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On the use of special crack tip elements in cracked elastic sheets

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Abstract

This paper presents a finite element method for determining the stress intensity factor in a cracked elastic sheet. Special cracked elements are placed around each crack tip; in each special element the stresses and displacements are derived from the exact stress function while the continuity of the displacements at the nodes is satisfied in a least square sense. A general procedure for evaluating the stiffness matrix of a cracked isotropic, or orthotropic, element is presented, and the numerical results obtained are compared with exact analytical results.

Résumé

Le mémoire présente une méthode par éléments finis pour déterminer le facteur d'intensité de contrainte dans un feuillard élastique fissuré. Des éléments spéciaux, présentant des fissures, sont disposés autour de chaque extrémité de fissures. Dans chacun de ces éléments spéciaux, les contraintes et les déplacements sont déduits de la fonction exacte d'une contrainte tandis que la continuité des déplacements aux noeuds satisfait à une règle des moindres carrés. Une procédure générale pour l'évaluation de la matrice de rigidité d'un élément fissuré à caractère isotrope ou orthotrope est présentée, et les résultats numériques obtenus sont comparés avec les résultats analytiques exacts.

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Authors and Affiliations

  1. Dept. of Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa

    R. Jones

  2. Dept. of Structures Theory, Aeronautical Research Laboratories, Melbourne, Victoria, Australia

    R. J. Callinan

Authors
  1. R. Jones
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  2. R. J. Callinan
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Jones, R., Callinan, R.J. On the use of special crack tip elements in cracked elastic sheets. Int J Fract 13, 51–64 (1977). https://doi.org/10.1007/BF00040875

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  • DOI: https://doi.org/10.1007/BF00040875

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