JP2021140285A - Mesh model generation apparatus and mesh model generation method - Google Patents

Abstract

To provide a mesh model generation apparatus and a mesh model generation method capable of generating a mesh model having a high analysis accuracy when analyzing the ground.SOLUTION: In a mesh model generation apparatus, a model generation unit includes first mesh division means that mesh-divides the ground into three-dimensional hexahedral elements E1, node setting means that determines if there is an intersection between a side S of the hexahedral element E1 and a geological boundary of the ground, and adds a node P to an intersection position when intersecting, second mesh division means that divides the hexahedral element E1 intersecting the geological boundary into both sides of a surface Fs connecting the nodes P, and generates a plurality of division elements E2, and basic element division means that further divides each of the plurality of division elements E2 into basic elements having 6 or less of surfaces, and sets the node P at each of vertices of the basic elements.SELECTED DRAWING: Figure 6

Description

The present invention relates to a mesh model generation device and a mesh model generation method.

There is a finite element method as a method of calculating the dynamic behavior of irregular ground and the interaction between the ground and the structure by reproducing the shape of the ground and the structure faithfully to some extent. The finite element method is a simple method that can be mathematically expressed by modeling a ground or structure with a complicated shape into a three-dimensional or two-dimensional shape model, and dividing this shape model into a mesh to create a mesh model. This is a method of generating shape elements (mesh) and numerically analyzing each element. As for the shape of the element, in the case of a three-dimensional shape model (hereinafter, this is appropriately referred to as a three-dimensional model), it is divided into elements having a shape such as a hexahedron, a pentahedron (square pyramid or triangular pillar), and a tetrahedron. In the case of a dimensional shape model (hereinafter, this is appropriately referred to as a two-dimensional model), it is divided into elements having a shape such as a quadrangle or a triangle.
The ground is created by nature and has a complex stratum composition. For this reason, it is difficult to divide the ground shape model into elements that can be analyzed. Therefore, the work of dividing the ground shape model into analyzable elements while considering the stratum composition is generally performed by the user using software embedded in the computer. However, it takes a huge amount of time and effort to divide the mesh of such a complicated and large-scale ground shape model. There is a technology to automatically mesh the model for mechanical structures, but there is no technology suitable for meshing a shape composed of complex irregular layer boundaries such as the ground. Is the current situation.

By the way, when the shape model of the ground is automatically divided into meshes, the element obtained by the mesh division is a hexahedron in the case of a three-dimensional analysis model from the viewpoint that flexible mesh division corresponding to the stratum composition is possible. In many cases, tetrahedral elements are used rather than elements, and in the case of a two-dimensional analysis model, triangular elements are used rather than quadrilateral elements.
However, the tetrahedral element (triangular element) has a problem that the analysis accuracy is lower than that of, for example, a hexahedral element (quadrilateral element). This is because the boundaries between the elements are approximately horizontal and vertical when the mesh is divided by hexahedral elements and quadrilateral elements, whereas the boundaries are horizontal and vertical when the mesh is divided by tetrahedral elements and triangular elements. This is because it is diagonal. When performing seismic response analysis on the ground, we mainly deal with the problem that shear waves and coarse and dense waves are uniformly incident in the vertical direction. Is difficult to propagate uniformly in the vertical direction. In addition, due to the non-linearity of the ground material, the shear rigidity decreases uniformly in the lateral direction and the damping constant increases in the hexahedral element and the quadrilateral element, but the shear rigidity and the damping constant in the lateral direction in the tetrahedral element and the triangular element. Becomes discontinuous.
In order to improve the analysis accuracy, there is a method of using tetrahedral elements and triangular elements and making the mesh size sufficiently small when generating the mesh, but the number of nodes and elements in the entire analysis model becomes enormous. There are problems that the execution time of the analysis program becomes very long and the load on the computer system that performs the analysis process becomes excessive.
Therefore, in order to improve the analysis accuracy, it is desirable to use as many hexahedral elements and quadrilateral elements as possible.

For example, in Patent Document 1, a hexahedron mesh is created as much as possible in all the divided partial regions, a tetrahedral mesh is created in the partial region where the hexahedral mesh could not be created, and the hexahedral mesh region and the tetrahedral mesh region are adjacent to each other. For the subregions to be used, a configuration is disclosed in which the number and position of the nodes on the adjacent surfaces thereof are matched.
As described above, it is desirable to use as many hexahedral elements as possible in order to improve the analysis accuracy. However, in the configuration disclosed in Patent Document 1, when the ground composed of complicated curved stratum boundaries is divided into meshes, the area between the regions divided by the hexahedral elements is divided by the tetrahedral elements. ing. Therefore, there are many tetrahedral elements with poor analysis accuracy.
Further, in Patent Document 2, the shape model to be meshed is divided into a plurality of blocks, and each of these blocks is meshed so that the arrangement of nodes and connections matches between adjacent blocks, and each of these blocks is meshed. A configuration is disclosed in which a mesh model corresponding to a large-scale shape model is generated by combining blocks.
However, in the configuration disclosed in Patent Document 2, the mesh division method of each block is limited to the tetrahedral element capable of automatic division because it is necessary to match the arrangement of the nodes and the connections between the blocks.
In Patent Document 3, after arranging hexahedron elements so as not to extend the region to each layer, the hexahedron element facing the region where the hexahedron element is not formed is replaced with a hexahedral element having a double size, and the tetrahedron element is replaced with a tetrahedron element. A configuration in which a tetrahedral element is arranged in a body mesh generation target area is disclosed.
However, in the configuration disclosed in Patent Document 3, the region between the regions divided by the hexahedral element needs to be divided by the tetrahedral element. Therefore, there are many tetrahedral elements with poor analysis accuracy.
As described above, in Patent Documents 1 to 3, since the number of tetrahedral elements increases, sufficient analysis accuracy may not be obtained. It is desired to further improve the analysis accuracy.

