WO2004084100A1 - Element division apparatus, method thereof, program thereof, and recording medium containing the program - Google Patents

Element division apparatus, method thereof, program thereof, and recording medium containing the program Download PDF

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Publication number
WO2004084100A1
WO2004084100A1 PCT/JP2003/003155 JP0303155W WO2004084100A1 WO 2004084100 A1 WO2004084100 A1 WO 2004084100A1 JP 0303155 W JP0303155 W JP 0303155W WO 2004084100 A1 WO2004084100 A1 WO 2004084100A1
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WIPO (PCT)
Prior art keywords
node
information
nodes
center
coordinate
Prior art date
Application number
PCT/JP2003/003155
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French (fr)
Japanese (ja)
Inventor
Shigeto Kikukawa
Hideo Ito
Original Assignee
Caedom Inc.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Caedom Inc. filed Critical Caedom Inc.
Priority to AU2003213399A priority Critical patent/AU2003213399A1/en
Priority to PCT/JP2003/003155 priority patent/WO2004084100A1/en
Publication of WO2004084100A1 publication Critical patent/WO2004084100A1/en

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Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
    • G06T17/205—Re-meshing

Definitions

  • the present invention relates to an element dividing device for performing a subdivision process on a finite element method analysis mesh formed by a plurality of nodes and elements, a method thereof, a program thereof, and a recording medium recording the program thereof.
  • the fully automatic mesh generation method specifies the overall mesh size and partial mesh size of the 3D shape of the structure that is the analysis model.
  • a computer automatically calculates a polygon or a polyhedron, which is a figure (element: element) composed of a line connecting these points, with a computer. Create a mesh.
  • a structure since a structure has a complicated shape having a curved surface, a concave portion, and the like, it is created by a tetrahedral element in consideration of computational efficiency.
  • the semi-automatic mesh generation method the three-dimensional shape of a structure is divided into predetermined portions and divided into simple two-dimensional or three-dimensional shapes. Then, a node is automatically calculated and created for each subdivided portion, and a mesh is created.
  • the manual mesh generation method refers to the 3D shape of the structure and Create a polygon element and a polyhedral element while connecting these nodes.
  • a mesh is created by creating a polygon element and a polyhedral element one by one so that the building blocks are stacked.
  • the mesh structure for the finite element method analysis is composed of a tetrahedral element having triangular faces, a pentahedral element having a triangular prism shape, and a quadrangular face. This is the hexahedral element that was created.
  • these polyhedrons better analysis results can be obtained by using a mesh composed of pentahedral elements than tetrahedral elements and hexahedral elements than pentahedral elements.
  • a mesh can be generated only with a hexahedral element if it has a simple three-dimensional shape, but a hexahedral element can be created as a complex shape having curved surfaces and concave portions is formed. Disappears.
  • the computation by the computer is interrupted halfway and the mesh cannot be generated, so tetrahedral elements are mainly used. For this reason, the mesh structure created by the fully automatic mesh generation method is difficult to obtain detailed analysis results, and can be used only for finite element analysis for limited applications.
  • the present invention provides an element dividing apparatus, which can easily and easily subdivide elements in a short time, and can easily and subdivide only three-dimensional elements into hexahedral elements in a short time. It is intended to provide the program and a recording medium on which the program is recorded. Disclosure of the invention
  • the present invention subdivides a mesh for finite element method analysis formed by a plurality of nodes and a plurality of elements formed in a closed plane region by selectively connecting any of the nodes.
  • An element dividing device for processing comprising: shape information recognizing means for obtaining point information of the plurality of nodes and shape information having surface information of the plurality of elements; Computing means for subdividing the element by operation of the shape information, wherein the computing means newly creates a midpoint between the adjacent nodes and a new node at the center of the element, and An element dividing device characterized by subdividing the element by connecting a node and the center node.
  • the arithmetic unit calculates the midpoint between the adjacent nodes and the center of the element based on the point information of the plurality of nodes and the surface information of the plurality of elements of the shape information acquired by the shape information recognizing unit. Is calculated to create new nodes respectively, and a calculation process for subdividing elements by connecting the middle node and the center node is performed. As a result, even a coarsely created mesh can be easily subdivided in a short time.
  • the point information includes coordinate information of the node
  • the calculating means generates a node at the middle point by averaging the coordinate values of the coordinate information of the adjacent nodes to form the element. It is preferable to create a central node by performing an operation of averaging the coordinate values of the coordinate information of the node.
  • the shape information having the point information including the coordinate information of the node is acquired, and the calculating means averages the coordinate values of the coordinate information of the adjacent nodes to create the middle node, thereby forming the element.
  • the center node is created by averaging the coordinate values of the coordinate information of the target node.
  • An element dividing device to be processed comprising: A shape information recognizing unit that obtains shape information having three-dimensional information of the element, and a calculating unit that subdivides the element by calculating the shape information obtained by the shape information recognizing unit.
  • a shape information recognizing unit that obtains shape information having three-dimensional information of the element
  • a calculating unit that subdivides the element by calculating the shape information obtained by the shape information recognizing unit.
  • the arithmetic unit based on the point information of the plurality of nodes of the shape information acquired by the shape information recognizing unit and the three-dimensional information of the plurality of elements, the midpoint between the adjacent nodes and the outer surface of the element A new node is created by calculating the center of the plane area and the center of gravity of the element, and a line connecting the center node and the center node, and a line connecting the center node and the center of gravity node.
  • the point information includes coordinate information of the node
  • the calculating unit generates a midpoint by averaging coordinate values of the coordinate information of the node, and calculates a plane area on an outer surface of the element. It is preferable that the center is created by an operation of averaging the coordinate values of the coordinate information of the constituent nodes, and that the center is created by an arithmetic operation of averaging the coordinate values of the coordinate information of the nodes forming the element.
  • the shape information having the point information including the coordinate information of the node is obtained, and the calculating means averages the coordinate values of the coordinate information of the adjacent nodes to create the middle node, thereby obtaining the outer surface of the element.
  • a center node is created by an operation that averages the coordinate values of the coordinate information of the nodes that make up the plane area of, and a node at the center of gravity is created by an operation that averages the coordinate values of the coordinate information that is the nodes that make up the element.
  • a method for subdividing a mesh for finite element method analysis comprising: The point information of the node and the shape information having the surface information of the element are obtained, and the midpoint between the adjacent nodes and the center of the element of the obtained shape information are calculated to obtain a new node. Setting, and performing an operation of subdividing the element by connecting the set middle node and the center node.
  • the element dividing method uses a computer to form a plurality of nodes and a plurality of elements formed into a closed polyhedron region by selectively connecting any of these nodes.
  • An element dividing method for subdividing a mesh for finite element method analysis comprising: acquiring shape information having point information of the plurality of nodes and three-dimensional information of the element; and acquiring the shape information adjacent to the acquired shape information.
  • the midpoint between the nodes, the center of the plane area of the outer surface of the element, and the center of gravity of the element are calculated and set as a new node, and the set node of the midpoint and the node at the center are set.
  • the operation of subdividing the above-mentioned element by a closed plane area newly formed by a connecting line and a line connecting the center node and the node of the center of gravity may be performed.
  • the element division program of the present invention causes a computer to execute the above-described element division method of the present invention.
  • the above-described element dividing method of the present invention can be executed by installing the program on a computer using a general-purpose computer, and the use of the present invention can be greatly promoted.
  • the number of computers is not limited to one, and includes, for example, a configuration in which a plurality of computers are combined in a network.
  • a recording medium of the present invention is characterized by recording the above-described element division program of the present invention.
  • FIG. 1 is a block diagram showing a schematic configuration of a three-dimensional element dividing device according to one embodiment of the present invention.
  • FIG. 2 is a schematic diagram showing tetrahedral elements constituting a mesh generated in a three-dimensional shape of original data according to the embodiment.
  • FIG. 3 is a schematic diagram showing pentahedral elements constituting a mesh generated in a three-dimensional shape of the original data according to the embodiment.
  • FIG. 4 is a schematic diagram showing hexahedral elements constituting a mesh generated in a three-dimensional shape of the original data according to the embodiment.
  • FIG. 5 is a schematic diagram showing a situation in which a tetrahedral element constituting a three-dimensional mesh of the original data is subdivided in the embodiment.
  • FIG. 6 is a schematic diagram showing a situation in which a pentahedral element constituting a three-dimensional mesh of the original data is subdivided in the embodiment.
  • FIG. 5 is a schematic diagram showing a situation in which a hexahedral element constituting a three-dimensional mesh of the original data is subdivided in the embodiment.
  • FIG. 8 is a schematic diagram showing a situation in which a three-dimensional shape of the original data of the preprocessing is created in the one embodiment.
  • FIG. 9 is a schematic diagram showing a situation in which a three-dimensional shape of the original data of the preprocessing is created in the embodiment.
  • FIG. 10 is a schematic diagram showing a situation in which a three-dimensional shape of the original data of the preprocessing is created in the embodiment.
  • FIG. 11 is a schematic diagram showing a situation in which a three-dimensional shape of the original data of the preprocessing is created in the embodiment.
  • FIG. 12 is a schematic diagram showing a situation in which a mesh is generated in the three-dimensional shape of the original data of the preprocessing according to the embodiment.
  • FIG. 13 is a schematic diagram showing a three-dimensional shape in which a mesh, which is original data of preprocessing, is generated in the embodiment.
  • FIG. 14 is a flowchart showing the operation of the subdivision processing in the embodiment.
  • FIG. 15 is a flowchart showing the operation of the node processing in the subdivision processing.
  • FIG. 16 is a flowchart showing the operation of element processing in the subdivision processing.
  • FIG. 17 is a flowchart showing the operation of the intermediate node processing in the subdivision processing.
  • FIG. 18 is a flowchart showing the operation of the output process in the subdivision process.
  • FIG. 19 is a schematic diagram showing a three-dimensional shape in which the mesh created by the preprocessing is generated.
  • FIG. 20 is a schematic diagram showing a three-dimensional shape of the mesh structure created by the subdivision processing.
  • FIG. 21 is a graph showing the transition of the number of meshes divided by the subdivision processing.
  • FIG. 22 is a graph showing the transition of the degree of distortion of the element divided by the subdivision processing.
  • FIG. 23 is a schematic diagram showing a situation in which a triangular element constituting a mesh of original data is subdivided in another embodiment.
  • FIG. 24 is a schematic diagram showing a situation in which quadrangular elements constituting a mesh of original data are subdivided in another embodiment.
  • FIG. 1 is a block diagram showing a schematic configuration of a three-dimensional element dividing device according to the present embodiment.
  • reference numeral 1 denotes a three-dimensional element decomposing device
  • the three-dimensional element decomposing device 1 includes an input means 2, a processing device main body 3, a display means 4, and an output means 5.
  • the input means 2 is connected to the processing device main body 3. Then, the input means 2 sets and inputs the original data of the three-dimensional shape in which the mesh is formed in advance to the processing device main body 3 by an input operation.
  • the input means 2 includes, for example, a processing device such as a reading device for reading original data stored on a magnetic disk or an optical disk as a storage medium by operating a keyboard or a mouse, a receiving device for receiving a signal transmitted from another computer, or the like. Any configuration that allows the main body 3 to set and input the original data can be used.
  • the original data entered in this setting is, for example, universal data that is used as standard in CAD (Computer Aided Design) that processes 3D shape data.
  • the data of the three-dimensional shape generated by generating a mesh by using the above method is used. Not only universal data but also any compatible data format such as parc data format can be supported.
  • the original data is composed of a series of polyhedral elements including at least one of tetrahedrons, pentahedrons, and hexahedrons that form a three-dimensional mesh.
  • these polyhedral elements are closed points surrounded by lines connecting the nodes of the vertices (nodes ode) (as shown in the figure) and these adjacent nodes. It is composed of three-dimensional information of polyhedron-shaped elements (elements) composed of planar regions.
  • the point information of the node is associated with the number information (1, 2, 3, 4, 4,...), which is a symbol for identifying the node as shown in FIGS. Coordinate information.
  • the three-dimensional information is information of a combination of numbers sequentially assigned to each node constituting the element. These nodes are represented by elements
  • the shape information of the set of polyhedrons used is the original data of the three-dimensional shape for which the mesh has been generated.
  • the processing apparatus main body 3 includes a three-dimensional shape data recognition means 11 as shape information recognition means, a calculation means 12, and a storage means 13.
  • the three-dimensional shape data recognizing means 11 reads the original data set and input by the input means 2 as a program developed on an OS (Operating System) for controlling the operation of the entire three-dimensional element dividing device 1. recognize. That is, it recognizes the shape information on the nodes and elements that make up the three-dimensional mesh of the original data.
  • the three-dimensional shape data recognition means 11 is connected to the storage means 13 and sends the recognized original data to the storage means 13 for storage.
  • the computing means 12 is a program developed on an OS (operating system) for controlling the operation of the entire three-dimensional element dividing device 1 as a program of the three-dimensional shape recognized by the three-dimensional shape data recognizing means 11. An operation for subdividing the mesh is performed.
  • the calculation means 12 includes a midpoint creation means 15, a center creation means 16, a center of gravity creation means 17, and an element creation means 18.
  • the midpoint creating means 15 performs a process of creating a new node at the midpoint between the nodes recognized by the three-dimensional shape data recognizing means 11. Specifically, as shown in Figs. 5 to 7, the coordinates of the midpoint between the coordinates of the coordinate information of the node recorded as universal data of the original data (in Figs. 5 to 7). (Calculate in Fig. 5 to Fig. 7.
  • the midpoint between the two nodes (xl, y1, zl) and (x2, y2, ⁇ 2) is the average of each node, that is, ((xl + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2).
  • the obtained midpoint is set as a new node ( ⁇ in FIGS. 5 to 7), for example, al, a2, a3, a4, a5, a6,. , New numbers are sequentially assigned, associated with the coordinate information of the calculation result, and set as new point information.
  • the center creation means 16 performs processing for creating a node at the center of each surface of each polygon element recognized by the three-dimensional shape data recognition means 11. Specifically, Figure 5 does not Then, as shown in Fig. 7, the coordinates of the center of the plane (the garden in Figs. 5 to 7), which is a plane area surrounded by the line connecting the nodes of the original data, are calculated.
