等方性弾性マトリックス中の任意の形状を持つ圧縮性液体介在物
Romina Ardeshiri Jouneghani1, Xu Wang2, Peter Schiavone1
1Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada.
まとめ
本研究では、複素変数を用いて弾性材料中の液体介在物の平面ひずみ問題を解く。この手法は、任意の形状の内部応力場を決定し、仮面線形および長方形の例で検証されている。
科学分野:
- 固体力学
- 連続体力学
- 数理物理学
背景:
- 介在物を含む弾性材料中の応力分布の理解は、材料科学および工学にとって重要である。
- 複素変数法は、弾性論における境界値問題の解決のための強力なツールを提供する。
研究 の 目的:
- 無限弾性マトリックス中の圧縮性液体介在物の平面ひずみ問題の解析のための一般的方法を開発すること。
- 任意の形状の介在物に対する内部静水圧応力および外部弾性場を決定すること。
主な方法:
- ムシュケリシヴィリの複素変数定式化を利用すること。
- 介在物領域を単位円に変換するために等角写像を用いること。
- 解析接続の修正技術を適用して線形代数方程式を導出すること。
主要な成果:
- らせん状液体介在物に対する閉形式解を導出した。
- n重対称介在物に対する数値結果は、写像関数項の影響を示した。
- 様々なアスペクト比を持つ長方形介在物に対する内部静水圧応力を決定した。
結論:
- 複素変数アプローチは、液体介在物を含む応力問題の解決のための堅牢なフレームワークを提供する。
- この方法は、様々な介在物の形状や対称性に適用可能な汎用性がある。
- 正確な応力場決定は、荷重下での材料挙動の予測に不可欠である。
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