Japanese Unexamined Patent Publication No. 8-16629 Japanese Patent No. 5637956 Japanese Unexamined Patent Publication No. 2011-39691

An object to be solved by the present invention is to provide a mesh model generation device and a mesh model generation method capable of generating a mesh model with high analysis accuracy when analyzing the ground.

The present invention determines the division pattern of the mesh from the intersection of the hexahedral element (square element in the case of two dimensions) generated by dividing the ground into a grid shape and the boundary of the stratum, and stores the corresponding division pattern. By dividing the elements of the stratum boundary based on the pattern storage unit, even if the stratum boundary is complicatedly inclined, a mesh model with an appropriate size from the viewpoint of analysis accuracy and analysis time can be created. Focusing on the point that it can be generated, the present invention was reached.
The present invention employs the following means in order to solve the above problems.
That is, the mesh model generation device of the present invention is a mesh model generation device that generates a two-dimensional or three-dimensional mesh model by dividing the ground in which the geological structure is represented by a two-dimensional or three-dimensional shape model into a mesh. A first mesh dividing means for dividing the ground into a two-dimensional quadrangular element or a three-dimensional hexahedral element in a grid pattern, an intersection of the sides of the quadrangular element or the hexahedral element and a stratum boundary of the ground. A quadrilateral element or a hexahedron element that intersects the stratum boundary is sandwiched between a line or a surface connecting the nodes with a node setting means that adds a node at the intersection position. However, the second mesh dividing means for generating a plurality of dividing elements by dividing into both sides, and each of the plurality of dividing elements are further divided into basic elements having 4 or less sides or 6 or less faces. , A basic element dividing means for setting nodes at each of the vertices of the basic element.
According to such a configuration, after the ground is divided into two-dimensional quadrilateral elements or three-dimensional hexahedral elements by the first mesh dividing means, the sides of the quadrilateral elements or hexahedral elements intersect with the stratum boundary. In the case, it is divided by a line or a surface connecting the nodes added at the intersection position, and a plurality of dividing elements are generated. When the quadrilateral element or hexahedron element obtained by mesh-dividing the ground into a grid shape includes a stratum boundary, the quadrilateral element or hexahedron element is divided along the stratum boundary. Each of the generated partitioning elements will be formed in a single formation.
By further dividing each of the plurality of dividing elements generated in this manner into basic elements having 4 or less sides or 6 or less faces, nodes are set at each of the vertices of the basic elements. The basic element obtained by this is a quadrilateral element or a triangular element having 4 or less sides in the case of a 2D model, and a hexahedron element or a pentahedron element having 6 or less faces in the case of a 3D model. , Or a tetrahedral element.
Therefore, according to such a configuration, only the quadrilateral element or the hexahedral element at which the stratum boundaries intersect is divided into the basic elements including the triangular element or the tetrahedral element, and the other elements are not divided while maintaining the original shape. Therefore, it is possible to generate a mesh model having many quadrilateral elements or hexahedral elements. This makes it possible to provide a mesh model generator capable of generating a mesh model with high analysis accuracy when analyzing the ground.

In one aspect of the invention, in the mesh model generator of the invention, the node setting means is at a depth position on the depth-direction side of the quadrilateral element or the hexahedral element at the depth position of the ground boundary. It is determined whether or not there is an intersection between the depth direction node setting means for setting the longitudinal node, the horizontal side of the quadrilateral element or the hexahedron element, and the stratum boundary, and if they intersect, at the intersection position. It is provided with a horizontal node setting means for adding a horizontal node.
According to such a configuration, a depth node is set at the depth position of the geological boundary of the ground on the depth side of the quadrilateral element or hexahedron element, and the horizontal side and the stratum boundary of the quadrilateral element or hexahedron element are set. By adding a horizontal node at the intersection with, it is possible to appropriately generate a dividing element even when the stratum boundary is complicatedly inclined.

Further, in one aspect of the present invention, in the mesh model generator of the present invention, each of the plurality of basic elements is a triangle or a quadrangle when the ground is a two-dimensional model, and the ground is a three-dimensional model. In the case of, a tetrahedron, a pentahedron, or a hexahedron whose surface is a quadrangle is further provided, and a division pattern storage unit for storing a division pattern for dividing the division element into a plurality of basic elements is further provided, and the basic element division is provided. The means further divides the divided element into new basic elements based on the divided pattern stored in the basic element pattern storage unit.
According to such a configuration, by registering the division pattern in the division pattern storage unit, each division element can be efficiently divided into basic elements having a shape effective for analysis. Therefore, it is possible to improve the analysis accuracy.

The mesh model generation method of the present invention is a mesh model generation method for generating a two-dimensional or three-dimensional mesh model by dividing the ground in which the geological structure is expressed by a two-dimensional or three-dimensional shape model into a mesh. Is divided into a two-dimensional quadrilateral element or a three-dimensional hexahedron element in a grid pattern, and the presence or absence of intersection between the side of the quadrilateral element or the hexahedron element and the geological boundary of the ground is determined and intersected. In, a node is added at the intersection position, and the quadrilateral element or the hexahedron element that intersects the stratum boundary is divided into both sides of a line or a surface connecting the nodes to generate a plurality of dividing elements. , Each of the plurality of division elements is further divided into basic elements having 4 or less sides or 6 or less faces, and nodes are set at each of the vertices of the basic elements.
According to such a configuration, it is possible to provide a mesh model generation method capable of generating a mesh model with high analysis accuracy when analyzing the ground.

According to the present invention, it is possible to provide a mesh model generation device and a mesh model generation method capable of generating a mesh model with high analysis accuracy when analyzing the ground.

