JP5482175B2 - Boundary particle search system, boundary particle search device, control method, and program - Google Patents

Description

  The present invention relates to a boundary particle search system, a boundary particle search device, a control method, and a program. In particular, the present invention relates to a boundary particle search system and a boundary particle search device that search for particles located at the boundary of an analysis model used in a numerical analysis using a particle method or the like, a control method for controlling the boundary particle search device, and the The present invention relates to a program for a boundary particle search device.

  There are many examples in which quality problems resulting from design defects have evolved into problems related to the existence of the company. Design quality verification methods and quality improvement are important issues. Under such circumstances, numerical analysis methods are used in a wide range of fields as design quality verification methods. Among many numerical analysis methods, the finite element method is used in a wide range of fields such as structural analysis, fluid analysis, and thermal analysis because of its versatility.

  However, in the finite element method, it is necessary to divide the analysis object into elements, and there is a problem that the time required for creating an analysis model becomes enormous in a complicated 3D shape. In recent years, with the spread of three-dimensional CAD, the design has been made three-dimensional, and an analysis model of the finite element method has been created based on detailed three-dimensional design data. Furthermore, the remarkable improvement in the processing capacity of the PC makes it possible to analyze an analysis model that faithfully reproduces the actual shape of the object to be analyzed in a three-dimensional space, or a structure model in which multiple parts are assembled. It tends to become larger and more complicated.

  Under such circumstances, in order to solve the above problems, many mesh-free methods, which are analysis methods that do not use elements, have been developed. Among the mesh-free methods, the particle method has been actively studied in recent years, and is one of the most noticeable mesh-free analysis methods.

  Since the particle method does not need to create an element as described above, there is an advantage that not only an analysis model can be easily created, but also a problem with large deformation that cannot be analyzed by the finite element method can be analyzed.

  In the case of analysis that handles large deformations of free surfaces and boundary surfaces, the particles that make up the boundary surface change every moment, so search for particles located on the boundary surface in the middle of the analysis and assign boundary conditions such as surface tension. There is a need to. FIG. 18 and FIG. 19 show an example of analyzing the shape of a droplet when surface tension is applied to the droplet using the particle method. FIG. 18 to FIG. 19 show that time has passed and the droplet shape is approaching a circle. In the state of FIG. 19 in which the particles positioned on the surface in the state of FIG. 18 have elapsed time, the particles move to the inside of the droplet along with the deformation of the droplet shape, or the particles positioned inside the droplet reach the surface. Has moved. In each step in the middle of the analysis, the accuracy of the analysis is improved by searching for particles located on the surface and applying surface tension.

  Conventionally, in the particle method, a method using a particle number density has been adopted as a method of defining particles constituting the boundary surface. The particle number density is defined by the following formula (1). W is a weight function. The particle number density is calculated as the sum of the particle weight functions within the radius of influence.

In the inside of the incompressible fluid, the particle number density is kept almost constant (n ₀ ), but the particle number density (n _i ) of the particles at the interface is lowered. By utilizing this, as shown in Equation (2) below, the particle number density: n _i is the inside of the particle number density coefficient in the n _0: grains satisfying the β smaller than the value obtained by multiplying a is , Defined as particles located on the interface.

  The coefficient β here is empirically confirmed to be effective as a method for defining a free boundary surface when a value of 0.9 to 0.97 is adopted (see, for example, Non-Patent Document 1). .

The following terms used in the following are defined as follows.
Search: An operation of searching for particles located at the boundary from a plurality of particles according to predetermined processing and determination.
Extraction: An operation for selecting particles satisfying a predetermined condition from a plurality of particles.

  FIG. 20 is a functional block diagram of a conventional boundary particle search system. FIG. 21 is a flowchart of a conventional boundary particle search system. Using the input unit 11, the analysis model data is imported into the boundary particle search system. The analysis model data to be imported is created according to a predetermined format including a particle identification number, a particle coordinate value, a material identification number, and the like. The processes A2 to A8 in the flowchart of FIG. 21 are sequentially performed on all N particles from the smallest particle identification number (in the following description, 1).

Particles existing in the region separately defined by the region setting unit 12 are extracted by the region particle extracting unit 13. The region here is a region defined based on the position coordinates of the selected particle, for example, a region within the influence radius centered on the selected particle generally adopted in the particle method. . Processes A3 to A7 are executed on the M particles extracted by the in-region particle extraction unit 13. Choose one of the extracted particles by particle density calculation unit 14 executes a process A4 of calculating the particle number density n _i in accordance with equation (1). The boundary particle determination unit 15, the calculated particle number density: performed n ₀ is determined whether or not A5 satisfying formula (2): and n _1, calculated reference particle number density at additional processing A1 If satisfied, it is determined that the particle is a boundary particle, and the output unit 16 updates the boundary particle list. If not satisfied, select other particles in the region. When the execution is completed for all M particles extracted by the in-region particle extraction unit 13, the process returns to the process A2, and the same process is repeated for the particle with the particle identification number 2. When the above process is completed for all N particles, the process ends.

