TETRA MESH GENERATOR, TETRA MESH GENERATION METHOD, AND PROGRAM

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First Claim
1. A tetra mesh generator comprising:
 an input unit to which shape definition data that defines a threedimensional shape is input; and
a processing unit that disposes a plurality of particles on an edge and a surface of the threedimensional shape defined by the shape definition data input to the input unit, disposes particles according to an internal distribution rule in an inner part spaced apart from the surface of the threedimensional shape, disposes particles at a position deviated from the position according to the internal distribution rule, in a space between the inner part and the surface of the threedimensional shape, and generates a tetra mesh having a center of the disposed particles as a vertex.
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Abstract
An input unit to which shape definition data that defines a threedimensional shape is input. A processing unit disposes a plurality of particles on an edge and a surface of the threedimensional shape defined by the input shape definition data, disposes particles according to an internal distribution rule in an inner part spaced apart from the surface of the threedimensional shape, disposes particles at a position deviated from the position according to the internal distribution rule, in a space between the inner part and the surface of the threedimensional shape, and generates a tetra mesh having a center of the disposed particles as a vertex.
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7 Claims
 1. A tetra mesh generator comprising:
an input unit to which shape definition data that defines a threedimensional shape is input; and a processing unit that disposes a plurality of particles on an edge and a surface of the threedimensional shape defined by the shape definition data input to the input unit, disposes particles according to an internal distribution rule in an inner part spaced apart from the surface of the threedimensional shape, disposes particles at a position deviated from the position according to the internal distribution rule, in a space between the inner part and the surface of the threedimensional shape, and generates a tetra mesh having a center of the disposed particles as a vertex.  View Dependent Claims (2, 3, 4, 5)
 6. A tetra mesh generation method comprising:
defining a threedimensional shape; disposing a plurality of particles on an edge and a surface of the threedimensional shape; disposing particles according to an internal distribution rule in an inner part spaced apart from the surface of the threedimensional shape, and disposing particles at a position deviated from the position according to the internal distribution rule, in a space between the inner part and the surface of the threedimensional shape; and generating a tetra mesh having a center of the disposed particles as a vertex.
 7. A program causing a computer to execute:
a function of inputting shape definition data that defines a threedimensional shape; a function of disposing a plurality of particles on an edge and a surface of the threedimensional shape defined by the input shape definition data, disposing particles according to an internal distribution rule in an inner part spaced apart from the surface of the threedimensional shape, disposing particles at a position deviated from the position according to the internal distribution rule, in a space between the inner part and the surface of the threedimensional shape, and generating a tetra mesh having a center of the particles as a vertex; and a function of outputting tetra mesh definition data that defines the generated tetra mesh.
1 Specification
The content of Japanese Patent Application No. 2018205606, on the basis of which priority benefits are claimed in an accompanying application data sheet, is in its entirety incorporated herein by reference.
Certain embodiment of the present invention relates to a tetra mesh generator, a tetra mesh generation method, and a program.
The related art discloses many tetra mesh generation methods. It is assumed that most of these tetra mesh generation methods are applied to a finite element method. Therefore, a molecular dynamics method based on a crystal lattice structure or a renormalization group molecular dynamics method (hereinafter, both are collectively referred to as a molecular dynamics method) may not be compatible.
If the analysis is performed by the molecular dynamics method using the tetra mesh generated by the method in the related art, the analysis accuracy may be remarkably lowered. In particular, a tetra mesh made by dividing a rectangular parallelepiped (see Japanese Unexamined Patent Publication No. 200375521) has low rigidity in the shear direction, and therefore analysis may break down if analysis is performed by the molecular dynamics method is performed using this mesh.
It is desirable to provide a tetra mesh generator, a tetra mesh generation method, and a program suitable for analysis by the molecular dynamics method or renormalization group molecular dynamics method.
According to one aspect of the present invention, there is provided a tetra mesh generator including:
 an input unit to which shape definition data that defines a threedimensional shape is input;
 a processing unit that disposes a plurality of particles on an edge and a surface of the threedimensional shape defined by the shape definition data input to the input unit, disposes particles according to an internal distribution rule in an inner part spaced apart from the surface of the threedimensional shape, disposes particles at a position deviated from the position according to the internal distribution rule, in a space between the inner part and the surface of the threedimensional shape, and generates a tetra mesh having a center of the disposed particles as a vertex.