It is a block diagram which shows the functional structure of the mesh model generation apparatus which concerns on embodiment of this invention. It is a figure which shows an example of the ground which the mesh model is generated by the mesh model generation apparatus of FIG. It is a figure which shows the state which mesh-divided the 3D model of FIG. 2 into a grid shape. It is a figure which shows an example of the mesh model generated by the mesh model generation apparatus of FIG. It is a figure which shows an example of the hexahedral element in which the stratum boundary is located inside. It is a figure which shows the plane which connects the node added at the position which intersects with the stratum boundary in the hexahedron element. It is a figure which shows an example of the division plane which divides the division element divided from a hexahedron element into a unit element. It is a figure which shows the example of the division pattern which divides a division element. It is a figure which shows the example of the division pattern which divides a division element. It is a figure which shows the example of the division pattern which divides a division element. It is a figure which shows the example of the division pattern which divides a division element. It is a figure which shows the example of the division pattern which divides a division element. It is a flowchart which shows the flow of the mesh model generation method which concerns on this Embodiment. It is a figure which shows an example of the 2D model of the ground for generating a mesh model by the mesh model generation apparatus of FIG. It is a figure which shows an example of the quadrilateral body element in which the stratum boundary is located inside. It is a figure which shows the example of the division pattern which divides a quadrilateral element. It is a figure which shows the modification which aggregates the nodes into one when there are two stratum boundaries in one element because there is a thin layer. It is a figure which shows the modification which aggregates the node of each side into one when there are a plurality of stratum boundaries in one element. It is a figure which shows the deformation example which moves the stratum boundary to the grid intersection side when a minute element or an irregular element occurs. It is a figure which shows the deformation example which moves the grid intersection to the formation boundary side when a minute element or an irregular element occurs. It is a figure which shows the deformation example when the plane shape of a grid is made into an irregular quadrangle. It is a figure which shows the deformation example when the plane shape of a grid is a triangle. It is a figure which shows the boring data of the ground in the Example of this invention. It is a figure which shows the stratum information obtained by boring in the Example of this invention. It is a figure which shows the information of the upper end depth of the stratum in the Example of this invention. It is a figure which shows the 3D model of the ground in the Example of this invention. It is a figure which shows the mesh model obtained in the Example of this invention.

The present invention is a mesh model generation device and a mesh model generation method for dividing an irregular ground having a complicated layer structure into a mesh. Specifically, in the present invention, when estimating the dynamic behavior problem of irregular ground and the interaction problem between the ground and the structure by numerical analysis, the irregular ground to be analyzed is subjected to mesh data with good analysis accuracy. We have developed a mesh model generation device and a mesh model generation method that can be created with little effort.
Hereinafter, a mode for carrying out the mesh model generation apparatus and the mesh model generation method according to the present invention will be described with reference to the accompanying drawings.
FIG. 1 shows a block diagram showing a functional configuration of the mesh model generator according to the embodiment of the present invention. FIG. 2 shows an example of a three-dimensional model which is a ground shape model for which a mesh model is generated by the mesh model generation device of FIG. FIG. 3 shows a state in which the three-dimensional model of FIG. 2 is mesh-divided into a grid shape. An example of the mesh model generated by the mesh model generator of FIG. 1 is shown in FIG.
The mesh model generation device 1 shown in FIG. 1 divides the ground G represented as a three-dimensional model into a mesh and generates a mesh model for performing seismic response analysis and the like. The mesh model generation device 1 is a computer device, and is a mesh model generation device 1 in which hardware including a CPU (Central Processing Unit), a memory, a storage device, and the like cooperate with a preset computer program. Demonstrate the required function as. The mesh model generation device 1 functionally includes a storage unit 2 and a model generation unit 3.
The storage unit 2 includes various storage devices such as a hard disk drive (HDD), a solid state drive (SSD), and a memory. The storage unit 2 includes a ground shape model storage unit 21 and a division pattern storage unit 22. The ground shape model storage unit 21 stores data of the three-dimensional model M10, which is a shape model of the ground G in the range to be analyzed, which is input from the outside. The division pattern storage unit 22 stores the data of the division pattern that divides the division element E2 into the unit element E3 as described later.

Here, as shown in FIG. 2, when the ground G in the range to be analyzed has a plurality of strata G1 to G3 in the vertical direction, the interface between the strata G1 to G3 located above and below each other. There is a stratum boundary Ge in. Such a three-dimensional model M10 of the ground G includes data indicating the depth (position in the depth direction Dv) of the stratum boundary Ge. The position of the stratum boundary Ge in the depth direction Dv is confirmed by performing a boring survey at a plurality of positions of the actual ground G. Data on the depth of the stratum boundary Ge between boring survey positions can be obtained by interpolation by methods such as inverse distance weighting (IDW), triangulated irregular network (TIN), spline interpolation, and kriging. Further, the three-dimensional model M10 is set (formed) so as to envelop the ground surface Gf of the ground G. That is, the three-dimensional model M10 is set to include a range above the ground surface Gf.

As shown in FIG. 4, the model generation unit 3 divides the three-dimensional model M10 of the ground G stored in the storage unit 2 into a mesh according to the stratum boundary Ge of the ground G, so that the plurality of hexahedral elements E1 and The process of generating the mesh model M12 including the dividing element E2 and the basic element E3 is executed. As shown in FIG. 1, the model generation unit 3 includes a first mesh dividing means 31, a node setting means 32, a second mesh dividing means 33, and a basic element dividing means 34.

