JP2004110212A

JP2004110212A - Hexahedral mesh generation method, three-dimensional object deformation analysis method, hexahedron mesh generation device, three-dimensional object deformation analysis device, computer program, and recording medium

Info

Publication number: JP2004110212A
Application number: JP2002269294A
Authority: JP
Inventors: Hideki Ueda; 上田　秀樹
Original assignee: Sumitomo Metal Industries Ltd
Current assignee: Nippon Steel Corp
Priority date: 2002-09-13
Filing date: 2002-09-13
Publication date: 2004-04-08

Abstract

【課題】立体物を複数の六面体の組み合わせで表現した六面体メッシュを自動で生成することを可能にし、しかも六面体メッシュが立体の形状を表現する質を向上させる六面体メッシュ生成方法、六面体メッシュ生成装置、コンピュータプログラム及び記録媒体、並びに前記六面体メッシュ生成方法を用いた立体物の変形の解析方法、解析装置、コンピュータプログラム及び記録媒体を提供する。
【解決手段】ボクセル法を用いることにより、立体物の形状を表現した立体形状Ｐの内部を六面体要素の組み合わせで充填した第１メッシュＭ１を生成し、立体形状Ｐの表面に位置する節点を含む六面体要素を第１メッシュＭ１に付加して第２メッシュＭ２を生成し、更に、図中に破線で示した、立体形状Ｐの輪郭などの立体形状Ｐを特徴づける特徴線上に、第２メッシュＭ２の表面上の節点を移動させ、六面体メッシュＭを生成する。
【選択図】　　　　図１A hexahedral mesh generation method and a hexahedral mesh generation device capable of automatically generating a hexahedral mesh expressing a three-dimensional object by a combination of a plurality of hexahedrons and further improving the quality of the hexahedral mesh expressing a three-dimensional shape, A computer program and a recording medium, and a method for analyzing deformation of a three-dimensional object using the hexahedral mesh generation method, an analyzing apparatus, a computer program, and a recording medium are provided.
A first mesh (M1) in which the interior of a three-dimensional shape (P) expressing the shape of a three-dimensional object is filled with a combination of hexahedral elements is generated by using a voxel method, and includes nodes located on the surface of the three-dimensional shape (P). A hexahedral element is added to the first mesh M1 to generate a second mesh M2. Further, the second mesh M2 is placed on a characteristic line that characterizes the three-dimensional shape P such as the outline of the three-dimensional shape P indicated by a broken line in the drawing. Is moved to generate a hexahedral mesh M.
[Selection diagram] Fig. 1

