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A stress boundary value problem for an ideal fibre-reinforced rectangular beam with a longitudinal notch

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Summary

The title problem is examined for a cross-section of an ideal fibre-reinforced rectangular beam with a symmetrical longitudinal notch, undergoing uniform tension. Using the ideal theory the displacement and stress fields are found to depend upon a single integral, which can be evaluated easily for the cases of a V-shaped notch and a line crack. It is anticipated that these solutions will be useful approximations to the corresponding results for similar highly anisotropic components. Simple fracture criteria are used to predict the possible modes of failure of these components.

Zusammenfassung

Das im Titel angezeigte Problem wird erörtert anhand eines idealen faserverstärkten rechteckigen Balkens mit einer symmetrsichen Längskerbe bei gleichmäßiger Spannung. Unter Verwendung der idealen Theorie stellt es sich heraus, daß die Verschiebungs- und Druckfelder von einem einzigen Integral abhängig sind, das für die Fälle, einer V-förmigen Kerbe und eines Linienrisses leicht zu berechnen ist. Voraussichtlich liefern diese Lösungen nützliche Annäherungen an die entsprechenden Ergebnisse bei ähnlich hoch anisotropischen Komponenten. Einfache Bruchkriterien werden verwendet, um die möglichen Arten des Versagens dieser Komponenten vorauszusagen.

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Authors and Affiliations

  1. Dept. of Theoretical Mechanics, University of Nottingham, UK

    James N. Thomas

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  1. James N. Thomas
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Thomas, J.N. A stress boundary value problem for an ideal fibre-reinforced rectangular beam with a longitudinal notch. Journal of Applied Mathematics and Physics (ZAMP) 25, 553–563 (1974). https://doi.org/10.1007/BF01596118

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  • DOI: https://doi.org/10.1007/BF01596118

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