The first mesh dividing means 31 divides the three-dimensional model M10 representing the ground G as shown in FIG. 2 into three-dimensional hexahedral elements in a grid shape as shown in FIG. The process of generating the grid division model M11 is performed. The hexahedral element E1 generated by mesh-dividing the three-dimensional model M10 by the first mesh dividing means 31 is generated in a rectangular parallelepiped shape. The first mesh dividing means 31 mesh-divides the three-dimensional model M10 representing the ground G into hexahedral elements E1 having a preset size. Here, the hexahedron element E1 is set to an appropriate size based on the viewpoints of analysis accuracy and analysis time. For example, in the case of an interaction problem, when the main object of analysis is, for example, the central part of the three-dimensional model M10, the grid spacing is made dense at the central part of the three-dimensional model M10, and the three-dimensional model M10 The solid spacing can also be sparse at the ends of.

FIG. 5 is a diagram showing an example of a hexahedral element in which a stratum boundary is located inside.
In the hexahedron element E1 set in the portion where the stratum boundary Ge is located, if the apex position of the hexahedron element E1 coincides with the depth position of the stratum boundary Ge, the mesh can be divided at the apex position. On the other hand, as shown in FIG. 5, when the apex position of the hexahedral element E1 does not match the depth position of the stratum boundary Ge, the stratum boundary Ge is located inside the hexahedral element E1. In this case, as will be described later, the hexahedron element E1 is divided by a plane along the stratum boundary Ge, and in preparation for this, the node setting means 32 sets the node P for the hexahedron element E1.
The node setting means 32 determines whether or not the side S of the hexahedron element E1 generated by the first mesh dividing means 31 intersects with the stratum boundary Ge, and the side S of the hexahedron element E1 intersects with the stratum boundary Ge. If so, the process of adding the node P to the intersection position is performed. The node setting means 32 includes a depth direction node setting means 32A and a horizontal node setting means 32B. When the side Sv of the depth direction Dv of the hexahedron element E1 and the stratum boundary Ge intersect, the depth direction node setting means 32A of the ground G on the side Sv of the depth direction Dv of the hexahedron element E1. A process of setting a node Pv in the depth direction is performed at the depth position of the stratum boundary Ge (the intersection of the side Sv and the stratum boundary Ge). The horizontal node setting means 32B determines whether or not the side Sh of the hexahedral element E1 in the horizontal direction Dh intersects the stratum boundary Ge, and when the side Sh in the horizontal direction Dh intersects the stratum boundary Ge, the horizontal node setting means 32B is horizontal. A process of adding a horizontal node Ph at the intersection of the side Sh of the direction Dh and the stratum boundary Ge is performed.

FIG. 6 is a diagram showing a surface connecting nodes added at positions intersecting with the stratum boundary in the hexahedral element.
The second mesh dividing means 33 is as shown in FIG. 6 when the node P is added to the side S of the hexahedron element E1 intersecting the stratum boundary Ge as shown in FIG. 5 by the node setting means 32. , The hexahedral element E1 is divided into both sides of the surface Fs connecting the nodes P, and a process of generating a plurality of divided elements E2 is performed.

FIG. 7 is a diagram showing an example of a division surface in which a division element divided from a hexahedron element is divided into unit elements.
As shown in FIG. 7, the basic element dividing means 34 has a polygon in which the number of faces of the plurality of dividing elements E2 generated by the second mesh dividing means 33 is 7 or more, or the number of sides is 5. In the case of a hexahedron having the above polygonal surfaces, each dividing element E2 is further divided into a basic element E3 having a polygon having 6 or less faces and 4 or less sides on each surface, and the basic element is further divided. A process of setting a node P at each of the vertices of E3 is performed. Here, each of the basic elements E3 is a tetrahedron, a pentahedron, or a hexahedron having a quadrangular surface. The basic element dividing means 34 further divides the dividing element E2 into the basic element E3 based on the dividing pattern stored in the dividing pattern storage unit 22.

A plurality of basic element models T corresponding to each of the basic elements E3 are stored in the division pattern storage unit 22. The shape that the dividing element E2 generated by the second mesh dividing means 33 can have varies depending on which side S of the hexahedral element E1 intersects with the stratum boundary Ge. Various types of the basic element model T are stored in the division pattern storage unit 22 so that all the shapes that can be considered as the division element E2 can be realized by combining a plurality of the basic element models T.
In the division pattern storage unit 22, each of the division elements E2 having various shapes and a combination of a plurality of basic element models T that can be combined to realize the division element E2 are associated with each other. This correspondence is stored as a division pattern of the division element E2.
The foundation element dividing means 34 determines which side S of the hexahedron element E1 intersects with the stratum boundary Ge, thereby specifying the shape of the dividing element E2. Then, the basic element dividing means 34 acquires a division pattern corresponding to the division element E2 from the division pattern storage unit 22 for each division element E2, and according to the acquired division pattern, divides the division element E2 into the division element E2. A plurality of basic element models T registered as patterns are applied.
Then, the basic element dividing means 34 generates a plurality of basic elements E3 by dividing the dividing element E2 along the boundary between the plurality of basic element models T fitted in the dividing element E2.

7 and 8 to 12 above are diagrams showing an example in which the hexahedron element is divided into the dividing element E2, and the dividing element E2 is further divided into the basic element E3 as needed. ..
As shown in FIGS. 7 to 12, a plurality of types of division patterns stored in the division pattern storage unit 22 are formed by combining a plurality of basic element models T so that each division element E2 can be divided into basic elements E3. It is set. Further, each basic element model T is prepared in advance as an element group divided into shapes that can be effectively analyzed by an analysis program of the finite element method. The basic element model T is formed by using a hexahedral element formed by a quadrangular surface, a pentahedral element such as a triangular prism and a quadrangular pyramid, and a tetrahedral element which is a triangular pyramid. The basic element E3 includes a rotated or inverted version of these basic element models T.
The basic element dividing means 34 sets nodes P at each of the vertices of the divided basic element E3.

