JP2008129779A - Method and apparatus for automatically converting mesh data of finite element analysis - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method and an apparatus for automatically converting mesh data of finite element analysis, in which triangular mesh data of a shape model to be analyzed are automatically converted into quadrilateral mesh data without moving the nodes of the triangle mesh data. <P>SOLUTION: Each triangular element of triangular mesh data obtained by dividing a shape model into meshes of triangular elements and its adjacent triangular element sharing the side of the original triangular element are used for temporarily forming a quadrilateral and the temporary quadrilateral wherein each of four internal angles is included within a conversion allowable range larger than a prescribed minimum angle and smaller than a prescribed maximum angle, a warp angle between two triangular elements forming the temporary quadrilateral is included within the conversion allowable range and any of the inner angles, the warp angle and an aspect ratio of the temporary quadrilateral is included in the conversion allowable range is determined as a quadrilateral element and substituted for the triangular elements in the triangular mesh data. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a finite element analysis mesh data conversion method and apparatus for automatically converting triangular mesh data obtained by dividing a shape model into triangular element meshes into quadrilateral mesh data.

  When performing CAE analysis using a mesh model based on the finite element method, for example, when analyzing the density distribution of a resin molded product according to the flow distance of the resin raw material during injection molding, a triangular mesh shape model that makes it easy to create an FEM program algorithm However, when analyzing deformation or distortion as a structural analysis for the resin molded product, a quadrilateral mesh that can predict the deformation behavior with high accuracy is preferable in terms of accuracy, and the field of application is wide. It has been known. Therefore, in order to leave information on the stress, heat, and other nodes at the time of injection molding analysis, as shown in FIG. 7, on the screen, the nodes of two adjacent triangular elements are used as they are, and the square elements are manually operated. Although it is possible to create quadrilateral mesh data by converting with the above, it naturally takes a long time for the work.

On the other hand, according to Patent Document 1, a step of creating a surface on a triangular mesh, a step of deleting nodes of the triangular mesh, a step of connecting adjacent surfaces to one surface among the created surfaces, and a surface A method of automatically converting a triangular mesh into a quadrilateral mesh having a step of defining a mesh for creating a quadrilateral mesh and a step of creating a mesh with respect to the surface for which the mesh creation definition has been performed is well known.
JP 2001-14494 A

  However, according to this automatic conversion method, since it is assumed that the nodes of the triangular element are deleted, the analysis results such as pressure distribution and temperature distribution at the CAE stage assuming the triangular mesh are obtained by the finite element method based on the quadrilateral mesh. There is a problem that cannot be used as analysis conditions for structural analysis.

  In view of these points, the present invention provides a mesh automatic conversion method and apparatus for finite element analysis that automatically converts triangular mesh data of a geometric model to be analyzed into quadrilateral mesh data without moving the nodes. With the goal.

  In order to achieve this object, the present invention provides a mesh data conversion method for finite element analysis in which triangular mesh data obtained by dividing a shape model into triangular element meshes is automatically converted into quadrilateral mesh data. For each element, a quadrangle is temporarily formed with an adjacent triangular element having a common side, and for each of the provisional quadrilaterals, the four interior angles are all larger than a predetermined minimum angle and larger than a predetermined maximum angle. Are within a small allowable conversion range, whether the bend angle between the two triangular elements forming the provisional rectangle is within the allowable conversion range, and any of the interior angle, the bend angle, and the aspect ratio of the temporary rectangle. The provisional quadrangle within the conversion allowable range is replaced with a triangular element in the triangular mesh data as a quadrilateral element. The conversion allowable range of interior angle, warp angle, and aspect ratio is set within a range where conversion to a quadrilateral element using the nodes of the triangular element is more effective than a triangular element, and analysis based on the quadrilateral element can be executed. As a result, quadrilateral mesh data at least partially replaced with quadrilateral elements is obtained.

