Mathematical and Numerical Analysis for a Curved Crack in Two-dimensional Elasticity

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  • 二次元曲線亀裂の数学解析と数値解析
  • 2ジゲン キョクセン キレツ ノ スウガク カイセキ ト スウチ カイセキ

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We deal with a problem of 2-dimensional elasticity with a curved crack and give mathematical analysis for the singularity of solutions at tips of the crack. The introduction of a weighted Sobolev space enables us to show the unique existence of a solution to the problem, and we give a mathematical proof for the asymptotic expansion of the solution. We give the definition, in the mathematical sense, of the stress intensity factors for a curved crack through our analysis. We also show error analysis for finite element solutions to the problem, and it leads us to numerical analysis based on mathematics for the stress intensity factors.

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