Next, the details of the mesh model generation method in the mesh model generation device 1 as described above will be described.
FIG. 13 is a flowchart showing the flow of the mesh model generation method according to the present embodiment.
As shown in FIG. 13, in the mesh model generation method in the present embodiment, first, the data of the three-dimensional model M10 of the ground G stored in the ground shape model storage unit 21 is called, and the first mesh dividing means 31 is used. As shown in FIG. 3, a plurality of hexahedrons are generated by dividing the three-dimensional model M10 of the ground G in the range to be analyzed into three-dimensional hexahedron elements in a grid shape to generate a grid division model M11. Generate element E1 (step S1).

Next, the node setting means 32 confirms the depth of the stratum boundary Ge just below each intersection of the grid in a state where the mesh-divided grid division model M11 is viewed from above (step S2). The node setting means 32 determines whether or not the depth of the stratum boundary Ge matches the position of the node P at the apex of the hexahedron element E1 for each hexahedron element E1 generated in step S1 (step S3). As a result, when the depth of the stratum boundary Ge coincides with the position of the node P at the apex of the hexahedron element E1, the process proceeds to step S5. In step S3, when the depth of the stratum boundary Ge does not match the position of the node P at the apex of the hexahedron element E1, the side Sv of the hexahedral element E1 in the depth direction Dv and the stratum boundary Ge intersect. Become. In that case, the depth direction node setting means 32A of the node setting means 32 is the depth position of the stratum boundary Ge of the ground G (the intersection of the side Sv and the stratum boundary Ge) on the side Sv of the hexahedral element E1 in the depth direction Dv. The depth direction node Pv is additionally set in the position) (step S4).
Next, the node setting means 32 confirms whether or not the side Sh of the hexahedral element E1 in the horizontal direction Dh intersects the stratum boundary Ge for each hexahedral element E1 generated in step S1 (step S5). Subsequently, the node setting means 32 determines, as a result of the confirmation in step S5, whether or not the side Sh of the hexahedral element E1 in the horizontal direction D and the stratum boundary Ge intersect (step S6). As a result, if the side Sh of the hexahedral element E1 in the horizontal direction Dh and the stratum boundary Ge do not intersect, the process proceeds to step S8. When the side Sh of the hexahedral element E1 in the horizontal direction D and the stratum boundary Ge intersect, the node setting means 32 adds the horizontal node Ph at the intersection of the side Sh of the horizontal Dh and the stratum boundary Ge. (Step S7).

In step S8, based on the determination results of steps S3 and S6 in each hexahedron element E1, it is confirmed whether each hexahedron element E1 intersects the stratum boundary Ge. As a result of the confirmation, it is determined whether or not each hexahedral element E1 intersects the stratum boundary Ge (step S9). As a result, for the hexahedron element E1 that does not intersect the stratum boundary Ge, the hexahedron element E1 generated by dividing into a grid shape in step S1 is adopted as it is (step S10).
On the other hand, regarding the hexahedron element E1 that intersects the stratum boundary Ge, the hexahedron element E1 is further divided into a plurality of division elements E2 by the second mesh dividing means 33 and the foundation element dividing means 34 from the situation of intersection with the stratum boundary Ge. And the basic element E3. To this end, first, the second mesh dividing means 33 connects the hexahedron element E1 to the surface Fs connecting the nodes P when the node P is added to the side S of the hexahedron element E1 intersecting the stratum boundary Ge. A plurality of division elements E2 are generated by dividing into both sides of the above.

When at least one of the generated plurality of dividing elements E2 is a polyhedron having 7 or more faces, or a hexahedron having a polygonal surface having 5 or more sides, the basic element dividing means 34 , The division element E2 is further divided into a plurality of basic elements E3 by the division pattern stored in the division pattern storage unit 22 in advance. The basic element dividing means 34 determines which side S of the hexahedron element E1 intersects with the stratum boundary Ge based on the node P additionally set on the side S. In this way, the dividing element E2, which is a polyhedron having 7 or more faces or a hexahedron having a polygonal surface having 5 or more sides, is specified from the state of intersection of the hexahedron element E1 and the stratum boundary Ge. The basic element dividing means 34 determines (identifies) the division pattern corresponding to the division element E2 whose shape is specified (step S11). Subsequently, the basic element dividing means 34 applies the basic element model T corresponding to the dividing pattern specified in step S11 to divide the dividing element E2 into a plurality of basic elements E3 (step S12). The basic element dividing means 34 sets nodes P at each of the vertices of the divided basic element E3.

As a result, the grid division model M11 is divided into any of the hexahedral element E1, the division element E2, and the base element E3 having 4 or less sides and 6 or less faces on each surface.
The model generation unit 3 confirms whether or not each of the hexahedron element E1, the division element E2, and the foundation element E3 generated as described above is below the ground surface Gf (step S13). As a result of the confirmation in step S13, it is determined whether or not each of the hexahedral element E1, the dividing element E2, and the foundation element E3 is below the ground surface Gf (step S14). As a result, the hexahedron element E1, the dividing element E2, and the foundation element E3, which are determined not to be closer to the ground surface Gf, are erased (step S15). As a result, the mesh model M12 as shown in FIG. 4 is generated.