  According to a third aspect of the present invention, there is provided an apparatus for carrying out the method according to the first aspect of the present invention, in the mesh data conversion apparatus for finite element analysis according to claim 3, wherein the triangular mesh data obtained by dividing the geometric model into triangular element meshes is automatically converted into quadrilateral mesh data. A storage device for storing mesh data obtained by dividing the mesh into meshes, processing element specifying means for sequentially specifying triangle elements to be processed with respect to the triangular mesh data stored in the storage device, and replacement of the triangular elements is allowed. In order to determine whether or not to obtain, conversion tolerance range data of an inner angle that is larger than a predetermined minimum angle of the quadrilateral element and smaller than the predetermined maximum angle, the warp angle between two triangular elements forming the provisional quadrangle Conversion allowable range data and conversion allowable range data smaller than a predetermined value of the aspect ratio of the provisional rectangle are held. Rectangle data creation means for temporarily forming a rectangle by two triangle elements, that is, a permissible data holding means and an adjacent triangle element having a common side for a designated triangle element, and the rectangle data creation means The calculation means for calculating the interior angle, the warp angle, and the aspect ratio of the provisional quadrangle created in step 4, and whether the four internal angles, warp angles, and aspect ratios of the provisional quadrilateral are within the allowable conversion range. Conversion judgment means for judging and replacing a provisional quadrangle within the allowable conversion range in the triangular mesh data with a triangular element stored in the storage device as a quadrilateral element.

  In order to further improve the accuracy of the structural analysis based on the converted quadrilateral mesh, according to claim 2, different conversion allowable ranges are set in a plurality of stages in which the conversion allowable range of at least one of the inner angle, the warp angle, and the aspect ratio is widened. In addition, for each triangular element that has not been converted to a quadrilateral element in the immediately preceding processing stage, it is determined whether or not it is within the conversion tolerance range of the belonging over a plurality of processing stages in order, and the provisional rectangle that is within the allowable internal angle range of the belonging Is replaced with a triangular element as a quadrilateral element, or according to claim 4, the conversion allowable data holding means has different conversion allowable ranges in a plurality of stages in which at least one of the internal allowable angle, the warp angle and the aspect ratio is widened. For each triangular element that holds data and the processing element designating means has not been converted to a quadrilateral element in the immediately preceding processing stage with respect to the conversion judging means. Order to determine whether it is within the conversion tolerance belongs over a plurality of processing stages.

  According to the invention of claim 1 or claim 3, by automatically converting two triangular elements that are effective in quadrilateral transformation into quadrilateral elements, the triangular mesh data is at least partially replaced with quadrilateral elements, By sharing the information associated with the nodes, structural analysis by finite element methods such as deformation and strain can be performed with high accuracy, and the analysis results by triangular mesh data can be diverted if necessary when analyzing by quadrilateral mesh . By making the internal angle, the warp angle, and the aspect ratio of the quadrangle acceptable conditions for conversion, automatic conversion can be performed in a state where the convergence of the analysis result is avoided so long as the advantage unique to the quadrilateral element can be utilized. In other words, without creating original mesh data consisting of flat quadrilateral elements, quadrilateral mesh data that at least partially contains quadrilateral elements that ensure element quality can be created based on triangular mesh data that is easy to create algorithms. It becomes.

  According to the invention of claim 2 or 4, the triangular elements to be processed are preferentially synthesized with the triangular elements of the adjacent conversion candidates that are relatively advantageous in terms of analysis accuracy, etc. The conversion effect to data can be improved.

  An apparatus for implementing a finite element analysis mesh automatic conversion method according to an embodiment of the present invention using a computer will be described with reference to FIGS. In this apparatus, as shown in FIG. 2, a computer 10 stores a memory 17a in which triangular mesh data obtained by dividing a three-dimensional shape model into triangular element meshes and mesh data including converted quadrilateral elements. A storage device 17 having a memory 17b, an input means 18 such as a keyboard for performing various input operations for conversion, a display unit 19 for displaying mesh data and the like, and the like.