According to another aspect of the present invention, there is provided a tetra mesh generation method including:
 defining a threedimensional shape;
 disposing a plurality of particles on an edge and a surface of the threedimensional shape;
 disposing particles according to an internal distribution rule in an inner part spaced apart from the surface of the threedimensional shape, and disposing particles at a position deviated from the position according to the internal distribution rule, in a space between the inner part and the surface of the threedimensional shape; and
 generating a tetra mesh having a center of the disposed particles as a vertex.
According to still another aspect of the invention, there is provided a program causing a computer to execute:
 a function of inputting shape definition data that defines a threedimensional shape;
 a function of disposing a plurality of particles on an edge and a surface of the threedimensional shape defined by the input shape definition data, disposing particles according to an internal distribution rule in an inner part spaced apart from the surface of the threedimensional shape, disposing particles at a position deviated from the position according to the internal distribution rule, in a space between the inner part and the surface of the threedimensional shape, and generating a tetra mesh having a center of the particles as a vertex; and
 a function of outputting tetra mesh definition data that defines a generated tetra mesh.
A tetra mesh having a shape reflecting the atomic arrangement to be simulated can be generated in the inner part of the threedimensional shape. In the space between the inner part and the surface, particles are displaced from the position according to the internal distribution rule, so the discontinuity of the mesh shape of the tetra mesh in the inner part and tetra mesh on the surface can be relaxed.
The accuracy of the simulation can be improved by disposing particles at the nodes of the tetra mesh and simulating the behavior of the particles using the molecular dynamics method or the renormalization group molecular dynamics method.
A tetra mesh generator and a tetra mesh generation method according to an embodiment will be described with reference to
The processing unit 21 performs a process of generating a tetra mesh based on the input conditions, and outputs the processing result to the output unit 22. The processing result includes tetra mesh definition data that defines the shape of the tetra mesh. The processing unit 21 includes, for example, a computer, and a program for causing the computer to execute various functions for generating a tetra mesh is stored in the storage unit 23. The output unit 22 is a communication device, a removable media writing device, and a display.
In step S1, the processing unit 21 acquires shape definition data that defines a threedimensional shape input from the input unit 20. The shape definition data is, for example, data in standard triangulated language (STL) format, and is created using threedimensional CAD. The data in STL format reproduces a threedimensional surface with a collection of small triangular elements.
In step S2 (
A normal vector can be defined for each triangular element of the shape definition data. If the angle formed by the normal vectors of adjacent triangular elements is equal to or smaller than a predetermined threshold value, the two triangular elements belong to the same section. In a case where the angle formed by the normal vectors of adjacent triangular elements is larger than a predetermined threshold value, the two triangular elements belong to the different sections. For example, the threshold value is about 30 degrees. The boundary of a section is defined as an edge.
In step S3 (
In step S4 (
Thus, based on the position of the particle 35 on the edge 32 or the already disposed particle 36 on the surface, the same processing is repeated until the surface of the threedimensional shape 30 is covered. By this processing, the region where the particle 36 on the surface is disposed expands (grows) from the particle 35 on the edge 32 which is the generation source. Ina case where the particle 35 or 36 is already disposed in the vicinity of the newly disposed particle 37, the particle 37 is not disposed. Here, “vicinity” means a range closer to the particle 35 than the interval between the particles 35 on the edge 32. A region grown from a common generation source is called a homogeneous region.
In step S5 (
The interaction potential between the particle 35 on the edge 32 and the particle 36 on the surface is defined. The virtual particle is moved by solving the equation of motion using this interaction potential. It is assumed that the particles 35 on the edge 32 do not move.
Only repulsive force is considered, by using a spring model as the interaction potential. Further, the size of particles other than the particles on the edge 32 is set to zero, and the particles are expanded with the passage of time, that is, the particle size is increased. When the pressure acting on the particles exceeds a predetermined threshold, the expansion of the particles is stopped. For example, when it expands until it contacts with an adjacent particle, the expansion of the particle is stopped. In a case of solving the equation of motion in a state where the particles are almost in contact with each other, the particle hardly moves even if the time step of the equation of motion is repeated. By setting the initial value of the size of the particle to zero, the particle can be easily displaced.