Next, the effects of the above-mentioned mesh model generation device and mesh model generation method will be described.
The mesh model generation device 1 as described above is a mesh model generation device 1 that generates a three-dimensional mesh model M12 by dividing the ground G in which the geological structure is represented by the three-dimensional shape model M10 into a mesh. In the case of determining whether or not the first mesh dividing means 31 that divides the mesh into the three-dimensional hexahedral element E1 and the side S of the hexahedral element E1 and the stratum boundary Ge of the ground G intersect with each other. Divides the node setting means 32 that adds the node P at the intersection position and the hexahedral element E1 that intersects the stratum boundary Ge on both sides of the surface Fs that connects the nodes P to generate a plurality of division elements E2. The second mesh dividing means 33 and the plurality of dividing elements E2 are further divided into the basic element E3 having 6 or less faces, and the node P is set at each of the vertices of the basic element E3. And.
According to such a configuration, after the ground G is divided into the three-dimensional hexahedral element E1 by the first mesh dividing means 31, the side S of the hexahedral element E1 and the stratum boundary Ge intersect when the ground G intersects. A node P is added at the intersection position, and the hexahedral element E1 intersecting the stratum boundary Ge is divided by the surface Fs connecting the nodes P to generate a plurality of division elements E2. When the hexahedral element E1 obtained by mesh-dividing the ground G into a grid shape includes the stratum boundary Ge, the hexahedron element E1 is divided along the stratum boundary Ge. Each of the generated plurality of dividing elements E2 will be formed by a single stratum.
By further dividing each of the plurality of dividing elements E2 generated in this manner into the basic element E3 having 6 or less faces, a node P is set at each of the vertices of the basic element E3. The basic element E3 thus obtained is a hexahedron element, a pentahedron element, or a tetrahedron element having 6 or less faces.
Therefore, according to such a configuration, only the hexahedral element E1 at which the stratum boundary Ge intersects can be divided into the basic element E3 including the tetrahedral element, and the other elements can be maintained in their original shape and not divided. , A mesh model M12 having many hexahedral elements E1 can be generated. This makes it possible to provide a mesh model generation device 1 capable of generating a mesh model M12 having high analysis accuracy when analyzing the ground G.

Further, the node setting means 32 includes the depth direction node setting means 32A for setting the depth direction node Pv at the depth position of the stratum boundary Ge of the ground G on the side Sv of the hexahedron element E1 in the depth direction Dv, and the hexahedron. A horizontal node setting means 32B for determining whether or not the side Sh of the element E1 in the horizontal direction Dh intersects with the stratum boundary Ge, and adding a horizontal node Ph at the intersection position is provided.
According to such a configuration, the depth direction node Pv is set at the depth position of the stratum boundary Ge of the ground G on the side Sv of the hexahedral element E1 in the depth direction Dv, and the side Sh of the horizontal direction Dh of the hexahedron element E1 is set. By adding the horizontal node Ph at the intersection of the stratum boundary Ge and the stratum boundary Ge, the dividing element E2 can be appropriately generated even when the stratum boundary Ge is complicatedly inclined.

Further, each of the plurality of basic elements E3 is a tetrahedron, a pentahedron, or a hexahedron having a quadrangular surface, and a division pattern storage unit that stores a division pattern for dividing the division element E2 into a plurality of basic elements E3. 22 is further provided, and the basic element dividing means 34 further divides the dividing element E2 into the basic element E3 based on the dividing pattern stored in the dividing pattern storage unit 22.
According to such a configuration, by registering the division pattern in the division pattern storage unit 22, each division element E2 can be efficiently divided into the basic element E3 having a shape effective for analysis. Therefore, it is possible to improve the analysis accuracy.

Further, the mesh model generation method as described above is a mesh model generation method in which the ground G in which the geological structure is expressed by the three-dimensional shape model M10 is divided into meshes to generate the three-dimensional mesh model M12, and the ground G is generated. Is divided into hexahedral elements E1 and the presence or absence of intersection between the side S of the hexahedral element E1 and the stratum boundary Ge is determined. The intersecting hexahedral elements E1 are divided on both sides of the surface Fs connecting the nodes P to generate a plurality of division elements E2, and each of the plurality of division elements E2 is a basic element E3 having 6 or less surfaces. Further, a node P is set for each of the vertices of the basic element E3.
According to such a configuration, it is possible to provide a mesh model generation method capable of generating a mesh model M12 having high analysis accuracy when analyzing the ground G.

(Modified example of the embodiment)
The mesh model generation device and the mesh model generation method of the present invention are not limited to the above-described embodiments described with reference to the drawings, and various modifications can be considered within the technical scope thereof.
For example, in the above embodiment, the mesh model M12 is generated by using the ground G as the three-dimensional model M10, but the present invention is not limited to this.
FIG. 14 is a diagram showing an example of a two-dimensional model of the ground for generating a mesh model by the mesh model generation device of FIG. FIG. 15 is a diagram showing an example of a quadrilateral element in which a stratum boundary is located inside.
When the mesh model generation device 1 shown in FIG. 1 mesh-divides the ground G represented as the two-dimensional model M21 to generate a mesh model, the first mesh dividing means 31 is as shown in FIG. , The ground G is mesh-divided into two-dimensional quadrangular elements E11 in a grid pattern. The node setting means 32 determines whether or not the side S of the quadrilateral element E11 intersects with the stratum boundary Ge, and if they intersect, the node P is added to the intersection position as shown in FIG.
More specifically, the depth direction node setting means 32A is on the side Sv of the depth direction Dv of the quadrilateral element E11 when the side Sv of the depth direction Dv of the quadrilateral element E11 and the stratum boundary Ge intersect. The process of setting the node Pv in the depth direction is performed at the depth position (intersection position between the side Sv and the stratum boundary Ge) of the stratum boundary Ge of the ground G. The horizontal node setting means 32B determines whether or not the side Sh in the horizontal direction Dh of the square element E11 intersects with the stratum boundary Ge, and when the side Sh in the horizontal direction Dh intersects with the stratum boundary Ge, the horizontal node setting means 32B is horizontal. A process of adding a horizontal node Ph at the intersection of the side Sh of the direction Dh and the stratum boundary Ge is performed.
The second mesh dividing means 33 divides the quadrangular element E11 intersecting the stratum boundary Ge on both sides of the line L connecting the nodes P to generate a plurality of dividing elements E12.