  This computer functions to configure the following units by operating a CPU, a memory, and the like in accordance with a predetermined program loaded. That is, the processing element designating means 11 for designating the triangular elements to be processed in order with respect to the triangular mesh data fetched into the memory 17b and the determination of whether or not the replacement of the triangular elements can be permitted. Conversion allowable range data defining the minimum allowable conversion angle and maximum angle of the interior angle, conversion allowable range data defined by the maximum allowable angle of the bend angle between two triangular elements that form the temporary rectangle for normal conversion, and provisional rectangle Two triangular elements, that is, conversion allowable data holding means 15 for holding conversion allowable range data defined by the maximum allowable aspect ratio, and adjacent triangular elements having the same side for the designated triangular element The quadrilateral data creating means 12 for forming a provisional quadrangle as a provisional quadrilateral element, and the four interior angles of the provisional quadrilateral based on the shape data. An internal angle calculation means 13 for calculating each of the angles, a bend angle calculation means 13a for calculating a bend angle between two flat triangular elements constituting the provisional rectangle, and an aspect ratio for the four sides of the provisional rectangle. The aspect ratio calculation means 13b and the provisional quadrilateral, the four interior angles are all within the allowable internal angle range, and the warp angle between the two triangular elements of the provisional quadrilateral is within the conversion allowable range. Whether or not the aspect ratio of the provisional quadrangle is within the allowable conversion range, and these three kinds of criteria parameters are preloaded into the memory 17b with the provisional quadrangle within the conversion allowable range as a quadrilateral element in advance. The conversion judging means 14 is configured to replace two triangular elements belonging to the existing triangle mesh data.

  This automatic mesh conversion device is intended to convert triangular mesh data of a three-dimensional shape model of an instrument panel injection-molded with, for example, PP resin shown in FIG. The first conversion allowable range data of ° and the maximum internal angle 110 ° and the second conversion allowable range data of the minimum internal angle 30 ° and the maximum internal angle 140 ° are held for the second processing stage. In addition, the first conversion allowable range data with a warp angle of 10 ° and the second with a warp angle of 30 °, which are angles formed by the respective normal vectors between two triangular elements synthesized with respect to the designated triangle element. Conversion allowable range data, r = 5 first conversion allowable range data defined by the allowable maximum value of the aspect ratio r = b / a, which is the ratio of the shortest side length a and the maximum side length b of the provisional rectangle, and r = 10 holds the second conversion tolerance.

  At the time of creating the triangular mesh data, the triangular element is defined as a flat surface by three nodes, but the neighbors are not necessarily the same surface. In this case, when the warp edge or bending angle between two triangular elements increases, that is, the warp angle increases, unlike the original quadrilateral mesh that does not depend on the conversion method of the present invention, the quadrilateral element with a corresponding distortion from the initial state. Therefore, there is a problem that further calculation is difficult and the analysis accuracy is lowered. Therefore, a warp angle of 10 ° or less is selected preferentially, and rather, conversion is not performed for, for example, 30 ° or more, in which the analysis with a triangle is preferable in terms of accuracy.

  In addition, when the inner angle is outside the conversion allowable range, the nodes of the provisional quadrangle that are facing each other will be appropriately approached, and when the aspect ratio is outside the conversion allowable range, the adjacent nodes will be close to each other. In some cases, the calculation results of the physical quantities of the two close nodes may change suddenly, and the analysis accuracy may be lowered rather than the triangular element due to the loss of continuity. In addition, the analysis results may not converge. . Therefore, the second conversion allowable range of the inner angle and the aspect ratio is set in consideration of these factors, so that the element quality is deteriorated to an unacceptable degree from the flat square, and an abnormal value is calculated by the physical quantity distribution function. In addition, in order to avoid deterioration of convergence, a quadrilateral element that ensures element quality is created.

  The processing element designating unit 11 sequentially designates the triangular elements of the triangular mesh data in the memory 17b fetched from the memory 17a, and forms a provisional rectangle for the designated triangular element with respect to the quadrilateral data creation unit 12, and the provisional quadrature. The interior angle calculation means 13 calculates the interior angle of the quadrangle, the curvature angle between two flat triangular elements is calculated by the curvature angle calculation means 13a, and the aspect ratio for the four sides is calculated by the aspect ratio calculation means 13b. . The conversion determination unit 14 replaces and stores the two triangular elements belonging to the quadrilateral element when a provisional quadrilateral whose inside angle, warp angle, and aspect ratio are all within the allowable internal angle range is detected.