Seiichi Koshizuka, “Particle Method”, Maruzen, February 2005, p. 31-32

  However, if the boundary particle is determined only by the particle number density, there is a possibility that there may be a particle that is not determined as the boundary particle although it is located at the boundary.

  In order to solve the above-described problem, according to the first aspect of the present invention, there is provided a boundary particle search system for searching for particles located at the boundary of an analysis model used in numerical analysis using a particle method or the like, the analysis model The search reference particle setting unit that extracts one or a plurality of particles located at the boundary from the position coordinates of all particles constituting the search reference particle, and the search reference particle extracted by the search reference particle setting unit is set as the starting point A vector setting unit that sets a search direction vector indicating a direction to search, an in-region particle extraction unit that extracts other particles existing in a region defined based on the position coordinates of the search reference particle, and a search reference particle Create each position vector of each particle in the region extracted by the in-region particle extraction unit, the size of the position vector, and the angle of the position vector and the search direction vector set by the vector setting unit Comprising a vector calculating unit for calculating for, and a boundary grain determination unit for determining a boundary particles by the size and angle of the vector the vector calculation unit has calculated.

  According to the second aspect of the present invention, there is provided a boundary particle search device for searching for particles located at the boundary of an analysis model used in numerical analysis using a particle method or the like, and the position coordinates of all particles constituting the analysis model A search reference particle setting unit that extracts one or a plurality of particles located at the boundary and uses the search reference particles extracted by the search reference particle setting unit as a search reference particle, and a search direction vector that indicates a search direction starting from the search reference particle Extracted by the vector setting unit for setting the search, the in-region particle extraction unit for extracting other particles existing in the region defined based on the position coordinates of the search reference particles, and the in-region particle extraction unit for the search reference particles A vector calculation unit for generating each position vector of each particle in the region and calculating the size of the position vector and the angle of the position vector and the search direction vector set by the vector setting unit; The size and angle of the vector torque calculation unit has calculated and a boundary particle determination unit that determines the boundary particles.

  According to a third aspect of the present invention, there is provided a control method for controlling a boundary particle search device that searches for particles located at the boundary of an analysis model used in numerical analysis using a particle method or the like, and constitutes an analysis model A search reference particle setting stage that extracts one or a plurality of particles located at the boundary from the position coordinates of all particles as search reference particles, and a search starting from the search reference particles extracted in the search reference particle setting stage A vector setting stage for setting a search direction vector indicating a direction to search, an in-area particle extraction stage for extracting other particles existing in an area defined based on the position coordinates of the search reference particles, and an area for the search reference particles Create each position vector of each particle in the region extracted in the inner particle extraction stage, and set the size of the position vector and the position vector and vector setting stage. Comprising the a vector calculating unit for calculating the angle of the search direction vector, and a boundary grain determination step of determining the magnitude and angle by the boundary grain of vector calculated in the vector calculation step.

  According to a fourth aspect of the present invention, there is provided a program for a boundary particle search device that searches for a particle located at the boundary of an analysis model used in a numerical analysis using a particle method or the like. The search reference particle setting unit that extracts one or more particles located at the boundary from the position coordinates of all the particles that make up the model and makes the search reference particle, the search reference particle extracted by the search reference particle setting unit is the starting point A vector setting unit for setting a search direction vector indicating a direction to search, an in-region particle extraction unit for extracting other particles existing in a region defined based on the position coordinates of the search reference particle, and an in-region for the search reference particle Create each position vector of each particle in the region extracted by the particle extraction unit, and set the size of the position vector and the angle between the position vector and the search direction vector set by the vector setting unit. Vector calculation section calculated for, to function as a boundary particle determination unit that determines a boundary particles by the size and angle of the vector the vector calculation unit has calculated.

  The above summary of the invention does not enumerate all the necessary features of the present invention, and sub-combinations of these feature groups can also be the invention.

  As is clear from the above description, according to the present invention, a vector is derived from the geometric coordinate values of each particle, and the angle between the magnitude of the vector and the vector serving as a reference for search is determined as a criterion for determining boundary particles. Therefore, the particles located at the boundary can be determined as boundary particles without leakage.