Description

【０００１】
【発明の属する技術分野】
本発明は、立体物の変形、特に型鍛造の工程における素材の形状変化を有限要素法により三次元解析するために、解析対象の立体物を複数の六面体要素の組み合わせで表現した六面体メッシュを生成する方法、その実施に使用する六面体メッシュ生成装置、コンピュータを該六面体メッシュ生成装置として実現するためのコンピュータプログラム、及び記録媒体、並びに前記六面体メッシュを用いて立体物の変形を解析する方法、立体物の変形の解析装置、コンピュータを該解析装置として実現するためのコンピュータプログラム、及び記録媒体に関する。
【０００２】
【従来の技術】
金属の加工方法の一つとして、円柱などの形状を有する素材に金型を用いたプレスによる鍛造を行う型鍛造があり、自動車のクランクシャフトなどの製品が型鍛造の工程で生産される。型鍛造の工程の最適化、又は型鍛造に用いる金型の最適な形状の設計のためには、素材の鍛造中の変形状態、又は鍛造後の成型状態を解析することが必要である。
【０００３】
従来、立体物の構造解析または流体解析などにおいては、立体物を複数の多面体の要素に分割して数値解析を行う有限要素法が主に用いられており、型鍛造における素材の変形の解析にも、有限要素法を用いた解析が行われている。有限要素法では、立体物を複数の四面体の要素に分割した四面体メッシュによる解析よりも、立体物を複数の六面体要素に分割した六面体メッシュによる解析の方が、解析精度が高くしかも解析時間が短いことが知られている。
【０００４】
立体物から六面体メッシュを生成する方法としては、いくつかの方法が知られており、特許文献１では、マッピング法を用いて六面体メッシュを生成する方法が開示されている。図２８は、マッピング法による六面体メッシュの生成の例を示す斜視図である。図２８（ａ）には、解析対象の立体物の形状を表現した立体形状Ｐを示している。まず、ＣＡＤ装置などを用いて立体形状Ｐを作成し、図２８（ｂ）に示す如く、立体形状Ｐを包含する六面体ブロックを作成する。次に、図２８（ｃ）に示す如く、前記六面体ブロックを複数の六面体に分割したメッシュを作成し、次に、作成したメッシュを立体形状Ｐに写像して、図２８（ｄ）に示す如き、解析対象の立体物を複数の六面体要素の組み合わせで表現した六面体メッシュを生成する。
【０００５】
六面体メッシュを生成する他の方法として、ボクセル法が知られている。非特許文献１では、ボクセル法を用いた六面体メッシュを生成する方法が開示されている。図２９は、ボクセル法による六面体メッシュの生成の例を二次元で示した模式図である。図中には簡単にするために二次元で示したが、実際は三次元で六面体メッシュの生成が行われる。ボクセル法では、まず、図２９（ａ）に示す如き立体形状Ｐに対して、図２９（ｂ）に示す如く、立体形状Ｐの内部を充填する複数の六面体要素を組み合わせたメッシュを生成する。次に、図２９（ｃ）に示す如く、メッシュの表面に位置する各節点に対応して、各節点を含んだ複数の要素面の法線ベクトルの平均の方向に、立体形状Ｐの表面上の新たな節点を作成し、図２９（ｄ）に示す如き、立体形状Ｐを複数の六面体要素の組み合わせで表現した六面体メッシュを生成する。また、特許文献２では、ボクセル法において、メッシュの表面に位置する各節点から最短距離にある立体形状の表面上の位置に新たな節点を作成して、六面体メッシュを生成する方法が開示されている。
【０００６】
【特許文献１】
特開２００１−９２９９４号公報
【特許文献２】
特開平１０−２５５０７７号公報
【非特許文献１】
シュナイダー（Ｒ．　Ｓｃｈｎｅｉｄｅｒｓ）、ブンテン（Ｒ．　Ｂｕｎｔｅｎ），「オートマティック　ジェネレーション　オブ　ヘキサヘドラル　フィニットエレメント　メッシュズ（Ａｕｔｏｍａｔｉｃ　ｇｅｎｅｒａｔｉｏｎ　ｏｆ　ｈｅｘａｈｅｄｒａｌ　　ｆｉｎｉｔｅｅｌｅｍｅｎｔ　ｍｅｓｈｅｓ）」，コンピュータエイデッドジオメトリックデザイン（Ｃｏｍｐｕｔｅｒ　Ａｉｄｅｄ　Ｇｅｏｍｅｔｒｉｃ　Ｄｅｓｉｇｎ），１９９５年１２月，ｐ．６９３−７０７
【０００７】
【発明が解決しようとする課題】
型鍛造における素材の変形の解析など、解析対象が大きく形状変更を行う解析を有限要素法を用いて行った場合、解析の計算中につぶれ要素が発生して計算が不正確になる場合がある。つぶれ要素は、体積が所定より小さくなった、又は形状が直方体から極端に変形した等の、六面体メッシュの変形に伴ってつぶれた六面体要素であり、つぶれ要素が発生した場合は、解析を中断し、中断時点での解析対象の形状を表現した六面体メッシュの再生成（以下、リメッシュと言う）を行い、リメッシュ後の六面体メッシュを用いて解析を再開する。解析を効率良く行うためには、リメッシュの作業を含めた全ての計算過程が自動で行われることが望ましい。
【０００８】
図３０は、マッピング法の問題点を示した斜視図である。マッピング法では、立体形状を包含する六面体ブロックを作成する必要があり、六面体ブロックの大きさを決定するためには、オペレータの操作を必要とする。特に、図３０（ａ）に示す如き複雑な形状を有する立体形状Ｐに対しては、該立体形状Ｐの形状を正確に表現した六面体メッシュを生成するために、図３０（ｂ）に示す如く立体形状Ｐを包含できる複数の六面体ブロックの組み合わせを作成する必要がある。複雑な立体形状に対して、いくつの六面体ブロックをどのように組み合わせればより正確な六面体メッシュを生成できるかという問題は、個々の立体形状について判断する必要があり、六面体メッシュの生成を自動化することが困難である。
【０００９】
メッシュの生成にボクセル法を用いた場合は、予め六面体ブロックを作成する必要がないため、マッピング法に比べて六面体メッシュの生成の自動化が容易である。しかし、立体形状の形状が複雑である場合、ボクセル法を用いて生成した六面体メッシュの形状と立体形状との間で差異が発生し、マッピング法を用いて生成した六面体メッシュに比べて立体物を表現する精度が劣るという問題がある。図３１は、ボクセル法の問題点を二次元で説明するための模式図である。複雑な形状を有する立体形状Ｐについて、図３１（ａ）に示す如く、メッシュの表面に位置する各節点を含む複数の面の法線ベクトルの平均の方向に新たな節点を作成した場合は、立体形状Ｐの形状が急峻に変化する付近では、新たな節点が遠方に作成され、図３１（ｂ）に示す如く、他の要素を突き抜ける等の異常な形状を有する要素が生成される。また、図３１（ｃ）に示す如く、メッシュの表面に位置する各節点から最短距離にある立体形状Ｐの表面上の位置に新たな節点を作成する場合は、図３１（ｄ）に示す如く、六面体の２面または３面が同一平面上に位置して角錐形状の要素が作成される場合がある。また、ボクセル法では、立体形状を特徴づけている輪郭部分に節点が生成されるとは限らないため、生成された六面体メッシュでは輪郭が喪失し、立体物の形状の特徴が損なわれるという問題がある。
【００１０】
更に、ボクセル法を用いて六面体メッシュを生成した場合、図２９（ｄ）に示した例で表面の要素の形が長方形からずれている様に、六面体メッシュの表面付近に生成される六面体要素は、直方体から形が大きく歪んで生成される。六面体メッシュを変形させる解析においては、表面付近の六面体要素が大変形するため、表面付近の六面体要素の形が直方体から大きく歪んでいる六面体メッシュを用いた場合は、表面付近の六面体要素につぶれ要素が発生し易くなる。このため、解析の計算精度が低下する、又は頻繁にリメッシュを行う必要が生じて解析の計算時間が長大になるという問題がある。
【００１１】
本発明は、斯かる事情に鑑みてなされたものであって、その目的とするところは、ボクセル法を用いることで六面体メッシュの生成の自動化を可能にした上で、立体形状の輪郭である特徴線上へ六面体メッシュの表面上の節点を移動させることにより、立体形状の特徴を保持できる六面体メッシュを生成する方法、六面体メッシュ生成装置、コンピュータを該六面体メッシュ生成装置として実現するためのコンピュータプログラム、及び記録媒体を提供することにある。
【００１２】
また、本発明の他の目的とするところは、ボクセル法を用いて六面体メッシュを生成する際に、メッシュの表面に位置する各節点を含む複数の面の法線ベクトルの平均の方向と、該節点から立体形状の表面への最短距離の方向とを、立体形状に応じた所定の比率で合成した方向に、新たな節点を作成することにより、立体物を表現する精度を向上させた六面体メッシュを生成する六面体メッシュ生成装置、コンピュータを該六面体メッシュ生成装置として実現するためのコンピュータプログラム、及び記録媒体を提供することにある。
【００１３】
また、本発明の他の目的とするところは、ボクセル法で利用するメッシュを、型鍛造で用いる型の形状に追従させた形状で生成することにより、型鍛造における素材の変形の解析に適した六面体メッシュを生成する六面体メッシュ生成装置、コンピュータを該六面体メッシュ生成装置として実現するためのコンピュータプログラム、及び記録媒体を提供することにある。
【００１４】
更に、本発明の他の目的とするところは、前記六面体メッシュ生成方法を用いて六面体メッシュの生成およびリメッシュを行うことにより、立体物の変形の解析を自動で行うことができる立体物の変形の解析方法、立体物の変形の解析装置、コンピュータを該解析装置として実現するためのコンピュータプログラム、及び記録媒体を提供することにある。
【００１５】
【課題を解決するための手段】
第１発明に係る六面体メッシュ生成方法は、記憶部及び演算部を備えたコンピュータを用いて、立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを生成する方法において、立体物の形状を規定した形状モデルを記憶部に記憶し、記憶部に記憶している形状モデルで表現される立体形状の内部に複数の六面体要素の組み合わせを充填した第１メッシュを演算部にて生成し、生成した第１メッシュの表面に位置する節点及び前記立体形状の表面に位置する節点を含む複数の六面体要素を前記第１メッシュに付加した第２メッシュを演算部にて生成し、前記立体形状の表面上で、前記立体形状を特徴づける特徴線及び特徴点を演算部にて抽出し、前記第２メッシュの表面上で前記特徴線又は特徴点の近傍に位置する節点を特徴線上の位置又は特徴点の位置へ移動させた六面体メッシュを演算部にて生成することを特徴とする。
【００１６】
第２発明に係る立体物の変形の解析方法は、記憶部及び演算部を備えたコンピュータを用い、立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを用いて、前記立体物の変形を解析する方法において、第１発明に係る六面体メッシュ生成方法を用いて、解析対象の立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを演算部にて生成して記憶部に記憶し、生成した六面体メッシュを変形させて前記立体物の変形を解析する計算を演算部にて行い、該計算が所定の段階に進む都度、変形させた六面体メッシュを構成する複数の六面体要素の中につぶれ要素が発生しているか否かを演算部にて判定し、つぶれ要素が発生している場合には、前記計算を中断して、前記六面体メッシュの形状を規定した形状モデルを記憶部に記憶し、記憶した形状モデルから、第１発明に記載の六面体メッシュ生成方法を用いて、変形途中の前記立体物を表現する新たな六面体メッシュを演算部にて生成して記憶部に記憶し、生成した新たな六面体メッシュを用いて前記計算を演算部にて再開することを特徴とする。
【００１７】
第３発明に係る六面体メッシュ生成装置は、立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを生成する装置において、立体物の形状を規定する形状モデルで表現される立体形状の内部に複数の六面体要素の組み合わせを充填した第１メッシュを生成する第１メッシュ生成手段と、生成した第１メッシュの表面に位置する節点及び前記立体形状の表面に位置する節点を含む複数の六面体要素を前記第１メッシュに付加した第２メッシュを生成する第２メッシュ生成手段と、前記立体形状を特徴づける特徴線及び特徴点を、前記立体形状の表面上で抽出する抽出手段と、前記第２メッシュの表面上で前記特徴線又は特徴点の近傍に位置する節点を特徴線上の位置又は特徴点の位置へ移動させた六面体メッシュを生成する移動手段とを備えることを特徴とする。
【００１８】
第４発明に係る六面体メッシュ生成装置は、前記抽出手段は、前記立体形状の表面上で、該表面の勾配の変化が所定以上である前記勾配の境界線を特徴線として抽出する手段と、抽出した特徴線の方向の変化が所定以上である点、及び特徴線の端点を特徴点として抽出する手段とを備え、前記移動手段は、前記第２メッシュの表面上で、抽出した特徴点から最短距離に位置する節点である第１節点を抽出する手段と、同一の特徴線上で隣り合う特徴点の夫々に係る第１節点同士を前記第２メッシュの表面の要素辺に沿って最短距離で結んだときに経由する複数の節点である第２節点を抽出する手段と、特徴点の位置へ第１節点を移動させる手段と、特徴線上で第２節点の夫々から最短距離に位置する点へ、第２節点の夫々を移動させる手段とを備えることを特徴とする。
【００１９】
第５発明に係る六面体メッシュ生成装置は、前記立体物は、型により成型される立体物であって、前記第１メッシュ生成手段は、前記立体形状を包含する六面体ブロックを作成する手段と、作成した六面体ブロックを、所定の分割数、又は所定の分割間隔で三次元格子状に分割して、前記六面体ブロックを複数の六面体要素の組み合わせで表現したブロック状メッシュを生成する手段と、生成したブロック状メッシュから所定の距離に、前記型の形状を表現した型形状モデルを配置する手段と、成型の工程で前記型が移動すべき方向に沿った前記ブロック状メッシュの表面上の節点と前記型形状モデルとの間の距離に対する所定の移動率で、前記方向に沿って前記節点を移動させる手段と、前記方向に沿った前記ブロック状メッシュが含む複数の節点間の距離の比を保存すべく、前記ブロック状メッシュの内部の節点を移動させる手段と、節点を移動させたブロック状メッシュが含む夫々の節点について、該節点が前記立体形状の内部に位置しているか否かを判定する手段と、前記立体形状の内部に位置していないと判定された節点を含む六面体要素を除去する手段とを備えることを特徴とする。
【００２０】
第６発明に係る六面体メッシュ生成装置は、前記第２メッシュ生成手段は、前記第１メッシュの表面上の一の節点を選択する手段と、選択した節点を含んでいる複数の要素面の夫々の法線ベクトルを平均した第１ベクトルを生成する手段と、前記節点から前記立体形状の表面へ延出した垂線の方向ベクトルである第２ベクトルを生成する手段と、前記節点の位置に応じた所定の合成比で第１ベクトル及び第２ベクトルを合成した合成ベクトルを生成する合成手段と、生成した合成ベクトルの方向へ前記節点から延出した線と前記立体形状の表面との交点に新たな節点を生成する手段と、前記第１メッシュの表面上の夫々の節点について、対応する新たな節点を生成する手段と、前記第１メッシュの表面上の要素辺、該要素辺の両端の各節点に対応する新たな節点同士を結んだ要素辺、及び前記第１メッシュの表面上の節点と該節点に対応する新たな節点とを結んだ要素辺から構成される複数の六面体要素を前記第１メッシュに付加する手段とを備えることを特徴とする。
【００２１】
第７発明に係る六面体メッシュ生成装置は、前記合成手段は、選択した節点から前記立体形状の表面までの第１ベクトルの方向に沿った距離を測定する手段と、測定した前記距離を所定値と比較する手段と、前記距離が所定値よりも小さい場合は、第１ベクトルを合成ベクトルとする手段と、前記距離が所定値以上である場合は、第２ベクトルを合成ベクトルとする手段とを備えることを特徴とする。
【００２２】
第８発明に係る立体物の変形の解析装置は、立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを用いて、前記立体物の変形を解析する装置において、第３乃至第７発明のいずれかに係る六面体メッシュ生成装置と、該六面体メッシュ生成装置を用いて、解析対象の立体物の形状を規定する形状モデルから、前記立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを生成する手段と、生成した六面体メッシュを変形させて前記立体物の変形を解析する計算を行う手段と、前記計算が所定の段階に進む都度、変形させた六面体メッシュを構成する複数の六面体要素の中につぶれ要素が発生しているか否かを判定する手段と、つぶれ要素が発生している場合には、前記計算を中断して、前記六面体メッシュの形状を規定した新たな形状モデルを記憶する手段と、前記六面体メッシュ生成装置を用いて、記憶した新たな形状モデルから、変形途中の前記立体物の形状を表現する新たな六面体メッシュを生成する手段と、生成した新たな六面体メッシュを用いて前記計算を再開する手段とを備えることを特徴とする。
【００２３】
第９発明に係るコンピュータプログラムは、コンピュータに、立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを生成させるコンピュータプログラムにおいて、コンピュータに、立体物の形状を規定する形状モデルで表現される立体形状の内部に複数の六面体要素の組み合わせを充填した第１メッシュを生成させる第１メッシュ生成手順と、コンピュータに、生成した第１メッシュの表面に位置する節点及び前記立体形状の表面に位置する節点を含む複数の六面体要素を前記第１メッシュに付加した第２メッシュを生成させる第２メッシュ生成手順と、コンピュータに、前記立体形状を特徴づける特徴線及び特徴点を、前記立体形状の表面上で抽出させる抽出手順と、コンピュータに、前記第２メッシュの表面上で前記特徴線又は特徴点の近傍に位置する節点を特徴線上の位置又は特徴点の位置へ移動させた六面体メッシュを生成させる移動手順とを含むことを特徴とする。
【００２４】
第１０発明に係るコンピュータプログラムは、前記抽出手順は、コンピュータに、前記立体形状の表面上で、該表面の勾配の変化が所定以上である前記勾配の境界線を特徴線として抽出させる手順と、コンピュータに、抽出した特徴線の方向の変化が所定以上である点、及び特徴線の端点を特徴点として抽出させる手順とを含み、前記移動手順は、コンピュータに、前記第２メッシュの表面上で、抽出した特徴点から最短距離に位置する節点である第１節点を抽出させる手順と、コンピュータに、同一の特徴線上で隣り合う特徴点の夫々に係る第１節点同士を前記第２メッシュの表面の要素辺に沿って最短距離で結んだときに経由する複数の節点である第２節点を抽出させる手順と、コンピュータに、特徴点の位置へ第１節点を移動させる手順と、コンピュータに、特徴線上で第２節点の夫々から最短距離に位置する点へ、第２節点の夫々を移動させる手順とを含むことを特徴とする。
【００２５】
第１１発明に係るコンピュータプログラムは、前記第１メッシュ生成手順は、コンピュータに、前記立体形状を包含する六面体ブロックを作成させる手順と、コンピュータに、作成した六面体ブロックを、所定の分割数、又は所定の分割間隔で三次元格子状に分割して、前記六面体ブロックを複数の六面体要素の組み合わせで表現したブロック状メッシュを生成させる手順と、コンピュータに、生成したブロック状メッシュから所定の距離に、前記立体物を成型する型の形状を表現した型形状モデルを配置させる手順と、コンピュータに、成型の工程で前記型が移動すべき方向に沿った前記ブロック状メッシュの表面上の節点と前記型形状モデルとの間の距離に対する所定の移動率で、前記方向に沿って前記節点を移動させる手順と、コンピュータに、前記方向に沿った前記ブロック状メッシュが含む複数の節点間の距離の比を保存すべく、前記ブロック状メッシュの内部の節点を移動させる手順と、コンピュータに、節点を移動させたブロック状メッシュが含む夫々の節点について、該節点が前記立体形状の内部に位置しているか否かを判定させる手順と、コンピュータに、前記立体形状の内部に位置していないと判定された節点を含む六面体要素を除去させる手順とを含むことを特徴とする。
【００２６】
第１２発明に係るコンピュータプログラムは、前記第２メッシュ生成手順は、コンピュータに、前記第１メッシュの表面上の一の節点を選択させる手順と、コンピュータに、選択した節点を含んでいる複数の要素面の夫々の法線ベクトルを平均した第１ベクトルを生成させる手順と、コンピュータに、前記節点から前記立体形状の表面へ延出した垂線の方向ベクトルである第２ベクトルを生成させる手順と、コンピュータに、前記節点の位置に応じた所定の合成比で第１ベクトル及び第２ベクトルを合成した合成ベクトルを生成させる合成手順と、コンピュータに、生成した合成ベクトルの方向へ前記節点から延出した線と前記立体形状の表面との交点に新たな節点を生成させる手順と、コンピュータに、前記第１メッシュの表面上の夫々の節点について、対応する新たな節点を生成させる手順と、コンピュータに、前記第１メッシュの表面上の要素辺、該要素辺の両端の各節点に対応する新たな節点同士を結んだ要素辺、及び前記第１メッシュの表面上の節点と該節点に対応する新たな節点とを結んだ要素辺から構成される複数の六面体要素を前記第１メッシュに付加させる手順とを含むことを特徴とする。
【００２７】
第１３発明に係るコンピュータプログラムは、前記合成手順は、コンピュータに、選択した節点から前記立体形状の表面までの第１ベクトルの方向に沿った距離を測定させる手順と、コンピュータに、測定した前記距離を所定値と比較させる手順と、コンピュータに、前記距離が所定値よりも小さい場合は、第１ベクトルを合成ベクトルとさせる手順と、コンピュータに、前記距離が所定値以上である場合は、第２ベクトルを合成ベクトルとさせる手順とを含むことを特徴とする。
【００２８】
第１４発明に係るコンピュータプログラムは、コンピュータに、立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを用いて、前記立体物の変形を解析させるコンピュータプログラムにおいて、コンピュータに、第９乃至第１３発明のいずれかに係るコンピュータプログラムを用いて、解析対象の立体物の形状を規定する形状モデルから、前記立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを生成させる手順と、コンピュータに、生成した六面体メッシュを変形させて前記立体物の変形を解析する計算を行わせる手順と、コンピュータに、前記計算が所定の段階に進む都度、変形させた六面体メッシュを構成する複数の六面体要素の中につぶれ要素が発生しているか否かを判定させる手順と、コンピュータに、つぶれ要素が発生している場合には、前記計算を中断して、前記六面体メッシュの形状を規定した新たな形状モデルを記憶させる手順と、コンピュータに、第９乃至第１３発明のいずれかに係るコンピュータプログラムを用いて、記憶した新たな形状モデルから、変形途中の前記立体物の形状を表現する新たな六面体メッシュを生成させる手順と、コンピュータに、生成した新たな六面体メッシュを用いて前記計算を再開させる手順とを備えることを特徴とする。
【００２９】
第１５発明に係るコンピュータでの読み取りが可能な記録媒体は、コンピュータに、立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを生成させるコンピュータプログラムを記録してあるコンピュータでの読み取りが可能な記録媒体において、コンピュータに、立体物の形状を規定する形状モデルで表現される立体形状の内部に複数の六面体要素の組み合わせを充填した第１メッシュを生成させる第１メッシュ生成手順と、コンピュータに、生成した第１メッシュの表面に位置する節点及び前記立体形状の表面に位置する節点を含む複数の六面体要素を前記第１メッシュに付加した第２メッシュを生成させる第２メッシュ生成手順と、コンピュータに、前記立体形状を特徴づける特徴線及び特徴点を、前記立体形状の表面上で抽出させる抽出手順と、コンピュータに、前記第２メッシュの表面上で前記特徴線又は特徴点の近傍に位置する節点を特徴線上の位置又は特徴点の位置へ移動させた六面体メッシュを生成させる移動手順とを含むコンピュータプログラムを記録してあることを特徴とする。
【００３０】
第１６発明に係るコンピュータでの読み取りが可能な記録媒体は、コンピュータに、立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを用いて、前記立体物の変形を解析させるコンピュータプログラムを記録してあるコンピュータでの読み取りが可能な記録媒体において、コンピュータに、第９乃至第１３発明のいずれかに係るコンピュータプログラムを用いて、解析対象の立体物の形状を規定する形状モデルから、前記立体物の形状を複数の六面体要素の組み合わせにて表現する六面体メッシュを生成させる手順と、コンピュータに、生成した六面体メッシュを変形させて前記立体物の変形を解析する計算を行わせる手順と、コンピュータに、前記計算が所定の段階に進む都度、変形させた六面体メッシュを構成する複数の六面体要素の中につぶれ要素が発生しているか否かを判定させる手順と、コンピュータに、つぶれ要素が発生している場合には、前記計算を中断して、前記六面体メッシュの形状を規定した新たな形状モデルを記憶させる手順と、コンピュータに、第９乃至第１３発明のいずれかに係るコンピュータプログラムを用いて、記憶した新たな形状モデルから、変形途中の前記立体物の形状を表現する新たな六面体メッシュを生成させる手順と、コンピュータに、生成した新たな六面体メッシュを用いて前記計算を再開させる手順とを含むコンピュータプログラムを記録してあることを特徴とする。
【００３１】
図１は、本発明の六面体メッシュ生成方法の概要を示す斜視図である。第１、第３、第４、第９、第１０及び第１５発明においては、図１（ａ）に示す如き、立体物の形状を表現した立体形状Ｐに対して、ボクセル法を用いることにより、図１（ｂ）に示す如く、立体形状Ｐの内部を六面体要素の組み合わせで充填した第１メッシュＭ１を生成し、図１（ｃ）に示す如く、立体形状Ｐの表面に位置する節点を含む六面体要素を第１メッシュＭ１に付加して第２メッシュＭ２を生成し、更に、図１（ｃ）に破線で示した、立体形状Ｐの輪郭などの立体形状Ｐの形状を特徴づける特徴線上に、第２メッシュＭ２の表面上の節点を移動させ、図１（ｄ）に示す如き六面体メッシュＭを生成する。これにより、立体形状Ｐの特徴を継承した六面体メッシュが生成される。
【００３２】
第５及び第１１発明においては、立体形状を包含する六面体ブロックを三次元格子状に分割したブロック状メッシュの表面上の節点を、該節点と立体物を成型する型の形状を規定する型形状モデルとの距離に比例した距離だけ前記型形状モデルに向かって移動させ、ブロック状メッシュの内部の節点も追従して移動させ、立体形状の内部に位置しない節点を含む六面体要素を除去して第１メッシュを生成することにより、六面体要素の形状および配置が前記型の形状に追従した六面体メッシュが生成される。
【００３３】
第６及び第１２発明においては、第１メッシュの表面上の節点に対応した新たな節点を立体形状の表面に生成して第２メッシュを生成する際に、節点の位置に応じて、該節点を含んだ複数の要素面の夫々の法線ベクトルを平均した第１ベクトルと前記節点から前記形状モデルの表面へ延ばした垂線の方向ベクトルである第２ベクトルとを合成した合成ベクトルを生成し、該合成ベクトルの方向に新たな節点を生成することにより、立体物を表現する精度が向上した六面体メッシュが生成される。
【００３４】
第７及び第１３発明においては、第１メッシュの表面上の節点に対応した新たな節点を立体形状の表面に生成する際に、節点から立体形状の表面までの第１ベクトルの方向に沿った距離を所定値と比較し、前記節点が立体形状に向かって突き出した部分にあって前記距離が所定値よりも小さい場合は、第１ベクトルを合成ベクトルとし、前記節点が立体形状から離れた奥まった部分にあって前記最短距離が所定値以上である場合は、第２ベクトルを合成ベクトルとすることにより、節点が位置しているまわりの状況に応じて適切な位置に新たな節点を生成して、立体物を表現する精度が向上した六面体メッシュが生成される。
【００３５】
第２、第８、第１４及び第１６発明においては、立体物の変形の解析を行うために、本発明に係る六面体メッシュ生成方法を用いて六面体メッシュの生成およびリメッシュを行うことにより、解析の計算を自動で行うことができる。
【００３６】
【発明の実施の形態】
以下本発明をその実施の形態を示す図面に基づき具体的に説明する。
図２は、本発明の六面体メッシュ生成装置の構成を示すブロック図であり、図中１は、本発明の六面体メッシュ生成装置である。六面体メッシュ生成装置１は、本発明に係る立体物の変形の解析装置の機能を兼ね備えており、コンピュータを用いて構成されている。六面体メッシュ生成装置１は、本発明に係る演算部であり、演算を行うＣＰＵ（演算部）１１と、本発明に係る記憶部であり、演算に伴って発生する一時的な情報を記憶するＲＡＭ（記憶部）１２と、ＣＤ−ＲＯＭドライブ等の外部記憶装置１３と、ハードディスク等の内部記憶装置１４とを備えており、ＣＤ−ＲＯＭ等の記録媒体２から本発明に係るコンピュータプログラム２０を外部記憶装置１３にて読み取り、読み取ったコンピュータプログラム２０を内部記憶装置１４に記憶し、ＲＡＭ１２にコンピュータプログラム２０をロードし、ロードしたコンピュータプログラム２０に基づいて六面体メッシュ生成装置１に必要な処理を実行する。六面体メッシュ生成装置１は、キーボード又はマウス等の入力装置１５と、液晶ディスプレイ又はＣＲＴディスプレイ等の出力装置１６とを備えており、データの入力を初めとするオペレータからの操作を受け付ける構成となっている。
【００３７】
また、六面体メッシュ生成装置１は、通信インタフェース１７を備え、通信インタフェース１７に接続しているサーバ装置３から本発明に係るコンピュータプログラム２０をダウンロードし、ＣＰＵ１１にて処理を実行する形態であってもよい。
【００３８】
次に、本発明に係る立体物の変形の解析方法を型鍛造における立体物の変形の解析を例にして説明する。図３は、型鍛造における立体物の変形を模式的に示した斜視図である。図中Ａは型鍛造により成型される立体物であり、上型及び下型により図中の矢印方向にプレスされて型鍛造が行われる。図４は、立体物の変形の解析方法の処理の手順を示すフローチャートである。本発明に係る立体物の変形の解析装置の機能を備えた六面体メッシュ生成装置１は、入力装置１５から、解析対象の立体物の形状を、該立体物が含む点の座標または曲線の方程式などで規定する形状モデル、及び前記立体物を成型する型の形状を表現する型形状モデルを読み込んでＲＡＭ１２に記憶する（Ｓ０１）。このとき、六面体メッシュ生成装置１は、形状モデル及び型形状モデルを内部記憶装置１４に記憶しておいて、記憶している形状モデル及び型形状モデルをＲＡＭ１２に読み込んでもよく、また、サーバ装置３が記憶している形状モデル及び型形状モデルを通信インタフェース１７を介して読み込んでも良い。また、六面体メッシュ生成装置１は、オペレータの操作により形状モデル及び型形状モデルを作成するＣＡＤ装置の機能を備えた形態であっても良い。六面体メッシュ生成装置１のＣＰＵ１１は、コンピュータプログラム２０をＲＡＭ１２へロードし、ロードしたコンピュータプログラム２０に従って、立体物の形状を複数の六面体要素の組み合わせで表現した六面体メッシュを生成し（Ｓ０２）、生成した六面体メッシュを型形状モデルを用いて変形させる解析の計算を行い（Ｓ０３）、型によるプレスが所定のプレス幅だけ行われた等、計算が所定の段階に達したときに、六面体メッシュにつぶれ要素が発生しているか否かを判定する（Ｓ０４）。つぶれ要素が発生している場合は（Ｓ０４：ＹＥＳ）、ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、処理をステップＳ０２に戻して、変形途中の六面体メッシュの形状を規定する新たな形状モデルから新たな六面体メッシュを生成するリメッシュの処理を行い、計算を再開する。ステップＳ０４にてつぶれ要素が発生していない場合は（Ｓ０４：ＮＯ）、ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、収束条件の判定などを行って計算の終了の判定を行い（Ｓ０５）、計算を終了して良い場合は（Ｓ０５：ＹＥＳ）、処理を終了し、計算が終了しない場合は（Ｓ０５：ＮＯ）、ステップＳ０３へ処理を戻して計算を続行する。
【００３９】
次に、本発明の六面体メッシュ生成方法を、型鍛造における立体物の変形の解析に用いる六面体メッシュの生成を例にして説明する。図５は、本発明の六面体メッシュ生成装置１が行う六面体メッシュ生成の処理の手順を示すフローチャートである。六面体メッシュ生成装置１のＣＰＵ１１は、コンピュータプログラム２０をＲＡＭ１２へロードし、ロードしたコンピュータプログラム２０に従って、ＲＡＭ１２に記憶している形状モデルで表現される立体形状の内部に複数の六面体要素の組み合わせを充填した第１メッシュを生成する第１メッシュ生成処理を行い（Ｓ１）、第１メッシュの表面に位置する節点及び前記立体形状の表面に位置する節点を含む複数の六面体要素を前記第１メッシュに付加した第２メッシュを生成する第２メッシュ生成処理を行い（Ｓ２）、第２メッシュの形状を立体形状の特徴に合わせて整形し、立体物の変形の解析に適した六面体メッシュを生成するメッシュ整形処理を行う（Ｓ３）。
【００４０】
図６は、ステップＳ１の第１メッシュ生成処理のサブルーチンの手順を示すフローチャートである。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、ＲＡＭ１２に記憶している形状モデルにおける、三次元の各軸方向の最小値および最大値を測定し（Ｓ１１）、測定した最小値及び最大値を包含する六面体ブロックを生成し（Ｓ１２）、生成した六面体ブロックを所定の幅または所定の数で三次元的に分割して、前記六面体ブロックを複数の六面体要素の組み合わせで表現したブロック状メッシュを生成する（Ｓ１３）。図７は、ブロック状メッシュを生成する手順を示した模式図である。図７（ａ）に示す、形状モデルで表現される立体形状Ｐに対して、各軸方向の最小値および最大値（Ｘｍｉｎ，Ｘｍａｘ），（Ｙｍｉｎ，Ｙｍａｘ），（Ｚｍｉｎ，Ｚｍａｘ）が測定され、図７（ｂ）に示す如く、測定した値を組み合わせた座標で囲まれた領域を包含する六面体ブロックＢが生成され、図７（ｃ）に示す如き、六面体ブロックＢが分割されたブロック状メッシュＢＭが生成される。
【００４１】
ＣＰＵ１１は、次に、立体物を成型する型の形状に従ってブロック状メッシュＢＭの形状を整形する処理を行う。図８は、ブロック状メッシュＢＭを整形する手順を示した模式図であり、簡単のために二次元面内でブロック状メッシュＢＭを示している。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、立体物を成型する型の形状を表現する型形状モデルを、型鍛造において型が立体物をプレスする方向へ移動させて、ブロック状メッシュＢＭに接触する位置に配置する（Ｓ１４）。図８（ａ）には、型鍛造で用いる型である上型および下型の形状を表現した上型形状モデルＦ１及び下型形状モデルＦ２を示している。ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、ブロック状メッシュＢＭの表面の節点のうち、型形状モデルに対向している節点を、型形状モデルに向かって所定の移動率で移動させる（Ｓ１５）。図８（ａ）に示した例では、上型形状モデルＦ１に対向した節点Ｐ１が全く移動しない場合を０、上型形状モデルＦ１に重なるまで移動する場合を１．０とする移動率Ｒｍにて、図８（ｂ）に示す如く、節点Ｐ１と上型形状モデルＦ１との間の距離Ｌ１、及び節点Ｐ１を移動した先の点Ｐａと上型形状モデルＦ１との間の距離Ｌａが、Ｌ１＊（１−Ｒｍ）＝Ｌａとなるように、節点Ｐ１をＺ軸方向へ移動させて、新たな節点Ｐａとする。下型形状モデルＦ２に対向した節点Ｐ６についても、同様に、節点Ｐ６と下型形状モデルＦ２との間の距離Ｌ７、及び節点Ｐ６を移動した先の点Ｐｆと下型形状モデルＦ２との間の距離Ｌｇが、Ｌ７＊（１−Ｒｍ）＝Ｌｇとなるように、節点Ｐ６をＺ軸方向へ移動させて、新たな節点Ｐｆとする。
【００４２】
ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、ブロック状メッシュＢＭの内部の節点を移動させる（Ｓ１６）。図８（ａ）に示した例では、図８（ｃ）に示す如く、節点Ｐ１及び節点Ｐ６の間に位置する節点Ｐ２，Ｐ３，Ｐ４及びＰ５を、Ｚ軸方向へ移動させて新たな節点Ｐｂ，Ｐｃ，Ｐｄ及びＰｅとし、節点Ｐａと節点Ｐｂとの間の距離Ｌｂ、節点Ｐｂと節点Ｐｃとの間の距離Ｌｃ、節点Ｐｃと節点Ｐｄとの間の距離Ｌｄ、節点Ｐｄと節点Ｐｅとの間の距離Ｌｅ、及び節点Ｐｅと節点Ｐｆとの間の距離Ｌｆ、並びに節点Ｐ１と節点Ｐ６との間の距離Ｌ８、及び節点Ｐａと節点Ｐｆとの間の距離Ｌｈについて、Ｌ２／Ｌ８＝Ｌｂ／Ｌｈ、Ｌ３／Ｌ８＝Ｌｃ／Ｌｈ、Ｌ４／Ｌ８＝Ｌｄ／Ｌｈ、Ｌ５／Ｌ８＝Ｌｅ／Ｌｈ、及びＬ６／Ｌ８＝Ｌｆ／Ｌｈの関係が成り立つようにする。結果、図８（ｄ）に実線で示す如く、ブロック状メッシュＢＭが型形状モデルの形状に追従して整形される。
【００４３】
ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、整形したブロック状メッシュＢＭを構成する複数の六面体要素のうち、どの六面体要素が立体形状Ｐの内部に位置するかを判定する内外判定処理を行う（Ｓ１７）。図９は、ステップＳ１７の内外判定処理のサブルーチンの手順を示すフローチャートである。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、ブロック状メッシュＢＭに含まれる複数の節点のうち一の節点を選択し（Ｓ１７１）、Ｘ，Ｙ，Ｚ軸方向へ、選択した節点を含む直線を伸長し（Ｓ１７２）、伸長した直線と立体形状Ｐの表面との二つの交点の間に前記節点が存在しているか否かを判定する（Ｓ１７３）。交点の間に前記節点が存在している場合は（Ｓ１７３：ＹＥＳ）、ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、前記節点は立体形状Ｐの内部に位置している節点であると判定し（Ｓ１７４）、交点の間に前記節点が存在していない場合は（Ｓ１７３：ＮＯ）、前記節点は立体形状Ｐの外部に位置している節点であると判定する（Ｓ１７５）。ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、全ての節点について内外判定を行ったか否かを判定し（Ｓ１７６）、全ての節点について内外判定を行っていない場合は（Ｓ１７６：ＮＯ）、処理をステップＳ１７１へ戻して内外判定を行っていない次の節点を選択し、全ての節点について内外判定を行っている場合は（Ｓ１７６：ＹＥＳ）、ステップＳ１７のサブルーチンの処理を終了し、第１メッシュ生成処理へ処理を戻す。なお、選択した節点から伸長した半直線と立体形状Ｐとの交点の数が奇数であるか偶数であるかによって前記節点の内外判定を行うなど、他の方法を用いた内外判定処理を行っても良い。
