JP2005259043A - Three-dimensional mesh generation method - Google Patents

Three-dimensional mesh generation method Download PDF

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JP2005259043A
JP2005259043A JP2004073054A JP2004073054A JP2005259043A JP 2005259043 A JP2005259043 A JP 2005259043A JP 2004073054 A JP2004073054 A JP 2004073054A JP 2004073054 A JP2004073054 A JP 2004073054A JP 2005259043 A JP2005259043 A JP 2005259043A
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Yasuhiro Takii
康弘 滝井
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Toyota Motor Corp
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Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of generating a three-dimensional mesh by simple calculation processing. <P>SOLUTION: In this method of generating the three-dimensional mesh, a two-dimensional data wherein a reference plane serving as a reference for generating the three-dimensional mesh is modeled with two-dimensional finite elements is read (S1), then normal direction data (sweep amount, division number, offset, group name and interface name) for specifying an array of three-dimensional finite elements along a normal direction of the reference plane are read (S2), the three-dimensional mesh is generated based the data therein (S3), and a three-dimensional mesh data is output (S3). <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

本発明は数値解析用の３次元メッシュ生成技術に関し、特に、計算処理の簡易化とデータ量の削減を図るための改良技術に関する。   The present invention relates to a three-dimensional mesh generation technique for numerical analysis, and more particularly to an improved technique for simplifying calculation processing and reducing the amount of data.

ＣＡＤ，ＣＡＥ等の分野において、解析対象の内部応力や熱応力その他の静的又は動的な構造解析を行うにあたり有限要素法が用いられている。この有限要素法は解析対象を有限要素の集合体にモデル化し、各有限要素に境界条件を与えて演算によりシミュレーション解析を行い、各有限要素の近似解を求めて全体の数値解析を行うものである。有限要素法による数値解析において、解析対象を有限要素の集合体にモデル化するための３次元メッシュ生成作業は多大な時間を費やすとともに、解析結果の精度に直接関わる重要な作業である。３次元メッシュの生成手法として各種の手法が研究されており、例えば、特開平５−１０１１５２号公報には、２次元メッシュに３本又は４本のガイド曲線を設定し、このガイド曲線に沿って２次元メッシュを変形移動させて立体軌跡を生成し、この立体軌跡により３次元メッシュを生成する手法が提案されている。
特開平５−１０１１５２号公報 In the field of CAD, CAE, etc., a finite element method is used for performing static or dynamic structural analysis such as internal stress, thermal stress or the like to be analyzed. In this finite element method, the object to be analyzed is modeled as a collection of finite elements, boundary conditions are given to each finite element, and simulation analysis is performed by computation. An approximate solution of each finite element is obtained, and the entire numerical analysis is performed. is there. In the numerical analysis by the finite element method, the three-dimensional mesh generation work for modeling the analysis target into a collection of finite elements is an important work directly related to the accuracy of the analysis result as well as spending a lot of time. Various methods have been studied as a method for generating a three-dimensional mesh. For example, in Japanese Patent Laid-Open No. 5-101152, three or four guide curves are set in a two-dimensional mesh, and along these guide curves. There has been proposed a method of generating a three-dimensional trajectory by deforming and moving a two-dimensional mesh and generating a three-dimensional mesh from the three-dimensional trajectory.
JP-A-5-101152

しかし、上述の計算手法では複雑なベクトル計算等を要する上に、扱うデータ量も膨大になるため、３次元メッシュを作成するには多大な労力と、高処理能力・大記憶容量のコンピュータシステムが要求される。   However, since the above calculation method requires complicated vector calculation and the amount of data to be handled is enormous, a large amount of labor is required to create a three-dimensional mesh, and a computer system with high processing capacity and large storage capacity is required. Required.

そこで、本発明は計算処理の簡易化とデータ量の削減を図るための３次元メッシュ生成方法を提案することを課題とする。   Accordingly, an object of the present invention is to propose a three-dimensional mesh generation method for simplifying calculation processing and reducing the amount of data.