It is a functional block of the boundary particle search system of the present invention. It is a flowchart of the boundary particle search system of this invention. It is a system display state figure of the analysis model of the example of the present invention. It is a flowchart of the boundary particle search system of the Example of this invention. It is an analysis model figure of the Example of this invention. It is explanatory drawing of the vector calculation of the Example of this invention. It is explanatory drawing of the vector calculation of the Example of this invention. It is explanatory drawing of the vector calculation of the Example of this invention. It is explanatory drawing of the vector calculation of the Example of this invention. It is explanatory drawing of the vector calculation of the Example of this invention. It is explanatory drawing of the vector calculation of the Example of this invention. It is boundary particle judgment explanatory drawing of the Example of this invention. It is boundary particle judgment explanatory drawing of the Example of this invention. It is boundary particle judgment explanatory drawing of the Example of this invention. It is explanatory drawing of the search direction and reference | standard vector of Example 1 of this invention. It is search direction vector explanatory drawing of Example 2 of this invention. It is a figure which shows an example of the hardware constitutions of the boundary particle search system which concerns on this embodiment. It is a figure which shows the droplet shape analysis example using a particle method. It is a figure which shows the droplet shape analysis example using a particle method. It is a functional block diagram of the conventional boundary particle search system. It is a flowchart of the conventional boundary particle search system.

  Hereinafter, the present invention will be described through embodiments of the invention. However, the following embodiments do not limit the claimed invention, and all combinations of features described in the embodiments are described. It is not necessarily essential for the solution of the invention.

  FIG. 1 is a functional block diagram of the boundary particle search system of the present invention. An input unit 21 that captures analysis model data, a search reference particle setting unit 22 that sets particles as a reference when searching for boundary particles from the captured analysis model data, a search direction vector that indicates a search direction, and Set by a vector setting unit 23 that sets orthogonal search reference vectors, a region setting unit 24 that sets a candidate particle existing region when searching for boundary particles from the captured analysis model data, and a region setting unit 24 A boundary based on the size and angle of the vector calculated by the vector calculation unit 26, a vector calculation unit 26 that performs vector calculation using the extracted particle group, and an in-region particle extraction unit 25 that extracts particles existing in the extracted region A boundary particle determination unit 27 that determines particles and an output unit 28 that outputs particle information determined as boundary particles are provided.

  FIG. 2 is a flowchart showing the best mode of the boundary particle search method of the present invention. Next, the operation of the best mode for carrying out the present invention will be described in detail with reference to FIGS. First, in the boundary particle search system, the analysis model data is imported into the boundary particle search system using the input unit 21. The analysis model data to be imported is created according to a predetermined format including a particle identification number, a particle coordinate value, a material identification number, and the like. After the import, it is displayed on the display device 7 in a two-dimensional XY coordinate system defined in the boundary particle search system. The search reference particle setting unit 22 executes preprocessing (B1 to B4) shown in FIG. From the coordinate values of all the particles of the analysis model, a process B2 for extracting particles having the maximum and minimum coordinate values in the respective axial directions is executed. The particles extracted by this process are stored as control points.

  The number of control points varies depending on the analysis model or from which part of the analysis model the boundary particle is extracted, but at least one particle must be extracted. From the extracted control points, a process B4 for determining one search reference particle as a search start point is executed. Further, the vector setting unit 23 sets the initial value of the search direction vector indicating the search direction using the search start point particle as the start point, and a search reference vector orthogonal to the search direction vector and serving as a reference for angle calculation. Processing B6 for setting an initial value is executed.

  When the particle having the minimum X coordinate value is set as the search reference particle, there is no particle in the negative direction of the X coordinate with respect to the particle. Therefore, as the initial value of the search direction vector, the unit vector (0, 1) is set, and the unit vector (-1, 0) in the negative direction of the X axis is set as the initial value of the search reference vector. Similarly, when the particle having the maximum Y coordinate value is set, there is no particle in the positive direction of the Y coordinate from the particle. Therefore, the unit vector (1, 0) in the X axis direction is used as the initial value of the search direction vector. ) And a unit vector (0, 1) in the positive direction of the Y axis is set as the initial value of the search reference vector.

  From the coordinate value of the control point extracted in process B2, process B7 for determining a path to be searched is executed. For example, when there is one control point, when the boundary particle is searched and the control point is determined to be the boundary particle again, it is assumed that the search path is completed. When there are a plurality of control points, control point 1 → control point 2 →. A search path that is a loop is set like control point X → control point 1 and is used for normal execution of search processing and determination of processing end.