  • the coordinates of each node constituting the surface are (xl, y1, ⁇ 1), ( ⁇ 2, y2, ⁇ 2) and ( ⁇ 3, y3, ⁇ 3)
  • the coordinates of the center are The average of each node, that is, ((xl + x2 + x3) / 3, (yl + y2 + y3) / 3, (z1 + z2 + z3) 3) is calculated.
  • the obtained center is set as a new node ( ⁇ in FIGS. 5 to 7). For example, as shown in FIGS. 5 to 7, b1, b2, b3, b4,.
  • a new number is assigned, associated with the coordinate information of the calculation result, and set as new point information.
  • the center-of-gravity creating means 17 performs a process of creating a node at the center of gravity of each polygon element recognized by the three-dimensional shape data recognizing means 11. Specifically, as shown in FIGS. 5 to 7, the coordinates of the center of gravity of the polygonal element of the original data ( ⁇ in FIGS. 5 to 7) are calculated.
  • the coordinates of each node constituting a polygon element are (xl, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y 4, z 4), the coordinates of the center of gravity are the average of each node, that is, ((xl + x2 + x3 + x4) / 4, (yl + y2 + y3 + y4) / A , (zl + z 2 + z 3 + z 4) / 4).
  • the obtained center of gravity is set as a new node ( ⁇ in FIG. 5 or FIG. 7), and a new number is assigned, for example, as shown by c 1 in FIG. 5 to FIG.
  • the element creation means 18 is a plane area surrounded by a line connecting the nodes newly created by the middle point creation means 15, the center creation means 16 and the center of gravity creation means 17. Create a hexahedral element to be partitioned. Specifically, as shown in FIGS. 5 to 7, a polyhedron defined by a line segment between each midpoint and the center and a line segment between each center and the center of gravity is As described above, new three-dimensional information is set in the order of the number assigned to the node, and a hexahedral element is formed by dividing it into plural It is.
  • the tetrahedral element is divided into four hexahedral elements
  • the pentahedral element is divided into six hexahedral elements
  • the hexahedral element is divided into eight elements. It is divided into hexahedral elements.
  • the processing data obtained by adding the point information and the three-dimensional information of the new node element to the original data in this way is sent to the storage means 13 and stored.
  • the storage means 13 stores programs such as OS (0 perating system) for controlling the operation of the entire three-dimensional element dividing device 1 and the three-dimensional shape data recognizing means 11 and the arithmetic means 12.
  • the storage means 13 temporarily stores the original data recognized by the three-dimensional shape data recognition means 11 and the processing data calculated by the calculation means 12.
  • the display means 4 is, for example, a liquid crystal display or the like, and appropriately displays original data, processed data, and the like under the control of the processing device body 3.
  • the output means 5 is, for example, a transmission device for transmitting various data such as original data and processed data to the outside, a printing device for printing, and the like. Output.
  • a pre-process of generating a mesh by converting a three-dimensional shape of a structure into digital data is performed. That is, for example, 3D CAD creation software / mesh creation software is started on a computer. Then, the computer reads the blueprint of the structure as digital data, and from the read information of the blueprint, sets the outer contour and creates a three-dimensional shape as shown in Fig. 8 to Fig. 11. I do. Then, create a node element based on the contour and surface of the 3D shape created as shown in Fig. 11. To form a mesh structure.
  • nodes are set in a three-dimensional shape, and each node is connected in order to create a cube, a hexahedral element.
  • a pentahedral element six nodes are selected, and in the case of a tetrahedral element, four nodes are selected and connected in order.
  • nodes and elements are sequentially created so as to form a three-dimensional shape by a plurality of elements, and a mesh is generated in the three-dimensional shape.
  • it may be created by a semi-automatic mesh generation method or a fully automatic mesh generation method.
  • the data of the three-dimensional shape for which the mesh is generated becomes the original data as shape information including the three-dimensional information of the elements of the plurality of polyhedrons and the point information of the nodes constituting the polyhedron.
  • the 3D element dividing device 1 is started by the input operation of the input means 2 and the universal file created by the above preprocessing is read. Enter settings.
  • the original data of the three-dimensional shape input by this setting is recognized by the three-dimensional shape data recognizing means 11 of the processing device main body 3.
  • the input operation of the input means 2 causes the three-dimensional shape data recognizing means 11 to read and open the original data of the three-dimensional shape (step S 1) and recognize the node elements (step S 1).
  • S 2 the input operation of the input means 2 causes the three-dimensional shape data recognizing means 11 to read and open the original data of the three-dimensional shape (step S 1) and recognize the node elements (step S 1).
  • step S2 if the three-dimensional shape data recognizing means 11 determines that the read data is not normal data, the calculating means 12 controls the display means 4 so that the data is not normal. Is displayed (step S3). Then, the data opened in step S1 is closed (step S4), and the process of dividing the mesh into three-dimensional elements is completed.
  • step S2 If it is determined in step S2 that the data is normal, the 3D shape In the data recognizing means 11, open the point information of the node constituting the original data of the data and the three-dimensional information of the element, that is, the temporary file for the node (step S3)
  • step S6 open the temporary file for the element (step S6).
  • the data recognized by the three-dimensional shape data recognition means 11 is temporarily stored in the storage means 13.
  • the three-dimensional shape data recognizing means 11 reads one line in which the processing state is recorded from the data of the opened universal file (step S7).
  • the calculating means 12 determines that the three-dimensional element division has been performed, performs an output process (step S9), and proceeds to step S4.
  • step S8 if the reading of one line of the opened universal file is not completed, the calculating means 12 determines that the data is unprocessed, and determines whether or not the information of one line is the point information of the original data. Judgment (step S10), if it is judged to be point information, node processing is performed (step S11), and if it is judged to be three-dimensional information of the original data (step S12), Perform element processing (step S13).
  • step S21 the presence or absence of unprocessed point information is determined (step S21), and the unprocessed point information opened in step S5 is recognized. That is, the process of writing to the node temporary file (step S22) and storing the node number and coordinate data of the point information of each node in the storage means 13 for calculation is repeated (step S23).
  • the arithmetic means 12 determines whether there is any unprocessed three-dimensional information (step S31), and corresponds to the node number of the three-dimensional information in step S23.
  • the coordinate data paired with the stored node number is read out (step S32).
  • the calculating means 12 calculates an intermediate node from the read coordinate data (step S33).
  • the calculating means 12 calculates the midpoint between adjacent nodes by the midpoint creating means 15 from the original data recognized by the three-dimensional shape data recognizing means 11. That is, as shown in FIGS. 5 to 7, the nodes constituting the elements (FIGS. The midpoint of the line connecting the hata in Fig. 7 ( ⁇ in Figs. 5 to 7) is obtained by calculating the average of the coordinate values as described above based on the coordinate information of the nodes at both ends of the line.
  • the calculation means 12 calculates the center by the center creation means 16 from the original data recognized by the three-dimensional shape data recognition means 11. That is, as shown in FIG. 5 to FIG. 7, the midpoint of the surface (the plane in FIG. 5 to FIG. 7), which is a plane area forming the element, is connected to the node (FIG. 5 to FIG. Based on the coordinate information of ⁇ ), the average of the coordinate values is calculated and obtained as described above.
  • the calculating means 12 calculates the center of gravity of the element from the original data recognized by the three-dimensional shape data recognizing means 11 by the center of gravity creating means 17. That is, as shown in FIGS. 5 and 7, the center of gravity of the element ( ⁇ in FIGS. 5 to 7) is used as the coordinate information of all the nodes (Ogina in FIGS. 5 to 7) that constitute this element. Based on this, the average of the coordinate values is calculated and obtained as described above.
  • step S34 The intermediate node calculated in this way is processed as an intermediate node (step S34).
  • the coordinate value of the middle application node is compared with the point coordinates stored in step S23 (step S334). Then, it is determined whether or not the coordinates are the same ('step S3422). If it is determined that the coordinates are the same, the node number of the stored point coordinates is adopted as the intermediate node (step S3343), and the intermediate node processing ends. If it is determined that the coordinates are not the same in step S 3 42, the coordinates are stored in the storage means 13 (step S 3 4 4), and the intermediate node is output to the node temporary file as a new node (step S 3 3 4 5).
  • the calculated midpoint, center, and center of gravity are used as the numbers (a1, a2, a3, a4, a5, a6) indicating the new nodes together with the coordinate values of the calculation results.
  • B 1, b 2, b 3, b 4,..., C 1) are created as coordinate information and set as a new node.
  • the coordinate information of the set midpoint, center, and center of gravity node ( ⁇ ⁇ ⁇ , ⁇ , ⁇ in FIG. 5 or FIG. 7) is temporarily stored in the storage means 13.
  • the arithmetic means 12 includes the original data and the new nodes created by the above-mentioned midpoint creation means 15, center creation means 16, and center of gravity creation means 17 (see FIGS. 5 to 7).
  • the element creating means 18 subdivides the polyhedral element of the original data to create a hexahedral element which is a plurality of polyhedral elements. In other words, as shown in Fig. 5 to Fig. 7, the line connecting the newly created midpoint node ( ⁇ in Fig. 5 to Fig.
  • the polyhedral element of the original data is divided into a plurality of hexahedral elements.
  • step S36 the process returns to step S31 to repeat the division operation.
  • three-dimensional information expressed in the numerical order assigned to the nodes constituting the hexahedral element is newly created and set as a new element .
  • the set three-dimensional information is stored in the storage means 13. In this way, the original data, the coordinate information of the node newly obtained by the calculation, and the three-dimensional information of a plurality of elements generated by the subdivision are temporarily combined with the coordinate information and the three-dimensional information of the original data as processing data.
  • a new midpoint, center, and center of gravity are newly set in the element of the original data, and the shape information is subdivided into a plane area formed by a line connecting the midpoint, the center, and the center of gravity. is there.
  • the arithmetic means 12 performs a process of displaying the processed data by appropriately controlling the display means 4 by the input operation of the input means 2.
  • the calculating means 12 performs a process of outputting processing data to the output means 5, such as printing on a printing device or transmitting the data to another computer, by an input operation by the input means 2.
  • step S9 the output processing of step S9 is performed.
  • the arithmetic means 12 reads the data opened in step S1 (step S41), and reopens the temporary file for reading (step S41).
  • step S42 open the universal file for output (step S43).
  • the arithmetic means 12 reads one line of the universal file (step S44), and until it recognizes information indicating that the processing of the three-dimensional element decomposition is completed (step S45), the node point information Is read (step S46).
  • step S44 the arithmetic means 12 reads one line of the universal file
  • step S45 the node point information Is read
  • step S46 the node point information Is read
  • step S47 the data of the node temporary file, which is the point information of the node
  • step S47 the universal file for output
  • all the node data in the universal file are skipped (step S48).
  • the calculating means 12 reads the three-dimensional information of the element (step S49).
  • all the data of the element temporary file which is the three-dimensional information of the element, is output to the universal file for output (step S50).
  • all the data of the elements in the universal file are skipped (step S51), and the process returns to step S44 to repeat the process and acquire data to be output.
  • the data acquired for this purpose is output from display means or output means.
  • the best analysis result is obtained when the mesh is composed of cube-shaped hexahedral elements.
  • This satisfies the requirements that the angles of all the faces constituting the cube are all right angles, and that the ratio of the longest side to the shortest side of each face is 1, that is, the length of each side is the same.
  • the angles of the constituent surfaces are not right angles, and the ratio of the longest side to the shortest side of each surface is not one.
  • the tetrahedral element and the pentahedral element are in a distorted state (the degree of distortion is smaller than 1) which largely deviates from the requirements for obtaining good analysis results. Therefore, good finite element analysis results can be obtained by using hexahedral elements that minimize distortion.
  • a new node is set at the position of the center and the center of gravity, and the line is formed by the line connecting the center and the center, and the line connecting the center and the center of gravity.
  • a series 1 shown by a dotted line and a series 2 shown by a solid line are graphs showing distortion of elements when a model having a different three-dimensional shape is subjected to subdivision processing.
  • the arithmetic unit 12 uses the three-dimensional shape data recognizing unit 11 to obtain the point information of the plurality of nodes of the original data and the three-dimensional Based on the information, a new node is created by calculating the midpoint between adjacent nodes, the center of the plane area on the outer surface of the element, and the center of gravity of the element.
  • the connecting line and the center An operation for subdividing the set and input original element is performed by using a closed plane area newly formed by the nodes connecting the nodes of and the nodes of the center of gravity. For this reason, even a coarsely created mesh can be easily subdivided in a short time, and all the elements can be subdivided into hexahedrons. Can be easily obtained.
  • the arithmetic means 12 Recognizing the original data having the point information including the coordinate information of the node, the arithmetic means 12 creates a node at the middle point by averaging the coordinate values of the coordinate information of the adjacent nodes, Creating the center node by averaging the coordinate values of the coordinate information of the nodes that make up the outer planar area, and creating the center of gravity node by averaging the coordinate values of the coordinate information of the nodes that make up the element carry out. Therefore, a new node for subdividing the mesh can be easily created in a short time by a simple calculation method of averaging the coordinate values, and the calculation processing efficiency can be easily improved.
  • the original data as the shape information includes the point information of a plurality of nodes and the closing of triangles and rectangles by lines connecting these nodes.
  • the point information has numbers (1, 2, 3,...) Assigned to the nodes and coordinate information as in the case of the first embodiment.
  • the surface information is information of a combination of the numbers of the nodes constituting the element.
  • the data is set and input by the input means 2 by the midpoint creating means 15 by the arithmetic means 12 and the element recognized by the shape data recognizing means in place of the three-dimensional shape data recognizing means 11.
  • the coordinates of the midpoint are used in the same manner as in the above embodiment. Is calculated and set as a new node.
  • the center creation means 16 calculates the coordinates of the center of the element (the mouth in FIGS. 14 and 15) and sets it as a new node in the same manner as in the first embodiment.
  • the element creating means 18 subdivides the area by a line connecting the midpoint and the center, that is, the closed plane area surrounded by the line is set as a new element and the number of the node number constituting this element is determined. Create and set combination surface information.
  • the adjacent nodes A new node is created by calculating the midpoint of the element and the center of the element, and an operation is performed to subdivide the element by connecting the midpoint node and the center node.
  • the elements subdivided by this method are all rectangular. That is, as described above, in the finite element method analysis, the element has a small distortion, and a good finite element analysis result can be obtained.
  • the calculation has been described by using the average of the coordinates of the adjacent nodes as the midpoint, the center, and the center of gravity, but any calculation method other than the calculation using the average can be used.
