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Three-dimensional elastic stress and displacement analysis of finite geometry solids containing cracks

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Abstract

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement distributions in various bodies containing cracks. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. When decoupling the equations and their boundary conditions is not possible, the use of a successive approximation procedure permits the analytical solution of the resulting ordinary differential equations. The results obtained show a considerable potential for using this method in the three-dimensional analysis of finite geometry solids and suggest a possible extension of this technique to nonlinear material behavior.

Résumé

On applique la méthode d'analyse par lignes aux équations d'équilibre élastique de Navier-Cauchy pour calculer la distribution des déplacements dans divers corps comportant des fissures.

L'application de la méthode à ces équations conduit à des couples d'équations différentielles ordinaires, dont les solutions sont obtenues pour des séries de lignes disposées dans une région discrète. Lorsqu'il n'est pas possible de découpler les équations et leurs conditions aux limites, le recours à une procédure d'approximation successive permet de trouver une solution analytique aux équations différentielles ordinaires.

Les résultats obtenus montrent les possibilités remarquables de l'emploi de la méthode pour l'analyse tridimensionnelle de solides à géométrie finie, et suggèrent des extensions possibles à l'étude du comportement des matériaux non linéaires.

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Authors and Affiliations

  1. Lewis Research Center, 44135, Cleveland, Ohio, USA

    John P. Gyekenyesi & Alexander Mendelson

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  1. John P. Gyekenyesi
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  2. Alexander Mendelson
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Gyekenyesi, J.P., Mendelson, A. Three-dimensional elastic stress and displacement analysis of finite geometry solids containing cracks. Int J Fract 11, 409–429 (1975). https://doi.org/10.1007/BF00033528

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  • DOI: https://doi.org/10.1007/BF00033528

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