The pressure Pi acting on the particle i is defined by the following expression.
Here, j means a particle that interacts with the particle i, V_{i }is the volume of the particle i, r_{ij }is the distance between the particle i and the particle j, and φ(r_{ij}) is the potential function between the particle i and the particle j.
When the equation of motion is solved to move particles on the surface of the threedimensional shape 30 (
Next, an example of a method for finding the triangular element closest to the position of the particle 40a deviating from the surface (
After solving the equation of motion, a cell 43 containing particles 40a (
In step S6 (
Delaunay triangulation is performed based on the position of the particles after the relaxation process. Specifically, first, three particles are selected, and a sphere including the center of the three particles on the surface is considered. However, the intersection of the plane and the sphere obtained from the center position of the three particles is assumed to be a great circle. If there is no other particle inside the sphere, a triangle with the center position of the selected three particles as the vertex is adopted as a part of the surface mesh.
However, in this method, a triangle that does not actually constitute the surface of the threedimensional shape 30 may be adopted as a part of the surface mesh. By deleting such triangles, a surface mesh is completed.
The distortion amount Q of the surface mesh created in this way is obtained by calculation. The distortion amount Q is defined by the following expression.
Here, θ_{max }and θ_{min }are the maximum value and the minimum value of the interior angles of the triangles constituting the surface mesh, respectively. θ_{e }is one interior angle of the equilateral triangle, that is, 60°. The distortion amount Q=0 when all the triangles of the surface mesh are regular triangles, and the distortion amount Q=1 when all the vertices of the triangles are arranged on one straight line.
It can be seen that the distortion amount Q decreases as the number of time steps of relaxation process increases. Further, it can be seen that the distortion amount Q of the surface mesh created by the method according to the present embodiment is smaller than the distortion amount Q of the surface mesh created using commercially available software in the related art. In a case where the analysis is performed by a molecular dynamics method using a tetra mesh, it is empirically found that the distortion amount Q is 0.5 or less. By the method according to the present embodiment, a surface mesh that satisfies this condition can be generated.
In step S7 (
Next, the particle arrangement method will be described more specifically. First, the particles are disposed so as to cover the inside of the threedimensional shape 30 (
Next, the particles overlapping with the particles 35 36 (
In step S8 (
In step S9 (
In step S10 (
In a case where the three tetrahedrons pass through two adjacent triangles of the surface mesh, the combination of the vertices of the three tetrahedrons is adjusted in the same manner. The same processing is performed in a case where a plurality of tetrahedrons pass through three or more adjacent triangles of the surface mesh.
In step S11 (
First, tetrahedrons positioned on the surface are extracted from the created tetrahedrons of the tetra mesh. For example, in a case where there is no other tetrahedron that shares one surface of the tetrahedron, the surface is determined to be a surface. If the surface determined to be a surface does not match the triangle of the surface mesh, the tetrahedron is deleted. When the tetrahedron is deleted, anew surface appears, so the new surface is compared with the triangle of the surface mesh. By repeating the process of deleting the tetrahedron, the outer tetrahedron of the threedimensional shape 30 is deleted, and only the inner tetrahedron remains.
Next, the excellent effects of the above embodiment will be described.
In the above embodiment, a tetra mesh having a shape reflecting the atomic arrangement to be simulated can be generated in the inner part of the threedimensional shape. Further, the particles can be disposed almost evenly on the surface or edge of the threedimensional shape. In the space between the inner part and the surface, particles are displaced from the position according to the internal distribution rule, so the discontinuity of the mesh shape of the tetra mesh in the inner part and tetra mesh on the surface can be relaxed.
The accuracy of the simulation can be improved by disposing particles at the nodes of the tetra mesh and simulating the behavior of the particles using the molecular dynamics method or the renormalization group molecular dynamics method.
The present invention is not limited to the embodiment described above. It will be apparent to those skilled in the art that various modifications, improvements, combinations, and the like can be made.
It should be understood that the invention is not limited to the abovedescribed embodiment, but may be modified into various forms on the basis of the spirit of the invention. Additionally, the modifications are included in the scope of the invention.