【００４４】
ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、立体形状Ｐの外部に位置していると判定した節点を含む六面体要素を除去して、第１メッシュを生成し（Ｓ１８）、ステップＳ１の第１メッシュ生成処理を終了して処理をメインの処理へ戻す。図１０は、第１メッシュの生成を示す模式図であり、簡単のために二次元面内でブロック状メッシュＢＭを示している。ブロック状メッシュＢＭに含まれる節点のうち、立体形状Ｐの内部に位置する節点を黒丸で、立体形状Ｐの外部に位置する節点を白丸で示しており、白丸を含む六面体要素が除去され、図中に斜線で塗りつぶした部分が第１メッシュとして残される。図１１は、第１メッシュＭ１の例を示す斜視図である。図７（ａ）に示した立体形状Ｐに対して生成された第１メッシュＭ１を示しており、第１メッシュの体積は立体形状Ｐよりも小さく、立体形状Ｐの内部を六面体要素の組み合わせで充填した形となっている。
【００４５】
図１２は、ステップＳ２の第２メッシュ生成処理のサブルーチンの手順を示すフローチャートである。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、第１メッシュＭ１の表面上の一の節点を選択し（Ｓ２１）、選択した節点を含む複数の要素面の夫々の法線ベクトルを平均した第１ベクトルＶ１を生成し（Ｓ２２）、前記節点から立体形状Ｐの表面へ延ばした垂線の方向ベクトルである第２ベクトルＶ２を生成する（Ｓ２３）。図１３は、第１ベクトルＶ１及び第２ベクトルＶ２の例を示す模式図であり、簡単のために二次元面内でベクトルの生成を示している。図中にａで示した節点について、節点ａを含んだ要素面の法線ベクトルを平均した第１ベクトルＶ１が生成され、節点ａから立体形状Ｐの表面への垂線の方向ベクトルである第２ベクトルＶ２が生成される。
【００４６】
ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、前記節点の位置に応じた合成比で第１ベクトルＶ１と第２ベクトルＶ２とを合成した合成ベクトルを生成する合成処理を行う（Ｓ２４）。図１４は、ステップＳ２４の合成処理のサブルーチンの手順を示すフローチャートである。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、節点から立体形状Ｐの表面までの第１ベクトルの方向に沿った距離Ｄを測定し（Ｓ２４１）、測定した距離Ｄが所定値よりも小さいか否かを判定し（Ｓ２４３）、距離Ｄが所定値よりも小さい場合は（Ｓ２４３：ＹＥＳ）、第１ベクトルＶ１を合成ベクトルＶｓとし（Ｓ２４５）、距離Ｄが所定値以上である場合は（Ｓ２４３：ＮＯ）、第２ベクトルＶ２を合成ベクトルＶｓとして（Ｓ２４７）、ステップＳ２４のサブルーチンの処理を終了し、第２メッシュ生成処理へ処理を戻す。図１５は、合成ベクトルＶｓの例を示す模式図であり、簡単のために二次元面内で合成ベクトルＶｓを示している。図１５（ａ）に示す如き、立体形状Ｐに向かって突き出した部分の節点ｂは、距離Ｄが小さいため、第１ベクトルＶ１が合成ベクトルＶｓとなる。図１５（ｂ）に示す如き、第１メッシュの形状が入り組んだ奥の部分の節点ｃは、第１ベクトルＶ１に沿った距離Ｄが大きいため、第２ベクトルＶ２が合成ベクトルＶｓとなる。
【００４７】
なお、ステップＳ２４の合成処理のサブルーチンにおいて、第１ベクトルＶ１と第２ベクトルＶ２とを合成する合成比を連続的に調整して合成ベクトルＶｓを生成する方法を用いてもよい。図１６は、合成比を連続的に調整する方法を用いた、ステップＳ２４の合成処理のサブルーチンの手順を示すフローチャートである。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、前記節点を含む要素辺の夫々について、該要素辺を含む二つの要素面がなす第１メッシュＭ１の内角である面挟角を測定し（Ｓ２４２）、測定した複数の面挟角のうち１８０°前後の所定範囲内にある面挟角を除いた他の面挟角について平均をとった、平均面挟角を計算する（Ｓ２４４）。図１７は、面挟角の例を示す模式的斜視図である。図１７（ａ）に示す如き、第１メッシュＭ１の角の部分の節点Ｎについては、節点Ｎを含む３本の要素辺の面挟角をθ１，θ２及びθ３として、平均面挟角θｍは、θｍ＝（θ１＋θ２＋θ３）／３と計算される。図１７（ｂ）に示す如き、第１メッシュＭ１の縁の部分の節点Ｎについては、面挟角θ１，θ２，θ３及びθ４のうち、１８０°前後であるθ３及びθ４を除いて、平均面挟角θｍは、θｍ＝（θ１＋θ２）／２と計算される。また、図１７（ｃ）に示す如き、形状が入り組んだ奥の部分の節点Ｎについては、２７０°前後のθ１及びθ２、９０°前後のθ３、並びに１８０°前後のθ４及びθ５から、平均面挟角θｍは、θｍ＝（θ１＋θ２＋θ３）／３と計算される。
【００４８】
ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、予めＲＡＭ１２又は内部記憶装置１４に記憶してある平均面挟角θｍと合成比Ｒｓとの関係に従って、合成比Ｒｓを決定し（Ｓ２４６）、決定した合成比Ｒｓを用いて、第１ベクトルＶ１と第２ベクトルＶ２を、合成ベクトルＶｓ＝（１−Ｒｓ）＊第１ベクトルＶ１＋Ｒｓ＊第２ベクトルＶ２の式に従って合成して、合成ベクトルＶｓを生成し（Ｓ２４８）。ステップＳ２４のサブルーチンの処理を終了し、第２メッシュ生成処理へ処理を戻す。図１８は、平均面挟角θｍと合成比Ｒｓとの関係の例を示す特性図であり、横軸に平均面挟角θｍ、縦軸に合成比Ｒｓを示している。平均面挟角θｍが０°〜９０°の範囲では、第１メッシュＭ１が立体形状Ｐに向かって突き出している部分であるため、合成ベクトルＶｓが第１ベクトルＶ１となるように、合成比を０．０とし、平均面挟角θｍが２７０°〜３６０°の範囲では、第１メッシュの形状が入り組んだ奥の部分であるため、合成ベクトルＶｓが第２ベクトルＶ２となるように合成比を１．０とし、平均面挟角θｍが９０°〜２７０°の範囲では、合成比Ｒｓは平均面挟角θｍに従って線形に変化させている。なお、９０°〜２７０°以外の範囲を変化させるようにしてもよく、また、双曲三角関数などを適用した非線形の関係を適用してもよい。
【００４９】
ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、合成ベクトルＶｓの方向へ前記節点から延ばした線と立体形状Ｐの表面との交点に、新たな節点を生成する（Ｓ２５）。図１５に示した例の場合、図１５（ａ）に示した節点ｂに対応して新たな節点ｂ’が生成され、図１５（ｂ）に示した節点ｃに対応して新たな節点ｃ’が生成される。ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、第１メッシュＭ１の表面上の全ての節点について、対応する新たな節点を生成したか否かを判定し（Ｓ２６）、全ての節点について新たな節点を生成していない場合は（Ｓ２６：ＮＯ）、処理をステップＳ２１へ戻して第１メッシュＭ１の表面上の次の節点を選択し、全ての節点について新たな節点を生成している場合は（Ｓ２６：ＹＥＳ）、第１メッシュＭ１の表面上の要素辺、該要素辺の両端の各節点に対応する新たな節点同士を結んだ要素辺、及び第１メッシュＭ１の表面上の節点と該節点に対応する新たな節点とを結んだ要素辺から構成される複数の六面体要素を第１メッシュＭ１に付加して、第２メッシュを生成し（Ｓ２７）、ステップＳ２の第２メッシュ生成処理を終了して処理をメインの処理へ戻す。図１９は、六面体要素の付加を示す模式図であり、簡単にするために二次元面内で第１メッシュＭ１を示している。図中に黒丸で示した第１メッシュＭ１の表面上の節点Ｎ１〜Ｎ８の夫々に対して、図中に白丸で示した新たな節点Ｎ’１〜Ｎ’８が生成され、第１メッシュＭ１の表面上の節点と該節点に対応する新たな節点とを結んだ要素辺を含む新たな六面体要素Ｅｎ，Ｅｎ，…が生成される。図２０は、第２メッシュＭ２の例を示す斜視図である。図１１に示した第１メッシュＭ１に対して生成された第２メッシュＭ２を示しており、第１メッシュＭ１と立体形状Ｐとの間の隙間に六面体要素を付加した構造となっている。
【００５０】
図２１は、ステップＳ３のメッシュ整形処理のサブルーチンの手順を示すフローチャートである。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、立体形状Ｐの形状を特徴づける特徴線を立体形状Ｐの表面上で抽出する特徴線抽出処理を行う（Ｓ３１）。図２２は、ステップＳ３１の特徴線抽出処理のサブルーチンの手順を示すフローチャートであり、図２３は、立体形状Ｐから特徴線を抽出する方法を示す斜視図である。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、立体形状Ｐの表面を構成している各面について、立体形状Ｐの外側向きの法線ベクトルを計算する（Ｓ３１１）。リメッシュの過程であって、変形途中の六面体メッシュの形状を規定する形状モデルを用いた処理を行っている場合は、図２３（ａ）に示す如く、変形途中の六面体メッシュを表現した立体形状Ｐの表面上の各要素面について、図中に矢印で示した法線ベクトルが計算される。ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、立体形状Ｐの表面上で隣接する面同士で、法線ベクトルの内積を計算し（Ｓ３１２）、面同士の間の角度が１８０°前後で面同士が略平坦につながっている場合以外を含む様に、内積が所定値以下となる面同士の境界の線分を抽出する（Ｓ３１３）。例えば、内積が０．３４以下となる線分を抽出する場合は、法線ベクトルの間の角度が７０°〜１８０°であり、面同士の間で立体形状Ｐの内側の角度が１１０°以下または２５０°以上となる場合の、面同士の境界の線分が抽出される。ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、抽出した線分の組み合わせを特徴線として（Ｓ３１４）、特徴線抽出処理のサブルーチンを終了してメッシュ整形処理へ処理を戻す。図２３（ａ）に示した立体形状Ｐの場合は、図２３（ｂ）に示す如く、要素面が平坦につながらずに角度を持ってつながっている境界である線分ｒ１〜ｒ８が抽出され、線分ｒ１〜ｒ７が連続した特徴線と、線分ｒ８単独からなる特徴線とが得られる。
【００５１】
ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、立体形状Ｐの形状を特徴づける特徴点を立体形状Ｐの表面上で抽出する特徴点抽出処理を行う（Ｓ３２）。図２４は、ステップＳ３２の特徴点抽出処理のサブルーチンの手順を示すフローチャートであり、図２５は、立体形状Ｐから抽出した特徴線および特徴点の例を示す模式図である。ＣＰＵ１１は、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、ステップＳ３１の特徴線抽出処理にて抽出した各線分の両端の点を、一本の線分のみに属しているか、又は三本以上の線分に共有されている点である特徴線の端点と、二本の線分に共有されている点である特徴線上の線上点とに分類し（Ｓ３２１）、分類した点のうち端点を特徴点として抽出する（Ｓ３２２）。図２５に示した例では、線分ｒ１〜ｒ８の端の点ｑ１〜ｑ１０のうち、点ｑ１，ｑ３，ｑ５，ｑ８，ｑ９及びｑ１０が端点に分類されて特徴点として抽出される。ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、特徴線上で連続している各線分について、特徴線に沿った同一の方向に向かう方向ベクトルを計算し（Ｓ３２３）、連続する線分同士で方向ベクトルの内積を計算し（Ｓ３２４）、線分同士の間の角度が１８０°前後で線分同士が略平坦につながっている場合以外を含む様に、内積が所定値以下となる線分同士が共有する線上点を特徴点として抽出し（Ｓ３２５）、特徴点抽出処理のサブルーチンを終了してメッシュ整形処理へ処理を戻す。例えば、内積が０．３４以下となる線上点を抽出する場合は、方向ベクトルの間の角度が７０°〜１８０°であり、連続する線分同士がなす内角が０°〜１１０°となる場合の、線分同士が共有する線上点が抽出される。図２５に示した例では、角度を持って連続している線分ｒ６及びｒ７が共有する点ｑ７が特徴点として抽出される。
【００５２】
図２６は、第２メッシュＭ２の整形を示す模式図であり、図２０に示した第２メッシュＭ２の一部を拡大して示し、立体形状Ｐから抽出した特徴線を破線で示している。ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、各特徴点から最短距離に位置する第２メッシュＭ２の表面上の節点である第１節点を抽出し（Ｓ３３）、同一の特徴線上で隣り合う特徴点の夫々に係る第１節点同士を、第２メッシュＭ２の表面の要素辺に沿って最短距離で結び（Ｓ３４）、このときに経由する複数の節点である第２節点を抽出する（Ｓ３５）。図２６（ａ）に示す如く、特徴点Ｋ１及びＫ２に対応して、最短距離の節点である第１節点Ｑ１及びＱ２が抽出され、第１節点Ｑ１及びＱ２を最短距離で結んだときに経由する節点である第２節点Ｑ３，Ｑ４及びＱ５が抽出される。ＣＰＵ１１は、次に、ＲＡＭ１２にロードしたコンピュータプログラム２０に従って、第１節点を特徴点の位置へ移動させ（Ｓ３６）、特徴線上にて第２節点から最短距離の位置へ、第２節点を移動させ（Ｓ３７）、ステップＳ３のメッシュ整形処理のサブルーチンを終了して、処理をメインの処理へ戻す。図２６（ｂ）に示す如く、第１節点Ｑ１及びＱ２は、特徴点Ｋ１及びＫ２の位置へ移動し、第２節点Ｑ３，Ｑ４及びＱ５は、第２節点の夫々から特徴線へ垂線を下ろした位置の点Ｏ３，Ｏ４及びＯ５へ移動する。
【００５３】
以上の処理をもって、ＣＰＵ１１は、六面体メッシュを完成させ、処理を終了する。図２７は、完成した六面体メッシュを示す斜視図である。図２０に示した第２メッシュＭ２を整形することによって完成した六面体メッシュＭを示しており、図２７（ａ）には、図２０に示した第２メッシュＭ２に重ねて、立体形状Ｐから抽出された特徴線を破線で示しており、図２７（ｂ）には、前記特徴線に形状を合わせた六面体メッシュＭを示している。六面体メッシュＭによって、立体形状Ｐの形状の特徴が表現される。
【００５４】
以上詳述した如く、本発明においては、第１メッシュＭ１の表面上の節点に対応した新たな節点を立体形状Ｐの表面に生成して第２メッシュＭ２を生成する際に、節点の位置に応じて、該節点を含んだ複数の要素面の夫々の法線ベクトルを平均した第１ベクトルＶ１と前記節点から立体形状Ｐの表面へ延ばした垂線の方向ベクトルである第２ベクトルＶ２とを合成した合成ベクトルＶｓを生成し、合成ベクトルＶｓの方向に新たな節点を生成することにより、節点が位置しているまわりの状況に応じて適切な位置に新たな節点を生成して、他の要素を突き抜ける等の異常な形状を有する要素、又は角錐形状の要素が作成されることを防止し、ボクセル法を用いて生成される六面体メッシュＭの質が向上される。また、立体形状Ｐを特徴づける、立体形状Ｐの輪郭などの特徴線、及び立体形状Ｐの頂点などの特徴点へ、第２メッシュＭ２の表面上の節点を移動させることで六面体メッシュＭを生成することにより、立体形状Ｐの形状の特徴が継承されて、六面体メッシュの質が更に向上される。
【００５５】
また、本発明においては、ブロック状メッシュＢＭの表面上の節点を、該節点と型形状モデルとの距離に比例した距離だけ前記型形状モデルに向かって移動させ、ブロック状メッシュＢＭの内部の節点も追従して移動させ、立体形状Ｐの内部に位置していない節点を含む六面体要素を除去して第１メッシュを生成することにより、第１メッシュの形状は前記型の形状に追従した形状となって、第１メッシュの表面に付加して六面体メッシュの表面に位置する六面体要素は、前記型の形状に略平行な面を有する六面体要素となり、前記型で立体物を変形させる解析の計算において、六面体メッシュの表面付近の六面体要素につぶれ要素が発生する頻度が従来よりも低下する。これにより、解析の計算精度が向上し、リメッシュを行う回数が減少して解析の計算時間が減少する。
【００５６】
更に、本発明においては、ボクセル法を用いて六面体メッシュの生成、及びリメッシュを行うことにより、六面体メッシュの生成およびリメッシュを含めた立体物の変形の解析の計算を自動で行うことができる。また、立体物の形状を表現する質が向上した六面体メッシュを用いるため、計算の精度が向上し、また、つぶれ要素が発生する頻度が低下してリメッシュを行う回数が減少し、解析の計算時間が短縮される。これにより、型鍛造の工程の最適化、又は型鍛造に用いる金型の最適な形状の設計に要する時間およびコストを抑制することができる。
【００５７】
本実施の形態においては、本発明の六面体メッシュ生成装置１は、立体物の変形の解析装置の機能を兼ね備えている形態を示したが、これに限るものではなく、六面体メッシュ生成装置１及び立体物の変形の解析装置を夫々別のコンピュータにて構成し、互いにデータを入出力してリメッシュと解析の計算とを行う形態としてもよい。
【００５８】
【発明の効果】
第１、第３、第４、第９、第１０及び第１５発明においては、立体物の形状を規定する形状モデルで表現される立体形状を特徴づける、輪郭などの特徴線、及び頂点などの特徴点に、六面体メッシュ表面上の節点を一致させることにより、立体形状の特徴が継承された六面体メッシュを生成することができる。
【００５９】
第５及び第１１発明においては、立体形状の内部を六面体要素の組み合わせで充填した第１メッシュについて、前記立体物を成型する型の形状に追従した形状の第１メッシュを生成することにより、第１メッシュの表面に付加されて六面体メッシュの表面に位置する六面体要素は、前記型の形状に略平行な面を有する六面体要素となり、前記型で立体物を変形させる解析の計算において、六面体メッシュの表面付近の六面体要素につぶれ要素が発生する頻度が従来よりも低下する。これにより、解析の計算精度が向上し、リメッシュを行う回数が減少して解析の計算時間が減少する。
【００６０】
第６及び第１２発明においては、第１メッシュの表面上の節点に対応した新たな節点を立体形状の表面に生成する際に、節点が位置しているまわりの状況に応じて適切な位置に新たな節点を生成して、他の要素を突き抜ける等の異常な形状を有する要素、又は角錐形状の要素が作成されることを防止し、ボクセル法を用いて生成される六面体メッシュの質を向上させることができる。
【００６１】
第７及び第１３発明においては、第１メッシュの表面上の節点に対応した新たな節点を立体形状の表面に生成する際に、節点が立体形状の表面に向かって突き出した部分にある場合は、該節点を含んだ複数の要素面の夫々の法線ベクトルを平均した方向に新たな節点を生成し、節点が立体形状の表面から離れた奥まった部分にある場合は、該節点から最短距離の位置に新たな節点を生成することにより、節点が位置しているまわりの状況に応じて適切な位置に新たな節点を生成して、六面体メッシュの質を向上させることができる。
【００６２】
第２、第８、第１４及び第１６発明においては、ボクセル法を用いて六面体メッシュの生成、及びリメッシュを行うことにより、六面体メッシュの生成およびリメッシュを含めた立体物の変形の解析の計算を自動で行うことができる。また、立体物の形状を表現する質が向上した六面体メッシュを用いるため、計算の精度が向上し、また、つぶれ要素が発生する頻度が低下してリメッシュを行う回数が減少し、解析の計算時間が短縮される。これにより、型鍛造の工程の最適化、又は型鍛造に用いる金型の最適な形状の設計に要する時間およびコストを抑制することができる等、本発明は優れた効果を奏する。
【図面の簡単な説明】
【図１】本発明の六面体メッシュ生成方法の概要を示す斜視図である。
【図２】本発明の六面体メッシュ生成装置の構成を示すブロック図でる。
【図３】型鍛造における立体物の変形を模式的に示した斜視図である。
【図４】立体物の変形の解析方法の処理の手順を示すフローチャートである。
【図５】本発明の六面体メッシュ生成装置が行う六面体メッシュ生成の処理の手順を示すフローチャートである。
【図６】ステップＳ１の第１メッシュ生成処理のサブルーチンの手順を示すフローチャートである。
【図７】ブロック状メッシュを生成する手順を示した模式図である。
【図８】ブロック状メッシュを整形する手順を示した模式図である。
【図９】ステップＳ１７の内外判定処理のサブルーチンの手順を示すフローチャートである。
【図１０】第１メッシュの生成を示す模式図である。
【図１１】第１メッシュの例を示す斜視図である。
【図１２】ステップＳ２の第２メッシュ生成処理のサブルーチンの手順を示すフローチャートである。
【図１３】第１ベクトル及び第２ベクトルの例を示す模式図である。
【図１４】ステップＳ２４の合成処理のサブルーチンの手順を示すフローチャートである。
【図１５】合成ベクトルの例を示す模式図である。
【図１６】合成比を連続的に調整する方法を用いた、ステップＳ２４の合成処理のサブルーチンの手順を示すフローチャートである。
【図１７】面挟角の例を示す模式的斜視図である。
【図１８】平均面挟角と合成比との関係の例を示す特性図である。
【図１９】六面体要素の付加を示す模式図である。
【図２０】第２メッシュの例を示す斜視図である。
【図２１】ステップＳ３のメッシュ整形処理のサブルーチンの手順を示すフローチャートである。
【図２２】ステップＳ３１の特徴線抽出処理のサブルーチンの手順を示すフローチャートである。
【図２３】立体形状から特徴線を抽出する方法を示す斜視図である。
【図２４】ステップＳ３２の特徴点抽出処理のサブルーチンの手順を示すフローチャートである。
【図２５】立体形状から抽出した特徴線および特徴点の例を示す模式図である。
【図２６】第２メッシュの整形を示す模式図である。
【図２７】完成した六面体メッシュを示す斜視図である。
【図２８】マッピング法による六面体メッシュの生成の例を示す斜視図である。
【図２９】ボクセル法による六面体メッシュの生成の例を二次元で示した模式図である。
【図３０】マッピング法の問題点を示した斜視図である。
【図３１】ボクセル法の問題点を二次元で説明するための模式図である。
【符号の説明】
１　六面体メッシュ生成装置（立体物の変形の解析装置）
１１　ＣＰＵ（演算部）
１２　ＲＡＭ（記憶部）
２　記録媒体
２０　コンピュータプログラム
Ｐ　立体形状
ＢＭ　ブロック状メッシュ
Ｍ１　第１メッシュ
Ｍ２　第２メッシュ
Ｍ　六面体メッシュ[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention generates a hexahedral mesh in which a three-dimensional object to be analyzed is represented by a combination of a plurality of hexahedral elements in order to three-dimensionally analyze a deformation of a three-dimensional object, particularly a shape change of a material in a die forging process by a finite element method. Hexahedral mesh generation device used for the implementation, a computer program for realizing a computer as the hexahedron mesh generation device, and a recording medium, and a method of analyzing deformation of a three-dimensional object using the hexahedral mesh, three-dimensional object And a computer program for realizing a computer as the analyzer, and a recording medium.
[0002]
[Prior art]
As one of the metal processing methods, there is a die forging in which a material having a shape such as a cylinder is forged by a press using a die, and a product such as a crankshaft of an automobile is produced in a die forging process. In order to optimize the process of die forging or to design an optimal shape of a die used for die forging, it is necessary to analyze a deformed state of a material during forging or a molded state after forging.
[0003]
Conventionally, in the structural analysis or fluid analysis of a three-dimensional object, a finite element method that divides a three-dimensional object into a plurality of polyhedral elements and performs a numerical analysis is mainly used, and is used for analysis of material deformation in die forging. Also, analysis using the finite element method is performed. In the finite element method, analysis using a hexahedral mesh that divides a solid object into multiple hexahedral elements has higher analysis accuracy and analysis time than analysis using a tetrahedral mesh that divides a solid object into multiple tetrahedral elements. Is known to be short.
[0004]
As a method for generating a hexahedral mesh from a three-dimensional object, several methods are known, and Patent Literature 1 discloses a method for generating a hexahedral mesh using a mapping method. FIG. 28 is a perspective view showing an example of generating a hexahedral mesh by the mapping method. FIG. 28A shows a three-dimensional shape P expressing the shape of a three-dimensional object to be analyzed. First, a three-dimensional shape P is created using a CAD device or the like, and a hexahedral block including the three-dimensional shape P is created as shown in FIG. Next, as shown in FIG. 28C, a mesh in which the hexahedron block is divided into a plurality of hexahedrons is created, and then the created mesh is mapped to a three-dimensional shape P, as shown in FIG. And generating a hexahedral mesh expressing the three-dimensional object to be analyzed by a combination of a plurality of hexahedral elements.
[0005]
As another method for generating a hexahedral mesh, a voxel method is known. Non-Patent Document 1 discloses a method for generating a hexahedral mesh using the voxel method. FIG. 29 is a schematic diagram showing a two-dimensional example of generating a hexahedral mesh by the voxel method. Although shown in two dimensions for simplicity in the drawing, a hexahedral mesh is actually generated in three dimensions. In the voxel method, first, a mesh is generated by combining a plurality of hexahedral elements filling the inside of the three-dimensional shape P with respect to the three-dimensional shape P as shown in FIG. 29 (a). Next, as shown in FIG. 29C, corresponding to each node located on the surface of the mesh, the surface of the solid shape P is moved in the average direction of the normal vectors of the plurality of element surfaces including each node. Is generated, and a hexahedral mesh in which the three-dimensional shape P is represented by a combination of a plurality of hexahedral elements is generated as shown in FIG. Further, Patent Document 2 discloses a method of generating a hexahedral mesh by creating a new node at a position on the surface of a three-dimensional shape that is the shortest distance from each node located on the surface of the mesh in the voxel method. I have.
[0006]
[Patent Document 1]
JP 2001-92994 A
[Patent Document 2]
JP-A-10-255077
[Non-patent document 1]
R. Schneiders, R. Bunten, "Automatic generation of hexahedral fine element meshes", Computerized geometric design, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Age, Digital Image Design, Digital Age, Digital Age, Digital Image Design (Digital Age, Digital Image Design, Digital Age, Digital Age, Digital Age, Digital Image Design, Digital Image Design, Digital Age, Digital Age, Digital Age, Digital Image Design, Digital Imaging Design, Digital Age, Digital Age, Digital Imaging Design, Digital Imaging Design, Digital Imaging Design, Digital Imaging Design, Inc.) , P. 693-707
[0007]
[Problems to be solved by the invention]
When analysis using a finite element method is performed, such as analysis of material deformation in die forging, in which the object to be analyzed changes shape significantly, a crushing element may occur during the calculation of the analysis and the calculation may be inaccurate . A crushed element is a hexahedral element that is crushed due to deformation of a hexahedral mesh, such as a volume that is smaller than a predetermined value or an extremely deformed shape from a rectangular parallelepiped.If a crushed element occurs, the analysis is interrupted. Then, a hexahedral mesh expressing the shape of the analysis target at the time of the interruption is regenerated (hereinafter, referred to as remeshing), and the analysis is restarted using the remeshed hexahedral mesh. In order to perform the analysis efficiently, it is desirable that all the calculation steps including the remeshing work are automatically performed.
[0008]
FIG. 30 is a perspective view showing a problem of the mapping method. In the mapping method, it is necessary to create a hexahedral block including a three-dimensional shape, and an operator operation is required to determine the size of the hexahedral block. In particular, for a three-dimensional shape P having a complicated shape as shown in FIG. 30A, in order to generate a hexahedral mesh accurately representing the shape of the three-dimensional shape P, as shown in FIG. It is necessary to create a combination of a plurality of hexahedral blocks that can include the three-dimensional shape P. The problem of how many hexahedral blocks can be combined to create a more accurate hexahedral mesh for complex three-dimensional shapes needs to be determined for each three-dimensional shape, and the generation of hexahedral meshes is automated. It is difficult.
[0009]