15 and 16 are views showing an example of a quadrangular element in which a stratum boundary is located inside.
When the number of sides of at least one of the generated plurality of dividing elements E12 is larger than 4 (pentagon or more), the basic element dividing means 34 has 4 sides of the dividing element E12 as shown in FIG. It is further divided into the following basic elements E13, and nodes P are set at each of the vertices of the basic element E13. Each of the plurality of foundation elements E13 is a triangle or a quadrangle when the ground G is the two-dimensional model M21.
The division pattern storage unit 22 stores a division pattern that divides the division element E12 into a plurality of basic elements E13. The basic element dividing means 34 further divides the dividing element E12 into the basic element E13 based on a plurality of basic element models T constituting the dividing pattern stored in the dividing pattern storage unit 22.

Such a mesh model generation device 1 is a mesh model generation device 1 that generates a two-dimensional mesh model by dividing the ground G in which the geological structure is represented by the two-dimensional shape model M21 into a mesh, and the ground G is divided into two. It is determined whether or not the first mesh dividing means 31 that divides the quadrilateral element E11 into a grid-like mesh, the side S of the quadrilateral element E11, and the stratum boundary Ge of the ground G intersect, and if they intersect, , The node setting means 32 that adds the node P at the intersection position and the quadrilateral element E11 that intersects the stratum boundary Ge are divided into both sides of the line L connecting the nodes P to generate a plurality of division elements E12. The second mesh dividing means 33 and each of the plurality of dividing elements E12 are further divided into basic elements E13 having 4 or less sides, and nodes P are set at each of the vertices of the basic element E3. Means 34 and.
According to such a configuration, after the ground G is divided into the two-dimensional quadrilateral element E11 by the first mesh dividing means 31, the side S of the quadrilateral element E11 and the stratum boundary Ge intersect when they intersect. A node P is added at the intersection position, and the quadrilateral element E11 intersecting the stratum boundary Ge is divided by the line L connecting the nodes P to generate a plurality of division elements E12. When the quadrilateral element E11 obtained by mesh-dividing the ground G into a grid shape includes the stratum boundary Ge, the quadrilateral element E11 is divided along the stratum boundary Ge. Each of the generated plurality of dividing elements E12 will be formed by a single stratum.
By further dividing each of the plurality of dividing elements E12 generated in this manner into the basic element E13 having 4 or less sides, a node P is set at each of the vertices of the basic element E13. The basic element E13 thus obtained is a quadrilateral element or a triangular element having four or less sides, that is, a quadrilateral element or a triangular element.
Therefore, according to such a configuration, only the quadrangular element E11 at which the stratum boundary Ge intersects is divided into the basic element E13 including the triangular element, and the other parts can be configured to maintain the original shape and not be divided. It is possible to generate a mesh model having many quadrilateral elements E11. This makes it possible to provide a mesh model generation device 1 capable of generating a mesh model with high analysis accuracy when analyzing the ground G.

Further, the node setting means 32 and the depth direction node setting means 32A set the depth direction node Pv at the depth position of the stratum boundary Ge of the ground G on the side Sv of the quadrilateral element E11 in the depth direction Dv. , The horizontal node setting means 32B, which determines whether or not the side Sh of the horizontal direction Dh of the quadrilateral element E11 intersects with the stratum boundary Ge, and adds the horizontal node Ph at the intersection position when they intersect. To be equipped.
According to such a configuration, the depth direction node Pv is set at the depth position of the stratum boundary Ge of the ground G on the side Sv of the depth direction Dv of the quadrilateral element E11, and the side Sh of the horizontal direction Dh of the quadrilateral element E11 is set. By adding the horizontal node Ph at the intersection of the stratum boundary Ge and the stratum boundary Ge, the dividing element E12 can be appropriately generated even when the stratum boundary Ge is complicatedly inclined.

Further, each of the plurality of basic elements E13 is a triangle or a quadrangle, and further includes a division pattern storage unit 22 for storing a division pattern for dividing the division element E12 into the plurality of basic elements E13, and the basic element division means 34. Further divides the division element E12 into the basic element E13 based on the division pattern stored in the basic element pattern storage unit 22.
According to such a configuration, by registering the division pattern in the division pattern storage unit 22, each division element E12 can be efficiently divided into the basic element E13 having a shape effective for analysis. Therefore, it is possible to improve the analysis accuracy.

Further, the mesh model generation method as described above is a mesh model generation method in which the ground G in which the geological structure is expressed by the two-dimensional shape model M21 is divided into meshes to generate a two-dimensional mesh model. The two-dimensional quadrilateral element E11 is divided into a mesh in a grid shape, and it is determined whether or not the side S of the quadrilateral element E11 intersects with the stratum boundary Ge of the ground G. In addition, the quadrilateral element E11 that intersects the stratum boundary Ge is divided into both sides of the line L connecting the nodes P to generate a plurality of division elements E12, and each of the plurality of division elements E12 has a number of sides. Is further divided into basic elements E13 having a value of 4 or less, and nodes P are set at each of the vertices of the basic element E13.
According to such a configuration, it is possible to provide a mesh model generation method capable of generating a mesh model having high analysis accuracy when analyzing the ground G.

(Other variants)
For example, as shown in FIG. 17, in the ground G in which the thin layer Gt exists, one hexahedral element E1 (or a quadrilateral element E11) may intersect two or more layer boundary Ges. For a thin layer Gt that is thinner than the thickness of one hexahedral element E1, it is considered that the influence on the behavior of the ground G is very small. Furthermore, thin flat elements may adversely affect the analysis accuracy, so it is considered appropriate to ignore them.
Therefore, for example, as shown in FIG. 17, two or more stratum boundary Ges may be aggregated into one. At this time, the coordinates of the node Pb after aggregation may be the average value of the coordinates of the plurality of nodes Pa before aggregation.