  Further, when storing such composite information, the conversion determination means 14 stores the triangle element number deleted by the replacement with the quadrilateral element in the memory 17b, so that the triangle in the second processing stage is stored. The element designation is canceled and the number of the converted quadrilateral element is added, and the number of elements adjacent to the designated triangular element and each element number are adjacent to the node of the quadrilateral element. The number of elements and the number of elements are stored in the memory 17b as new mesh information.

  The processing element designating unit 11 determines that the judgment criterion output from the conversion permissible data holding unit 15 is within the second conversion allowable range when the triangular elements that have not been converted remain at the end of the first processing stage in the memory 17b. By switching, the remaining elements are sequentially specified again to form a provisional rectangle, and the determination process in the second processing stage is performed.

  The operation of the finite element analysis automatic mesh conversion apparatus configured as described above will be described with reference to the flowchart of FIG. For example, the mesh model (FIG. 4A) of the side portion 1 of the instrument panel to be converted shown in FIG. 6 is designated in order for each element of the triangular mesh data in that region (S1). A provisional quadrilateral is created in order for each of the three sides (S2), and then the interior angle, the warp angle, and the aspect ratio of the four locations are calculated to determine whether or not they are within the first conversion allowable range (S3).

  For example, as shown in FIG. 3, for the triangular element 5, the provisional quadrature synthesized with the triangular element 5 a is determined to have an interior angle outside the first allowable interior angle range, and then the provisional square synthesized with the triangular element 5 b. When it is determined that (indicated by a bold line) is within the first allowable internal angle range, and the warp angle and aspect ratio are also determined to be within the first conversion allowable range, the designated triangular element in the triangular mesh data at that time 5 is replaced with a square element which is regarded as a substantially original square element composed of one adjacent triangular element 5b (S4), and these triangle elements are converted into converted data together with the related information described above. Stored. When the determination is completed for all the triangular elements, the triangular mesh data (FIG. 4A) is converted into the square mesh data (FIG. 4B) in the first processing stage.

  Subsequently, when there are remaining unconverted triangular elements (S5, S6), the remaining elements are designated in order, and the second processing stage is determined based on the switched second allowable conversion range data. Is done. As a result, as shown in FIG. 4C, the area to be converted into a quadrilateral element extends to a curved surface having a relatively small curvature, an area in which the plate thickness is increased, and the like, and the accuracy of the structural analysis by the quadrilateral element is effective. Conversion to quadrilateral elements that are ensured and the analysis result may not converge is avoided, and quadrilateral mixed mesh data is created. In some cases, if no non-converted triangular element remains, it is converted into complete quadrilateral mesh data on the premise that two elements are combined.

  4A, the aspect ratio does not increase as a whole. However, as shown in FIG. 5, in the instrument panel side portion 1, a rib whose thickness increases more abruptly in a stepped manner than the general surface, for example, in a narrow range T1 on the back surface thereof. Are formed, and a relatively extremely small triangle is adjacent to each other, and the shortest side length a of the provisional quadrangle becomes extremely short with respect to the maximum side length b, so that the aspect ratio is greater than 5. The determination is made based on the second allowable conversion range.

  In the above-described embodiment, the two-stage processing is performed. However, the conversion determining unit 14 widens the conversion allowable range of, for example, only the bend angle in the second processing stage, and sets the second processing stage. The conversion tolerance range data that is different in multiple stages by a combination of interior angle, warp angle, and aspect ratio, which is widened in two or more stages, such as the third processing stage by widening the conversion tolerance range of only the ratio, etc. Based on each triangle element that has not been converted to a quadrilateral element in the immediately preceding processing stage, it is determined whether or not it is within the permissible conversion allowable range over a plurality of processing stages in order, and is temporarily within the permissible internal angle range of the belonging It is also possible to replace a quadrangle with a triangular element as a quadrilateral element.