When the voxel method is used to generate the mesh, it is not necessary to create a hexahedral block in advance, so that the generation of the hexahedral mesh is easier to automate than the mapping method. However, when the shape of the three-dimensional shape is complicated, a difference occurs between the shape of the hexahedral mesh generated using the voxel method and the three-dimensional shape, and the three-dimensional object is compared with the hexahedral mesh generated using the mapping method. There is a problem that the representation accuracy is poor. FIG. 31 is a schematic diagram for explaining a problem of the voxel method in two dimensions. For a three-dimensional shape P having a complicated shape, as shown in FIG. 31 (a), when a new node is created in the average direction of normal vectors of a plurality of surfaces including each node located on the surface of the mesh, In the vicinity where the shape of the three-dimensional shape P changes abruptly, a new node is created far away, and as shown in FIG. 31B, an element having an abnormal shape such as penetrating another element is generated. Further, as shown in FIG. 31C, when a new node is created at a position on the surface of the three-dimensional shape P which is the shortest distance from each node located on the surface of the mesh, as shown in FIG. 31D. In some cases, two or three faces of a hexahedron are positioned on the same plane to create a pyramidal element. Also, in the voxel method, nodes are not always generated at the contour part characterizing the three-dimensional shape, so the generated hexahedral mesh loses the contour and the characteristic of the shape of the three-dimensional object is damaged. is there.
[0010]
Furthermore, when the hexahedral mesh is generated using the voxel method, the hexahedral element generated near the surface of the hexahedral mesh is similar to the example shown in FIG. The shape is greatly distorted from a rectangular parallelepiped. In the analysis that deforms the hexahedral mesh, the hexahedral element near the surface undergoes large deformation, so when using a hexahedral mesh in which the shape of the hexahedral element near the surface is greatly distorted from a rectangular parallelepiped, the collapsed element is used for the hexahedral element near the surface Is more likely to occur. For this reason, there is a problem that the calculation accuracy of the analysis is reduced, or that it is necessary to frequently perform remeshing, and the calculation time of the analysis becomes longer.
[0011]
The present invention has been made in view of such circumstances, and an object of the present invention is to make it possible to automate the generation of a hexahedral mesh by using a voxel method, and to obtain a feature that is a contour of a three-dimensional shape. By moving the nodes on the surface of the hexahedral mesh onto the line, a method of generating a hexahedral mesh capable of retaining the feature of the three-dimensional shape, a hexahedral mesh generation device, a computer program for realizing a computer as the hexahedron mesh generation device, and It is to provide a recording medium.
[0012]
Another object of the present invention is to generate a hexahedral mesh using the voxel method, and to determine the average direction of normal vectors of a plurality of surfaces including nodes located on the surface of the mesh. A hexahedral mesh that improves the accuracy of expressing a three-dimensional object by creating new nodes in the direction that combines the direction of the shortest distance from the node to the surface of the three-dimensional shape at a predetermined ratio according to the three-dimensional shape And a computer program for realizing a computer as the hexahedral mesh generation device, and a recording medium.
[0013]
Another object of the present invention is to generate a mesh used in the voxel method in a shape that follows the shape of the die used in the die forging, thereby being suitable for analyzing the deformation of the material in the die forging. An object of the present invention is to provide a hexahedral mesh generation device that generates a hexahedral mesh, a computer program for realizing a computer as the hexahedral mesh generation device, and a recording medium.
[0014]
Further, another object of the present invention is to generate and remesh a hexahedral mesh using the above-mentioned hexahedral mesh generation method, thereby automatically analyzing the deformation of a three-dimensional object. An object of the present invention is to provide an analysis method, a three-dimensional object deformation analysis device, a computer program for realizing a computer as the analysis device, and a recording medium.
[0015]
[Means for Solving the Problems]
The method for generating a hexahedral mesh according to the first invention is a method for generating a hexahedral mesh in which a shape of a three-dimensional object is represented by a combination of a plurality of hexahedral elements using a computer having a storage unit and an arithmetic unit. A shape model defining a shape is stored in a storage unit, and a first mesh in which a combination of a plurality of hexahedral elements is filled in a three-dimensional shape represented by the shape model stored in the storage unit is generated by an arithmetic unit. A second mesh in which a plurality of hexahedral elements including nodes located on the surface of the generated first mesh and nodes located on the surface of the three-dimensional shape are added to the first mesh; The feature line and the feature points that characterize the three-dimensional shape are extracted by the calculation unit on the surface of the above, and nodes located near the feature line or the feature points on the surface of the second mesh are extracted. And generating a hexahedral mesh is moved to the position or feature point position of the symptoms line by the computing unit.
[0016]
The method for analyzing the deformation of a three-dimensional object according to the second invention uses a computer having a storage unit and a calculation unit, and uses a hexahedral mesh that expresses the shape of the three-dimensional object by combining a plurality of hexahedral elements. In the method for analyzing the deformation of the object, the arithmetic unit generates and stores a hexahedral mesh expressing the shape of the three-dimensional object to be analyzed by a combination of a plurality of hexahedral elements using the hexahedral mesh generation method according to the first invention. The calculation unit analyzes the deformation of the three-dimensional object by deforming the generated hexahedral mesh in the calculation unit. Each time the calculation proceeds to a predetermined stage, a plurality of hexahedrons forming the deformed hexahedron mesh are calculated. The arithmetic unit determines whether or not a crushed element has occurred in the element.If a crushed element has occurred, the calculation is interrupted, and the shape of the hexahedral mesh is defined. A shape model is stored in a storage unit, and a new hexahedral mesh expressing the three-dimensional object being deformed is generated by the calculation unit from the stored shape model using the hexahedral mesh generation method according to the first invention. The calculation is restarted by the calculation unit by using the new hexahedral mesh that is stored in the storage unit and generated.
[0017]
A hexahedral mesh generation device according to a third aspect of the present invention is a device for generating a hexahedral mesh that represents a shape of a three-dimensional object by a combination of a plurality of hexahedral elements. First mesh generation means for generating a first mesh filled with a combination of a plurality of hexahedral elements, and a plurality of hexahedrons including nodes located on the surface of the generated first mesh and nodes located on the surface of the three-dimensional shape Second mesh generation means for generating a second mesh in which elements are added to the first mesh, extraction means for extracting feature lines and feature points characterizing the three-dimensional shape on the surface of the three-dimensional shape, A hexahedral mesh is generated by moving nodes located in the vicinity of the feature line or the feature point on the surface of the two meshes to the position on the feature line or the position of the feature point. Characterized in that it comprises a moving means.
[0018]
A hexahedral mesh generation apparatus according to a fourth aspect of the present invention, wherein the extracting means extracts, on the surface of the three-dimensional shape, a boundary line of the gradient whose gradient of the surface is greater than or equal to a predetermined value as a characteristic line; Means for extracting a point where the change in the direction of the feature line is equal to or greater than a predetermined value, and an end point of the feature line as a feature point, wherein the moving means is provided on the surface of the second mesh in the shortest distance from the extracted feature point. Means for extracting a first node which is a node located at a distance, and connecting the first nodes relating to each of the adjacent feature points on the same feature line with the shortest distance along the element side of the surface of the second mesh; Means for extracting a second node, which is a plurality of nodes passing through at the time, means for moving the first node to the position of the feature point, and a point located at the shortest distance from each of the second nodes on the feature line, Means for moving each of the second nodes; Characterized in that it comprises.
[0019]
In the hexahedral mesh generating apparatus according to a fifth aspect, the three-dimensional object is a three-dimensional object molded by a mold, and the first mesh generating unit generates a hexahedral block including the three-dimensional shape; Means for generating a block-shaped mesh in which the hexahedral block is divided into a three-dimensional lattice at a predetermined number of divisions or a predetermined division interval, and the hexahedral block is expressed by a combination of a plurality of hexahedral elements; Means for arranging a mold shape model representing the shape of the mold at a predetermined distance from the mesh, a node on the surface of the block-like mesh along a direction in which the mold should move in a molding step, and the mold Means for moving the nodes along the direction at a predetermined rate of movement with respect to the distance to the shape model; Means for moving the nodes inside the block-shaped mesh in order to save the ratio of the distance between the nodes, and for each node included in the block-shaped mesh whose nodes have been moved, the nodes are located inside the three-dimensional shape. It is characterized by comprising means for determining whether or not it is located, and means for removing a hexahedral element including a node determined not to be located inside the three-dimensional shape.
[0020]
In a hexahedral mesh generation device according to a sixth aspect, the second mesh generation means includes means for selecting one node on the surface of the first mesh, and each of a plurality of element surfaces including the selected node. Means for generating a first vector by averaging normal vectors; means for generating a second vector which is a direction vector of a perpendicular extending from the node to the surface of the three-dimensional shape; and a predetermined vector corresponding to the position of the node. Synthesizing means for generating a synthesized vector obtained by synthesizing the first vector and the second vector at a synthesizing ratio, and a new node at an intersection of a line extending from the node in the direction of the generated synthesized vector and the surface of the three-dimensional shape Means for generating, for each node on the surface of the first mesh, a means for generating a new corresponding node, and for each element side on the surface of the first mesh, each node at both ends of the element side. A plurality of hexahedral elements comprising element sides connecting corresponding new nodes, and element sides connecting nodes on the surface of the first mesh and new nodes corresponding to the nodes, to the first mesh And means for adding to.
[0021]
In a hexahedral mesh generation device according to a seventh aspect, the synthesizing unit measures a distance along a direction of a first vector from a selected node to a surface of the three-dimensional shape, and the measured distance is a predetermined value. Means for comparing, means for making the first vector a combined vector when the distance is smaller than a predetermined value, and means for making the second vector a combined vector when the distance is greater than or equal to a predetermined value. It is characterized by the following.
[0022]
An apparatus for analyzing deformation of a three-dimensional object according to an eighth invention is a device for analyzing deformation of the three-dimensional object using a hexahedral mesh that expresses the shape of the three-dimensional object by a combination of a plurality of hexahedral elements. A hexahedral mesh generation device according to any one of the seven inventions, and a shape model defining the shape of a three-dimensional object to be analyzed using the hexahedral mesh generation device to combine the shape of the three-dimensional object with a combination of a plurality of hexahedral elements. Means for generating a hexahedral mesh to be represented; means for performing a calculation for deforming the generated hexahedral mesh to analyze the deformation of the three-dimensional object; and forming a deformed hexahedral mesh each time the calculation proceeds to a predetermined stage. Means for determining whether or not a crushed element has occurred in a plurality of hexahedral elements; and, if a crushed element has occurred, suspending the calculation and Generating a new hexahedral mesh representing the shape of the three-dimensional object being deformed from the stored new shape model using the means for storing a new shape model defining the shape of the mesh and the hexahedral mesh generation device. And a means for restarting the calculation using the generated new hexahedral mesh.
[0023]
A computer program according to a ninth invention is a computer program for causing a computer to generate a hexahedral mesh that expresses the shape of a three-dimensional object by a combination of a plurality of hexahedral elements. A first mesh generation procedure for generating a first mesh filled with a combination of a plurality of hexahedral elements inside a three-dimensional shape to be created; and a computer that outputs a node located on the surface of the generated first mesh and a surface of the three-dimensional shape. A second mesh generation procedure for generating a second mesh in which a plurality of hexahedral elements including located nodes are added to the first mesh; and a computer instructing the computer on a feature line and a feature point characterizing the three-dimensional shape. An extraction procedure to extract on the surface, and a computer on the surface of the second mesh Serial, characterized in that it comprises a transfer procedures to generate the feature line or hexahedral meshes of nodes located in the vicinity of the feature point is moved to the position of the position or feature point feature line.
[0024]
A computer program according to a tenth aspect, wherein the extracting step causes a computer to extract, on the surface of the three-dimensional shape, a boundary line of the gradient whose gradient of the surface is not less than a predetermined value as a characteristic line; Causing the computer to extract a point where the change in the direction of the extracted feature line is equal to or greater than a predetermined value, and an end point of the feature line as a feature point. Extracting a first node which is a node located at the shortest distance from the extracted feature points, and causing a computer to connect the first nodes related to each of the adjacent feature points on the same feature line to the surface of the second mesh. Extracting a plurality of second nodes passing through when connected at the shortest distance along the element side of the element, and moving the first node to the position of the feature point by a computer If, on the computer, each of the second node in the feature line to a point located the shortest distance, characterized in that it comprises a procedure for moving each of the second node.
[0025]