上記の課題を解決するため、本発明の３次元メッシュ生成方法は解析対象を３次元有限要素にモデル化した３次元メッシュを生成するための３次元メッシュ生成方法であって、３次元メッシュを生成する基準となる基準平面を２次元有限要素にモデル化した２次元メッシュと、この基準平面の法線方向における３次元有限要素の配列を規定する情報とに基づいて３次元メッシュを生成する。この方法によれば、３次元メッシュを生成する基準となる基準平面を２次元有限要素にモデル化した２次元メッシュと、この基準平面の法線方向における３次元有限要素の配列を規定する情報とを保持していればよいので、３次元メッシュの格子座標データを保持する従来例と比較して、取り扱うデータ量を大幅に削減でき、計算負荷も大幅に低減できる。   In order to solve the above problems, the 3D mesh generation method of the present invention is a 3D mesh generation method for generating a 3D mesh in which an analysis target is modeled as a 3D finite element. A three-dimensional mesh is generated based on a two-dimensional mesh obtained by modeling a reference plane serving as a reference to be a two-dimensional finite element and information defining an array of three-dimensional finite elements in the normal direction of the reference plane. According to this method, a two-dimensional mesh obtained by modeling a reference plane serving as a reference for generating a three-dimensional mesh into a two-dimensional finite element, and information defining an array of three-dimensional finite elements in the normal direction of the reference plane; Therefore, the amount of data to be handled can be greatly reduced and the calculation load can be greatly reduced as compared with the conventional example in which lattice coordinate data of a three-dimensional mesh is held.

本発明の方法を適用できる３次元メッシュとしては、基準平面を２次元有限要素にモデル化した２次元メッシュと、基準平面に平行な任意の断面を２次元有限要素にモデル化した２次元メッシュとが同一となるメッシュモデルに適用できる。３次元メッシュがこのようなメッシュ構造を備えている場合には、３次元メッシュの格子座標データを全て保持しなくても、解析対象の基準平面を２次元有限要素にモデル化した２次元メッシュと、この基準平面の法線方向における３次元有限要素の配列を規定する情報とに基づいて解析対象の３次元メッシュを生成することが可能となる。   The three-dimensional mesh to which the method of the present invention can be applied includes a two-dimensional mesh in which a reference plane is modeled as a two-dimensional finite element, a two-dimensional mesh in which an arbitrary cross section parallel to the reference plane is modeled as a two-dimensional finite element, Can be applied to mesh models with the same. When the three-dimensional mesh has such a mesh structure, the two-dimensional mesh in which the reference plane to be analyzed is modeled as a two-dimensional finite element without having to hold all the lattice coordinate data of the three-dimensional mesh, Based on the information defining the arrangement of the three-dimensional finite elements in the normal direction of the reference plane, a three-dimensional mesh to be analyzed can be generated.

基準平面の法線方向における３次元有限要素の配列を規定する情報としては、例えば、３次元有限要素のスイープ量、分割数、オフセット、グループ名、及び界面名を含む情報を用いることができる。また、数値解析対象の対象として、各種の物理現象に応用可能であるが、例えば、燃料電池に適用することにより、燃料電池の３次元温度分布や熱応力を数値シミュレーションすることができる。   As information defining the arrangement of the three-dimensional finite elements in the normal direction of the reference plane, for example, information including the sweep amount, the number of divisions, the offset, the group name, and the interface name of the three-dimensional finite element can be used. Moreover, the present invention can be applied to various physical phenomena as an object of numerical analysis, but for example, by applying it to a fuel cell, a three-dimensional temperature distribution and thermal stress of the fuel cell can be numerically simulated.

本発明によれば３次元メッシュを生成する基準となる基準平面を２次元有限要素にモデル化した２次元メッシュと、この基準平面の法線方向における３次元有限要素の配列を規定する情報とに基づいて３次元メッシュを生成するため、３次元メッシュの計算処理を簡易化できる。また、取り扱うデータ量も小容量化できる。   According to the present invention, a two-dimensional mesh obtained by modeling a reference plane serving as a reference for generating a three-dimensional mesh into a two-dimensional finite element, and information defining an array of three-dimensional finite elements in the normal direction of the reference plane. Since the three-dimensional mesh is generated based on this, the calculation process of the three-dimensional mesh can be simplified. In addition, the amount of data handled can be reduced.