  Next, the process proceeds to the search execution part. A region defined based on the position coordinates of the search reference particles is set by the region setting unit 24. A boundary particle search is performed on the particle group existing in this region, and the boundary particle is determined. The region particle extraction unit 25 executes a process B8 for extracting particles within the region radius. As the region defined based on the position coordinates of the search reference particles, for example, the inside of a circle around the search reference particles is adopted.

  The vector calculation unit 26 obtains a position vector of the extracted particle relative to the search start point particle, executes a process B10 for calculating the size, and executes a process B11 for calculating an angle between the position vector and the search reference vector. . The above vector calculation is performed on all particles extracted from the region (B9 to B12).

  Based on the angle between the size of the in-region particle position vector calculated in the process B10 and the search reference vector calculated in the process B11, the boundary particle determination unit 27 executes the process B13 for determining the particles located at the boundary. Then, the process B14 for outputting the information of the particles determined to be the boundary to the extraction list is executed.

  Processing B15 is executed to update the position vector of the particle determined to be located at the boundary by the boundary particle determination unit 27 with respect to the search reference particle as the search direction vector used for the next search, and is also orthogonal to the search direction vector. Process B16 for updating the search reference vector is executed. A process B <b> 17 is performed in which the particles determined to be positioned on the boundary by the boundary particle determination unit 27 are updated as search reference particles in the next step.

  This completes the first search step. For the updated search reference particles, the above processing is sequentially repeated to search for boundary particles. The search path is compared with the search path set in the process B7, and the search process is terminated when the control point that is the end point of the search path is determined to be a boundary particle.

  Next, a first embodiment will be described with reference to FIGS. FIG. 3 is a system display state diagram of the analysis model according to the embodiment of the present invention. The boundary particle search system executes each function by selecting a button of the command unit 31 or inputting a numerical value directly into the numerical value display unit of the setting unit 34.

  Usually, the boundary particle search system has a global coordinate system 32, and a particle group is displayed on the display unit 33 as an analysis model according to the coordinate system. Information such as the number of particles of the imported analysis model is automatically displayed on the setting unit 34. A format in which the radius of the area defined by the area setting unit 24 is directly input to the setting unit 34 can also be adopted.

  FIG. 4 is a flowchart of the boundary particle search according to the first embodiment. When the execution button of the setting unit 34 is pressed, processing starts according to the flowchart shown in FIG. In the present embodiment, the boundary particle search system will be described as one independent system, but includes a form in which the processing shown in FIG. 4 is executed as a subroutine that constitutes a part of an analysis system that executes numerical calculation.

Definitions of variables in the flowchart shown in FIG. 4 are as follows.
N: Total number of particles in analysis model M: Number of particles extracted from region R ₁ : Size of vector R of boundary particle first candidate Initial value = 0
R ₂ ... Size of the boundary particle second candidate vector R Initial value = 0
φ ₁ ... Angle between vector Q and vector R of boundary particle first candidate Initial value = 2π
φ ₂ ... Angle between vector Q and vector R of boundary particle second candidate Initial value = 2π

  Import the analysis model data of the structure to be analyzed into the boundary particle search system. FIG. 3 shows a state where the imported analysis model is displayed on the display device 7. The total number of particles: N is 172.

  For the called analysis model, the search reference particle setting unit investigates the coordinate values of all the particles, and executes a process C2 for extracting particles having the maximum and minimum coordinate values in both the X and Y directions. In the analysis model of FIG. 3, the four particles shown in FIG. 5 and particle identification numbers 1, 30, 40, and 50 are extracted. The extracted particles are stored as control points, and a process C4 for determining search reference particles that are search start points from the four control points is executed. As shown in FIG. 5, the particle identification number 1 (hereinafter referred to as particle 1) is set as the search reference particle in the first step.

  Next, processing C5 and C6 for initial setting of the search direction vector: P starting from the particle 1 and the search reference vector: Q are executed. As shown in FIG. 3, since there is no particle in the negative X direction from the search reference particle 1, the Y-axis positive direction is taken as the initial value of the search direction, and the search direction vector: P has a size of 1 The unit vector (0, 1) is taken as the initial value of the search reference direction, the X-axis negative direction is taken, and the unit vector (-1, 0) of size 1 is adopted as the search reference vector: Q.

  Further, as a search path, a process C7 for setting a closed loop of control point 1 → control point 30 → control point 40 → control point 50 → control point 1 in the direction of search direction vector: P is executed. This completes the preprocessing part of the search.