A computer program according to an eleventh invention is characterized in that the first mesh generation step includes a step of causing a computer to create a hexahedral block including the three-dimensional shape, and a step of causing the computer to divide the created hexahedral block into a predetermined number of divisions or a predetermined number. The procedure of dividing the hexahedral block into a three-dimensional lattice at a division interval to generate a block mesh expressed by a combination of a plurality of hexahedral elements, and causing a computer to a predetermined distance from the generated block mesh, A procedure for arranging a mold shape model representing the shape of a mold for molding a three-dimensional object, and causing a computer to determine nodes on the surface of the block-like mesh and the mold shape along a direction in which the mold should move in a molding process. Moving the node along the direction at a predetermined rate of movement with respect to the distance to the model; Moving the nodes inside the block mesh to save the ratio of the distance between the plurality of nodes included in the block mesh along the direction, and moving the nodes to the computer. For each node included in the block-shaped mesh, a procedure for determining whether the node is located inside the three-dimensional shape, and causing the computer to determine whether the node is determined not to be located inside the three-dimensional shape. And removing a hexahedral element including the same.
[0026]
A computer program according to a twelfth aspect, wherein the second mesh generation step includes a step of causing a computer to select one node on the surface of the first mesh, and a step of causing the computer to select a plurality of elements including the selected node. A procedure for generating a first vector by averaging respective normal vectors of a surface, a procedure for causing a computer to generate a second vector that is a direction vector of a perpendicular extending from the node to the surface of the three-dimensional shape, A synthesizing procedure for generating a synthesized vector obtained by synthesizing the first vector and the second vector at a predetermined synthesizing ratio according to the position of the node; and a computer extending a line extending from the node in the direction of the generated synthesized vector. Generating a new node at the intersection of the first mesh and the surface of the three-dimensional shape. A procedure for generating a new corresponding node for the point; and causing the computer to perform an element side on the surface of the first mesh, an element side connecting the new nodes corresponding to the nodes at both ends of the element side, and Adding, to the first mesh, a plurality of hexahedral elements composed of element sides connecting nodes on the surface of the first mesh and new nodes corresponding to the nodes.
[0027]
A computer program according to a thirteenth invention is characterized in that the synthesizing step includes: causing a computer to measure a distance along a first vector from a selected node to the surface of the three-dimensional shape; Is compared with a predetermined value, a procedure in which the computer causes the first vector to be a composite vector when the distance is smaller than the predetermined value, and a procedure in which the computer causes the second vector to be used when the distance is equal to or more than the predetermined value. And converting the vector into a composite vector.
[0028]
A computer program according to a fourteenth invention is a computer program for causing a computer to analyze a deformation of a three-dimensional object using a hexahedral mesh that expresses the shape of the three-dimensional object by a combination of a plurality of hexahedral elements. Using a computer program according to any one of the thirteenth to thirteenth aspects, a hexahedral mesh that represents the shape of the three-dimensional object by a combination of a plurality of hexahedral elements is generated from a shape model that defines the shape of the three-dimensional object to be analyzed. A procedure for causing a computer to perform a calculation for deforming the generated hexahedral mesh to analyze the deformation of the three-dimensional object, and for causing the computer to construct a deformed hexahedral mesh each time the calculation proceeds to a predetermined stage. Procedure for determining whether or not a collapsed element has occurred among multiple hexahedral elements If the computer has a collapsed element, the procedure for interrupting the calculation and storing a new shape model defining the shape of the hexahedral mesh is stored in the computer. Using a computer program according to any of the above, a procedure for generating a new hexahedral mesh representing the shape of the three-dimensional object being deformed from the stored new shape model, and using the generated new hexahedral mesh for the computer And restarting the calculation.
[0029]
The computer-readable recording medium according to the fifteenth invention is a computer-readable recording medium that stores a computer program that causes a computer to generate a hexahedral mesh that expresses the shape of a three-dimensional object by combining a plurality of hexahedral elements. A first mesh generation procedure for causing a computer to generate a first mesh in which a combination of a plurality of hexahedral elements is filled in a three-dimensional shape represented by a shape model that defines a shape of a three-dimensional object; A second mesh generation step for causing a computer to generate a second mesh in which a plurality of hexahedral elements including nodes located on the surface of the generated first mesh and nodes located on the surface of the three-dimensional shape are added to the first mesh; A computer, the characteristic line and the characteristic point characterizing the three-dimensional shape, the three-dimensional shape An extraction procedure for extracting on the surface, and a computer generating a hexahedral mesh in which nodes located near the feature line or the feature point on the surface of the second mesh are moved to the position on the feature line or the position of the feature point. And a computer program including a moving procedure to be performed.
[0030]
A computer-readable recording medium according to a sixteenth aspect of the present invention is a computer program for causing a computer to analyze the deformation of a three-dimensional object using a hexahedral mesh that represents the shape of the three-dimensional object by a combination of a plurality of hexahedral elements. In a computer-readable recording medium having recorded therein, the computer uses a computer program according to any of the ninth to thirteenth aspects to convert a shape model that defines the shape of a three-dimensional object to be analyzed from A procedure for generating a hexahedral mesh expressing the shape of the three-dimensional object by a combination of a plurality of hexahedral elements, and a procedure for causing a computer to perform a calculation for deforming the generated hexahedral mesh and analyzing the deformation of the three-dimensional object, Whenever the calculation proceeds to a predetermined stage, the computer constructs a deformed hexahedral mesh A procedure for determining whether or not a crushed element has occurred in a plurality of hexahedral elements, and, when a crushed element has occurred, suspending the calculation and changing the shape of the hexahedral mesh. A procedure for storing a prescribed new shape model, and using a computer program according to any of the ninth to thirteenth aspects, the computer represents the shape of the three-dimensional object being deformed from the stored new shape model. A computer program is recorded which includes a procedure for generating a new hexahedral mesh to be performed and a procedure for restarting the calculation using the generated new hexahedral mesh.
[0031]
FIG. 1 is a perspective view showing an outline of a hexahedral mesh generation method of the present invention. In the first, third, fourth, ninth, tenth, and fifteenth inventions, a voxel method is used for a three-dimensional shape P expressing the shape of a three-dimensional object as shown in FIG. As shown in FIG. 1 (b), a first mesh M1 in which the inside of the three-dimensional shape P is filled with a combination of hexahedral elements is generated, and as shown in FIG. The second mesh M2 is generated by adding the hexahedron element including the first mesh M1 to the first mesh M1, and further on a feature line characterizing the shape of the three-dimensional shape P such as the outline of the three-dimensional shape P indicated by a broken line in FIG. Next, the nodes on the surface of the second mesh M2 are moved to generate a hexahedral mesh M as shown in FIG. As a result, a hexahedral mesh that inherits the features of the three-dimensional shape P is generated.
[0032]
In the fifth and eleventh inventions, a node on the surface of a block-shaped mesh obtained by dividing a hexahedral block including a three-dimensional shape into a three-dimensional lattice is defined by a mold shape that defines the shape of a mold for molding the three-dimensional object with the node. Moved toward the mold shape model by a distance proportional to the distance to the model, follow and move the nodes inside the block-shaped mesh, and remove the hexahedral elements including nodes that are not located inside the three-dimensional shape. By generating one mesh, a hexahedral mesh in which the shape and arrangement of hexahedral elements follow the shape of the mold is generated.
[0033]
In the sixth and twelfth inventions, when a new node corresponding to a node on the surface of the first mesh is generated on the surface of the three-dimensional shape to generate the second mesh, the node is determined according to the position of the node. A combined vector is generated by combining a first vector obtained by averaging respective normal vectors of a plurality of element surfaces including a second vector which is a direction vector of a perpendicular extending from the node to the surface of the shape model, By generating new nodes in the direction of the composite vector, a hexahedral mesh with improved accuracy of representing a three-dimensional object is generated.
[0034]
In the seventh and thirteenth inventions, when a new node corresponding to the node on the surface of the first mesh is generated on the surface of the three-dimensional shape, the new node along the direction of the first vector from the node to the surface of the three-dimensional shape is generated. The distance is compared with a predetermined value, and when the node is located at a portion protruding toward the three-dimensional shape and the distance is smaller than the predetermined value, the first vector is set as a composite vector, and the node is deepened away from the three-dimensional shape. If the shortest distance is equal to or greater than a predetermined value in the portion where the node is located, a new node is generated at an appropriate position according to the situation around the node by using the second vector as a composite vector. As a result, a hexahedral mesh with improved accuracy of representing a three-dimensional object is generated.
[0035]
In the second, eighth, fourteenth, and sixteenth inventions, in order to analyze deformation of a three-dimensional object, the hexahedral mesh is generated and remeshed by using the hexahedral mesh generation method according to the present invention, whereby the analysis is performed. Calculation can be performed automatically.
[0036]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, the present invention will be specifically described with reference to the drawings showing the embodiments.
FIG. 2 is a block diagram showing the configuration of the hexahedral mesh generation device of the present invention. In the figure, reference numeral 1 denotes a hexahedral mesh generation device of the present invention. The hexahedral mesh generation device 1 also has the function of the three-dimensional object deformation analysis device according to the present invention, and is configured using a computer. The hexahedral mesh generation device 1 is a calculation unit according to the present invention, which is a CPU (calculation unit) 11 that performs a calculation, and a storage unit according to the present invention, which is a RAM that stores temporary information generated with the calculation. (Storage unit) 12, an external storage device 13 such as a CD-ROM drive, and an internal storage device 14 such as a hard disk. The computer program 20 according to the present invention is externally stored from a recording medium 2 such as a CD-ROM. The computer program 20 read by the storage device 13 is stored in the internal storage device 14, the computer program 20 is loaded into the RAM 12, and processing necessary for the hexahedral mesh generation device 1 is executed based on the loaded computer program 20. . The hexahedral mesh generation device 1 includes an input device 15 such as a keyboard or a mouse, and an output device 16 such as a liquid crystal display or a CRT display, and is configured to receive an operation from an operator including data input. I have.
[0037]
Further, the hexahedral mesh generation device 1 may include a communication interface 17, download the computer program 20 according to the present invention from the server device 3 connected to the communication interface 17, and execute the processing by the CPU 11. Good.
[0038]
Next, a method of analyzing deformation of a three-dimensional object according to the present invention will be described by taking as an example the analysis of deformation of a three-dimensional object in die forging. FIG. 3 is a perspective view schematically showing deformation of a three-dimensional object in die forging. A in the figure is a three-dimensional object formed by die forging, and is pressed by an upper die and a lower die in the direction of the arrow in the drawing to perform die forging. FIG. 4 is a flowchart illustrating a procedure of a process of a method for analyzing deformation of a three-dimensional object. The hexahedral mesh generation device 1 having the function of the three-dimensional object deformation analysis device according to the present invention uses the input device 15 to convert the shape of the three-dimensional object to be analyzed into the coordinates of points included in the three-dimensional object or the equation of a curve. Then, the shape model specified by the formula (1) and the mold shape model expressing the shape of the mold for molding the three-dimensional object are read and stored in the RAM 12 (S01). At this time, the hexahedral mesh generation device 1 may store the shape model and the shape model in the internal storage device 14 and read the stored shape model and the shape model into the RAM 12. May be read via the communication interface 17. Further, the hexahedral mesh generation device 1 may have a form having a function of a CAD device that creates a shape model and a mold shape model by an operation of an operator. The CPU 11 of the hexahedral mesh generation device 1 loads the computer program 20 into the RAM 12, generates a hexahedral mesh expressing the shape of the three-dimensional object by a combination of a plurality of hexahedral elements according to the loaded computer program 20 (S02). Calculation of analysis for deforming the hexahedral mesh using the mold shape model is performed (S03), and when the calculation reaches a predetermined stage, such as when the press by the mold is performed for a predetermined press width, the crushed element is deformed to the hexahedral mesh. It is determined whether or not an error has occurred (S04). If a crushing element has occurred (S04: YES), the CPU 11 returns the process to step S02 according to the computer program 20 loaded in the RAM 12, and executes the processing from the new shape model that defines the shape of the hexahedral mesh being deformed. The remeshing process for generating a new hexahedral mesh is performed, and the calculation is restarted. If the collapse element has not occurred in step S04 (S04: NO), the CPU 11 determines convergence conditions and the like according to the computer program 20 loaded in the RAM 12, and determines the end of the calculation (S05). If the calculation can be ended (S05: YES), the process is ended. If the calculation is not ended (S05: NO), the process returns to step S03 to continue the calculation.
[0039]
Next, the hexahedral mesh generation method of the present invention will be described with reference to an example of generation of a hexahedral mesh used for analysis of deformation of a three-dimensional object in die forging. FIG. 5 is a flowchart showing a procedure of hexahedral mesh generation processing performed by the hexahedral mesh generation device 1 of the present invention. The CPU 11 of the hexahedral mesh generation device 1 loads the computer program 20 into the RAM 12 and fills a combination of a plurality of hexahedral elements into the three-dimensional shape represented by the shape model stored in the RAM 12 according to the loaded computer program 20. A first mesh generation process for generating the first mesh is performed (S1), and a plurality of hexahedral elements including nodes located on the surface of the first mesh and nodes located on the surface of the three-dimensional shape are added to the first mesh. Performing a second mesh generation process for generating a modified second mesh (S2), shaping the shape of the second mesh according to the characteristics of the three-dimensional shape, and generating a hexahedral mesh suitable for analyzing deformation of the three-dimensional object. Processing is performed (S3).
