS / 5)
Here, min is a function that returns the minimum value of the argument. Further, the vertex coordinate values (Xc, Yc, Zc) of the quadrangular pyramid mesh are obtained by the following equation.
(Equation 2)
Xc = Xp + (Xp−Xq) / Dh × Ht
Yc = Yp + (Yp−Yq) / Dh × Ht
Zc = Zp + (Zp−Zq) / Dh × Ht
The above equation means that the vector in the vertex direction of the tetrahedral mesh is determined from the center of gravity points Np and Nq of the surface of the hexahedral mesh, and the height of the tetrahedral mesh is determined based on the dimensions of the hexahedral mesh. A quadrangular pyramid mesh is generated from the vertices obtained by the above equation and the corresponding nodes (N1, N2, N3, N4) of the hexahedral mesh. Note that this example is an example of a primary element, but in the case of a secondary element, it is obtained in the same way as in the case of a primary element using eight node coordinate values from N1 to N8 without considering intermediate nodes. .
[0021]
FIG. 8 is a diagram showing a state after generating the quadrangular pyramid meshes 801 and 802 in all necessary portions on the hexahedral mesh in FIG. A quadrangular pyramid mesh is not generated for a portion not adjacent to the tetrahedral mesh region. As shown in the method for determining the coordinates of the tetrahedral mesh vertices (FIG. 7), the dimensions of the tetrahedral mesh depend on the dimensions of the hexahedral mesh, and the vertices of the tetrahedral mesh form the hexahedral mesh 8 Since the vertices are obtained, each vertex is not uniform.
[0022]
FIG. 9 is a diagram showing a state in which a hexahedral mesh and a tetrahedral mesh are connected using a tetragonal pyramid mesh. In FIG. 9, the quadrangular pyramid mesh is indicated by hatching. A hexahedral mesh 901 is bonded to the lower surface of the quadrangular pyramid mesh, and tetrahedral meshes 902, 903, 904, and 905 are bonded to the remaining four surfaces, respectively. Here, for convenience, only four tetrahedral meshes at the joint are shown, but these are a part of the tetrahedral mesh located at the boundary between the hexahedral mesh region and the tetrahedral mesh region. A mesh is generated in the entire region of the tetrahedral mesh generation target by connecting another tetrahedral mesh.
[0023]
FIG. 10 is a mesh model of a final form with respect to the model of FIG. 5 completed by adding tetrahedral meshes 1001 and 1002 to the state of FIG. In the case of automatic tetrahedral mesh generation for an arbitrary shape, the regularity of the mesh is inferior to that of a hexahedral mesh, but the applicability of automatic mesh generation is high, so this is effective. The algorithm for generating the tetrahedral mesh is known, and therefore detailed description is omitted. For example, a Delaunay method, an advancing front method, or the like can be used.
[0024]
【The invention's effect】
As described above, according to the method for generating a mesh for analysis of the present invention, a quadrangular pyramid mesh in which one surface is a quadrilateral surface and the other four surfaces are a triangular surface is connected to a connecting portion of a hexahedral mesh and a tetrahedral mesh. And the tetragonal surface of the tetragonal pyramid mesh is connected to the tetragonal surface of the hexahedral mesh, and the triangular surface of the tetragonal pyramid mesh is connected to the triangular surface of the tetrahedral mesh. However, it is possible to join two types of meshes without generating free sides. Furthermore, by making the quadrangular pyramid mesh the same topological structure as the hexahedral mesh, analysis using an analysis program that does not support the quadrangular pyramid mesh becomes possible.
[0025]
According to the method for generating a mesh for analysis of the present invention, a hexahedral mesh is first generated, and then a quadrangular pyramid mesh is arranged on the surface of the hexahedral mesh adjacent to the tetrahedral mesh. After the tetrahedral mesh is placed on the triangular surface of the mesh, the tetrahedral mesh is generated in the area where the tetrahedral mesh can be generated, so that it is possible to automate the mesh generation while improving the stability in analysis. Become. Further, since the hexahedral mesh and the tetrahedral mesh are joined without using the MPC, the amount of calculation can be reduced as compared with the case where the MPC is used, so that the processing time can be reduced.
[0026]
Further, according to the analysis mesh generation apparatus of the present invention, input means for inputting a shape model in an interactive format, and shape model creation means for automatically creating a three-dimensional geometric model and generating a hexahedral mesh Area setting means and hexahedral mesh generating means, tetrahedral mesh generating means for generating a quadrangular pyramid mesh at a connecting portion of tetrahedral mesh and hexahedral mesh, and tetrahedral mesh generation automatically generating the tetrahedral mesh By providing the means, the hexahedral mesh having no free side and the tetrahedral mesh can be connected, and the stability in analysis is improved. Further, the analysis processing using the finite element method can be automated. Further, since the hexahedral mesh and the tetrahedral mesh are joined without using the MPC, the amount of calculation can be reduced as compared with the case where the MPC is used.
[Brief description of the drawings]
FIG. 1 is a block diagram illustrating a configuration example of an analysis mesh generation device according to the present invention.
FIG. 2 is a flowchart illustrating a mesh generation process.
FIG. 3 is a diagram showing a data representation of a hexahedral mesh and a quadrangular pyramid mesh generated by degenerating the mesh.
FIG. 4 is a diagram showing a data representation of a hexahedral mesh having a node also at the center of a side of the mesh and a quadrangular pyramid mesh generated by degenerating the hexahedral mesh.
FIG. 5 is a shape diagram showing an example of a shape model to be subjected to finite element analysis.
6 is an explanatory diagram in which a mesh division number is set for each side of the mesh region in FIG. 5 and a hexahedral mesh is generated using a mapping method.
FIG. 7 is an explanatory diagram showing a method of determining coordinates of vertices of a quadrangular pyramid mesh.
FIG. 8 is a diagram showing a state after generating a quadrangular pyramid mesh for all necessary portions on a hexahedral mesh.
FIG. 9 is a diagram showing a state in which a hexahedral mesh and a tetrahedral mesh are connected using a tetragonal pyramid mesh.
FIG. 10 is a mesh model of a final form completed by adding a tetrahedral mesh to the state of FIG. 8;
[Explanation of symbols]
Reference Signs List 1 analysis processor 2 model database 3 shape input / display device 11 shape model input unit 12 automatic mesh generation unit 21 shape model data 22 mesh models 501, 502 hexahedral mesh regions 503, 504 tetrahedral mesh regions 601, 602 tetrahedral mesh A hexahedral mesh 901 adjacent to the area A tetrahedral mesh 902 to 905 A tetrahedral mesh