  • the midpoint is not limited to a position that bisects a line segment between adjacent nodes, but any position on the line segment between nodes and the center is a line segment such as the center position of an inscribed triangle.
  • the position and the center of gravity in the plane constituting the element other than the line segment and the center of gravity of the element other than the plane, such as the position of the center of gravity of the mass when the element is filled with uniform mass Can be in any position.
  • the calculation method is easy and the processing speed can be improved. Also, by setting the midpoint to the bisecting position of the line segment, the center to the position of the center of the inscribed triangle, and the center of gravity to the position of the mass center of gravity, the distortion of the element after subdivision is closer to 1 This is preferable because a small number of hexahedral elements can be obtained.
  • the specific structure and procedure for implementing the present invention can be appropriately changed to another structure or the like as long as the object of the present invention can be achieved. Industrial applicability
  • the present invention can be used as an element division device and an element division method for performing a subdivision process on a mesh for finite element method analysis formed of a plurality of nodes and elements. It can be used for finite element method analysis using a mesh structure divided by polygons and polyhedrons, such as structural analysis of structures, electromagnetic field analysis, and fluid analysis.

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Abstract

Original data containing 3-dimensional shape node point information and element 3-dimensional information constituting a mesh created by 3-dimensional CAD creation software or the like is set/input into a 3-dimensional original element division apparatus (1) and the data is recognized by 3-dimensional shape data recognition means (11). According to coordinate information on the recognized original data node point information, the middle point between adjacent nodes, a center of surface constituting an element, and center of gravity of the element are calculated by using the average of coordinate values, thereby setting a new node. The element is divided into hexahedron elements by a surface composed of a line connecting the middle point node and the center node and a line connecting the center node and the center-of-gravity node.

Description

明 細 書 要素分割装置、 その方法、 そのプログラムおよびそのプログラムを記録した記録 媒体 技術分野  Description Element dividing apparatus, method thereof, program thereof, and recording medium recording the program
本発明は、 複数の節点および要素にて形成される有限要素法解析用のメッシュ を細分割処理する要素分割装置、 その方法、 そのプログラムおよびそのプロダラ ムを記録した記録媒体に関する。 背景技術  The present invention relates to an element dividing device for performing a subdivision process on a finite element method analysis mesh formed by a plurality of nodes and elements, a method thereof, a program thereof, and a recording medium recording the program thereof. Background art
従来、 例えば構造物の構造解析や電磁場解析、 流体解析などの各種解析におい て、 構造物の 2次元形状あるいは 3次元形状を複数の多角形や多面体で分割した メッシュ構造を利用した有限要素法により実施している。 この有限要素法解析用 のメッシュ生成方法としては、 各種方法が知られており、 大別して完全自動メッ シュ生成方法、 半自動メッシュ生成方法および手動メッシュ生成方法の 3つの方 法がある。  Conventionally, in various analyzes such as structural analysis of structures, electromagnetic field analysis, fluid analysis, etc., the finite element method using a mesh structure in which the two-dimensional or three-dimensional shape of the structure is divided by multiple polygons or polyhedrons We are implementing. Various methods are known as mesh generation methods for the finite element method analysis. There are roughly three methods: a fully automatic mesh generation method, a semi-automatic mesh generation method, and a manual mesh generation method.
完全自動メッシュ生成方法は、 解析モデルである構造物の 3次元形状の全体的 なメッシュの大きさや部分的なメッシュの大きさを指定する。 このことにより、 節点 （ノード: node) と、 これら点を結ぶ線にて構成される図形 （エレメント ： el ement)である多角形や多面体とを、 コンピュータを用いて自動的に演算して作成 し、 メッシュを作成する。 なお、 一般的には、 構造物は曲面や凹部などを有した 複雑な形状であることから、 演算性に鑑みて 4面体ェレメントで作成される。 半自動メッシュ生成方法は、 構造物の 3次元形状を所定の部分毎にパーティ シヨン (partition)すなわち個々が単純な 2次元形状や 3次元形状となるように区 切って細分化する。 そして、 細分化した部分毎にノ一ドぉよぴェレメントを自動 的に演算して作成し、 メッシュを作成する。  The fully automatic mesh generation method specifies the overall mesh size and partial mesh size of the 3D shape of the structure that is the analysis model. As a result, a computer automatically calculates a polygon or a polyhedron, which is a figure (element: element) composed of a line connecting these points, with a computer. Create a mesh. In general, since a structure has a complicated shape having a curved surface, a concave portion, and the like, it is created by a tetrahedral element in consideration of computational efficiency. In the semi-automatic mesh generation method, the three-dimensional shape of a structure is divided into predetermined portions and divided into simple two-dimensional or three-dimensional shapes. Then, a node is automatically calculated and created for each subdivided portion, and a mesh is created.
手動メッシュ生成方法は、 構造物の 3次元形状を参照しつつ、 手動によりノー ドを順次作成し、 これらノードを繋ぎながら多角形エレメントゃ多面体エレメン トを作成する。 すなわち、 積み木を積み上げるように 1つ 1つの多角形エレメン トゃ多面体エレメントを作成してメッシュを作成する。 The manual mesh generation method refers to the 3D shape of the structure and Create a polygon element and a polyhedral element while connecting these nodes. In other words, a mesh is created by creating a polygon element and a polyhedral element one by one so that the building blocks are stacked.
ところで、上記従来のメッシュ生成方法において、有限要素法解析用のメッシュ 構造は、 構成するエレメントが三角形の面にて構成された 4面体エレメント、 三 角柱形状の 5面体エレメント、 四角形の面にて構成された 6面体エレメントであ る。 そして、 これら多面体において、 4面体エレメントより 5面体エレメント、 5面体エレメントより 6面体エレメントにて構成したメッシュを用いた方が良好 な解析結果が得られる。  By the way, in the above-mentioned conventional mesh generation method, the mesh structure for the finite element method analysis is composed of a tetrahedral element having triangular faces, a pentahedral element having a triangular prism shape, and a quadrangular face. This is the hexahedral element that was created. In these polyhedrons, better analysis results can be obtained by using a mesh composed of pentahedral elements than tetrahedral elements and hexahedral elements than pentahedral elements.
しかしながら、 上記従来のメッシュ生成方法では、 単純な 3次元形状であれば 6面体エレメントのみでもメッシュを生成できるが、 曲面や凹部を有するような 複雑な形状となるにしたがって、 6面体エレメントを作成できなくなる。 特に、 完全自動メッシュ生成方法を利用する場合には、 コンピュータによる演算が途中 で中断してメッシュを生成できなくなるため、 4面体エレメントが主体となる。 このため、 完全自動メッシュ生成方法にて作成されたメッシュ構造は、 詳細な解 析結果が得られ難く、 限られた用途の有限要素法解析にのみしか利用できない。 このことから、 従来において、 複雑な形状でも手動により部分毎に区画した領 域で自動計算させる半自動メッシュ生成方法や、 比較的に 6面体エレメントが主 体で一部に 4面体エレメントゃ 5面体エレメントが存在する手動メッシュ生成方 法が採られている。 特に、 有限要素法解析において詳細で良好な結果が得られる 六面体エレメントが主体となるメッシュ構造を形成できる手動メッシュ生成方法 が広く利用されている。 しかしながら、 この手動メッシュ生成方法では、 手動に より 1つ 1つのエレメントを作成することを何万回と繰り返さなければならず、 メッシュを作成するには非常に多大な時間および労力を要する問題がある。 本発明は、 このような問題点に鑑みて、 短時間で容易に要素を細分割できる、 また 3次元形状でも 6面体のェレメントのみに短時間で容易に細分割できる要素 分割装置、 その方法、 そのプログラムおよびそのプログラムを記録した記録媒体 を提供することを目的とする。 発明の開示 However, according to the conventional mesh generation method described above, a mesh can be generated only with a hexahedral element if it has a simple three-dimensional shape, but a hexahedral element can be created as a complex shape having curved surfaces and concave portions is formed. Disappears. In particular, when a fully automatic mesh generation method is used, the computation by the computer is interrupted halfway and the mesh cannot be generated, so tetrahedral elements are mainly used. For this reason, the mesh structure created by the fully automatic mesh generation method is difficult to obtain detailed analysis results, and can be used only for finite element analysis for limited applications. For this reason, in the past, semi-automatic mesh generation methods in which even complex shapes were automatically calculated manually in areas divided into parts, a relatively hexahedral element was mainly used, and a tetrahedral element was partially used, and a pentahedral element was partially used. There is a manual mesh generation method that exists. In particular, a manual mesh generation method capable of forming a mesh structure mainly composed of hexahedral elements, which provides detailed and good results in finite element analysis, is widely used. However, in this manual mesh generation method, it is necessary to repeatedly create each element manually tens of thousands of times, and there is a problem that it takes a great deal of time and effort to create a mesh. . In view of the above problems, the present invention provides an element dividing apparatus, which can easily and easily subdivide elements in a short time, and can easily and subdivide only three-dimensional elements into hexahedral elements in a short time. It is intended to provide the program and a recording medium on which the program is recorded. Disclosure of the invention
本発明は、 複数の節点と、 これら節点のうちのいずれかが選択的に連結されて 閉じた平面領域に構成された複数の要素とにて形成される有限要素法解析用の メッシュを細分割処理する要素分割装置であって、 前記複数の節点の点情報およ ぴ前記複数の要素の面情報を有した形状情報を取得する形状情報認識手段と、 こ の形状情報認識手段にて取得した形状情報を演算により前記要素を細分割する演 算手段とを具備し、 前記演算手段は、 隣接する前記節点間の中点および前記要素 の中心に新たに節点をそれぞれ作成し、 前記中点の節点およぴ前記中心の節点を 結んで前記要素を細分割することを特徴とした要素分割装置である。  The present invention subdivides a mesh for finite element method analysis formed by a plurality of nodes and a plurality of elements formed in a closed plane region by selectively connecting any of the nodes. An element dividing device for processing, comprising: shape information recognizing means for obtaining point information of the plurality of nodes and shape information having surface information of the plurality of elements; Computing means for subdividing the element by operation of the shape information, wherein the computing means newly creates a midpoint between the adjacent nodes and a new node at the center of the element, and An element dividing device characterized by subdividing the element by connecting a node and the center node.
この発明では、 演算手段により、 形状情報認識手段にて取得された形状情報の 複数の節点の点情報および複数の要素の面情報に基づいて、 隣接する節点間の中 点と、 要素の中心とを演算して新たに節点をそれぞれ作成し、 中点の節点および 中心の節点を結んで要素を細分割する演算処理を実施する。 このことにより、 粗 く作成されたメッシユでも容易に短時間で細分割処理される。  According to the present invention, the arithmetic unit calculates the midpoint between the adjacent nodes and the center of the element based on the point information of the plurality of nodes and the surface information of the plurality of elements of the shape information acquired by the shape information recognizing unit. Is calculated to create new nodes respectively, and a calculation process for subdividing elements by connecting the middle node and the center node is performed. As a result, even a coarsely created mesh can be easily subdivided in a short time.
本発明の要素分割装置において、 点情報は、 節点の座標情報を含み、 演算手段 は、 隣接する前記節点の座標情報の座標値を平均する演算により中点の節点を作 成し、 要素を構成する前記節点の座標情報の座標値を平均する演算により中心の 節点を作成することが望ましい。  In the element dividing device of the present invention, the point information includes coordinate information of the node, and the calculating means generates a node at the middle point by averaging the coordinate values of the coordinate information of the adjacent nodes to form the element. It is preferable to create a central node by performing an operation of averaging the coordinate values of the coordinate information of the node.
この発明では、 節点の座標情報を含む点情報を有した形状情報を取得し、 演算 手段により、 隣接する節点の座標情報の座標値を平均する演算により中点の節点 を作成し、 要素を構成する節点の座標情報の座標値を平均する演算により中心の 節点を作成する。 このことにより、 単純な演算により、 メッシュを細分割するた めの新たな節点が容易に短時間で作成される。 本発明は、 複数の節点と、 これら節点のうちのいずれかが選択的に連結されて 閉じた多面体領域に構成された複数の要素とにて形成される有限要素法解析用の メッシュを細分割処理する要素分割装置であって、 複数の節点の点情報および前 記要素の立体情報を有した形状情報を取得する形状情報認識手段と、 この形状情 報認識手段にて取得した形状情報を演算により前記要素を細分割する演算手段と を具備し、 前記演算手段は、 隣接する前記節間の中点、 前記要素の外面の平面領 域の中心、 および、 前記要素の重心に新たに節点をそれぞれ作成し、 前記中点の 節点および前記中心の節点を結ぶ線と前記中心の節点およぴ前記重心の節点を結 ぶ線とにて新たに構成される閉じた平面領域により前記要素を細分割することを 特徴とした要素分割装置である。 According to the present invention, the shape information having the point information including the coordinate information of the node is acquired, and the calculating means averages the coordinate values of the coordinate information of the adjacent nodes to create the middle node, thereby forming the element. The center node is created by averaging the coordinate values of the coordinate information of the target node. As a result, new nodes for subdividing the mesh can be easily created in a short time with a simple operation. The present invention subdivides a mesh for finite element method analysis formed by a plurality of nodes and a plurality of elements formed in a closed polyhedron region by selectively connecting any of the nodes. An element dividing device to be processed, comprising: A shape information recognizing unit that obtains shape information having three-dimensional information of the element, and a calculating unit that subdivides the element by calculating the shape information obtained by the shape information recognizing unit. Are the midpoints between the adjacent nodes, the center of the planar area of the outer surface of the element, and a new node at the center of gravity of the element, and a line connecting the midpoint node and the center node And a line connecting the center node and the center of gravity node, and further subdivides the element by a closed planar area.
この発明では、 演算手段により、 形状情報認識手段にて取得された形状情報の 複数の節点の点情報および複数の要素の立体情報に基づいて、 隣接する節点間の 中点と、 要素の外面の平面領域の中心と、 要素の重心を演算して新たに節点をそ れぞれ作成し、 中点の節点および中心の節点を結ぶ線と、 中心の節点および重心 の節点を結ぶ線とにて新たに構成される閉じた平面領域により要素を細分割する 演算処理を実施する。 'このことにより、 粗く作成されたメッシュでも容易に短時 間で細分割されるとともに、 要素の全ては、 有限要素法解析で良好な結果が得ら れる 6面体に分割される。  According to the present invention, the arithmetic unit, based on the point information of the plurality of nodes of the shape information acquired by the shape information recognizing unit and the three-dimensional information of the plurality of elements, the midpoint between the adjacent nodes and the outer surface of the element A new node is created by calculating the center of the plane area and the center of gravity of the element, and a line connecting the center node and the center node, and a line connecting the center node and the center of gravity node. Performs arithmetic processing to subdivide elements by a newly configured closed planar area. 'This means that even coarse meshes can be easily subdivided in a short time, and all elements can be subdivided into hexahedrons that can be obtained by finite element analysis.