[0040]
FIG. 6 is a flowchart showing the procedure of a subroutine of the first mesh generation processing in step S1. The CPU 11 measures the minimum value and the maximum value of each of the three-dimensional axial directions in the shape model stored in the RAM 12 according to the computer program 20 loaded in the RAM 12 (S11), and includes the measured minimum value and maximum value. (S12), the generated hexahedral block is three-dimensionally divided by a predetermined width or a predetermined number, and a block-like mesh in which the hexahedral block is expressed by a combination of a plurality of hexahedral elements is generated. (S13). FIG. 7 is a schematic diagram showing a procedure for generating a block-shaped mesh. The minimum and maximum values (Xmin, Xmax), (Ymin, Ymax), (Zmin, Zmax) in each axial direction are measured for the three-dimensional shape P represented by the shape model shown in FIG. As shown in FIG. 7B, a hexahedral block B including an area surrounded by coordinates obtained by combining the measured values is generated, and as shown in FIG. A mesh BM is generated.
[0041]
Next, the CPU 11 performs a process of shaping the shape of the block-shaped mesh BM according to the shape of the mold for molding the three-dimensional object. FIG. 8 is a schematic diagram showing a procedure for shaping the block-shaped mesh BM, and shows the block-shaped mesh BM in a two-dimensional plane for simplification. In accordance with the computer program 20 loaded into the RAM 12, the CPU 11 moves a mold shape model expressing the shape of a mold for molding a three-dimensional object in a direction in which the mold presses the three-dimensional object in mold forging, and contacts the block-shaped mesh BM. (S14). FIG. 8A shows an upper mold shape model F1 and a lower mold shape model F2 expressing the shapes of an upper mold and a lower mold, which are molds used for mold forging. Next, among the nodes on the surface of the block-shaped mesh BM, the CPU 11 moves the node facing the mold model at a predetermined moving rate toward the mold model according to the computer program 20 loaded on the RAM 12. (S15). In the example shown in FIG. 8A, the movement rate Rm is set to 0 when the node P1 facing the upper mold model F1 does not move at all, and to 1.0 when it moves until it overlaps with the upper mold model F1. As shown in FIG. 8B, the distance L1 between the node P1 and the upper mold model F1 and the distance La between the point Pa to which the node P1 has been moved and the upper mold model F1 are: The node P1 is moved in the Z-axis direction so that L1 * (1-Rm) = La, and is set as a new node Pa. Similarly, with respect to the node P6 facing the lower mold model F2, the distance L7 between the node P6 and the lower mold model F2 and the distance between the point Pf to which the node P6 is moved and the lower mold model F2 are also determined. The node P6 is moved in the Z-axis direction so that the distance Lg of L7 becomes L7 * (1-Rm) = Lg, and is set as a new node Pf.
[0042]
Next, the CPU 11 moves the nodes inside the block-shaped mesh BM according to the computer program 20 loaded into the RAM 12 (S16). In the example illustrated in FIG. 8A, as illustrated in FIG. 8C, the nodes P2, P3, P4, and P5 located between the nodes P1 and P6 are moved in the Z-axis direction to form a new node. Let Pb, Pc, Pd, and Pe be the distance Lb between the node Pa and the node Pb, the distance Lc between the node Pb and the node Pc, the distance Ld between the node Pc and the node Pd, and the node Pd and the node Pe. L2 / L8 between the distance Le between the node Pe, the distance Lf between the node Pe and the node Pf, the distance L8 between the node P1 and the node P6, and the distance Lh between the node Pa and the node Pf. = Lb / Lh, L3 / L8 = Lc / Lh, L4 / L8 = Ld / Lh, L5 / L8 = Le / Lh, and L6 / L8 = Lf / Lh. As a result, as shown by a solid line in FIG. 8D, the block-shaped mesh BM is shaped following the shape of the mold shape model.
[0043]
Next, the CPU 11 determines which hexahedral element among a plurality of hexahedral elements constituting the shaped block-shaped mesh BM is located inside the three-dimensional shape P according to the computer program 20 loaded into the RAM 12. Is performed (S17). FIG. 9 is a flowchart showing the procedure of a subroutine of the inside / outside determination process in step S17. The CPU 11 selects one of the plurality of nodes included in the block-shaped mesh BM according to the computer program 20 loaded in the RAM 12 (S171), and draws a straight line including the selected node in the X, Y, and Z axis directions. It is extended (S172), and it is determined whether or not the node exists between two intersections of the extended straight line and the surface of the three-dimensional shape P (S173). If the node exists between the intersections (S173: YES), the CPU 11 determines that the node is a node located inside the three-dimensional shape P according to the computer program 20 loaded into the RAM 12. (S174) If the node does not exist between the intersections (S173: NO), it is determined that the node is a node located outside the three-dimensional shape P (S175). Next, the CPU 11 determines whether or not the inside / outside determination has been performed for all the nodes according to the computer program 20 loaded in the RAM 12 (S176). If the inside / outside determination has not been performed for all the nodes (S176: NO). Then, the process returns to step S171 to select the next node for which the inside / outside determination has not been performed, and if the inside / outside determination has been performed for all the nodes (S176: YES), the processing of the subroutine of step S17 ends, and The process returns to the one mesh generation process. Note that the inside / outside determination processing using another method is performed, such as performing the inside / outside determination of the node based on whether the number of intersections of the half line extended from the selected node and the solid shape P is odd or even. Is also good.
[0044]
Next, the CPU 11 removes the hexahedral element including the node determined to be located outside the three-dimensional shape P according to the computer program 20 loaded into the RAM 12, generates a first mesh (S18), and proceeds to step S1. Is completed, and the process returns to the main process. FIG. 10 is a schematic diagram showing generation of the first mesh, and shows a block-like mesh BM in a two-dimensional plane for simplicity. Among the nodes included in the block-shaped mesh BM, nodes located inside the three-dimensional shape P are indicated by black circles, and nodes located outside the three-dimensional shape P are indicated by white circles, and hexahedral elements including the white circles are removed. The part shaded inside is left as the first mesh. FIG. 11 is a perspective view showing an example of the first mesh M1. FIG. 7B shows a first mesh M1 generated for the three-dimensional shape P shown in FIG. 7A, wherein the volume of the first mesh is smaller than the three-dimensional shape P, and the inside of the three-dimensional shape P is formed by a combination of hexahedral elements. It has a filled shape.
[0045]
FIG. 12 is a flowchart illustrating a procedure of a subroutine of the second mesh generation processing in step S2. The CPU 11 selects one node on the surface of the first mesh M1 according to the computer program 20 loaded on the RAM 12 (S21), and averages the normal vectors of the plurality of element surfaces including the selected node. A vector V1 is generated (S22), and a second vector V2, which is a direction vector of a perpendicular extending from the node to the surface of the three-dimensional shape P, is generated (S23). FIG. 13 is a schematic diagram illustrating an example of the first vector V1 and the second vector V2, and illustrates generation of the vector in a two-dimensional plane for simplicity. For the node indicated by a in the figure, a first vector V1 is generated by averaging normal vectors of element surfaces including the node a, and a second vector V1 which is a direction vector of a perpendicular from the node a to the surface of the solid shape P is generated. A vector V2 is generated.
[0046]
Next, in accordance with the computer program 20 loaded in the RAM 12, the CPU 11 performs a synthesizing process of generating a synthesized vector obtained by synthesizing the first vector V1 and the second vector V2 at a synthesis ratio corresponding to the position of the node (S24). . FIG. 14 is a flowchart showing the procedure of the subroutine of the combining process in step S24. The CPU 11 measures the distance D along the direction of the first vector from the node to the surface of the three-dimensional shape P according to the computer program 20 loaded in the RAM 12 (S241), and determines whether the measured distance D is smaller than a predetermined value. Is determined (S243), if the distance D is smaller than the predetermined value (S243: YES), the first vector V1 is set as the composite vector Vs (S245), and if the distance D is equal to or larger than the predetermined value (S243: NO), the second vector V2 is set as the composite vector Vs (S247), the processing of the subroutine of step S24 ends, and the processing returns to the second mesh generation processing. FIG. 15 is a schematic diagram illustrating an example of the composite vector Vs, and illustrates the composite vector Vs in a two-dimensional plane for simplicity. As shown in FIG. 15A, the node b of the portion protruding toward the three-dimensional shape P has a small distance D, so that the first vector V1 becomes the composite vector Vs. As shown in FIG. 15B, the distance c along the first vector V1 is large at the node c in the deep part where the shape of the first mesh is complicated, so that the second vector V2 becomes the composite vector Vs.
[0047]
In the subroutine of the combining process in step S24, a method of generating a combined vector Vs by continuously adjusting the combining ratio for combining the first vector V1 and the second vector V2 may be used. FIG. 16 is a flowchart showing the procedure of the subroutine of the combining process in step S24 using the method of continuously adjusting the combining ratio. In accordance with the computer program 20 loaded in the RAM 12, the CPU 11 measures, for each of the element sides including the node, a face included angle which is an inner angle of the first mesh M1 formed by the two element faces including the element side (S242). Then, an average of the other included angles except for the included angles that are within a predetermined range of about 180 ° among the plurality of measured included angles is calculated (S244). FIG. 17 is a schematic perspective view showing an example of a face included angle. As shown in FIG. 17A, as for the node N at the corner portion of the first mesh M1, the surface included angles of three element sides including the node N are defined as θ1, θ2 and θ3, and the average surface included angle θm is , Θm = (θ1 + θ2 + θ3) / 3. As shown in FIG. 17B, with respect to the node N at the edge portion of the first mesh M1, the average surface is excluded from the included angles θ1, θ2, θ3 and θ4 except for θ3 and θ4 which are around 180 °. The included angle θm is calculated as θm = (θ1 + θ2) / 2. Further, as shown in FIG. 17C, the node N at the deep part where the shape is intricate is calculated from θ1 and θ2 around 270 °, θ3 around 90 °, and θ4 and θ5 around 180 °, and The included angle θm is calculated as θm = (θ1 + θ2 + θ3) / 3.
[0048]
Next, the CPU 11 determines the combining ratio Rs according to the relationship between the average plane included angle θm and the combining ratio Rs stored in the RAM 12 or the internal storage device 14 in advance according to the computer program 20 loaded into the RAM 12 (S246). Using the determined combination ratio Rs, the first vector V1 and the second vector V2 are combined according to the equation of a combined vector Vs = (1−Rs) * first vector V1 + Rs * second vector V2, and a combined vector Vs Is generated (S248). The process of the subroutine of step S24 ends, and the process returns to the second mesh generation process. FIG. 18 is a characteristic diagram illustrating an example of the relationship between the average plane included angle θm and the composition ratio Rs, in which the horizontal axis indicates the average plane included angle θm and the vertical axis indicates the composite ratio Rs. When the average plane included angle θm is in the range of 0 ° to 90 °, since the first mesh M1 is a portion protruding toward the three-dimensional shape P, the combining ratio is set so that the combined vector Vs becomes the first vector V1. In the range of 270 ° to 360 ° where the included angle θm is 270 ° to 360 °, the combination ratio is set so that the composite vector Vs becomes the second vector V2 because the composite mesh Vs is a deep part where the shape of the first mesh is complicated. When the average plane included angle θm is in the range of 90 ° to 270 °, the combining ratio Rs is linearly changed according to the average plane included angle θm. Note that a range other than 90 ° to 270 ° may be changed, or a non-linear relationship using a hyperbolic trigonometric function or the like may be applied.
[0049]
Next, the CPU 11 generates a new node at the intersection of the line extending from the node in the direction of the composite vector Vs and the surface of the three-dimensional shape P according to the computer program 20 loaded into the RAM 12 (S25). In the case of the example shown in FIG. 15, a new node b ′ is generated corresponding to the node b shown in FIG. 15A, and a new node c is generated corresponding to the node c shown in FIG. 'Is generated. Next, the CPU 11 determines whether or not corresponding new nodes have been generated for all the nodes on the surface of the first mesh M1 according to the computer program 20 loaded into the RAM 12 (S26). If a new node has not been generated (S26: NO), the process returns to step S21, the next node on the surface of the first mesh M1 is selected, and new nodes are generated for all nodes. In this case (S26: YES), the element side on the surface of the first mesh M1, the element side connecting new nodes corresponding to the nodes at both ends of the element side, and the node on the surface of the first mesh M1 A plurality of hexahedral elements composed of element sides connecting the and a new node corresponding to the node are added to the first mesh M1 to generate a second mesh (S27). 2 to end the mesh generation process and the process returns to the main processing. FIG. 19 is a schematic diagram showing the addition of a hexahedral element, and shows the first mesh M1 in a two-dimensional plane for simplicity. For each of the nodes N1 to N8 on the surface of the first mesh M1 indicated by black circles in the figure, new nodes N'1 to N'8 indicated by white circles in the figure are generated, and the first mesh M1 Are generated, including the element sides connecting the nodes on the surface of and the new nodes corresponding to the nodes. FIG. 20 is a perspective view illustrating an example of the second mesh M2. 12 illustrates a second mesh M2 generated for the first mesh M1 illustrated in FIG. 11, and has a structure in which a hexahedral element is added to a gap between the first mesh M1 and the three-dimensional shape P.
[0050]