本発明の実施形態は解析対象を３次元有限要素にモデル化した３次元メッシュを生成するための手法を提案するものであり、３次元メッシュを生成する基準となる基準平面を２次元有限要素にモデル化した２次元メッシュと、この基準平面に平行な任意の断面を２次元有限要素にモデル化した２次元メッシュとが同一となるメッシュ構造を備えた３次元メッシュを対象としている。このようなメッシュ構造を備えた３次元メッシュにおいては、基準平面を２次元有限要素にモデル化した２次元メッシュの格子座標データ（以下、２次元メッシュデータと称する。）と、基準平面の法線方向における３次元有限要素の配列を規定する情報（以下、法線方向データと称する。）に基づいて、解析対象の３次元メッシュを生成することができる。但し、３次元メッシュ内の全ての領域において３次元有限要素が形成されている必要はなく、一部の領域において３次元有限要素が形成されていない領域が存在していてもよい。   The embodiment of the present invention proposes a method for generating a three-dimensional mesh in which an analysis target is modeled as a three-dimensional finite element. A reference plane serving as a reference for generating a three-dimensional mesh is changed to a two-dimensional finite element. The target is a three-dimensional mesh having a mesh structure in which a modeled two-dimensional mesh and a two-dimensional mesh in which an arbitrary cross section parallel to the reference plane is modeled as a two-dimensional finite element are the same. In a three-dimensional mesh having such a mesh structure, two-dimensional mesh lattice coordinate data (hereinafter referred to as two-dimensional mesh data) in which the reference plane is modeled as a two-dimensional finite element, and the normal of the reference plane. A three-dimensional mesh to be analyzed can be generated based on information defining the arrangement of three-dimensional finite elements in the direction (hereinafter referred to as normal direction data). However, it is not necessary that the three-dimensional finite element is formed in all the regions in the three-dimensional mesh, and there may be a region where the three-dimensional finite element is not formed in some regions.

ここで、図３を参照しつつ、基準平面の２次元メッシュデータと、法線方向データとに基づいて解析対象の３次元メッシュを生成する手法について説明する。同図（ｄ）は解析対象を３次元有限要素にモデル化した３次元メッシュ４０を示しており、その底面は３次元メッシュ４０を生成する基準となる基準平面４１を構成している。基準平面４１の法線方向にはＨ１〜Ｈ４から成る４種類の３次元メッシュが積層されており、基準平面４１に平行な任意の断面の２次元メッシュは全て同一である。図中、格子が記されてない箇所は３次元メッシュが形成されていない箇所を示している。同図（ａ）は法線方向から視た基準平面４１を示している。基準平面４１は領域Ａ、領域Ｂ、及び領域Ｃの３つの領域に分割される（説明の便宜上、２次元メッシュの図示は省略している）。同図（ｂ）は３次元メッシュＨ１〜Ｈ４の法線方向の配列を示している。図中、ハッチングを付した箇所は３次元メッシュが形成されている領域を示している。   Here, a method for generating a three-dimensional mesh to be analyzed based on two-dimensional mesh data on the reference plane and normal direction data will be described with reference to FIG. FIG. 4D shows a three-dimensional mesh 40 in which the analysis target is modeled as a three-dimensional finite element. The bottom surface of the three-dimensional mesh 40 forms a reference plane 41 that serves as a reference for generating the three-dimensional mesh 40. Four types of three-dimensional meshes composed of H1 to H4 are stacked in the normal direction of the reference plane 41, and the two-dimensional meshes of arbitrary cross sections parallel to the reference plane 41 are all the same. In the figure, a portion where no lattice is marked indicates a portion where a three-dimensional mesh is not formed. FIG. 4A shows the reference plane 41 viewed from the normal direction. The reference plane 41 is divided into three regions, region A, region B, and region C (a two-dimensional mesh is not shown for convenience of explanation). FIG. 2B shows an arrangement in the normal direction of the three-dimensional meshes H1 to H4. In the figure, hatched portions indicate regions where a three-dimensional mesh is formed.