本発明の要素分割装置において、 点情報は、 節点の座標情報を含み、 演算手段 は、 前記節点の座標情報の座標値を平均する演算により中点を作成し、 要素の外 面の平面領域を構成する前記節点の座標情報の座標値を平均する演算により中心 を作成し、 要素を構成する前記節点の座標情報の座標値を平均する演算により作 成することが望ましい。  In the element dividing device according to the aspect of the invention, the point information includes coordinate information of the node, and the calculating unit generates a midpoint by averaging coordinate values of the coordinate information of the node, and calculates a plane area on an outer surface of the element. It is preferable that the center is created by an operation of averaging the coordinate values of the coordinate information of the constituent nodes, and that the center is created by an arithmetic operation of averaging the coordinate values of the coordinate information of the nodes forming the element.
この発明では、 節点の座標情報を含む点情報を有した形状情報を取得し、 演算 手段により、 隣接する節点の座標情報の座標値を平均する演算により中点の節点 を作成し、 要素の外面の平面領域を構成する節点の座標情報の座標値を平均する 演算により中心の節点を作成し、 要素を構成する節点の座標情報の座標値を平均 する演算により重心の節点を作成する。このことにより、単純な演算により、メッ シュを細分割するための新たな節点が容易に短時間で作成される。 本発明の要素分割方法は、 コンピュータを用いて、 複数の節点と、 これら節点 のうちのいずれかが選択的に連結されて閉じた平面領域に構成された複数の要素 とにて形成される有限要素法解析用のメッシュを細分割処理する要素分割方法で あって、 前記複数の節点の点情報および前記要素の面情報を有した形状情報を取 得し、 この取得した形状情報の隣接する前記節点間の中点およぴ前記要素の中心 を演算して新たな節点と設定し、 これら設定された前記中点の節点と前記中心の 節点とを結んで前記要素を細分割する演算を実施することを特徴とする。 According to the present invention, the shape information having the point information including the coordinate information of the node is obtained, and the calculating means averages the coordinate values of the coordinate information of the adjacent nodes to create the middle node, thereby obtaining the outer surface of the element. A center node is created by an operation that averages the coordinate values of the coordinate information of the nodes that make up the plane area of, and a node at the center of gravity is created by an operation that averages the coordinate values of the coordinate information that is the nodes that make up the element. As a result, a new node for subdividing the mesh can be easily created in a short time by a simple operation. The element dividing method according to the present invention includes a plurality of nodes using a computer. And a plurality of elements selectively closed and configured in a closed planar area.A method for subdividing a mesh for finite element method analysis, the method comprising: The point information of the node and the shape information having the surface information of the element are obtained, and the midpoint between the adjacent nodes and the center of the element of the obtained shape information are calculated to obtain a new node. Setting, and performing an operation of subdividing the element by connecting the set middle node and the center node.
本発明の要素分割方法は、 コンピュータを用いて、 複数の節点と、 これら節点 のうちのいずれかが選択的に連結されて閉じた多面体領域に構成された複数の要 素とにて形成される有限要素法解析用のメッシュを細分割処理する要素分割方法 であって、 前記複数の節点の点情報および前記要素の立体情報を有した形状情報 を取得し、 この取得した形状情報の隣接する前記節点間の中点、 前記要素の外面 の平面領域の中心、 および、 前記要素の重心を演算して新たな節点と設定し、 こ れら設定された前記中点の節点および前記中心の節点を結ぶ線と前記中心の節点 およぴ前記重心の節点を結ぶ線とにて新たに構成される閉じた平面領域により前 記要素を細分割する演算を実施するとしてもよい。  The element dividing method according to the present invention uses a computer to form a plurality of nodes and a plurality of elements formed into a closed polyhedron region by selectively connecting any of these nodes. An element dividing method for subdividing a mesh for finite element method analysis, comprising: acquiring shape information having point information of the plurality of nodes and three-dimensional information of the element; and acquiring the shape information adjacent to the acquired shape information. The midpoint between the nodes, the center of the plane area of the outer surface of the element, and the center of gravity of the element are calculated and set as a new node, and the set node of the midpoint and the node at the center are set. The operation of subdividing the above-mentioned element by a closed plane area newly formed by a connecting line and a line connecting the center node and the node of the center of gravity may be performed.
このような本発明においては、 前述した本発明の要素分割装置と同様の作用効 果を享受できる。 本発明の要素分割プログラムは、 前述した本発明の要素分割方法をコンビユー タに実行させることを特徴とする。  According to the present invention, the same operation and effect as those of the above-described element dividing device of the present invention can be obtained. The element division program of the present invention causes a computer to execute the above-described element division method of the present invention.
この発明では、 例えば汎用のコンピュータを利用してコンピュータにインス トールすることにより前述した本発明の要素分割方法をコンピュータに実行させ ることができ、 本発明の利用促進を大幅に図ることができる。  According to the present invention, for example, the above-described element dividing method of the present invention can be executed by installing the program on a computer using a general-purpose computer, and the use of the present invention can be greatly promoted.
なお、本発明において、コンピュータは、 1つに限らず、例えば複数のコンビユー タをネットワーク状に組み合わせた構成なども含む。  In the present invention, the number of computers is not limited to one, and includes, for example, a configuration in which a plurality of computers are combined in a network.
本発明の記録媒体は、 前述した本発明の要素分割プログラムを記録したことを 特徴とする。  A recording medium of the present invention is characterized by recording the above-described element division program of the present invention.
この発明では、 前述した本発明の要素分割方法をコンピュータに実行させるた めの要素分割プログラムの流通性および取扱性が向上し、 本発明の利用促進を大 幅に図ることができる。 図面の簡単な説明 According to the present invention, there is provided a method for causing a computer to execute the above-described element dividing method of the present invention. The distribution and handling of the element division program are improved, and the use of the present invention can be largely promoted. BRIEF DESCRIPTION OF THE FIGURES
図 1は本発明の一実施の形態に係る 3次元要素分割装置の概略構成を示すブ 口ック図である。  FIG. 1 is a block diagram showing a schematic configuration of a three-dimensional element dividing device according to one embodiment of the present invention.
図 2は前記一実施の形態における元データの 3次元形状に生成されたメッシュ を構成する 4面体のエレメントを示す模式図である。  FIG. 2 is a schematic diagram showing tetrahedral elements constituting a mesh generated in a three-dimensional shape of original data according to the embodiment.
図 3は前記一実施の形態における元データの 3次元形状に生成されたメッシュ を構成する 5面体のエレメントを示す模式図である。  FIG. 3 is a schematic diagram showing pentahedral elements constituting a mesh generated in a three-dimensional shape of the original data according to the embodiment.
図 4は前記一実施の形態における元データの 3次元形状に生成されたメッシュ を構成する 6面体のエレメントを示す模式図である。  FIG. 4 is a schematic diagram showing hexahedral elements constituting a mesh generated in a three-dimensional shape of the original data according to the embodiment.
図 5は前記一実施の形態における元データの 3次元形状のメッシュを構成する 4面体のエレメントを細分割する状況を示す模式図である。  FIG. 5 is a schematic diagram showing a situation in which a tetrahedral element constituting a three-dimensional mesh of the original data is subdivided in the embodiment.
図 6は前記一実施の形態における元データの 3次元形状のメッシュを構成する 5面体のエレメントを細分割する状況を示す模式図である。  FIG. 6 is a schematic diagram showing a situation in which a pentahedral element constituting a three-dimensional mesh of the original data is subdivided in the embodiment.
図 Ίは前記一実施の形態における元データの 3次元形状のメッシュを構成する 6面体のエレメントを細分割する状況を示す模式図である。  FIG. 5 is a schematic diagram showing a situation in which a hexahedral element constituting a three-dimensional mesh of the original data is subdivided in the embodiment.
図 8は前記一実施の形態における前処理の元データの 3次元形状を作成する状 況を示す模式図である。  FIG. 8 is a schematic diagram showing a situation in which a three-dimensional shape of the original data of the preprocessing is created in the one embodiment.
図 9は前記一実施の形態における前処理の元データの 3次元形状を作成する状 況を示す模式図である。  FIG. 9 is a schematic diagram showing a situation in which a three-dimensional shape of the original data of the preprocessing is created in the embodiment.
図 1 0は前記一実施の形態における前処理の元データの 3次元形状を作成する 状況を示す模式図である。  FIG. 10 is a schematic diagram showing a situation in which a three-dimensional shape of the original data of the preprocessing is created in the embodiment.
図 1 1は前記一実施の形態における前処理の元データの 3次元形状を作成する 状況を示す模式図である。  FIG. 11 is a schematic diagram showing a situation in which a three-dimensional shape of the original data of the preprocessing is created in the embodiment.
図 1 2は前記一実施の形態における前処理の元データの 3次元形状にメッシュ を生成する状況を示す模式図である。 図 1 3は前記一実施の形態における前処理の元データであるメッシュが生成さ れた 3次元形状を示す模式図である。 FIG. 12 is a schematic diagram showing a situation in which a mesh is generated in the three-dimensional shape of the original data of the preprocessing according to the embodiment. FIG. 13 is a schematic diagram showing a three-dimensional shape in which a mesh, which is original data of preprocessing, is generated in the embodiment.
図 1 4は前記一実施の形態における細分割処理の動作を示すフローチャートで ある。  FIG. 14 is a flowchart showing the operation of the subdivision processing in the embodiment.
図 1 5は前記細分割処理におけるノ一ド処理の動作を示すフローチヤ一トであ る。  FIG. 15 is a flowchart showing the operation of the node processing in the subdivision processing.
図 1 6は前記細分割処理におけるエレメント処理の動作を示すフローチヤ一ト である。  FIG. 16 is a flowchart showing the operation of element processing in the subdivision processing.
図 1 7は前記細分割処理における中間ノード処理の動作を示すフローチヤ一ト である。  FIG. 17 is a flowchart showing the operation of the intermediate node processing in the subdivision processing.
図 1 8は前記細分割処理における出力処理の動作を示すフローチャートであ る。  FIG. 18 is a flowchart showing the operation of the output process in the subdivision process.
図 1 9は前記前処理により作成したメッシュが生成された 3次元形状を示す模 式図である。  FIG. 19 is a schematic diagram showing a three-dimensional shape in which the mesh created by the preprocessing is generated.
図 2 0は前記細分割処理により作成したメッシュ構造の 3次元形状を示す模式 図である。  FIG. 20 is a schematic diagram showing a three-dimensional shape of the mesh structure created by the subdivision processing.
図 2 1は前記細分割処理により分割されるメッシュの数の推移を示すグラフで める。  FIG. 21 is a graph showing the transition of the number of meshes divided by the subdivision processing.
図 2 2は前記細分割処理により分割されるエレメントの歪み度の推移を示すグ ラフである。  FIG. 22 is a graph showing the transition of the degree of distortion of the element divided by the subdivision processing.
図 2 3は他の実施の形態における元データのメッシュを構成する三角形のエレ メントを細分割する状況を示す模式図である。  FIG. 23 is a schematic diagram showing a situation in which a triangular element constituting a mesh of original data is subdivided in another embodiment.
図 2 4は他の実施の形態における元データのメッシュを構成する四角形のエレ メントを細分割する状況を示す模式図である。 発明を実施するための最良の形態  FIG. 24 is a schematic diagram showing a situation in which quadrangular elements constituting a mesh of original data are subdivided in another embodiment. BEST MODE FOR CARRYING OUT THE INVENTION
以下、 本発明の一実施の形態を図面に基づいて説明する。 〔 3次元要素分割装置の構成〕 Hereinafter, an embodiment of the present invention will be described with reference to the drawings. [Configuration of 3D element dividing device]
図 1は、 本実施の形態における 3次元要素分割装置の概略構成を示すプロック 図である。 この図 1において、 1は 3次元要素分解装置で、 この 3次元要素分解 装置 1は、 入力手段 2と、 処理装置本体 3と、 表示手段 4と、 出力手段 5とを備 えている。  FIG. 1 is a block diagram showing a schematic configuration of a three-dimensional element dividing device according to the present embodiment. In FIG. 1, reference numeral 1 denotes a three-dimensional element decomposing device, and the three-dimensional element decomposing device 1 includes an input means 2, a processing device main body 3, a display means 4, and an output means 5.
入力手段 2は、 処理装置本体 3に接続されている。 そして、 入力手段 2は、 入 力操作により、 あらかじめメッシュが形成された 3次元形状の元データを処理装 置本体 3に設定入力する。 この入力手段 2としては、 例えばキーボードやマウス の操作により記憶媒体としての磁気ディスクや光ディスクに記憶された元データ を読み出す読取装置、 他のコンピュータから送信される信号を受信する受信装置 など、 処理装置本体 3に元データを設定入力させるいずれの構成でもできる。 なお、 この設定入力される元データは、 例えば 3次元形状のデータを処理する C A D (Computer Aided Design) において標準的に利用されるユニバーサルデー タで、 別途 3次元 C A D作成ソフトウエアゃメッシュ作成ソフトウエアなどによ りメッシュが生成されて形成された 3次元形状のデータが用いられる。 なお、 ュ 二バーサルデータに限らず、 例えばパルクデータ形式など、 互換可能ないずれの 形式のデータに対応できる。  The input means 2 is connected to the processing device main body 3. Then, the input means 2 sets and inputs the original data of the three-dimensional shape in which the mesh is formed in advance to the processing device main body 3 by an input operation. The input means 2 includes, for example, a processing device such as a reading device for reading original data stored on a magnetic disk or an optical disk as a storage medium by operating a keyboard or a mouse, a receiving device for receiving a signal transmitted from another computer, or the like. Any configuration that allows the main body 3 to set and input the original data can be used. Note that the original data entered in this setting is, for example, universal data that is used as standard in CAD (Computer Aided Design) that processes 3D shape data. The data of the three-dimensional shape generated by generating a mesh by using the above method is used. Not only universal data but also any compatible data format such as parc data format can be supported.