FIG. 21 is a flowchart showing the procedure of the subroutine of the mesh shaping process in step S3. The CPU 11 performs a feature line extraction process of extracting a feature line characterizing the shape of the three-dimensional shape P on the surface of the three-dimensional shape P according to the computer program 20 loaded in the RAM 12 (S31). FIG. 22 is a flowchart showing the procedure of the subroutine of the characteristic line extraction processing in step S31, and FIG. 23 is a perspective view showing a method of extracting characteristic lines from the three-dimensional shape P. The CPU 11 calculates the outward normal vector of the three-dimensional shape P for each surface constituting the surface of the three-dimensional shape P according to the computer program 20 loaded into the RAM 12 (S311). In the remeshing process, when a process using a shape model that defines the shape of the hexahedral mesh in the middle of deformation is performed, as shown in FIG. Is calculated for each element plane on the surface of. Next, the CPU 11 calculates the inner product of the normal vectors between adjacent surfaces on the surface of the three-dimensional shape P according to the computer program 20 loaded into the RAM 12 (S312), and the angle between the surfaces is about 180 °. Then, a line segment at a boundary between the surfaces whose inner product is equal to or less than a predetermined value is extracted so as to include cases other than the case where the surfaces are connected substantially flat (S313). For example, when extracting a line segment whose inner product is 0.34 or less, the angle between the normal vectors is 70 ° to 180 °, and the angle inside the three-dimensional shape P between the surfaces is 110 ° or less. Alternatively, a line segment at the boundary between the surfaces when the angle is 250 ° or more is extracted. Next, according to the computer program 20 loaded into the RAM 12, the CPU 11 sets the combination of the extracted line segments as a feature line (S314), terminates the feature line extraction process subroutine, and returns to the mesh shaping process. In the case of the three-dimensional shape P shown in FIG. 23 (a), as shown in FIG. 23 (b), the line segments r1 to r8, which are boundaries where the element surfaces are connected at an angle without being connected flat, are extracted. , A characteristic line having continuous line segments r1 to r7 and a characteristic line composed of only line segment r8 are obtained.
[0051]
Next, the CPU 11 performs a feature point extraction process of extracting feature points characterizing the shape of the three-dimensional shape P on the surface of the three-dimensional shape P according to the computer program 20 loaded into the RAM 12 (S32). FIG. 24 is a flowchart showing the procedure of the subroutine of the feature point extraction process in step S32, and FIG. 25 is a schematic diagram showing an example of feature lines and feature points extracted from the three-dimensional shape P. According to the computer program 20 loaded into the RAM 12, the CPU 11 converts the points at both ends of each line segment extracted in the feature line extraction processing in step S31 into one line segment or into three or more line segments. An end point of the feature line that is a shared point and a point on a line on the feature line that is a point shared by two line segments are classified (S321), and the end point among the classified points is extracted as a feature point. (S322). In the example shown in FIG. 25, points q1, q3, q5, q8, q9, and q10 among the points q1 to q10 at the ends of the line segments r1 to r8 are classified into the end points and extracted as feature points. Next, the CPU 11 calculates a direction vector directed to the same direction along the feature line for each continuous line segment on the feature line according to the computer program 20 loaded on the RAM 12 (S323), The inner product of the directional vectors is calculated in step S324, and the line segment whose inner product is equal to or less than a predetermined value is included, including the case where the angle between the line segments is around 180 ° and the line segments are connected substantially flat. The points on the line shared by each other are extracted as feature points (S325), and the subroutine of the feature point extraction processing ends, and the processing returns to the mesh shaping processing. For example, when extracting a point on a line where the inner product is 0.34 or less, the angle between the direction vectors is 70 ° to 180 °, and the inner angle between continuous line segments is 0 ° to 110 °. The point on the line shared by the line segments is extracted. In the example shown in FIG. 25, a point q7 shared by line segments r6 and r7 that are continuous at an angle is extracted as a feature point.
[0052]
FIG. 26 is a schematic diagram showing the shaping of the second mesh M2, in which a part of the second mesh M2 shown in FIG. 20 is shown in an enlarged manner, and feature lines extracted from the three-dimensional shape P are shown by broken lines. Next, the CPU 11 extracts a first node, which is a node on the surface of the second mesh M2 located at the shortest distance from each feature point, according to the computer program 20 loaded into the RAM 12 (S33), and on the same feature line. The first nodes relating to each of the adjacent feature points are connected to each other at the shortest distance along the element side of the surface of the second mesh M2 (S34), and a second node which is a plurality of nodes passing at this time is extracted. (S35). As shown in FIG. 26A, the first nodes Q1 and Q2, which are the shortest distance nodes, are extracted corresponding to the feature points K1 and K2, and the first nodes Q1 and Q2 are connected at the shortest distance. The second nodes Q3, Q4 and Q5, which are the nodes to be changed, are extracted. Next, the CPU 11 moves the first node to the position of the feature point in accordance with the computer program 20 loaded in the RAM 12 (S36), and moves the second node to the position of the shortest distance from the second node on the feature line. (S37) The subroutine of the mesh shaping process in step S3 ends, and the process returns to the main process. As shown in FIG. 26B, the first nodes Q1 and Q2 move to the positions of the feature points K1 and K2, and the second nodes Q3, Q4 and Q5 draw perpendiculars from each of the second nodes to the feature line. Move to the points O3, O4 and O5 at the positions indicated.
[0053]
With the above processing, the CPU 11 completes the hexahedral mesh and ends the processing. FIG. 27 is a perspective view showing the completed hexahedral mesh. FIG. 27A shows a hexahedral mesh M completed by shaping the second mesh M2 shown in FIG. 20, and FIG. 27A shows the hexahedral mesh M extracted from the three-dimensional shape P by overlapping the second mesh M2 shown in FIG. The characteristic line thus drawn is indicated by a broken line, and FIG. 27B shows a hexahedral mesh M whose shape is matched to the characteristic line. The feature of the shape of the three-dimensional shape P is expressed by the hexahedral mesh M.
[0054]
As described above in detail, in the present invention, when a new node corresponding to the node on the surface of the first mesh M1 is generated on the surface of the three-dimensional shape P and the second mesh M2 is generated, the position of the node is Accordingly, a first vector V1 obtained by averaging respective normal vectors of a plurality of element surfaces including the node and a second vector V2 which is a direction vector of a perpendicular extending from the node to the surface of the three-dimensional shape P are synthesized. And generating a new node in the direction of the synthesized vector Vs, thereby generating a new node at an appropriate position according to the situation around the position of the node, and generating another node. An element having an abnormal shape, such as penetrating through, or a pyramid-shaped element is prevented from being created, and the quality of the hexahedral mesh M generated using the voxel method is improved. Further, a hexahedron mesh M is generated by moving a node on the surface of the second mesh M2 to a feature line such as a contour of the three-dimensional shape P and a feature point such as a vertex of the three-dimensional shape P, which characterizes the three-dimensional shape P. By doing so, the characteristics of the shape of the three-dimensional shape P are inherited, and the quality of the hexahedral mesh is further improved.
[0055]
Further, in the present invention, the nodes on the surface of the block-shaped mesh BM are moved toward the mold shape model by a distance proportional to the distance between the nodes and the mold shape model, and the nodes inside the block-shaped mesh BM are moved. Also, the first mesh is generated by removing the hexahedral element including the nodes not located inside the three-dimensional shape P to generate the first mesh, so that the shape of the first mesh is the same as the shape following the shape of the mold. The hexahedral element added to the surface of the first mesh and located on the surface of the hexahedral mesh becomes a hexahedral element having a surface substantially parallel to the shape of the mold, and is used in a calculation of an analysis for deforming a three-dimensional object with the mold. In addition, the frequency of occurrence of the crushing element in the hexahedral element near the surface of the hexahedral mesh is lower than that in the related art. As a result, the calculation accuracy of the analysis is improved, the number of times of remeshing is reduced, and the calculation time of the analysis is reduced.
[0056]
Further, in the present invention, by generating and remeshing the hexahedral mesh using the voxel method, it is possible to automatically calculate the generation of the hexahedral mesh and the analysis of the deformation of the three-dimensional object including the remesh. In addition, since a hexahedral mesh with improved quality for expressing the shape of a three-dimensional object is used, the accuracy of calculation is improved, and the frequency of occurrence of collapse elements is reduced, the number of times of remeshing is reduced, and the calculation time for analysis is reduced. Is shortened. As a result, it is possible to suppress the time and cost required for optimizing the die forging process or designing an optimal shape of a die used for die forging.
[0057]
In the present embodiment, the hexahedral mesh generation device 1 of the present invention has been described as an embodiment having the function of a three-dimensional object deformation analysis device, but is not limited thereto. The apparatus for analyzing the deformation of an object may be configured by separate computers, and data may be input and output to and from each other to perform remeshing and analysis calculations.
[0058]
【The invention's effect】
In the first, third, fourth, ninth, tenth, and fifteenth inventions, characteristic lines such as contours and vertices that characterize a three-dimensional shape represented by a shape model that defines the shape of a three-dimensional object are provided. By matching the nodes on the surface of the hexahedral mesh with the feature points, it is possible to generate a hexahedral mesh in which the features of the three-dimensional shape are inherited.
[0059]
In the fifth and eleventh inventions, the first mesh that fills the inside of the three-dimensional shape with a combination of hexahedral elements generates a first mesh that follows the shape of the mold for molding the three-dimensional object. The hexahedral element added to the surface of the one mesh and located on the surface of the hexahedral mesh is a hexahedral element having a surface substantially parallel to the shape of the mold, and in the calculation of the analysis for deforming the three-dimensional object with the mold, The frequency of occurrence of the crushing element in the hexahedral element near the surface is lower than before. As a result, the calculation accuracy of the analysis is improved, the number of times of remeshing is reduced, and the calculation time of the analysis is reduced.
[0060]
In the sixth and twelfth inventions, when a new node corresponding to the node on the surface of the first mesh is generated on the surface of the three-dimensional shape, the new node is set to an appropriate position according to the situation around the position of the node. Generate new nodes to prevent elements with abnormal shapes such as penetrating other elements or pyramid-shaped elements from being created, and improve the quality of hexahedral meshes generated using the voxel method Can be done.
[0061]
In the seventh and thirteenth inventions, when a new node corresponding to a node on the surface of the first mesh is generated on the surface of the three-dimensional shape, if the node is located at a portion protruding toward the surface of the three-dimensional shape, Generating a new node in the direction of averaging the respective normal vectors of the plurality of element surfaces including the node, and if the node is located in a deep part away from the surface of the three-dimensional shape, the shortest distance from the node By generating a new node at the position, the new node can be generated at an appropriate position according to the situation around the position of the node, and the quality of the hexahedral mesh can be improved.
[0062]
In the second, eighth, fourteenth, and sixteenth inventions, the generation of the hexahedral mesh and the remeshing using the voxel method are used to calculate the generation of the hexahedral mesh and the analysis of the deformation of the solid object including the remesh. It can be done automatically. In addition, since a hexahedral mesh with improved quality for expressing the shape of a three-dimensional object is used, the accuracy of calculation is improved, and the frequency of occurrence of collapse elements is reduced, the number of times of remeshing is reduced, and the calculation time for analysis is reduced. Is shortened. As a result, the present invention has excellent effects such as optimizing the die forging process or suppressing the time and cost required for designing an optimal shape of a die used for die forging.
[Brief description of the drawings]
FIG. 1 is a perspective view showing an outline of a hexahedral mesh generation method of the present invention.
FIG. 2 is a block diagram illustrating a configuration of a hexahedral mesh generation device according to the present invention.
FIG. 3 is a perspective view schematically showing deformation of a three-dimensional object in die forging.
FIG. 4 is a flowchart showing a processing procedure of a method for analyzing deformation of a three-dimensional object.
FIG. 5 is a flowchart showing a procedure of hexahedral mesh generation processing performed by the hexahedral mesh generation device of the present invention.
FIG. 6 is a flowchart illustrating a procedure of a subroutine of a first mesh generation process in step S1.
FIG. 7 is a schematic diagram showing a procedure for generating a block-shaped mesh.
FIG. 8 is a schematic diagram showing a procedure for shaping a block-shaped mesh.
FIG. 9 is a flowchart showing the procedure of a subroutine of an inside / outside determination process in step S17.
FIG. 10 is a schematic diagram illustrating generation of a first mesh.
FIG. 11 is a perspective view showing an example of a first mesh.
FIG. 12 is a flowchart illustrating a procedure of a subroutine of a second mesh generation process in step S2.
FIG. 13 is a schematic diagram illustrating an example of a first vector and a second vector.
FIG. 14 is a flowchart illustrating a procedure of a subroutine of a combining process in step S24.
FIG. 15 is a schematic diagram illustrating an example of a combined vector.
FIG. 16 is a flowchart showing a procedure of a subroutine of a combining process in step S24 using a method of continuously adjusting a combining ratio.
FIG. 17 is a schematic perspective view illustrating an example of a face included angle.
FIG. 18 is a characteristic diagram illustrating an example of a relationship between an average plane included angle and a composition ratio.
FIG. 19 is a schematic diagram showing addition of a hexahedral element.
FIG. 20 is a perspective view showing an example of a second mesh.
FIG. 21 is a flowchart illustrating a procedure of a subroutine of a mesh shaping process in step S3.
FIG. 22 is a flowchart showing the procedure of a subroutine of a feature line extraction process in step S31.
FIG. 23 is a perspective view showing a method of extracting a feature line from a three-dimensional shape.
FIG. 24 is a flowchart showing the procedure of a subroutine of a feature point extraction process in step S32.
FIG. 25 is a schematic diagram illustrating an example of a feature line and a feature point extracted from a three-dimensional shape.
FIG. 26 is a schematic diagram showing shaping of a second mesh.
FIG. 27 is a perspective view showing a completed hexahedral mesh.
FIG. 28 is a perspective view showing an example of generating a hexahedral mesh by a mapping method.
FIG. 29 is a schematic diagram two-dimensionally illustrating an example of generating a hexahedral mesh by the voxel method.
FIG. 30 is a perspective view showing a problem of the mapping method.
FIG. 31 is a schematic diagram for explaining a problem of the voxel method in two dimensions.
[Explanation of symbols]
1. Hexahedral mesh generation device (analysis device for deformation of three-dimensional objects)
11 CPU (arithmetic unit)
12 RAM (storage unit)
2 Recording media
20 Computer programs
P solid shape
BM Block mesh
M1 1st mesh
M2 2nd mesh
M hexahedral mesh