  Next, the process of the search execution part will be described. Particles existing in a region of radius: r around the particle 1 as the search reference particle determined in the preprocessing are extracted. The particles extracted here become the search target of the boundary particles and become candidates for the boundary particles. Therefore, the determination of this region is important, and it must be set so that particles located at the boundary always exist in the region. When the radius: r is set small, the number of search target particles is reduced and the calculation time is shortened. However, there are cases where particles to be selected as boundary particles do not exist in the region. Conversely, if the radius r is set large, the number of particles to be searched increases and the calculation time increases. Radius: As a value set as r, a value 2.0 to 3.5 times the basic particle interval is adopted. The basic particle interval is a value set at the time of creating the analysis model, and the inside of the model in which the particles are filled is an inter-particle distance at which particles are created at almost equal intervals with this value. Let M be the number of particles that exist in the region and are candidates for boundary particles. In this embodiment, a circle centered on the search reference particle is adopted as the region. However, if a boundary particle candidate is included, the center can be moved, or a region other than the circle can be defined.

  One of the particles in the region is selected, and the processes C9 to C16 are performed on the M particles extracted from the region.

The position vector: R of the selected particle with respect to the search reference particle is obtained, and the inner product Q · R and the outer product Q × R of the position vector size | R | and the search reference vector: Q are calculated. The angle θ between the vectors Q and R is obtained from the calculated inner product and outer product. If it demonstrates using FIG. 6, let the search reference | standard particle | grains be O (hatched hatching) and the particle | grains (black circle) in an area | region. The subscript of the particle in the region is a particle identification number, which is the number given to all particles without duplication. A particle 2 in the region is selected, a vector R ₁ is obtained, and an angle θ ₁ between the vector Q and the vector R ₁ is obtained. The process C13 for determining | θ ₁ | ≦ φ ₁ is executed. Since this is the first process, 2π is set as an initial value in φ ₁ so that the determination process C13 is always true.

In the case of the particle 2, it is determined to be true by the determination of | θ ₁ | ≦ φ ₁ , and the particle 2 is stored as the first candidate of the boundary particle by the processing C15, and the vector size | R | , Stored as R ₁ and φ ₁ , respectively.

Next, as shown in FIG. 6, the particles 3 are selected. Similarly, a position vector: R ₂ with respect to the search reference particle is obtained, and an inner product Q · R ₂ and an outer product Q × R ₂ of the vector magnitude | R ₂ | and the search reference vector: Q are calculated. An angle θ ₂ between the vectors Q and R is obtained from the calculated inner product and outer product. In process C13 for determining | θ ₂ | ≦ φ ₁ , θ ₁ is set for φ ₁ in the process for particle 1, so that | θ ₂ |> | θ ₁ | The process for this ends.

Subsequently, as shown in FIG. 7, the particle 4 is selected, and the vector magnitude | R ₃ | and the angle θ ₃ are similarly calculated. In process C13 for determining | θ ₃ | ≦ φ ₁ , | θ ₃ | ≦ | θ ₁ | The size R ₁ and the angle phi ₁ vector particles 1 which have been stored as the first candidate boundary particles ever run the process C14 to substitute R ₂ and phi ₂ as a second candidate border particles, particles 4 A process C15 is executed to store the vector size | R ₃ | and the angle θ ₃ of R ₁ and φ ₁ as boundary particle first candidates, respectively.

  When the above processing is performed on all M particles in the region, the particle 5 is finally stored as the boundary particle first candidate and the particle 6 is stored as the boundary particle second candidate, as shown in FIG. Become.

When the vector sizes R ₁ and R ₂ of the two boundary particle candidates are compared and R ₁ ≦ R ₂ is satisfied, the process C 17 is performed to determine the particle 5 as the boundary particle first candidate as the boundary particle, A process C18 for adding the information of the particle 5 to the boundary particle list is executed. At this time, information on the particles 1 and 5 is stored in the boundary particle list.

  The next step C19 is executed to update the position vector of the particle 5 with respect to the particle 1 as the search direction vector P, and the search reference vector Q is rotated 90 degrees counterclockwise. The process C20 for updating to a new vector is executed. As the search reference particle, a process C21 for updating to the particle 5 determined as the boundary particle is executed. The same processing is executed for the new search reference particles, and the boundary particles are sequentially searched.

  The process of determining the particle 10 in FIG. 5 as the boundary particle and searching for the next boundary particle will be described. As shown in FIG. 9, particles existing in a region of radius: r centering on the particle 10 are extracted.

  Select one of the particles in the region and perform the following process on the particles that are in the region. However, since particles that have already been determined to be boundary particles also exist in the region, they are already determined to be boundary particles. For particles (hatched hatching), the processing is transferred to the next particle without performing the following processing.