It is a flowchart explaining operation | movement of the mesh automatic conversion apparatus of the finite element analysis by embodiment of this invention. It is a figure explaining the structure of the same apparatus. It is a figure explaining operation | movement of the apparatus. It is a figure explaining the conversion process of the mesh by the same apparatus. It is a figure explaining the judgment operation | movement of the aspect-ratio of the apparatus. It is a perspective view which shows partially the instrument panel used as the premise of the mesh model used as the conversion object of this invention. It is a figure explaining the conversion method by the manual operation to the square mesh data of the conventional triangle mesh data.

Explanation of symbols

1 Side of the instrument panel
5, 5a, 5b Triangular element

Claims (4)

In the mesh data conversion method of finite element analysis that automatically converts triangle mesh data obtained by dividing the shape model into meshes of triangular elements to quadrilateral mesh data,
For each triangular element, temporarily form a quadrangle with adjacent triangular elements that share the same side,
Regarding the provisional quadrangle, whether the four interior angles are larger than a predetermined minimum angle and within a conversion allowable range smaller than the predetermined maximum angle, and the two triangles forming the provisional quadrangle Determining whether the warp angle between the elements is within a conversion allowable range, and whether the aspect ratio of the provisional rectangle is within a conversion allowable range smaller than a predetermined value;
Mesh data conversion of finite element analysis, wherein the provisional quadrangle whose all of the interior angle, the warp angle, and the aspect ratio are within the allowable conversion range is replaced with the triangular element in triangular mesh data as a quadrilateral element Method.   Based on multiple conversion tolerances that have widened the conversion tolerance range of at least one of interior angle, warp angle, and aspect ratio, each triangle element that has not been converted to a quadrilateral element in the immediately preceding processing stage is subjected to multiple processes in order. 2. The finite state according to claim 1, wherein it is determined whether or not it is within the permissible conversion range belonging to each step, and the provisional quadrangle within the permissible internal angle range of the belonging is replaced with the triangular element as a quadrilateral element. Mesh data conversion method for element analysis. In a mesh data conversion device for finite element analysis that automatically converts triangle mesh data obtained by dividing a shape model into meshes of triangular elements to quadrilateral mesh data,
A storage device that stores mesh data obtained by dividing a shape model into meshes, a processing element specifying unit that sequentially specifies triangle elements to be processed with respect to the triangular mesh data stored in the storage device, and replacement of the triangle elements In order to determine whether or not the two can be allowed, conversion tolerance range data of an inner angle that is larger than the predetermined minimum angle of the quadrilateral element and smaller than the predetermined maximum angle, the two triangular elements forming the provisional quadrangle Conversion allowable data holding means for holding conversion allowable range data of the bend angle between and a conversion rectangle data smaller than a predetermined value of the aspect ratio of the provisional quadrangle, and the adjacent triangle elements that share the same side A quadrilateral data creating means for forming the provisional quadrilateral by two triangular elements together with the triangular element, and the quadrilateral data creation Calculating means for calculating an interior angle, a warp angle, and an aspect ratio of the provisional quadrilateral created in steps, and for the provisional quadrilateral, the four internal angles, the warp angle, and the aspect ratio are all within the conversion allowable range. Conversion judging means for judging whether or not the temporary quadrangle within the conversion allowable range in the triangle mesh data is replaced with the triangular element stored in the storage device as a quadrilateral element. A mesh data converter for finite element analysis characterized by the above. The conversion allowable data holding means holds different conversion allowable range data in a plurality of stages in which the conversion allowable range of at least one of the internal angle, the warp angle and the aspect ratio is widened,
The processing element designating unit causes the conversion determining unit to determine whether or not each triangular element that has not been converted to the quadrilateral element in the immediately preceding processing step is within the conversion allowable range to which it belongs over a plurality of processing steps in order. The mesh data conversion apparatus for finite element analysis according to claim 3.

Images