Claims

In a method of generating a hexahedral mesh that expresses the shape of a three-dimensional object by a combination of a plurality of hexahedral elements using a computer including a storage unit and an arithmetic unit,
A shape model defining the shape of the three-dimensional object is stored in the storage unit,
A first mesh in which a combination of a plurality of hexahedral elements is filled in a three-dimensional shape represented by a shape model stored in a storage unit is generated by an arithmetic unit,
A second mesh in which a plurality of hexahedral elements including nodes located on the surface of the generated first mesh and nodes located on the surface of the three-dimensional shape are added to the first mesh is generated by an arithmetic unit;
On a surface of the three-dimensional shape, a feature line and a feature point characterizing the three-dimensional shape are extracted by an arithmetic unit,
A hexahedral mesh in which a calculation unit generates a hexahedral mesh in which a node located near the feature line or the feature point on the surface of the second mesh is moved to a position on the feature line or a position of the feature point. Generation method.

Using a computer equipped with a storage unit and a calculation unit, using a hexahedral mesh to represent the shape of the three-dimensional object by a combination of a plurality of hexahedral elements, in the method of analyzing the deformation of the three-dimensional object,
Using the hexahedral mesh generation method according to claim 1, a hexahedral mesh that expresses the shape of the three-dimensional object to be analyzed by a combination of a plurality of hexahedral elements is generated by an arithmetic unit and stored in a storage unit,
Performing a calculation to analyze the deformation of the three-dimensional object by deforming the generated hexahedral mesh in the arithmetic unit,
Each time the calculation proceeds to a predetermined stage, the arithmetic unit determines whether or not a collapsed element has occurred in a plurality of hexahedral elements constituting the deformed hexahedral mesh,
If a collapse element has occurred, the calculation is interrupted, and a shape model that defines the shape of the hexahedral mesh is stored in a storage unit.
From the stored shape model, using the hexahedral mesh generation method according to claim 1, a new hexahedral mesh representing the three-dimensional object being deformed is generated by the calculation unit and stored in the storage unit,
A method for analyzing deformation of a three-dimensional object, wherein the calculation is restarted by a calculation unit using the generated new hexahedral mesh.

In a device that generates a hexahedral mesh that represents the shape of a three-dimensional object by combining a plurality of hexahedral elements,
First mesh generation means for generating a first mesh filled with a combination of a plurality of hexahedral elements inside a three-dimensional shape represented by a shape model defining a shape of a three-dimensional object;
Second mesh generation means for generating a second mesh obtained by adding a plurality of hexahedral elements including nodes located on the surface of the generated first mesh and nodes located on the surface of the three-dimensional shape to the first mesh;
Extracting means for extracting a characteristic line and a characteristic point characterizing the three-dimensional shape on a surface of the three-dimensional shape,
Moving means for generating a hexahedral mesh in which nodes located in the vicinity of the feature line or feature point on the surface of the second mesh are moved to positions on the feature line or positions of the feature points. Mesh generator.

The extracting means,
On the surface of the three-dimensional shape, a means for extracting a boundary line of the gradient in which the gradient of the surface is greater than or equal to a predetermined value as a characteristic line,
Means for extracting a change in the direction of the extracted feature line by a predetermined value or more, and means for extracting an end point of the feature line as a feature point,
The moving means,
Means for extracting a first node which is a node located at the shortest distance from the extracted feature point on the surface of the second mesh;
A second node, which is a plurality of nodes through which the first nodes related to each of the adjacent feature points on the same feature line are connected at the shortest distance along the element side of the surface of the second mesh, is extracted. Means,
Means for moving the first node to the position of the feature point;
4. The hexahedral mesh generation apparatus according to claim 3, further comprising: means for moving each of the second nodes to a point located at the shortest distance from each of the second nodes on the characteristic line.

The three-dimensional object is a three-dimensional object molded by a mold,
The first mesh generation means includes:
Means for creating a hexahedral block including the three-dimensional shape,
The created hexahedral block is divided into a three-dimensional lattice at a predetermined number of divisions or a predetermined division interval, and a means for generating a block-shaped mesh expressed by combining the hexahedral block with a plurality of hexahedral elements,
Means for arranging a mold shape model representing the shape of the mold at a predetermined distance from the generated block-shaped mesh,
In the molding step, the nodes are moved along the direction at which the mold moves along the direction in which the mold should move along the direction at a predetermined rate of movement with respect to the distance between the nodes on the surface of the block-shaped mesh and the mold shape model. Means,
Means for moving nodes inside the block mesh to preserve a ratio of distances between the plurality of nodes included in the block mesh along the direction,
Means for determining whether or not each of the nodes included in the block-shaped mesh whose nodes have been moved is located inside the three-dimensional shape,
The hexahedral mesh generation device according to claim 3, further comprising: a unit configured to remove a hexahedral element including a node determined not to be located inside the three-dimensional shape.

The second mesh generation means includes:
Means for selecting one node on the surface of the first mesh;
Means for generating a first vector by averaging respective normal vectors of a plurality of element surfaces including the selected node;
Means for generating a second vector that is a direction vector of a perpendicular extending from the node to the surface of the three-dimensional shape;
Synthesizing means for generating a synthesized vector obtained by synthesizing the first vector and the second vector at a predetermined synthesis ratio according to the position of the node;
Means for generating a new node at the intersection of a line extending from the node in the direction of the generated composite vector and the surface of the three-dimensional shape,
Means for generating a corresponding new node for each node on the surface of the first mesh;
An element side on the surface of the first mesh, an element side connecting new nodes corresponding to nodes at both ends of the element side, and a node on the surface of the first mesh and a new node corresponding to the node. The hexahedral mesh generation apparatus according to any one of claims 3 to 5, further comprising: a unit for adding a plurality of hexahedral elements composed of element sides connecting the nodes to the first mesh.

The combining means includes:
Means for measuring the distance along the direction of the first vector from the selected node to the surface of the three-dimensional shape;
Means for comparing the measured distance with a predetermined value,
Means for setting the first vector as a composite vector when the distance is smaller than a predetermined value;
7. The hexahedral mesh generation device according to claim 6, further comprising: when the distance is equal to or more than a predetermined value, using a second vector as a composite vector. 8.

In a device for analyzing the deformation of the three-dimensional object, using a hexahedral mesh expressing the shape of the three-dimensional object by a combination of a plurality of hexahedral elements,
A hexahedral mesh generation device according to any one of claims 3 to 7,
Means for generating a hexahedral mesh that represents the shape of the three-dimensional object by a combination of a plurality of hexahedral elements, from the shape model that defines the shape of the three-dimensional object to be analyzed, using the hexahedral mesh generation device;
Means for performing a calculation to analyze the deformation of the three-dimensional object by deforming the generated hexahedral mesh,
Each time the calculation proceeds to a predetermined stage, means for determining whether or not a collapsed element has occurred in a plurality of hexahedral elements constituting the deformed hexahedral mesh,
In the case where a collapse element has occurred, the calculation is interrupted, and a means for storing a new shape model defining the shape of the hexahedral mesh,
Using the hexahedral mesh generation device, from the stored new shape model, a means for generating a new hexahedral mesh representing the shape of the three-dimensional object in the middle of deformation,
Means for resuming the calculation using the generated new hexahedral mesh.

In a computer program that causes a computer to generate a hexahedral mesh that expresses the shape of a three-dimensional object by a combination of a plurality of hexahedral elements,
A first mesh generation procedure for causing a computer to generate a first mesh filled with a combination of a plurality of hexahedral elements inside a three-dimensional shape represented by a shape model defining a shape of a three-dimensional object;
A second mesh generation step for causing a computer to generate a second mesh in which a plurality of hexahedral elements including nodes located on the surface of the generated first mesh and nodes located on the surface of the three-dimensional shape are added to the first mesh; ,
An extraction procedure for causing a computer to extract feature lines and feature points characterizing the three-dimensional shape on the surface of the three-dimensional shape,
A computer generating a hexahedral mesh in which a node located on the surface of the second mesh in the vicinity of the characteristic line or the characteristic point is moved to a position on the characteristic line or a position of the characteristic point. And a computer program.

The extraction procedure includes:
A step of causing a computer to extract, as a characteristic line, a boundary line of the gradient on which the change in the gradient of the surface is equal to or more than a predetermined value, on the surface of the three-dimensional shape;
Including a step of causing the computer to extract a point where the change in the direction of the extracted feature line is equal to or greater than a predetermined value, and an end point of the feature line as a feature point,
The moving procedure includes:
Causing the computer to extract, on the surface of the second mesh, a first node which is a node located at the shortest distance from the extracted feature point;
A second node, which is a plurality of nodes that pass through the computer when the first nodes related to each of the adjacent feature points on the same feature line are connected at the shortest distance along the element side of the surface of the second mesh. To extract the
Moving the first node to the position of the feature point by the computer;
10. The computer program according to claim 9, further comprising the step of: causing the computer to move each of the second nodes to a point located at a shortest distance from each of the second nodes on the characteristic line.

The first mesh generation procedure includes:
A procedure for causing a computer to create a hexahedral block including the three-dimensional shape,
A procedure for causing the computer to divide the created hexahedral block into a predetermined number of divisions or a three-dimensional lattice at a predetermined division interval, and to generate a block-shaped mesh in which the hexahedral block is represented by a combination of a plurality of hexahedral elements. ,
A procedure for causing a computer to arrange a mold shape model representing a shape of a mold for molding the three-dimensional object at a predetermined distance from the generated block-shaped mesh,
In a computer, at a predetermined moving rate with respect to a distance between a node on the surface of the block-shaped mesh and a mold shape model along a direction in which the mold should move in a molding process, the node along the direction is provided. To move the
Moving a node inside the block mesh to a computer to store a ratio of a distance between the plurality of nodes included in the block mesh along the direction;
A procedure for causing the computer to determine whether each of the nodes included in the block-shaped mesh whose nodes have been moved is located within the three-dimensional shape,
11. The computer program according to claim 9, further comprising: causing a computer to remove a hexahedral element including a node determined not to be located inside the three-dimensional shape.

The second mesh generation procedure includes:
Causing the computer to select one node on the surface of the first mesh;
Causing the computer to generate a first vector by averaging respective normal vectors of the plurality of element surfaces including the selected node;
Causing the computer to generate a second vector that is a direction vector of a perpendicular extending from the node to the surface of the three-dimensional shape;
A synthesizing procedure for causing a computer to generate a synthesized vector obtained by synthesizing the first vector and the second vector at a predetermined synthesis ratio according to the position of the node;
A procedure for causing a computer to generate a new node at an intersection of a line extending from the node in the direction of the generated composite vector and the surface of the three-dimensional shape,
Causing the computer to generate, for each node on the surface of the first mesh, a corresponding new node;
The computer informs the element side on the surface of the first mesh, the element side connecting new nodes corresponding to the nodes at both ends of the element side, and the nodes on the surface of the first mesh and the nodes. 12. A computer program according to claim 9, further comprising: adding a plurality of hexahedral elements formed of element sides connecting new nodes to the first mesh.

The synthesis procedure comprises:
Causing the computer to measure a distance along a first vector direction from the selected node to the surface of the three-dimensional shape;
Causing the computer to compare the measured distance with a predetermined value;
Causing the computer to make the first vector a composite vector if the distance is smaller than a predetermined value;
13. The computer program according to claim 12, further comprising: when the distance is equal to or greater than a predetermined value, causing the computer to convert the second vector into a composite vector.

A computer program that causes a computer to analyze the deformation of the three-dimensional object using a hexahedral mesh expressing the shape of the three-dimensional object by a combination of a plurality of hexahedral elements,
Using a computer program according to any one of claims 9 to 13 to a computer, the shape of the three-dimensional object is represented by a combination of a plurality of hexahedral elements from a shape model that defines the shape of the three-dimensional object to be analyzed. A procedure for generating a hexahedral mesh,
A procedure for causing a computer to perform a calculation for deforming the generated hexahedral mesh and analyzing the deformation of the three-dimensional object,
A procedure for causing the computer to determine whether or not a collapsed element has occurred in a plurality of hexahedral elements constituting the deformed hexahedral mesh each time the calculation proceeds to a predetermined stage,
Computer, if a collapse element has occurred, suspending the calculation, a procedure for storing a new shape model that defines the shape of the hexahedral mesh,
A step of causing a computer to generate a new hexahedral mesh representing the shape of the three-dimensional object being deformed from the stored new shape model, using the computer program according to any one of claims 9 to 13;
Causing the computer to restart the calculation using the generated new hexahedral mesh.

In a computer-readable recording medium that stores a computer program that causes a computer to generate a hexahedral mesh that expresses the shape of a three-dimensional object by combining a plurality of hexahedral elements,
A first mesh generation procedure for causing a computer to generate a first mesh filled with a combination of a plurality of hexahedral elements inside a three-dimensional shape represented by a shape model defining a shape of a three-dimensional object;
A second mesh generation step for causing a computer to generate a second mesh in which a plurality of hexahedral elements including nodes located on the surface of the generated first mesh and nodes located on the surface of the three-dimensional shape are added to the first mesh; ,
An extraction procedure for causing a computer to extract feature lines and feature points characterizing the three-dimensional shape on the surface of the three-dimensional shape,
A computer generating a hexahedral mesh by moving a node located near the feature line or the feature point on the surface of the second mesh to a position on the feature line or a position of the feature point. A recording medium readable by a computer, characterized by being recorded.

Computer, using a hexahedral mesh expressing the shape of the three-dimensional object by a combination of a plurality of hexahedral elements, in a computer-readable recording medium that has recorded a computer program that analyzes the deformation of the three-dimensional object,
Using a computer program according to any one of claims 9 to 13 to a computer, the shape of the three-dimensional object is represented by a combination of a plurality of hexahedral elements from a shape model that defines the shape of the three-dimensional object to be analyzed. A procedure for generating a hexahedral mesh,
A procedure for causing a computer to perform a calculation for deforming the generated hexahedral mesh and analyzing the deformation of the three-dimensional object,
A procedure for causing the computer to determine whether or not a collapsed element has occurred in a plurality of hexahedral elements constituting the deformed hexahedral mesh each time the calculation proceeds to a predetermined stage,
Computer, if a collapse element has occurred, suspending the calculation, a procedure for storing a new shape model that defines the shape of the hexahedral mesh,
A step of causing a computer to generate a new hexahedral mesh representing the shape of the three-dimensional object being deformed from the stored new shape model, using the computer program according to any one of claims 9 to 13;
A computer-readable recording medium characterized by recording a computer program including a step of restarting the calculation using a newly generated hexahedral mesh in a computer.