  As described above, the position vector of the particle 10 with respect to the particle 9 may be adopted as the next search direction vector: P. However, the change in the direction and size of the search direction vector in the previous step indicated by a dotted line. Can be predicted from. For example, as shown in FIG. 9, when the boundary is changing along a substantially circular shape, the search direction vector: P is considered to change with a substantially constant angular change, so the next search direction vector is indicated by a solid line in the figure. Vector P.

Similarly, the position vector: R of the selected particle with respect to the search reference particle is obtained, and the inner product Q · R and the outer product Q × R of the vector size | R | and the search reference vector: Q are calculated. The angle θ between the vectors Q and R is obtained from the calculated inner product and outer product. The particle 14 having the minimum | θ | is the boundary particle first candidate, and the particle 15 having the minimum | θ | is the boundary particle second candidate. Also in this case, when the vector sizes R ₁ and R ₂ of the boundary particle candidate are compared, R ₁ ≦ R ₂ is satisfied, so the particle 14 is determined as the boundary particle.

  Next, a process of determining the particle 20 in FIG. 5 as a boundary particle and searching for the next boundary particle will be described. As shown in FIG. 10, particles existing in a region of radius: r centering on the particles 20 are extracted.

Similarly, the particle 25 having the minimum | θ | is the boundary particle first candidate, and the particle 24 having the minimum | θ | is the boundary particle second candidate. In this case, when the sizes R ₁ and R ₂ of the boundary particle candidate vectors are compared, R ₁ > R ₂ , and the boundary particles are determined by the following processing. As shown in FIG. _11, when a R 1> _{R 2,} as shown in FIGS. 12 to 14, between _{R 1} and the elementary particles Distance: to case analysis on the relationship between _{l 0.}

When R ₁ ≦ l ₀ (in the case of FIG. 12), the particle 25 is determined as the boundary particle. Since the interval between the particles 20 and the particles 25 is less than or equal to the basic particle interval, the inner particles 24 do not need to be used as boundaries.

When R ₁ > α × ₁₀ (in the case of FIG. 14), the particle 24 is determined as the boundary particle. Since the interval between the particle 20 and the particle 25 is farther than the basic particle interval, the inner particle 24 is used as a boundary.

In the case of l ₀ <R ₁ <α × l ₀ (in the case of FIG. 13), as shown in FIG. 13, the region inside the isosceles triangle (cross-hatching) with R ₁ as the base and low angle: ω When the particle 24 exists in the boundary region, the particle 24 is defined as a boundary particle. When the particle 24 does not exist, the particle 25 is defined as a boundary particle.

The above α and ω take numerical values in the following range.
30 ° ≦ ω ≦ 45 ° 1.2 ≦ α ≦ 2.0

  The above processing is performed as a search path: control point 1 → control point 30 → control point 40 → control point 50 → control point 1 whether all the control points 1 have been passed.

A method for obtaining the angle θ between the vectors Q and R from the inner product and outer product of the search reference vector: Q and the position vector: R will be described in detail below. As shown in FIG. 15, a local coordinate system is considered in which the search reference particle is the origin and the search direction vector: P and the search reference vector: Q are axial directions. Each quadrant is divided into Zone1 to Zone4. Since tan θ ′ is obtained from the inner product and outer product, θ ′ is calculated by an inverse function. With respect to the obtained θ ′, it is determined which Zone is located from the sign of the inner product and outer product, and θ is obtained according to the following equation.
Zone1: inner product> 0 and outer product ≦ 0 θ = θ ′
Zone2: inner product ≦ 0 and outer product ≦ 0 θ = − (π−θ ′)
Zone3: inner product ≦ 0 and outer product> 0 θ = − (π−θ ′)
Zone4: inner product> 0 and outer product> 0 θ = − (2.0π−θ ′)

  Next, a second embodiment will be described with reference to FIG. In the first embodiment described above, two vectors, a search direction vector and a search reference vector orthogonal to the search direction vector, are used. However, it is also possible to use a search direction vector alone as a search reference vector. In process C11 in the flowchart of FIG. 4, in the first embodiment, the angle is calculated from the inner product and outer product of the search reference vector and the particle position vector extracted from the region, but in the second embodiment, the search direction vector and A search direction vector and a position vector angle are calculated from the inner product and outer product of the position vectors. As shown in FIG. 16, considering a rectangular coordinate system centered on the search reference particle and having the search direction vector in the axial direction, each quadrant is divided into Zone 1 to Zone 4 as in FIG. 15. As in the case of the first embodiment, tan θ ′ is obtained from the inner product and outer product, and θ ′ is calculated by an inverse function. With respect to the obtained θ ', it is determined which Zone is located from the sign of the inner product and outer product, and θ is obtained.

