有限な変形弾性に対する境界コンフォーム四角形による浸水同ジオメトリック解析
Yusuf T Elbadry1, Pablo Antolín2, Oliver Weeger1
1Cyber-Physical Simulation, Department of Mechanical Engineering and Graduate School Computational Engineering, Technical University of Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany.
Archive of applied mechanics = Ingenieur-Archiv
|September 3, 2025
まとめ
この研究は,効率的な数値シミュレーションのための境界コンフォーム四角化によるスプラインベースの浸透型同位幾何分析を導入します. この方法は,複雑な幾何学と非線形弾性問題を最小限の計算コストで正確に処理します.
科学分野:
- 計算力学
- 数値分析
- 固体力学
背景:
- 複雑な幾何学の数値シミュレーションは,メッシングのために計算的に高価です.
- 浸透した境界と架空のドメインの方法は,カルテシアングリッドを使用しますが,切断されたセル統合の精度で苦労します.
- 非線形的な問題は,カット・セル・メソッドの精度と堅固さの問題を悪化させる.
研究 の 目的:
- 複雑な幾何学を持つ小規模および大規模な変形弾性問題をシミュレートするための効率的で正確な数学的方法を開発する.
- 切り取られた要素の処理における従来の浸水およびカットセル方法の限界を克服する.
- 境界コンフォーム四角形によるスプラインベースの浸透型同地測量分析を導入する.
主な方法:
- 体型適合の有限要素メッシュの必要性を排除するスプラインベースの浸透型同ジオメトリック分析を使用した.
- トリムした要素の境界コンフォーム四角形のために高次元のB-spline再パラメータ化を使用した.
- 正確な統合のために再パラメータ化された切断要素に古典的なガウス二乗法を適用した.
主要な成果:
- 2D 線形および非線形弾性問題における h と k 精度における最適な収束率を達成した.
- 罰則と変形マップのリセットと組み合わせると,有限な変形の問題に対する堅実性が実証されています.
- 大変変形状態での微細構造材料の多スケール均質化への適用性を示した.
結論:
- 提案された境界コンフォーム四角形による浸透型同地測量分析は,複雑な幾何学シミュレーションに高い効率と精度を提供します.
- この方法は,大きな変形を含む線形と非線形の弾性の両方をしっかりと処理します.
- マルチスケール材料分析などの高度なアプリケーションのための多用途のフレームワークを提供します.
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