Claims (2)

An analysis mesh generation device for generating mesh data for finite element analysis based on a model of a three-dimensional geometric shape to be analyzed, comprising: input means for inputting data related to the model; and a shape model for generating the model. Creating means, area setting means for specifying an area for generating a hexahedral mesh, hexahedral mesh generating means for generating a hexahedral mesh, and searching for a hexahedral mesh adjacent to the tetrahedral area, And a tetrahedral mesh generating means for generating a tetrahedral mesh in an area in contact with the quadrangular pyramid mesh, wherein the tetrahedral mesh generating means comprises: Based on the dimensions of the generated hexahedral mesh, the positions of the vertices shared by the four triangular faces are determined, and the vertices and the corresponding vertices are determined. While generating based on the nodes of the hexahedral mesh, the positions of the vertices are set to the coordinates of the center of gravity of each of the bottom and top surfaces of the hexahedral mesh, the height of the hexahedral mesh, and the height of the quadrangular pyramid mesh. A mesh generation device for analysis, wherein the calculation is based on the calculation. An analysis mesh generation device for generating mesh data for finite element analysis based on a model of a three-dimensional geometric shape to be analyzed, comprising: input means for inputting data related to the model; and a shape model for generating the model. Creating means, area setting means for specifying an area for generating a hexahedral mesh, hexahedral mesh generating means for generating a hexahedral mesh, and searching for a hexahedral mesh adjacent to the tetrahedral area, And a tetrahedral mesh generating means for generating a tetrahedral mesh in an area in contact with the quadrangular pyramid mesh.
The quadrangular pyramid mesh generating means generates the quadrangular pyramid mesh such that all the identification numbers of the nodes belonging to one surface of the hexahedron have the same value and have the same topological structure as the hexahedral mesh. An analysis mesh generation device, characterized in that:

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