Summary
The paper presents an analytic solution for the stresses in a thick plate of infinite size containing a spherical inclusion or cavity eccentrically located between the surfaces. The plate is subject to a stress system symmetrical about the axis of revolution of the plate while the surfaces are stress-free. In the inclusion problem, the inclusion is assumed to be rigid and no slip occurs between the plate, and inclusion. In the cavity problem, the surface of cavity is assumed to be stress-free. The solutions of both problems are illustrated by numerical examples for the cases of all-round tension and circular bending.
Part I of the paper presents the solution of the cavity problem.
Zusammenfassung
Die Arbeit behandelt die analytische Bestimmung der Spannungen in einer unbegrenzten dicken Platte mit einem außermittig gelegenen sphärischen Einschluß oder einer sphärischen Höhlung. Die Platte wird durch Spannungen, die symmetrisch bezüglich ihrer Drehachse liegen, beansprucht. Die beiden Begrenzungsflächen der Platte sind spannungsfrei. Der Einschluß wird starr angenommen; Gleiten zwischen Einschluß und Platte soll nicht auftreten. Die Oberfläche der Höhlung sei spannungsfrei. Als numerische, Beispiele für beide Probleme werden allseitiger Zug und Biegung gerechnet.
Der erste Teil der Arbeit bringt die Lösung des Höhlungsproblems.
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Ling, CB., Tsai, CP. Stresses in a thick plate containing an eccentric spherical inclusion or cavity Part I. Acta Mechanica 7, 169–186 (1969). https://doi.org/10.1007/BF01176666
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DOI: https://doi.org/10.1007/BF01176666