そして、 この元データは、 3次元形状のメッシュを構成する 4面体、 5面体お ょぴ 6面体のうちの少なくともいずれか 1種類を含む多面体のエレメントが積み 木が積まれたように複数連続したデータである。 これら多面体のエレメントは、 図 2ないし図 4に示すように、 頂点に位置する節点 （ノード ode) (図中のき） の点情報と、 これら隣接するノードを結ぶ線にて囲まれた閉じた平面領域にて構 成される多面体形状の要素 （エレメント ： element) の立体情報とにて構成されて いる。  The original data is composed of a series of polyhedral elements including at least one of tetrahedrons, pentahedrons, and hexahedrons that form a three-dimensional mesh. Data. As shown in Fig. 2 to Fig. 4, these polyhedral elements are closed points surrounded by lines connecting the nodes of the vertices (nodes ode) (as shown in the figure) and these adjacent nodes. It is composed of three-dimensional information of polyhedron-shaped elements (elements) composed of planar regions.
ここで、 ノードの点情報は、 図 2ないし図 4に示すようなノードを特定する記 号である番号情報 （1， 2 , 3， 4， ···） と、 このノードの番号情報に関連付け られた座標情報とを含む。 立体情報は、 エレメントを構成する各ノードに順次付 される番号の組み合わせの情報である。 これらのノードおょぴエレメントにて表 される多面体の集合の形状情報がメッシュが生成された 3次元形状の元データと なる。 Here, the point information of the node is associated with the number information (1, 2, 3, 4, 4,...), Which is a symbol for identifying the node as shown in FIGS. Coordinate information. The three-dimensional information is information of a combination of numbers sequentially assigned to each node constituting the element. These nodes are represented by elements The shape information of the set of polyhedrons used is the original data of the three-dimensional shape for which the mesh has been generated.
一方、 処理装置本体 3は、 形状情報認識手段としての 3次元形状データ認識手 段 1 1と、 演算手段 1 2と、 記憶手段 1 3とを備えている。  On the other hand, the processing apparatus main body 3 includes a three-dimensional shape data recognition means 11 as shape information recognition means, a calculation means 12, and a storage means 13.
そして、 3次元形状データ認識手段 1 1は、 3次元要素分割装置 1全体の動作 制御を行う O S (Operating System) 上に展開されるプログラムとして、入力手段 2により設定入力された元データを読み取って認識する。 すなわち、 元データの 3次元形状のメッシュを構成するノードおよびエレメントに関する形状情報を認 識する。 そして、 この 3次元形状データ認識手段 1 1は、 記憶手段 1 3に接続さ れ、 認識した元データを記憶手段 1 3に送くつて記憶させる。  The three-dimensional shape data recognizing means 11 reads the original data set and input by the input means 2 as a program developed on an OS (Operating System) for controlling the operation of the entire three-dimensional element dividing device 1. recognize. That is, it recognizes the shape information on the nodes and elements that make up the three-dimensional mesh of the original data. The three-dimensional shape data recognition means 11 is connected to the storage means 13 and sends the recognized original data to the storage means 13 for storage.
また、 演算手段 1 2は、 3次元要素分割装置 1全体の動作制御を行う O S (Op erating System) 上に展開されるプログラムとして、 3次元形状データ認識手段 1 1にて認識した 3次元形状のメッシュを細分割処理するための演算を実施する。 この演算手段 1 2は、 中点作成手段 1 5と、 中心作成手段 16と、 重心作成手段 1 7と、 エレメント作成手段 18とを備えている。  The computing means 12 is a program developed on an OS (operating system) for controlling the operation of the entire three-dimensional element dividing device 1 as a program of the three-dimensional shape recognized by the three-dimensional shape data recognizing means 11. An operation for subdividing the mesh is performed. The calculation means 12 includes a midpoint creation means 15, a center creation means 16, a center of gravity creation means 17, and an element creation means 18.
中点作成手段 1 5は、 3次元形状データ認識手段 1 1にて認識した各ノード間 の中点に新たなノードを作成する処理をする。 具体的には、 図 5ないし図 7に示 すように、 元データのユニバーサルデータとして記録されているノードの座標情 報の各座標 （図 5ないし図 7中のき） 間の中点の座標 （図 5ないし図 7中の を演算する。  The midpoint creating means 15 performs a process of creating a new node at the midpoint between the nodes recognized by the three-dimensional shape data recognizing means 11. Specifically, as shown in Figs. 5 to 7, the coordinates of the midpoint between the coordinates of the coordinate information of the node recorded as universal data of the original data (in Figs. 5 to 7). (Calculate in Fig. 5 to Fig. 7.
例えば、 （x l, y 1 , z l) および （x 2， y 2 , ζ 2) の二つのノード間 の中点は、 各ノードの平均、 すなわち （ （x l + x 2) /2, (y 1 + y 2) / 2, (z 1 + z 2) /2) と演算されて求められる。 そして、 この求められた中 点を新たなノード （図 5ないし図 7中の▲) として、 例えば図 5ないし図 7中に a l、 a 2、 a 3、 a 4、 a 5、 a 6、 …と示すように、 順次新たな番号が付さ れ、 演算結果の座標情報と関連付けされ、 新たな点情報として設定される。  For example, the midpoint between the two nodes (xl, y1, zl) and (x2, y2, ζ2) is the average of each node, that is, ((xl + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2). Then, the obtained midpoint is set as a new node (▲ in FIGS. 5 to 7), for example, al, a2, a3, a4, a5, a6,. , New numbers are sequentially assigned, associated with the coordinate information of the calculation result, and set as new point information.
中心作成手段 1 6は、 3次元形状データ認識手段 1 1にて認識した各多角形ェ レメントの各表面の中心にノードを作成する処理をする。 具体的には、 図 5ない し図 7に示すように、 元データのノード間を結ぶ線にて囲まれた平面領域である 面の中心の座標 （図 5ないし図 7中の園） を演算する。 The center creation means 16 performs processing for creating a node at the center of each surface of each polygon element recognized by the three-dimensional shape data recognition means 11. Specifically, Figure 5 does not Then, as shown in Fig. 7, the coordinates of the center of the plane (the garden in Figs. 5 to 7), which is a plane area surrounded by the line connecting the nodes of the original data, are calculated.
例えば、 面を構成する各ノードの座標が （x l , y 1 , ζ 1) 、 (χ 2 , y 2 , ζ 2) および （χ 3， y 3 , ζ 3) である場合、 中心の座標は各ノードの平均、 すなわち ( (x l + x 2 + x 3 ) /3 , (y l + y 2 + y 3) / 3 , ( z 1 + z 2 + z 3) 3) と演算されて求められる。 そして、 この求められた中心を新た なノード （図 5ないし図 7中の▲) として、 例えば図 5ないし図 7中に b 1、 b 2、 b 3、 b 4、 …と示すように、 順次新たな番号が付され、 演算結果の座標情 報と関連付けされ、 新たな点情報として設定される。  For example, if the coordinates of each node constituting the surface are (xl, y1, ζ1), (χ2, y2, ζ2) and (χ3, y3, ζ3), the coordinates of the center are The average of each node, that is, ((xl + x2 + x3) / 3, (yl + y2 + y3) / 3, (z1 + z2 + z3) 3) is calculated. Then, the obtained center is set as a new node (▲ in FIGS. 5 to 7). For example, as shown in FIGS. 5 to 7, b1, b2, b3, b4,. A new number is assigned, associated with the coordinate information of the calculation result, and set as new point information.
重心作成手段 1 7は、 3次元形状データ認識手段 1 1にて認識した各多角形ェ レメントの重心にノードを作成する処理をする。 具体的には、 図 5ないし図 7に 示すように、元データの多角形エレメントの重心の座標（図 5ないし図 7中の★) を演算する。  The center-of-gravity creating means 17 performs a process of creating a node at the center of gravity of each polygon element recognized by the three-dimensional shape data recognizing means 11. Specifically, as shown in FIGS. 5 to 7, the coordinates of the center of gravity of the polygonal element of the original data (★ in FIGS. 5 to 7) are calculated.
例えば、 多角形エレメントを構成する各ノードの座標が （x l , y 1 , z 1 ) 、 (x 2 , y 2 , z 2) 、 (x 3 , y 3 , z 3) および (x 4 , y 4， z 4) であ る場合、 重心の座標は各ノードの平均、 すなわち （ （x l + x 2 + x 3 + x 4) /4， (y l + y 2 + y 3 + y 4) /A , ( z l + z 2 + z 3 + z 4) / 4) と 演算されて求められる。 そして、 この求められた重心を新たなノード （図 5ない し図 7中の★) として、 例えば図 5ないし図 7中に c 1と示すように、 新たな番 号が付され、 演算結果の座標情報と関違付けされ、 新たな点情報として設定され る。 エレメント作成手段 1 8は、 中点作成手段 1 5、 中心作成手段 1 6および重心 作成手段 1 7により新たに作成されたノ一ドを結ぶ線分で囲まれた平面領域であ る面にて区画される 6面体のエレメントを作成する。 具体的には、 図 5ないし図 7に示すように、 各中点と中心との間の線分、 および、 各中心と重心との間の線 分で囲まれる面にて区画される多面体を、 上述したようにノードに付される番号 順で表して新たな立体情報として設定し、 6面体のエレメントが複数分割形成さ れる。 For example, the coordinates of each node constituting a polygon element are (xl, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y 4, z 4), the coordinates of the center of gravity are the average of each node, that is, ((xl + x2 + x3 + x4) / 4, (yl + y2 + y3 + y4) / A , (zl + z 2 + z 3 + z 4) / 4). Then, the obtained center of gravity is set as a new node (★ in FIG. 5 or FIG. 7), and a new number is assigned, for example, as shown by c 1 in FIG. 5 to FIG. Correlated with the coordinate information, it is set as new point information. The element creation means 18 is a plane area surrounded by a line connecting the nodes newly created by the middle point creation means 15, the center creation means 16 and the center of gravity creation means 17. Create a hexahedral element to be partitioned. Specifically, as shown in FIGS. 5 to 7, a polyhedron defined by a line segment between each midpoint and the center and a line segment between each center and the center of gravity is As described above, new three-dimensional information is set in the order of the number assigned to the node, and a hexahedral element is formed by dividing it into plural It is.
すなわち、 図 5ないし図 7に示すように、 4面体のエレメントは 4つの 6面体 のエレメントに分割され、 5面体のエレメントは 6つの 6面体のエレメントに分 割され、 6面体のェレメントは 8つの 6面体のエレメントに分割される。 このよ うに新たなノードぉょぴエレメントの点情報および立体情報を元データに加えた 処理データは、 記憶手段 1 3に送られて記憶される。  That is, as shown in Figures 5 through 7, the tetrahedral element is divided into four hexahedral elements, the pentahedral element is divided into six hexahedral elements, and the hexahedral element is divided into eight elements. It is divided into hexahedral elements. The processing data obtained by adding the point information and the three-dimensional information of the new node element to the original data in this way is sent to the storage means 13 and stored.
そして、記憶手段 1 3は、 3次元要素分割装置 1全体の動作制御を行う O S (0 perating System) や、 3次元形状データ認識手段 1 1および演算手段 1 2などの プログラムを記憶する。 また、 記憶手段 1 3は、 3次元形状データ認識手段 1 1 にて認識した元データおよび演算手段 1 2にて演算した処理データなどを一時的 に記憶する。  The storage means 13 stores programs such as OS (0 perating system) for controlling the operation of the entire three-dimensional element dividing device 1 and the three-dimensional shape data recognizing means 11 and the arithmetic means 12. The storage means 13 temporarily stores the original data recognized by the three-dimensional shape data recognition means 11 and the processing data calculated by the calculation means 12.
一方、 表示手段 4は、 例えば液晶ディスプレイなどで、 処理装置本体 3による 制御にて、 元データや処理データなどを適宜表示する。  On the other hand, the display means 4 is, for example, a liquid crystal display or the like, and appropriately displays original data, processed data, and the like under the control of the processing device body 3.
また、 出力手段 5は、 例えば元データや処理データなどの各種データを、 外部 に送信する送信装置や、 印刷する印刷装置などで、 処理装置本体 3による制御に て、 元データや処理データを適宜出力する。  Further, the output means 5 is, for example, a transmission device for transmitting various data such as original data and processed data to the outside, a printing device for printing, and the like. Output.
〔 3次元要素分割装置の動作〕 [Operation of 3D element dividing device]
次に、 上記実施の形態における 3次元要素分割装置 1の動作について図面を参 照して説明する。  Next, the operation of the three-dimensional element dividing device 1 in the above embodiment will be described with reference to the drawings.
(前処理）  (Preprocessing)
まず、 本発明の 3次元要素分割を実施するに際して、 構造物の 3次元形状をデ ジタルデータ化してメッシュを生成する前処理を実施する。 すなわち、 例えばコ ンピュータに 3次元 C A D作成ソフトウエアゃメッシュ作成ソフトウエアなどを 起動させる。 そして、 構造物の設計図をコンピュータにデジタルデータとして読 み取らせ、 この読み取った設計図の情報から、 図 8ないし図 1 1に順次示すよう にして、 外郭を設定して 3次元形状を作成する。 そして、 図 1 1に示すように作 成された 3次元形状の外郭や表面を基準として、 ノードおょぴエレメントを作成 してメッシュ構造とする。 First, when performing the three-dimensional element division of the present invention, a pre-process of generating a mesh by converting a three-dimensional shape of a structure into digital data is performed. That is, for example, 3D CAD creation software / mesh creation software is started on a computer. Then, the computer reads the blueprint of the structure as digital data, and from the read information of the blueprint, sets the outer contour and creates a three-dimensional shape as shown in Fig. 8 to Fig. 11. I do. Then, create a node element based on the contour and surface of the 3D shape created as shown in Fig. 11. To form a mesh structure.