同図（ｃ）は３次元メッシュＨ１〜Ｈ４の法線方向データを示しており、スイープ量、分割数、オフセット、グループ名、及び界面名が例示されている。スイープ量は３次元メッシュの法線方向の高さ（押し出し量）を示す。分割数は３次元有限要素を法線方向に積層した数を示す。オフセットは各領域における３次元メッシュの有無を示す（○は該当する領域に３次元メッシュが存在することを示し、×は該当する領域に３次元メッシュが存在しないことを示している。）。グループ名は同一のグループ（又は属性）を構成する３次元有限要素の集合名称を示す。例えば、格子数をｎ、押し出し領域数をｍ、２次元格子座標を（Ｘ，Ｙ）、押し出し方向座標をＺ（ｎ）、ｉ番目の領域をＡ（ｉ）、押し出し方向界面座標をｃ（ｍ）とし、Ａ（ｉ）に属する任意の（Ｘ，Ｙ）について、あるＺ（ｎ）がｃ（ｍ−１）〜ｃ（ｍ）に含まれるとき、座標値（Ｘ，Ｙ，Ｚ（ｎ））はＡ（ｍ）に含まれる。界面名は隣接するグループ同士の界面の名称を示す（説明の便宜上、界面名の図示は省略している。）。同図に示す例について、３次元メッシュＨ４を例に挙げて詳述すると、３次元メッシュＨ４のスイープ量は４ｍｍ、分割数は５である。また、３次元メッシュＨ４の領域Ａ，Ｂにはメッシュが存在し、領域Ｃにはメッシュが存在しない。この領域Ａ，Ｂの３次元メッシュは共にＮｏ．３のグループに属している。このように、３次元メッシュ４０は基準平面４１の２次元メッシュと、法線方向データに基づいて、基準平面４１上に３次元有限要素を法線方向に積層していくことにより得られるため、簡易な計算処理により３次元メッシュ４０を生成できる。   FIG. 4C shows normal direction data of the three-dimensional meshes H1 to H4, and illustrates the sweep amount, the number of divisions, the offset, the group name, and the interface name. The sweep amount indicates the height (extrusion amount) in the normal direction of the three-dimensional mesh. The number of divisions indicates the number of three-dimensional finite elements stacked in the normal direction. The offset indicates the presence or absence of a three-dimensional mesh in each region (◯ indicates that a three-dimensional mesh exists in the corresponding region, and x indicates that a three-dimensional mesh does not exist in the corresponding region). The group name indicates a set name of three-dimensional finite elements constituting the same group (or attribute). For example, the number of grids is n, the number of extrusion areas is m, the two-dimensional grid coordinates are (X, Y), the extrusion direction coordinates are Z (n), the i-th area is A (i), and the extrusion direction interface coordinates are c ( m), and for any (X, Y) belonging to A (i), when a certain Z (n) is included in c (m−1) to c (m), the coordinate values (X, Y, Z ( n)) is included in A (m). The interface name indicates the name of the interface between adjacent groups (for convenience of description, the interface name is not shown). The example shown in the figure will be described in detail by taking the three-dimensional mesh H4 as an example. The sweep amount of the three-dimensional mesh H4 is 4 mm and the number of divisions is five. Further, a mesh exists in the areas A and B of the three-dimensional mesh H4, and no mesh exists in the area C. The three-dimensional meshes of the areas A and B are both No. It belongs to 3 groups. Thus, since the three-dimensional mesh 40 is obtained by laminating three-dimensional finite elements in the normal direction on the reference plane 41 based on the two-dimensional mesh of the reference plane 41 and the normal direction data, The three-dimensional mesh 40 can be generated by a simple calculation process.