  According to the present invention, when the particle method is used for analyzing the behavior of a fluid accompanied by large deformation, particles existing at the boundary can be efficiently searched from the analysis model of the particle method, and contact determination with the wall surface can be performed. It is effective when applying boundary conditions such as surface tension.

  FIG. 17 shows an example of a hardware configuration when the boundary particle search system is configured by an electronic information processing apparatus such as a computer. The boundary particle search system includes a CPU (Central Processing Unit) peripheral part, an input / output part, and a legacy input / output part. The CPU peripheral section includes a CPU 902, a RAM (Random Access Memory) 903, a graphic controller 904, and a display device 905 that are connected to each other by a host controller 901. The input / output unit includes a communication interface 907, a hard disk drive 908, and a CD-ROM (Compact Disk Read Only Memory) drive 909 connected to the host controller 901 by the input / output controller 906. The legacy input / output unit includes a read only memory (ROM) 910, a flexible disk drive 911, and an input / output chip 912 that are connected to the input / output controller 906.

  The host controller 901 connects the RAM 903, the CPU 902 that accesses the RAM 903 at a high transfer rate, and the graphic controller 904. The CPU 902 operates based on programs stored in the ROM 910 and the RAM 903 to control each unit. The graphic controller 904 acquires image data generated by the CPU 902 or the like on a frame buffer provided in the RAM 903 and displays the image data on the display device 905. Instead of this, the graphic controller 904 may include a frame buffer for storing image data generated by the CPU 902 or the like.

  The input / output controller 906 connects the host controller 901 to the hard disk drive 908, the communication interface 907, and the CD-ROM drive 909, which are relatively high-speed input / output devices. The hard disk drive 908 stores programs and data used by the CPU 902. The communication interface 907 is connected to the network communication device 991 to transmit / receive programs or data. The CD-ROM drive 909 reads a program or data from the CD-ROM 992 and provides it to the hard disk drive 908 and the communication interface 907 via the RAM 903.

  The input / output controller 906 is connected to a ROM 910, a flexible disk drive 911, and a relatively low-speed input / output device such as an input / output chip 912. The ROM 910 stores a boot program executed when the boundary particle search system is started, or a program depending on the hardware of the boundary particle search system. The flexible disk drive 911 reads a program or data from the flexible disk 993 and provides it to the hard disk drive 908 and the communication interface 907 via the RAM 903. The input / output chip 912 connects various input / output devices via the flexible disk drive 911 or a parallel port, a serial port, a keyboard port, a mouse port, and the like.

  A program executed by the CPU 902 is stored in a recording medium such as a flexible disk 993, a CD-ROM 992, or an IC (Integrated Circuit) card and provided by a user. The program stored in the recording medium may be compressed or uncompressed. The program is installed in the hard disk drive 908 from the recording medium, read into the RAM 903, and executed by the CPU 902. The program executed by the CPU 902 includes the boundary particle search system, the input unit 21, the search reference particle setting unit 22, the vector setting unit 23, the region setting unit 24, and the in-region particle extraction described with reference to FIGS. Function as a unit 25, vector calculation unit 26, boundary particle determination unit 27, and output unit 28.

  The program shown above may be stored in an external storage medium. As a storage medium, in addition to a flexible disk 993 and a CD-ROM 992, an optical recording medium such as a DVD (Digital Versatile Disk) or a PD (Phase Disk), a magneto-optical recording medium such as an MD (MiniDisk), a tape medium, and an IC card A semiconductor memory or the like can be used. Further, a boundary particle search system may be provided as a program via a network using a storage medium such as a hard disk or a RAM provided in a server system connected to a dedicated communication network or the Internet as a recording medium.

  As mentioned above, although this invention was demonstrated using embodiment, the technical scope of this invention is not limited to the range as described in the said embodiment. It will be apparent to those skilled in the art that various modifications or improvements can be added to the above embodiment. It is apparent from the description of the scope of claims that embodiments with such changes or improvements can be included in the technical scope of the present invention.

21 Input unit 22 Search reference particle setting unit 23 Vector setting unit 24 Region setting unit 25 In-region particle extraction unit 26 Vector calculation unit 27 Boundary particle determination unit 28 Output unit 901 Host controller 902 CPU
903 RAM
904 Graphic controller 905 Display device 906 Input / output controller 907 Communication interface 908 Hard disk drive 909 CD-ROM drive 910 ROM
911 Flexible disk drive 912 I / O chip 991 Network communication device 992 CD-ROM
993 Flexible disk

Claims (9)