例えば、 手動の場合には、 図 1 2に示すように、 3次元形状に 8個のノードを 設定し、 各ノードを順番に結んで 1つの立方体である 6面体のエレメントを作成 する。 なお、 5面体のエレメントの場合には 6個のノード、 4面体のエレメント の場合には 4個のノードを選択して順番に結んで作成する。 そして、 図 1 3に示 すように、 複数のエレメントにより 3次元形状を構成するようにノードおよびェ レメントを順次作成して、 3次元形状にメッシュを生成させる。なお、半自動メッ シュ生成方法や完全自動メッシュ生成方法により作成してもよい。  For example, in the case of manual operation, as shown in Fig. 12, eight nodes are set in a three-dimensional shape, and each node is connected in order to create a cube, a hexahedral element. In the case of a pentahedral element, six nodes are selected, and in the case of a tetrahedral element, four nodes are selected and connected in order. Then, as shown in FIG. 13, nodes and elements are sequentially created so as to form a three-dimensional shape by a plurality of elements, and a mesh is generated in the three-dimensional shape. In addition, it may be created by a semi-automatic mesh generation method or a fully automatic mesh generation method.
このメッシュが生成された 3次元形状のデ一タは、 複数の多面体のェレメント の立体情報と、 多面体を構成するノードの点情報とを含んだ形状情報としての元 データとなる。  The data of the three-dimensional shape for which the mesh is generated becomes the original data as shape information including the three-dimensional information of the elements of the plurality of polyhedrons and the point information of the nodes constituting the polyhedron.
(細分化処理）  (Subdivision processing)
次に、 上記前処理により作成された 3次元形状に生成されたメッシュを 3次元 要素分割する動作について、 図ないし図に示すフローチャートを参照して説明す る。  Next, the operation of dividing the mesh generated into the three-dimensional shape created by the preprocessing into three-dimensional elements will be described with reference to the drawings and the flowcharts shown in the drawings.
まず、 図 1 4のフローチャートに示すように、 入力手段 2の入力操作により、 3次元要素分割装置 1を起動させ、 上記前処理により作成したユニバーサルファ ィルを読み取らせ、 3次元要素分割装置 1に設定入力する。 この設定入力された 3次元形状の元データは、 処理装置本体 3の 3次元形状データ認識手段 1 1によ り認識される。 具体的には、 入力手段 2の入力操作により、 3次元形状データ認 識手段 1 1により、 3次元形状の元データを読み取って開き （ステップ S 1 ) 、 ノードおょぴエレメントを認識する （ステップ S 2 ) 。  First, as shown in the flowchart of FIG. 14, the 3D element dividing device 1 is started by the input operation of the input means 2 and the universal file created by the above preprocessing is read. Enter settings. The original data of the three-dimensional shape input by this setting is recognized by the three-dimensional shape data recognizing means 11 of the processing device main body 3. Specifically, the input operation of the input means 2 causes the three-dimensional shape data recognizing means 11 to read and open the original data of the three-dimensional shape (step S 1) and recognize the node elements (step S 1). S 2).
このステップ S 2において、 3次元形状データ認識手段 1 1は、 この読み取つ たデータが正常なデータでないと判断した場合には、 演算手段 1 2は表示手段 4 を制御して、 データが正常でない旨のエラーメッセージを表示させる (ステップ S 3 ) 。 そして、 ステップ S 1で開いたデータをクローズし (ステップ S 4 ) 、 メッシュを 3次元要素分割する処理を終了する。  In this step S2, if the three-dimensional shape data recognizing means 11 determines that the read data is not normal data, the calculating means 12 controls the display means 4 so that the data is not normal. Is displayed (step S3). Then, the data opened in step S1 is closed (step S4), and the process of dividing the mesh into three-dimensional elements is completed.
また、 ステップ S 2で、 データが正常であると判断した場合には、 3次元形状 データ認識手段 1 1にて、 データのうちの元データを構成するノ一ドの点情報お ょぴエレメントの立体情報、 すなわち、 ノード用一時ファイルを開く （ステップIf it is determined in step S2 that the data is normal, the 3D shape In the data recognizing means 11, open the point information of the node constituting the original data of the data and the three-dimensional information of the element, that is, the temporary file for the node (step
S 5) とともに、 エレメント用一時ファイルを開く (ステップ S 6) 。 なお、 3 次元形状データ認識手段 1 1にて認識したデータは、 一旦記憶手段 1 3に記憶さ れる。 With S5), open the temporary file for the element (step S6). The data recognized by the three-dimensional shape data recognition means 11 is temporarily stored in the storage means 13.
この後、 3次元形状データ認識手段 1 1は、開いたユニバーサルファイルのデー タから処理状態が記録された一行を読み取る （ステップ S 7) 。 この読み取りが 完了した場合には、 演算手段 1 2は 3次元要素分割が実施されたものと判断し、 出力処理し （ステップ S 9) 、 ステップ S 4に進む。  Thereafter, the three-dimensional shape data recognizing means 11 reads one line in which the processing state is recorded from the data of the opened universal file (step S7). When this reading is completed, the calculating means 12 determines that the three-dimensional element division has been performed, performs an output process (step S9), and proceeds to step S4.
また、 ステップ S 8で、 演算手段 1 2は、 開いたユニバーサルファイルの一行 の読み取りが完了しない場合にはデータが未処理であると判断し、 一行の情報が 元データの点情報か否かを判断し （ステップ S 10) 、 点情報であると判断した 場合にはノード処理を実施し （ステップ S 1 1) 、 元データの立体情報であると 判断した場合には （ステップ S 1 2) 、 エレメント処理を実施する （ステップ S 1 3) 。  In step S8, if the reading of one line of the opened universal file is not completed, the calculating means 12 determines that the data is unprocessed, and determines whether or not the information of one line is the point information of the original data. Judgment (step S10), if it is judged to be point information, node processing is performed (step S11), and if it is judged to be three-dimensional information of the original data (step S12), Perform element processing (step S13).
すなわち、 ノード処理では、 図 1 5のフローチャートに示すように、 未処理の 点情報の有無を判断し （ステップ S 2 1) 、 ステップ S 5で開いた未処理の点情 報を認識、すなほちノード用一時ファイルに書き込み（ステップ S 22)、各ノー ドの点情報のノード番号および座標データを演算のために記憶手段 1 3に記憶さ せる処理を繰り返す （ステップ S 23) 。  That is, in the node processing, as shown in the flowchart of FIG. 15, the presence or absence of unprocessed point information is determined (step S21), and the unprocessed point information opened in step S5 is recognized. That is, the process of writing to the node temporary file (step S22) and storing the node number and coordinate data of the point information of each node in the storage means 13 for calculation is repeated (step S23).
そして、 図 1 6のフローチャートのエレメント処理に示すように、 演算手段 1 2は、 未処理の立体情報の有無を判断し （ステップ S 3 1) 、 立体情報のノード 番号に対応しステップ S 23で格納したノード番号と対をなす座標データを読み 出す (ステップ S 32) 。 そして、 演算手段 1 2は、 読み出した座標データから、 中間ノードを演算する （ステップ S 33) 。  Then, as shown in the element processing of the flowchart in FIG. 16, the arithmetic means 12 determines whether there is any unprocessed three-dimensional information (step S31), and corresponds to the node number of the three-dimensional information in step S23. The coordinate data paired with the stored node number is read out (step S32). Then, the calculating means 12 calculates an intermediate node from the read coordinate data (step S33).
具体的には、 演算手段 1 2は、 3次元形状データ認識手段 1 1にて認識した元 データから、 中点作成手段 1 5により隣接するノード間の中点を演算する。 すな わち、 図 5ないし図 7に示すように、 エレメントを構成するノード （図 5ないし 図 7中の秦） を結ぶ線の中点 （図 5ないし図 7中の▲) を、 線の両端のノードの 座標情報に基づいて、 上述したように座標値の平均を演算して求める。 Specifically, the calculating means 12 calculates the midpoint between adjacent nodes by the midpoint creating means 15 from the original data recognized by the three-dimensional shape data recognizing means 11. That is, as shown in FIGS. 5 to 7, the nodes constituting the elements (FIGS. The midpoint of the line connecting the hata in Fig. 7 (▲ in Figs. 5 to 7) is obtained by calculating the average of the coordinate values as described above based on the coordinate information of the nodes at both ends of the line.
さらに、 演算手段 1 2は、 3次元形状データ認識手段 1 1にて認識した元デー タから、 中心作成手段 1 6により中心を演算する。 すなわち、 図 5ないし図 7に 示すように、 エレメントを構成する平面領域である表面の中点 (図 5ないし図 7 中の驪） を、 この表面を構成するノード （図 5ないし図 7中の ©) の座標情報に 基づいて、 上述したように座標値の平均を演算して求める。  Further, the calculation means 12 calculates the center by the center creation means 16 from the original data recognized by the three-dimensional shape data recognition means 11. That is, as shown in FIG. 5 to FIG. 7, the midpoint of the surface (the plane in FIG. 5 to FIG. 7), which is a plane area forming the element, is connected to the node (FIG. 5 to FIG. Based on the coordinate information of ©), the average of the coordinate values is calculated and obtained as described above.
また、 演算手段 1 2は、 3次元形状データ認識手段 1 1にて認識した元データ から、 重心作成手段 1 7によりエレメントの重心を演算する。 すなわち、 図 5な いし図 7に示すように、 エレメントの重心 （図 5ないし図 7中の★) を、 このェ レメントを構成する全ノード （図 5ないし図 7中の翁） の座標情報に基づいて、 上述したように座標値の平均を演算して求める。  The calculating means 12 calculates the center of gravity of the element from the original data recognized by the three-dimensional shape data recognizing means 11 by the center of gravity creating means 17. That is, as shown in FIGS. 5 and 7, the center of gravity of the element (★ in FIGS. 5 to 7) is used as the coordinate information of all the nodes (Ogina in FIGS. 5 to 7) that constitute this element. Based on this, the average of the coordinate values is calculated and obtained as described above.
このようにして算出した中間ノードは、 中間ノード処理される （ステップ S 3 4 ) 。 このステップ S 3 4の中間ノード処理は、 図 1 7のフローチャートに示す ように、中願ノードの座標値と、ステップ S 2 3で格納した点座標とを比較し（ス テツプ S 3 4 1 ) 、 同一座標か否かを判断する （'ステップ S 3 4 2 ) 。 そして、 同一座標であると判断した場合には、 格納してある点座標のノード番号を中間 ノードとして採用し （ステップ S 3 4 3 ) 、 中間ノード処理を終了する。 また、 ステップ S 3 4 2で同一座標でないと判断した場合には、 記憶手段 1 3に記憶し (ステップ S 3 4 4 ) 、 中間ノードを新たなノードとしてノード用一時ファイル に出力する （ステップ S 3 4 5 ) 。  The intermediate node calculated in this way is processed as an intermediate node (step S34). In the intermediate node processing of step S34, as shown in the flowchart of FIG. 17, the coordinate value of the middle application node is compared with the point coordinates stored in step S23 (step S334). Then, it is determined whether or not the coordinates are the same ('step S3422). If it is determined that the coordinates are the same, the node number of the stored point coordinates is adopted as the intermediate node (step S3343), and the intermediate node processing ends. If it is determined that the coordinates are not the same in step S 3 42, the coordinates are stored in the storage means 13 (step S 3 4 4), and the intermediate node is output to the node temporary file as a new node (step S 3 3 4 5).
具体的には、 この演算された中点、 中心および重心は、 演算結果の座標値とと もに新たなノードを示す番号 （a 1， a 2 , a 3 , a 4 , a 5 , a 6 , ·· ·， b 1 , b 2 , b 3 , b 4， ···， c 1 ) が関連付けされた座標情報が作成され、新たなノー ドとして設定される。 この設定された中点、 中心および重心のノード （図 5ない し図 7中の△, □， ☆) の座標情報は、 記憶手段 1 3に一旦記憶される。  Specifically, the calculated midpoint, center, and center of gravity are used as the numbers (a1, a2, a3, a4, a5, a6) indicating the new nodes together with the coordinate values of the calculation results. ,..., B 1, b 2, b 3, b 4,..., C 1) are created as coordinate information and set as a new node. The coordinate information of the set midpoint, center, and center of gravity node (ノ ー ド, □, ☆ in FIG. 5 or FIG. 7) is temporarily stored in the storage means 13.
そして、 上述したようにして作成した中間ノードを利用して、 図 1 6のフロー チャートに示すように、 分割エレメントを作成する （ステップ S 3 5 ) 。 具体的には、 演算手段 1 2は、 元データと、 上記中点作成手段 1 5、 中心作成 手段 1 6および重心作成手段 1 7にて作成された新たなノード （図 5ないし図 7 中の▲, ■， ★) の座標情報とに基づいて、エレメント作成手段 1 8により元デー タの多面体のェレメントを細分割して複数の多面体のエレメントである 6面体の エレメントを作成する処理をする。 すなわち、 図 5ないし図 7に示すように、 新 たに作成された中点のノード （図 5ないし図 7中の▲) および中心のノード （図 5ないし図 7中の圜） を結ぶ線と、 中心のノード (図 5ないし図 7中の口） およ ぴ重心のノード (図 5ないし図 7中の★) を結ぶ線とにて新たに構成される閉じ た平面領域である面にて、 元データの多面体のエレメントを複数の 6面体のエレ メントに区画する。 Then, using the intermediate node created as described above, a divided element is created as shown in the flowchart of FIG. 16 (step S35). Specifically, the arithmetic means 12 includes the original data and the new nodes created by the above-mentioned midpoint creation means 15, center creation means 16, and center of gravity creation means 17 (see FIGS. 5 to 7). Based on the coordinate information (▲, ■, ★), the element creating means 18 subdivides the polyhedral element of the original data to create a hexahedral element which is a plurality of polyhedral elements. In other words, as shown in Fig. 5 to Fig. 7, the line connecting the newly created midpoint node (▲ in Fig. 5 to Fig. 7) and the central node (the annex in Fig. 5 to Fig. 7) , The center node (the mouth in Fig. 5 to Fig. 7) and the line connecting the center of gravity node (★ in Fig. 5 to Fig. 7). The polyhedral element of the original data is divided into a plurality of hexahedral elements.
