Abstract
This paper deals with a procedure to calculate the elastic stress intensity factors for arbitrary-shaped cracks in plane stress and plane strain problems. An assumed displacement hybrid finite element model is employed wherein the unknowns in the final algebraic system of equations are the nodal displacements and the elastic stress intensity factors. Special elements, which contain proper singular displacement and stress fields, are used in a fixed region near the crack tip; and the interelement displacement compatibility is satisfied through the use of a Lagrangean multiplier technique. Numerical examples presented include: central as well as edge cracks in tension plates and a quarter-circular crack in a tension plate. Excellent correlations were obtained with available solutions in all the cases. A discussion on the convergence of the present solution is also included.
Résumé
Le mémoire a trait à une procédure pour le calcul des facteurs d'intensité des contraintes élastiques dans le cas de fissures de formes arbitraires soumises à état plan de tension ou de déformation. Un modèle de déplacements hypothétiques à éléments finis hybrides est utilisé, dans lequel les inconnues dans le système final d'équations algébriques sont les déplacements nodaux et les facteurs d'intensité des contraintes. Des éléments spéciaux, comportant leurs propres déplacements et champs de contraintes singuliers, sont utilisés dans une région déterminée voisine de l'extrémité de la fissure; la compatibilité de déplacement entre les éléments est satisfaite en recourant à la technique de multiplication d'un Lagrangien. Des exemples numériques sont présentés, notamment: fissures centrales ou de bord dans des tôles soumises à tension, fissure en quart de cercle dans une tôle tendue. D'excellentes corrélations ont été établies avec les solutions disponibles pour chaque cas traité. On procède également à une discussion sur la convergence de la solution proposée.
Zusammenfassung
Dieser Bericht behandelt ein Verfahren zur Rechnung der elastischen Spannungsintensitatsfaktoren von Rissen beliebiger Form in ebenen Spannungs- und ebenen Verformungsproblemen. Man benützt ein festgelegtes Verschiebungsmodell hybrider endlicher Elementen indem die Unbekannten im Endgleichungssystem die Knotenverschiebungen und die elastischen Spannungsintensitätsfaktoren sind. Besondere Elemente, die eigene singuläre Verschiebungen und Spannungsfelder enthalten, werden in einem festgelegten Gebiet an der Rißspitze benützt, und die Komptabilität der Verschiebungen zwischen Elementen werden durch ein Multiplikationsverfahren von Lagrange erfüllt. Die angegebene Rechenbeispiele enthalten: Mittel- sowohl als Randrisse in Platten unter Zugspannung, und ein Viertelkreisriß in einer Platte unter Zugspannung. Ausgezeichnete Korrelation ergab sich mit allen zur Verfügung stehenden Lösungen in allen Fällen. Die Konvergenz der angegebenen Lösung wird auch besprochen.
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This work was supported by the U.S. Air Force Office of Scientific Research, Grant AFOSR-73-2478.
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Atluri, S.N., Kobayashi, A.S. & Nakagaki, M. An assumed displacement hybrid finite element model for linear fracture mechanics. Int J Fract 11, 257–271 (1975). https://doi.org/10.1007/BF00038893
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DOI: https://doi.org/10.1007/BF00038893