A boundary particle search system for searching for particles located at the boundary of an analysis model used in numerical analysis using a particle method,
A search reference particle setting unit that extracts one or a plurality of particles located at the boundary from the position coordinates of all particles constituting the analysis model, and sets the search reference particles as a search reference particle;
A vector setting unit for setting a search direction vector indicating a search direction starting from the search reference particle extracted by the search reference particle setting unit;
An in-region particle extraction unit for extracting other particles existing in the region defined based on the position coordinates of the search reference particles;
Create each position vector of each particle in the region extracted by the in-region particle extraction unit with respect to the search reference particle, and calculate the size of the position vector and the angle of the position vector and the search direction vector set by the vector setting unit A vector calculator to perform,
A boundary particle search system comprising a boundary particle determination unit that determines boundary particles based on the magnitude and angle of the vector calculated by the vector calculation unit. The vector setting unit sets a search reference vector orthogonal to the search direction vector,
The in-region particle extraction unit extracts other particles existing in the region defined based on the position coordinates of the search reference particles,
The vector calculation unit creates each position vector of each particle extracted from the region by the intra-region particle extraction unit with respect to a search reference particle, and sets the size of the position vector, the position vector, and the vector setting unit. Calculate the angle of the search reference vector
The boundary particle search system according to claim 1, wherein the boundary particle determination unit determines boundary particles based on the magnitude and angle of the vector calculated by the vector calculation unit. 2. The boundary particle search system according to claim 1, wherein the vector setting unit updates a position vector of a newly determined search reference particle with respect to a search reference particle before determination as a search direction vector in a search process. The vector setting unit analyzes a difference based on a search direction vector size and an angle change history in a search process, predicts a next search direction, and newly updates the search direction vector. The boundary particle search system according to 1. In the search process, the vector setting unit newly updates the position vector of the newly determined search reference particle with respect to the search reference particle before determination as a new search direction vector, and newly adds a vector orthogonal to the updated search direction vector. The boundary particle search system according to claim 2, wherein the boundary particle search system is updated as a search reference vector. In the search process, the vector setting unit analyzes the difference based on the size of the search direction vector and the history of angle changes, predicts the next search direction, and newly updates the search direction vector. The boundary particle search system according to claim 2, wherein a vector orthogonal to the search direction vector is newly updated as a search reference vector. A boundary particle search device that searches for particles located at the boundary of an analysis model used in numerical analysis using a particle method,
A search reference particle setting unit that extracts one or a plurality of particles located at the boundary from the position coordinates of all particles constituting the analysis model, and sets the search reference particles as a search reference particle;
A vector setting unit for setting a search direction vector indicating a search direction starting from the search reference particle extracted by the search reference particle setting unit;
An in-region particle extraction unit for extracting other particles existing in the region defined based on the position coordinates of the search reference particles;
Create each position vector of each particle in the region extracted by the in-region particle extraction unit with respect to the search reference particle, and calculate the size of the position vector and the angle of the position vector and the search direction vector set by the vector setting unit A vector calculator to perform,
A boundary particle search device comprising: a boundary particle determination unit that determines boundary particles based on the magnitude and angle of the vector calculated by the vector calculation unit. A control method for controlling a boundary particle search device that searches for particles located at the boundary of an analysis model used in numerical analysis using a particle method or the like,
A search reference particle setting stage in which one or a plurality of particles located at the boundary are extracted from the position coordinates of all particles constituting the analysis model and set as a search reference particle,
A vector setting step for setting a search direction vector indicating a search direction starting from the search reference particle extracted in the search reference particle setting step;
In-region particle extraction stage for extracting other particles existing in the region defined based on the position coordinates of the search reference particles;
Create each position vector of each particle in the region extracted in the region particle extraction step with respect to the search reference particle, the size of the position vector, and the angle of the position vector and the search direction vector set in the vector setting step A vector calculation unit for calculating
A control method comprising a boundary particle determination step of determining boundary particles based on the magnitude and angle of the vector calculated in the vector calculation step. A program for a boundary particle search device that searches for particles located at the boundary of an analysis model used in numerical analysis using a particle method or the like, the boundary particle search device comprising:
A search reference particle setting unit that extracts one or a plurality of particles located at the boundary from the position coordinates of all particles constituting the analysis model, and sets the search reference particles.
A vector setting unit for setting a search direction vector indicating a search direction starting from the search reference particle extracted by the search reference particle setting unit;
An in-region particle extraction unit for extracting other particles existing in the region defined based on the position coordinates of the search reference particles;
Create each position vector of each particle in the region extracted by the in-region particle extraction unit with respect to the search reference particle, and calculate the size of the position vector and the angle of the position vector and the search direction vector set by the vector setting unit Vector calculator,
A program that functions as a boundary particle determination unit that determines boundary particles based on the magnitude and angle of a vector calculated by the vector calculation unit.

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