この後、 分割したエレメントをエレメント用一時ファイルに出力し (ステップ S 3 6 ) 、 ステップ S 3 1に戻って分割動作を繰り返す。 すなわち、 細分割され て形成される 6面体のエレメントは、 この 6面体のエレメントを構成するノード に付される番号順で表された立体情報が新たに作成され、 新たなエレメントとし て設定される。 この設定された立体情報は、 記憶手段 1 3にー且記憶される。 このように、 元データと、 演算により新たに得られたノードの座標情報および 細分割により生成された複数のエレメントの立体情報を、 元データの座標情報お よび立体情報と合わせて処理データとして一旦記憶しておく。この処理データは、 元データのエレメントに新たに中点、 中心および重心が設定され、 これら中点、 中心およぴ重心を結ぶ線にて構成される平面領域にて細分割された形状情報であ る。  Thereafter, the divided elements are output to an element temporary file (step S36), and the process returns to step S31 to repeat the division operation. In other words, for the hexahedral element formed by subdivision, three-dimensional information expressed in the numerical order assigned to the nodes constituting the hexahedral element is newly created and set as a new element . The set three-dimensional information is stored in the storage means 13. In this way, the original data, the coordinate information of the node newly obtained by the calculation, and the three-dimensional information of a plurality of elements generated by the subdivision are temporarily combined with the coordinate information and the three-dimensional information of the original data as processing data. Remember. In this processed data, a new midpoint, center, and center of gravity are newly set in the element of the original data, and the shape information is subdivided into a plane area formed by a line connecting the midpoint, the center, and the center of gravity. is there.
そして、 演算手段 1 2は、 入力手段 2による入力操作により、 適宜表示手段 4 を制御して処理データを表示させる処理をする。 また、 演算手段 1 2は、 入力手 段 2による入力操作により、 印刷装置などにて印刷させたり別のコンピュータに 送信するなど、 出力手段 5に処理データを出力される処理をする。  Then, the arithmetic means 12 performs a process of displaying the processed data by appropriately controlling the display means 4 by the input operation of the input means 2. The calculating means 12 performs a process of outputting processing data to the output means 5, such as printing on a printing device or transmitting the data to another computer, by an input operation by the input means 2.
すなわち、 図 1 8のフローチヤ一トに示すように、 ステップ S 9の出力処理を 実施する。 この出力処理では、 演算手段 1 2は、 ステップ S 1で開いたデータを 読み取り （ステップ S 4 1 ) 、 一時ファイルを読取用として再び開き （ステップ S 4 2 ) 、 出力用のユニバーサルファイルを開く （ステップ S 4 3 ) 。 That is, as shown in the flowchart of FIG. 18, the output processing of step S9 is performed. In this output processing, the arithmetic means 12 reads the data opened in step S1 (step S41), and reopens the temporary file for reading (step S41). S42), open the universal file for output (step S43).
そして、 演算手段 1 2は、 ユニバーサルファイルの一行を読み取り （ステップ S 4 4 ) 、 3次元要素分解の処理の終了である旨の情報を認識するまで （ステツ プ S 4 5 ) 、 ノードの点情報を読み取る （ステップ S 4 6 ) 。 このノードの点情 報を読み取ったら、 ノードの点情報であるノード用一時ファイルのデータを全て 出力用ユニバーサルファイルに出力する （ステップ S 4 7 ) 。 そして、 ュニバー サルファイル内のノードのデータを全てスキップする (ステップ S 4 8 ) 。  Then, the arithmetic means 12 reads one line of the universal file (step S44), and until it recognizes information indicating that the processing of the three-dimensional element decomposition is completed (step S45), the node point information Is read (step S46). When the point information of this node is read, all the data of the node temporary file, which is the point information of the node, is output to the universal file for output (step S47). Then, all the node data in the universal file are skipped (step S48).
さらに、演算手段 1 2は、エレメントの立体情報を読み取る (ステップ S 4 9 )。 このエレメントの立体情報を読み取ったら、 エレメントの立体情報であるエレメ ント用一時ファイルのデータを全て出力用ユニバーサルファイルに出力する （ス テツプ S 5 0 ) 。 そして、 ユニバーサルフアイノレ内のエレメントのデータを全て スキップし （ステップ S 5 1 ) 、 ステップ S 4 4に戻って処理を繰り返し、 出力 するためのデータを取得する。 この用にして取得したデータを表示手段や出力手 段から出力させる。  Further, the calculating means 12 reads the three-dimensional information of the element (step S49). When the three-dimensional information of the element is read, all the data of the element temporary file, which is the three-dimensional information of the element, is output to the universal file for output (step S50). Then, all the data of the elements in the universal file are skipped (step S51), and the process returns to step S44 to repeat the process and acquire data to be output. The data acquired for this purpose is output from display means or output means.
このようにして、 例えば図 1 9に示す 3次元形状のメッシュが図 2 0に示す 3 次元形状のメッシュに細分割される。  In this way, for example, the three-dimensional mesh shown in FIG. 19 is subdivided into the three-dimensional mesh shown in FIG.
ここで、有限要素法解析において、立方体形状の 6面体のエレメントによりメッ シュが構成されたものが最も良好な解析結果が得られる。 これは、 立方体を構成 する各面の角における角度が全て直角であること、 および、 各面の最長辺と最短 辺との比が 1すなわち各辺の長さが同一であることの要件を満たしている。 しか しながら、 4面体のエレメントや 5面体のエレメントでは、 構成する面の角にお ける角度が直角とはならず、かつ、各面の最長辺と最短辺との比が 1とはならい。 このことから、 4面体のエレメントや 5面体のエレメントでは、 良好な解析結果 を得るための要件から大きく外れた歪んだ状態（歪み度が 1より小さレ、） となる。 このため、 最も歪みが小さくなる 6面体のエレメントにて構成することにより、 良好な有限要素解析結果が得られることとなる。  Here, in the finite element method analysis, the best analysis result is obtained when the mesh is composed of cube-shaped hexahedral elements. This satisfies the requirements that the angles of all the faces constituting the cube are all right angles, and that the ratio of the longest side to the shortest side of each face is 1, that is, the length of each side is the same. ing. However, in the case of tetrahedral elements and pentahedral elements, the angles of the constituent surfaces are not right angles, and the ratio of the longest side to the shortest side of each surface is not one. For this reason, the tetrahedral element and the pentahedral element are in a distorted state (the degree of distortion is smaller than 1) which largely deviates from the requirements for obtaining good analysis results. Therefore, good finite element analysis results can be obtained by using hexahedral elements that minimize distortion.
したがって、 上述したように、 中点、 中心おょぴ重心の位置に新たなノードを 設定し、 中点と中心とを結ぶ線、 および、 中心と重心とを結ぶ線にて構成される 面の位置でエレメントを分割することにより、 4面体のエレメントゃ 5面体のェ レメントでも 6面体のエレメントに分割できる。このため、 3次元形状のメッシュ の歪みが小さくなり、 良好な有限要素解析結果を得ることができる。 Therefore, as described above, a new node is set at the position of the center and the center of gravity, and the line is formed by the line connecting the center and the center, and the line connecting the center and the center of gravity. By dividing the element at the position of the surface, even a tetrahedral element ゃ a pentahedral element can be divided into a hexahedral element. As a result, the distortion of the three-dimensional mesh is reduced, and good finite element analysis results can be obtained.
そして、 この細分割処理を繰り返すことにより、 図 2 1に示すように、 細分割 されるメッシュの数は、 指数関数的に増大する。 このため、 数回の細分割処理で も、 細かい 3次元形状のメッシュを作成でき、 手動メッシュ生成方法のように元 データのメッシュが粗くても、 極めて詳細な 3次元形状のメッシュを容易に得る ことができる。 したがって、 構造物の外郭に比較的に近い 3次元形状のメッシュ が得られる手動メッシュ生成方法では、 元データの 3次元形状のメッシュを粗い 状態としても良好な細分化ができるので、 元データの作成時間を極めて短縮でき る。  By repeating this subdivision process, the number of subdivided meshes increases exponentially as shown in FIG. As a result, a fine three-dimensional mesh can be created even with several subdivision processes, and an extremely detailed three-dimensional mesh can be easily obtained even if the original data mesh is coarse as in the manual mesh generation method. be able to. Therefore, in the manual mesh generation method that can obtain a three-dimensional mesh relatively close to the outline of the structure, it is possible to satisfactorily subdivide the three-dimensional mesh of the original data even if the mesh is coarse, so that the original data is created. Time can be significantly reduced.
さらに、 細分割処理を繰り返すことにより、 図 2 2に示すように、 エレメント の歪み状態が歪みのない 「1」 により近付くことも認められる。 なお、 この図 2 2において、 点線で示す系列 1および実線で示す系列 2は、 異なる 3次元形状の モデルを細分割処理した際のエレメントの歪みを示すグラフである。 このことか らも、 上述したように、 自動メッシュ作成方法や半自動メッシュ作成方法、 手動 メッシュ作成方法で作成され、 4面体のエレメントのみで構成されたメッシュや、 4面体のエレメントあるいは 5面体のエレメントさらには 6面体のエレメントが 混在するようなメッシュでも、 細分割処理により 6面体のエレメントのみのメッ シュが得られ、 さらには細分割処理を繰り返すことによりさらに歪みを少なくで き、 良好な有限要素解析結果を容易に得ることができる。  Furthermore, by repeating the subdivision process, it is also recognized that the distortion state of the element approaches “1” without distortion, as shown in FIG. In FIG. 22, a series 1 shown by a dotted line and a series 2 shown by a solid line are graphs showing distortion of elements when a model having a different three-dimensional shape is subjected to subdivision processing. From this, as described above, meshes created by the automatic meshing method, semi-automatic meshing method, and manual meshing method, and composed of tetrahedral elements only, tetrahedral elements or pentahedral elements Furthermore, even for a mesh in which hexahedral elements are mixed, a mesh of only hexahedral elements can be obtained by the subdivision processing.Furthermore, by repeating the subdivision processing, distortion can be further reduced, and a good finite element Analysis results can be easily obtained.
〔 3次元要素分割装置の効果〕 [Effects of 3D element dividing device]
上述したように、 本発明の 3次元要素分割装置 1では、 演算手段 1 2により、 3次元形状データ認識手段 1 1にて取得された元データの複数のノードの点情報 および複数のエレメントの立体情報に基づいて、 隣接するノード間の中点と、 ェ レメントの外面の平面領域の中心と、 エレメントの重心をそれぞれ演算して新た にノードをそれぞれ作成し、 中点のノードおよび中心のノードを結ぶ線と、 中心 のノードおよび重心のノードを結ぶ線とにて新たに構成される閉じた平面領域に より、 設定入力された元のエレメントを細分割する演算処理を実施する。 このた め、 粗く作成されたメッシュでも容易に短時間で細分割できるとともに、 エレメ ントの全てを 6面体に細分割でき、 元データを特に有限要素法解析で良好な結果 が得られる処理データとして容易に得ることができる。 As described above, in the three-dimensional element dividing device 1 of the present invention, the arithmetic unit 12 uses the three-dimensional shape data recognizing unit 11 to obtain the point information of the plurality of nodes of the original data and the three-dimensional Based on the information, a new node is created by calculating the midpoint between adjacent nodes, the center of the plane area on the outer surface of the element, and the center of gravity of the element. The connecting line and the center An operation for subdividing the set and input original element is performed by using a closed plane area newly formed by the nodes connecting the nodes of and the nodes of the center of gravity. For this reason, even a coarsely created mesh can be easily subdivided in a short time, and all the elements can be subdivided into hexahedrons. Can be easily obtained.
そして、 ノードの座標情報を含む点情報を有した元データを認識し、 演算手段 1 2により、 隣接するノ一ドの座標情報の座標値を平均する演算による中点の ノードの作成、 エレメントの外面の平面領域を構成するノードの座標情報の座標 値を平均する演算による中心のノードの作成、および、エレメントを構成するノー ドの座標情報の座標値を平均する演算による重心のノードの作成を実施する。 こ のため、 座標値の平均という単純な演算方法により、 メッシュを細分割するため の新たなノードを容易に短時間で作成でき、 演算処理効率を容易に向上できる。  Recognizing the original data having the point information including the coordinate information of the node, the arithmetic means 12 creates a node at the middle point by averaging the coordinate values of the coordinate information of the adjacent nodes, Creating the center node by averaging the coordinate values of the coordinate information of the nodes that make up the outer planar area, and creating the center of gravity node by averaging the coordinate values of the coordinate information of the nodes that make up the element carry out. Therefore, a new node for subdividing the mesh can be easily created in a short time by a simple calculation method of averaging the coordinate values, and the calculation processing efficiency can be easily improved.
〔実施形態の変形〕 (Modification of Embodiment)
なお、 本発明は、 上述した各実施の形態に限定されるものではなく、 本発明の 目的を達成できる範囲で以下に示される変形をも含むものである。  It should be noted that the present invention is not limited to the embodiments described above, but includes the following modifications as long as the object of the present invention can be achieved.
例えば、 上記図 1ないし図 2 2に示す実施の形態において、 3次元形状のメッ シュを細分割する構成について説明したが、 例えばワイヤーフレームやポリゴン などのように、 三角形などの多角形が連続するメッシュ構造でも、 要素となる多 角形を複数に分割してメッシュを細分割する構成としてもできる。  For example, in the embodiment shown in FIGS. 1 to 22 described above, a configuration in which a three-dimensional mesh is subdivided has been described.For example, polygons such as triangles are continuous like a wire frame or a polygon. Even with a mesh structure, a configuration in which a polygon that is an element is divided into a plurality of pieces and a mesh is subdivided can be adopted.
具体的には、 例えば図 2 3およぴ図 2 4に示すように、 形状情報である元デー タとしては、 複数のノードの点情報およびこれらノードを結ぶ線にて三角形や四 角形の閉じた平面領域に構成されたエレメントの面情報とを有している。 点情報 は、 上記一実施の形態と同様にノードに付された番号 （1， 2 , 3， ···) と座標 情報とを有している。 面情報は、 エレメントを構成するノードの番号の組み合わ せの情報である。  Specifically, for example, as shown in FIGS. 23 and 24, the original data as the shape information includes the point information of a plurality of nodes and the closing of triangles and rectangles by lines connecting these nodes. Surface information of the elements configured in the flat area. The point information has numbers (1, 2, 3,...) Assigned to the nodes and coordinate information as in the case of the first embodiment. The surface information is information of a combination of the numbers of the nodes constituting the element.