Further, as shown in FIG. 18, two or more stratum boundary Ges may intersect one hexahedral element E1 (or quadrangular element E11) at a break in a discontinuous layer or the like. As the number of intersecting geological boundaries Ge increases, many division patterns must be prepared accordingly. Therefore, two or more node Pc may be aggregated so that the number of nodes P added by the intersection of the stratum boundary Ge is, for example, one per side. The coordinates of the node Pd after aggregation may be the average value of the coordinates of a plurality of node Pc before aggregation.

Further, as shown in FIG. 19, minute elements and irregular elements Es may be generated depending on the positional relationship between the hexahedral element E1 (or the quadrilateral element E11) and the stratum boundary Ge. The presence of such an element Es may reduce the analysis accuracy, and therefore it is desirable to eliminate it as much as possible. Therefore, when a minute element or an irregular element Es is generated, the stratum boundary Ge may be moved to the node side of the hexahedral element E1 and the element Es may be deleted. Alternatively, as shown in FIG. 20, the node X of the hexahedral element E1 may be moved to the stratum boundary Ge side to delete the element Es.

Further, in general, in order to shorten the calculation time and save the storage area when analyzing the ground G, it is conceivable to reduce the number of elements, or to model the structure and analyze it integrally with the ground G. .. In such a case, the hexahedral element or quadrangle element in the grid division model generated by the first mesh division means 31 is converted into a non-rectangular quadrangle E4 or triangle E5 as shown in FIGS. 21 and 22. , It is possible to change it partially.
The mesh model generation device and the mesh model generation method as described above include the node setting means 32, the second mesh dividing means 33, and the basic element dividing means even when the elements having such a shape are included. It is possible to deal with it as described above in 34.
In addition to this, as long as the gist of the present invention is not deviated, the configuration described in the above embodiment can be selected or changed to another configuration as appropriate.

Since a mesh model of the ground was generated using the configuration of the above embodiment of the present invention, an example thereof is shown below.
The ground G was surveyed at the plane position as shown in FIG. 23, and boring data at a plurality of positions were obtained.
The stratum information obtained by boring at each position is as shown in FIG. In this embodiment, the top depths of the strata between boring are interpolated by the inverse distance weighting method using each boring position and the top depth of each layer at each boring position. As a result, as shown in FIG. 25, information on the upper end depth of the stratum was obtained.
A three-dimensional model of such ground is shown in FIG. The central part, which is the main target of analysis, is a dense grid, and the points away from the central part are sparse grids to shorten the calculation time and save the storage area.
With respect to such a three-dimensional model, the ground was divided into meshes by the mesh model generation method shown in the above embodiment, and a mesh model as shown in FIG. 27 was generated.

1 Mesh model generator Fs surface 22 Division pattern storage unit G Ground 31 First mesh division means G1 to G3 Formation 32 Node setting means Ge Formation boundary 32A Depth direction node setting means M10 3D model (shape model)
32B Horizontal node setting means M12 Mesh model 33 Second mesh dividing means M21 Two-dimensional model (shape model)
34 Basic element dividing means L line Dh Horizontal P node Dv Depth direction Ph Horizontal node E1 Hexahedron element Pv Depth direction node E11 Rectangle element S side E2, E12 Dividing element Sh Horizontal side E3, E13 Basic element Sv depth Horizontal side

Claims (4)

A mesh model generator that generates a two-dimensional or three-dimensional mesh model by dividing the ground, which expresses the geological structure with a two-dimensional or three-dimensional shape model, into meshes.
A first mesh dividing means for dividing the ground into a two-dimensional quadrangular element or a three-dimensional hexahedral element in a grid pattern.
A node setting means that determines whether or not the side of the quadrilateral element or the hexahedron element intersects with the stratum boundary of the ground, and if it intersects, adds a node at the intersection position.
A second mesh dividing means for generating a plurality of dividing elements by dividing the quadrangular element or the hexahedral element intersecting the stratum boundary on both sides of a line or a surface connecting the nodes.
A basic element dividing means that further divides each of the plurality of dividing elements into basic elements having 4 or less sides or 6 or less faces, and sets nodes at each of the vertices of the basic element.
A mesh model generator, characterized in that it comprises. The node setting means
Depth direction node setting means for setting a depth direction node at a depth position of the geological boundary of the ground on the depth direction side of the quadrilateral element or the hexahedron element.
A horizontal node setting means that determines whether or not the horizontal side of the quadrilateral element or the hexahedral element intersects with the stratum boundary, and if it intersects, adds a horizontal node at the intersection position.
The mesh model generator according to claim 1, wherein the mesh model generator is provided. Each of the plurality of basic elements is a triangle or a quadrangle when the ground is a two-dimensional model, and a tetrahedron, a pentahedron, or a hexahedron whose surface is a quadrangle when the ground is a three-dimensional model. ,
A division pattern storage unit that stores a division pattern for dividing the division element into a plurality of basic elements is further provided.
The mesh model generation device according to claim 1 or 2, wherein the basic element dividing means further divides the divided element into new basic elements based on the divided pattern stored in the basic element pattern storage unit. .. It is a mesh model generation method that generates a two-dimensional or three-dimensional mesh model by dividing the ground in which the geological structure is expressed by a two-dimensional or three-dimensional shape model.
The ground is divided into a two-dimensional quadrangular element or a three-dimensional hexahedral element into a grid-like mesh.
It is determined whether or not the side of the quadrilateral element or the hexahedral element intersects the stratum boundary of the ground, and if it intersects, a node is added at the intersection position.
The quadrilateral element or the hexahedron element that intersects the stratum boundary is divided into both sides of a line or a surface connecting the nodes to generate a plurality of division elements.
A mesh model generation method in which each of the plurality of divided elements is further divided into basic elements having 4 or less sides or 6 or less faces, and nodes are set at each of the vertices of the basic elements.

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