図１は本実施形態の３次元メッシュ生成装置の機能ブロック図、図２は３次元メッシュ生成ルーチンを示している。３次元メッシュ生成装置１０は３次元メッシュ生成処理を行うプロセッサ２０と、３次元メッシュ生成に必要な各種のプログラム及びデータ類を格納するメモリ３０を備えている。メモリ３０には、３次元メッシュ生成方法を実行する３次元メッシュ生成プログラム３１と、基準平面の２次元メッシュデータ３２と、法線方向データ３３が格納され、更に、所定メモリ領域は３次元メッシュデータの出力領域３４が割り当てられている。プロセッサ２０は３次元メッシュ生成プログラムを解釈、実行することにより３次元メッシュ生成手段２１として機能する。３次元メッシュ生成手段２１は２次元メッシュデータ３２を読み取り（Ｓ１）、次いで、法線方向データを読み取って（Ｓ２）、これらのデータに基づいて３次元メッシュを生成し（Ｓ３）、３次元メッシュデータ出力領域３４に３次元メッシュデータを出力する（Ｓ４）。具体的には、２次元格子座標を（Ｘ，Ｙ）、押し出し方向座標をＺ（ｎ）、ｉ番目の領域をＡ（ｉ）、押し出し界面座標をｃとし、Ａ（ｉ）に属する任意の（Ｘ，Ｙ）について、あるＺ（ｎ）でｆｌａｇ（Ａ（ｉ），ｃ）＝１である場合は、座標値（Ｘ，Ｙ，Ｚ（ｎ））を出力する。ここで、領域Ａ（ｉ）の押し出し界面座標ｃに格子がある場合をｆｌａｇ（Ａ（ｉ），ｃ）＝１とし、格子がない場合をｆｌａｇ（Ａ（ｉ），ｃ）＝０とする。   FIG. 1 is a functional block diagram of the three-dimensional mesh generation apparatus of this embodiment, and FIG. 2 shows a three-dimensional mesh generation routine. The three-dimensional mesh generation apparatus 10 includes a processor 20 that performs a three-dimensional mesh generation process, and a memory 30 that stores various programs and data necessary for three-dimensional mesh generation. The memory 30 stores a three-dimensional mesh generation program 31 for executing a three-dimensional mesh generation method, two-dimensional mesh data 32 of a reference plane, and normal direction data 33. Further, the predetermined memory area has three-dimensional mesh data. Output area 34 is allocated. The processor 20 functions as the three-dimensional mesh generation means 21 by interpreting and executing the three-dimensional mesh generation program. The three-dimensional mesh generation means 21 reads the two-dimensional mesh data 32 (S1), then reads the normal direction data (S2), and generates a three-dimensional mesh based on these data (S3). Three-dimensional mesh data is output to the data output area 34 (S4). Specifically, the two-dimensional grid coordinate is (X, Y), the extrusion direction coordinate is Z (n), the i-th region is A (i), the extrusion interface coordinate is c, and any arbitrary belonging to A (i) For (X, Y), if flag (A (i), c) = 1 at a certain Z (n), the coordinate value (X, Y, Z (n)) is output. Here, flag (A (i), c) = 1 is set when there is a grid at the extrusion interface coordinate c of the area A (i), and flag (A (i), c) = 0 is set when there is no grid. .

本実施形態によれば簡易な計算処理で３次元メッシュを生成できる。また、３次元メッシュを生成する基準となる基準平面を２次元有限要素にモデル化した２次元メッシュと、この基準平面の法線方向における３次元有限要素の配列を規定する情報とを保持していればよいので、３次元メッシュの格子座標データを保持する従来例と比較して、取り扱うデータ量を大幅に削減できる。   According to this embodiment, a three-dimensional mesh can be generated by a simple calculation process. In addition, a two-dimensional mesh obtained by modeling a reference plane as a reference for generating a three-dimensional mesh into a two-dimensional finite element, and information for defining an array of three-dimensional finite elements in the normal direction of the reference plane are held. Therefore, the amount of data to be handled can be greatly reduced as compared with the conventional example that holds the lattice coordinate data of the three-dimensional mesh.

本実施形態の３次元メッシュ生成装置の機能ブロック図である。It is a functional block diagram of the three-dimensional mesh production | generation apparatus of this embodiment. 本実施形態の３次元メッシュ生成処理ルーチンである。It is a three-dimensional mesh generation processing routine of this embodiment. 本実施形態の３次元メッシュの説明図である。It is explanatory drawing of the three-dimensional mesh of this embodiment.