そして、 演算手段 1 2の中点作成手段 1 5により、 入力手段 2にて設定入力さ れ 3次元形状データ認識手段 1 1に代えた形状データ認識手段にて認識した元 データのノード （図 1 4およぴ図 1 5中の秦） の座標情報に基づいて、 上記一実 施の形態と同様に、 中点 （図 1 4および図 1 5中の▲) の座標を演算して新たな ノードとして設定する。 さらに、 中心作成手段 1 6により、 上記一実施の形態と 同様に、 エレメントの中心 （図 1 4および図 1 5中の口） の座標を演算して新た なノードとして設定する。 そして、 エレメント作成手段 1 8により、 中点およ-び 中心を結ぶ線にて細分割、 すなわち線にて囲まれた閉ざされた平面領域を新たな エレメントとしてこのエレメントを構成するノードの番号の組み合わせの面情報 を作成して設定する。 Then, the data is set and input by the input means 2 by the midpoint creating means 15 by the arithmetic means 12 and the element recognized by the shape data recognizing means in place of the three-dimensional shape data recognizing means 11. Based on the coordinate information of the data node (hata in FIGS. 14 and 15), the coordinates of the midpoint (▲ in FIGS. 14 and 15) are used in the same manner as in the above embodiment. Is calculated and set as a new node. Further, the center creation means 16 calculates the coordinates of the center of the element (the mouth in FIGS. 14 and 15) and sets it as a new node in the same manner as in the first embodiment. Then, the element creating means 18 subdivides the area by a line connecting the midpoint and the center, that is, the closed plane area surrounded by the line is set as a new element and the number of the node number constituting this element is determined. Create and set combination surface information.
このように、 演算手段 1 2により、 設定入力されて形状データ認識手段にて認 識した元データの複数のノードの点情報おょぴ複数のエレメントの面情報に基づ いて、 隣接するノード間の中点と、 エレメントの中心とを演算して新たにノード をそれぞれ作成し、 中点のノードおよび中心のノードを結んでエレメントを細分 割する演算処理を実施する。 このことにより、 粗く作成されたメッシュでも容易 に短時間で細分割処理できる。 さらに、 この方法により、 細分割されたエレメン トは、 全て四角形となる。 すなわち、 上述したように、有限要素法解析において、 歪みが小さいエレメントとなり、 良好な有限要素解析結果を得ることができるよ うになる。  In this way, based on the point information of a plurality of nodes of the original data and the surface information of a plurality of elements, which are set and input by the calculating means 12 and recognized by the shape data recognizing means, the adjacent nodes A new node is created by calculating the midpoint of the element and the center of the element, and an operation is performed to subdivide the element by connecting the midpoint node and the center node. As a result, a finely divided mesh can be easily and quickly subdivided. Furthermore, the elements subdivided by this method are all rectangular. That is, as described above, in the finite element method analysis, the element has a small distortion, and a good finite element analysis result can be obtained.
また、 中点、 中心および重心として、 隣接するノードの座標の平均により演算 して説明したが、平均による演算以外のいずれの演算方法でもできる。すなわち、 中点としては、 隣接するノード間の線分を二等分する位置に限らず、 ノード間の 線分上のいずれの位置、 中心としては、 例えば内接三角形の中心の位置など線分 以外のエレメントを構成する面内のいずれの位置、 重心としては、 例えばエレメ ント内が均一な質量で充填された状態とした場合の質量重心の位置など線分およ ぴ面以外のエレメント内のいずれの位置でもできる。 なお、 平均にて求める上記 実施の形態では、 計算方法が容易で処理速度を向上できる。 また、 中点として線 分の二等分の位置、 中心として内接三角形の中心の位置、 重心として質量重心の 位置とすることにより、 細分割後のエレメントの歪み度がより 1に近い歪みの少 ない 6面体のエレメントが得られるので好ましい。 その他、 本発明の実施の際の具体的な構造おょぴ手順は、 本発明の目的を達成 できる範囲で他の構造などに適宜変更できる。 産業上の利用可能性 Also, the calculation has been described by using the average of the coordinates of the adjacent nodes as the midpoint, the center, and the center of gravity, but any calculation method other than the calculation using the average can be used. In other words, the midpoint is not limited to a position that bisects a line segment between adjacent nodes, but any position on the line segment between nodes and the center is a line segment such as the center position of an inscribed triangle. The position and the center of gravity in the plane constituting the element other than the line segment and the center of gravity of the element other than the plane, such as the position of the center of gravity of the mass when the element is filled with uniform mass Can be in any position. Note that, in the above-described embodiment in which the average is obtained, the calculation method is easy and the processing speed can be improved. Also, by setting the midpoint to the bisecting position of the line segment, the center to the position of the center of the inscribed triangle, and the center of gravity to the position of the mass center of gravity, the distortion of the element after subdivision is closer to 1 This is preferable because a small number of hexahedral elements can be obtained. In addition, the specific structure and procedure for implementing the present invention can be appropriately changed to another structure or the like as long as the object of the present invention can be achieved. Industrial applicability
本発明は、 複数の節点および要素にて形成される有限要素法解析用のメッシュ を細分割処理する要素分割装置、 要素分割方法として利用でき、 構造物の 2次元 形状あるいは 3次元形状を複数の多角形や多面体で分割したメッシュ構造を利用 した有限要素法解析、 例えば構造物の構造解析や電磁場解析、 流体解析などの各 種解析に利用できる。  INDUSTRIAL APPLICABILITY The present invention can be used as an element division device and an element division method for performing a subdivision process on a mesh for finite element method analysis formed of a plurality of nodes and elements. It can be used for finite element method analysis using a mesh structure divided by polygons and polyhedrons, such as structural analysis of structures, electromagnetic field analysis, and fluid analysis.

Claims

請 求 の 範 囲 The scope of the claims
1 . 複数の節点と、 これら節点のうちのいずれかが選択的に連結されて閉じた 平面領域に構成された複数の要素とにて形成される有限要素法解析用のメッシュ を細分割処理する要素分割装置であって、 1. Subdivide the mesh for the finite element method analysis formed by a plurality of nodes and a plurality of elements formed in a closed plane area by selectively connecting any of the nodes. An element dividing device,
前記複数の節点の点情報および前記複数の要素の面情報を有した形状情報を取 得する形状情報認識手段と、  Shape information recognition means for obtaining shape information having point information of the plurality of nodes and surface information of the plurality of elements;
この形状情報認識手段にて取得した形状情報を演算により前記要素を細分割す る演算手段とを具備し、  Computing means for subdividing the element by computation on the shape information obtained by the shape information recognizing means,
前記演算手段は、 隣接する前記節点間の中点おょぴ前記要素の中心に新たに節 点をそれぞれ作成し、 前記中点の節点および前記中心の節点を結んで前記要素を 細分割する  The calculating means creates a new node at the center of the element, which is a midpoint between adjacent nodes, and subdivides the element by connecting the node at the midpoint and the node at the center.
ことを特徴とした要素分割装置。  An element dividing device characterized by the above.
2 . 請求項 1に記載の要素分割装置において、  2. The element dividing device according to claim 1,
点情報は、 節点の座標情報を含み、  The point information includes coordinate information of the node,
演算手段は、 前記節点の座標情報の座標値を平均する演算により中点の節点を 作成し、 要素を構成する前記節点の座標情報の座標値を平均する演算により中心 の節点を作成する  The calculating means creates a middle node by an operation of averaging the coordinate values of the coordinate information of the nodes, and creates a central node by an operation of averaging the coordinate values of the coordinate information of the nodes constituting the element.
ことを特徴とした要素分割装置。 ， An element dividing device characterized by the above. ,
3 . 複数の節点と、 これら節点のうちのいずれかが選択的に連結されて閉じた 多面体領域に構成された複数の要素とにて形成される有限要素法解析用のメッ シュを細分割処理する要素分割装置であって、 3. Subdivision processing of mesh for finite element analysis formed by multiple nodes and multiple elements configured in closed polyhedral region by selectively connecting any of these nodes Element dividing device,
複数の節点の点情報および前記要素の立体情報を有した形状情報を取得する形 状情報認識手段と、  Shape information recognizing means for obtaining shape information including point information of a plurality of nodes and three-dimensional information of the element;
この形状情報認識手段にて取得した形状情報を演算により前記要素を細分割す る演算手段とを具備し、  Computing means for subdividing the element by computation on the shape information obtained by the shape information recognizing means,
前記演算手段は、隣接する前記節間の中点、前記要素の外面の平面領域の中心、 および、 前記要素の重心に新たに節点をそれぞれ作成し、 前記中点の節点おょぴ 前記中心の節点を結ぶ線と前記中心の節点および前記重心の節点を結ぶ線とにて 新たに構成される閉じた平面領域により前記要素を細分割する The calculating means creates a new node at the midpoint between the adjacent nodes, the center of the plane area on the outer surface of the element, and a new node at the center of gravity of the element. The element is subdivided by a closed plane area newly formed by a line connecting the center node and a line connecting the center node and the node of the center of gravity.
ことを特徴とした要素分割装置。  An element dividing device characterized by the above.
4 . 請求項 3に記載の要素分割装置において、  4. The element dividing device according to claim 3,
点情報は、 節点の座標情報を含み、  The point information includes coordinate information of the node,
演算手段は、前記節点の座標情報の座標値を平均する演算により中点を作成し、 要素の外面の平面領域を構成する前記節点の座標情報の座標値を平均する演算に より中心を作成し、 要素を構成する前記節点の座標情報の座標値を平均する演算 により作成する  The arithmetic means creates a midpoint by an operation of averaging the coordinate values of the coordinate information of the nodes, and creates a center by an operation of averaging the coordinate values of the coordinate information of the nodes constituting the planar area on the outer surface of the element. , Which are created by averaging the coordinate values of the coordinate information of the nodes constituting the element
ことを特徴とした要素分割装置。  An element dividing device characterized by the above.
5 . コンピュータを用いて、 複数の節点と、 これら節点のうちのいずれかが選 択的に連結されて閉じた平面領域に構成された複数の要素とにて形成される有限 要素法解析用のメッシュを細分割処理する要素分割方法であって、  5. Using a computer, a finite element method analysis formed by a plurality of nodes and a plurality of elements formed in a closed plane region by selectively connecting any of these nodes. An element division method for subdividing a mesh,
前記複数の節点の点情報および前記要素の面情報を有した形状情報を取得し、 この取得した形状情報の隣接する前記節点間の中点および前記要素の中心を演 算して新たな節点と設定し、  Acquires shape information having the point information of the plurality of nodes and the surface information of the element, calculates a midpoint between the adjacent nodes of the acquired shape information and the center of the element, and obtains a new node. Set,
これら設定された前記中点の節点と前記中心の節点とを結んで前記要素を細分 割する演算を実施する  Performing an operation of subdividing the element by connecting the set middle node and the center node.
ことを特徴とする要素分割方法。  An element division method characterized by the following.
6 . 請求項 5に記載の要素分割方法において、 6. In the element dividing method according to claim 5,
コンピュータは、 節点の座標情報を含む点情報を有した形状情報を取得し、 隣 接する前記節点の座標情報の座標値を平均して中点の節点を演算し、 要素を構成 する前記節点の座標情報の座標値を平均して中心の接点を演算する  The computer obtains shape information having point information including the coordinate information of the node, calculates the middle node by averaging the coordinate values of the coordinate information of the adjacent node, and calculates the coordinates of the node constituting an element. Calculate the center contact point by averaging the coordinate values of information
ことを特徴とする要素分割方法。  An element division method characterized by the following.
7 . コンピュータを用いて、 複数の節点と、 これら節点のうちのいずれかが選 択的に連結されて閉じた多面体領域に構成された複数の要素とにて形成される有 限要素法解析用のメッシュを細分割処理する要素分割方法であって、 7. For the finite element method analysis formed by using a computer, a plurality of nodes and a plurality of elements formed in a closed polyhedral region by selectively connecting any of these nodes. Element division method for subdividing the mesh of
前記複数の節点の点情報および前記要素の立体情報を有した形状情報を取得 し、 Acquire point information of the plurality of nodes and shape information including three-dimensional information of the element And
この取得した形状情報の隣接する前記節点間の中点、 前記要素の外面の平面領 域の中心、 および、 前記要素の重心を演算して新たな節点と設定し、  The midpoint between the adjacent nodes of the acquired shape information, the center of the planar area on the outer surface of the element, and the center of gravity of the element are calculated and set as a new node,
これら設定された前記中点の節点およぴ前記中心の節点を結ぶ線と前記中心の 節点おょぴ前記重心の節点を結ぶ線とにて新たに構成される閉じた平面領域によ り前記要素を細分割する演算を実施する  A closed plane area newly constituted by a line connecting the set middle node and the center node and a line connecting the center node and the center of gravity node is used. Perform operations to subdivide elements
ことを特徴とする要素分割方法。  An element division method characterized by the following.
8 . 請求項 7に記載の要素分割方法において、 8. In the element dividing method according to claim 7,
コンピュータは、 節点の座標情報を含む点情報を有した形状情報を取得し、 隣 接する前記節点の座標情報の座標値を平均して中点の節点を演算し、 要素の外面 の平面領域を構成する前記節点の座標情報の座標値を平均して中心の接点を演算 し、 要素を構成する前記節点の座標情報の座標値を平均して重心の節点を演算す る  The computer obtains shape information having point information including the coordinate information of the node, calculates the middle node by averaging the coordinate values of the coordinate information of the adjacent nodes, and configures a plane area on the outer surface of the element. Average the coordinate values of the coordinate information of the nodes to calculate the center contact point, and calculate the nodes of the center of gravity by averaging the coordinate values of the coordinate information of the nodes forming the element.
ことを特徴とする要素分割方法。  An element division method characterized by the following.
9 . 請求項 5ないし請求項 8のいずれかに記載の要素分割方法をコンピュータ に実行させる 9. Cause a computer to execute the element division method according to any one of claims 5 to 8.
ことを特徴とする要素分割プロダラム。  An element division program characterized by the following.
1 0 . 請求項 9に記載の要素分割プログラムを記録した 10. The element division program according to claim 9 was recorded.
ことを特徴とした要素分割プログラムを記録した記録媒体。  A recording medium having recorded thereon an element division program.
PCT/JP2003/003155 2003-03-17 2003-03-17 Element division apparatus, method thereof, program thereof, and recording medium containing the program WO2004084100A1 (en)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH07121579A (en) * 1993-10-22 1995-05-12 Asahi Glass Co Ltd Method for generating finite element mesh
JP2001076029A (en) * 1999-08-16 2001-03-23 Mtu Motoren & Turbinen Union Muenchen Gmbh Generating method for three-dimenisonal mesh for finite element analysis

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH07121579A (en) * 1993-10-22 1995-05-12 Asahi Glass Co Ltd Method for generating finite element mesh
JP2001076029A (en) * 1999-08-16 2001-03-23 Mtu Motoren & Turbinen Union Muenchen Gmbh Generating method for three-dimenisonal mesh for finite element analysis

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