符号の説明Explanation of symbols

１０…３次元メッシュ生成装置 ２０…プロセッサ ２１…３次元メッシュ生成手段 ３０…メモリ ３１…３次元メッシュ生成プログラム ３２…３次元メッシュデータ ３３…法線方向データ ３４…３次元メッシュデータ出力領域 ４０…３次元メッシュ ４１…基準平面 DESCRIPTION OF SYMBOLS 10 ... Three-dimensional mesh production | generation apparatus 20 ... Processor 21 ... Three-dimensional mesh production | generation means 30 ... Memory 31 ... Three-dimensional mesh production | generation program 32 ... Three-dimensional mesh data 33 ... Normal direction data 34 ... Three-dimensional mesh data output area 40 ... 3 Dimensional mesh 41 ... Reference plane

Claims (4)

解析対象を３次元有限要素にモデル化した３次元メッシュを生成するための３次元メッシュ生成方法であって、前記３次元メッシュを生成する基準となる基準平面を２次元有限要素にモデル化した２次元メッシュと、前記基準平面の法線方向における前記３次元有限要素の配列を規定する情報とに基づいて前記３次元メッシュを生成する、３次元メッシュ生成方法。   A 3D mesh generation method for generating a 3D mesh in which an analysis target is modeled as a 3D finite element, wherein a reference plane used as a reference for generating the 3D mesh is modeled as a 2D finite element 2 A three-dimensional mesh generation method for generating the three-dimensional mesh based on a three-dimensional mesh and information defining an array of the three-dimensional finite elements in a normal direction of the reference plane. 請求項１に記載の３次元メッシュ生成方法であって、前記３次元メッシュは前記基準平面を２次元有限要素にモデル化した２次元メッシュと、前記基準平面に平行な任意の断面を２次元有限要素にモデル化した２次元メッシュとが同一となるメッシュモデルである、３次元メッシュ生成方法。   2. The three-dimensional mesh generation method according to claim 1, wherein the three-dimensional mesh includes a two-dimensional mesh obtained by modeling the reference plane as a two-dimensional finite element, and an arbitrary cross section parallel to the reference plane. A three-dimensional mesh generation method, which is a mesh model in which a two-dimensional mesh modeled as an element is the same. 請求項１又は請求項２に記載の３次元メッシュ生成方法であって、前記基準平面の法線方向における前記３次元有限要素の配列を規定する情報は、前記基準平面の法線方向における３次元有限要素のスイープ量、分割数、オフセット、グループ名、及び界面名を含む、３次元メッシュ生成方法。   3. The three-dimensional mesh generation method according to claim 1, wherein the information defining the arrangement of the three-dimensional finite elements in the normal direction of the reference plane is three-dimensional in the normal direction of the reference plane. A three-dimensional mesh generation method including a sweep amount of a finite element, the number of divisions, an offset, a group name, and an interface name. 請求項１乃至請求項３のうち何れか１項に記載の３次元メッシュ生成方法であって、前記解析対象は燃料電池である、３次元メッシュ生成方法。

4. The three-dimensional mesh generation method according to claim 1, wherein the analysis target is a fuel cell. 5.

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105787176A (en) * 2016-02-25 2016-07-20 辽宁工程技术大学 Three-dimensional stability calculation method of side slope containing down-dip weak layer of open pit coal mine
WO2016133679A1 (en) * 2015-02-20 2016-08-25 Siemens Product Lifecycle Management Software Inc. Computer-aided simulation of additive manufacturing processes
US10409933B2 (en) 2014-09-19 2019-09-10 Siemens Product Lifecycle Management Software Inc. Computer-aided simulation of additive manufacturing processes

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10409933B2 (en) 2014-09-19 2019-09-10 Siemens Product Lifecycle Management Software Inc. Computer-aided simulation of additive manufacturing processes
WO2016133679A1 (en) * 2015-02-20 2016-08-25 Siemens Product Lifecycle Management Software Inc. Computer-aided simulation of additive manufacturing processes
CN105787176A (en) * 2016-02-25 2016-07-20 辽宁工程技术大学 Three-dimensional stability calculation method of side slope containing down-dip weak layer of open pit coal mine
CN105787176B (en) * 2016-02-25 2018-11-30 辽宁工程技术大学 A kind of three-dimensional stability calculation method of the open coal mine containing suitable weak layer side slope of inclining

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