Summary
The problem of a plane inclusion where an oversized circular disk is contained inside a hole of an infinite plate was studied. Both the disk and plate are made of elastic and isotropic materials of different mechanical properties. The inclusion contains a certain number of thermal sources, and the contact between the inclusion and the plate is considered as thermally ideal. The complex potentials f (z), Φ 0(z) and Ψ 0(z) were derived under the form of Cauchy integrals which were used for defining the thermal and mechanical stress fields. For the particular case of the inclusion we have established a system of singular integral equations describing completely the problem. As an example we have examined the case of a circular inclusion where, under closed form, we have calculated the distribution of stresses and displacements, and, on the other hand, we have established an interesting analogy between the thermal and the purely mechanical problems.
Übersicht
Untersucht wird das Problem des Einschlusses einer Kreisscheibe mit Übermaß in einer unendlichen Platte mit Loch. Scheibe und Platte bestehen aus isotropem elastischem Werkstoff mit unterschiedlichen Materialkonstanten. Der Einschluß enthält eine bestimmte Anzahl von Wärmequellen und sein Kontakt mit der Platte wird als thermisch ideal angenommen. Die komplexen Potentiale f (z), Φ0(z) und Ψ 0(z), die die vollständige Beschreibung der mechanischen und thermischen Spannungsfelder erlauben, werden in der Form von Cauchy-Integralen hergeleitet. Für den speziellen Fall eines Einschlusses beschreibt ein System singulärer Integralgleichungen das Problem vollständig. Als Beispiel wird ein kreisförmiger Einschluß behandelt, für den die Spannungs- und Verschiebungsverteilung in geschlossener Form berechnet wird. Darüber hinaus wird eine interessante Analogie zwischen dem thermischen und rein mechanischen Problem aufgezeigt.
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Theocaris, P.S., Bardzokas, D. Affinities in contact stresses between thermal and mechanical problems for the inclusion-matrix stress field. Ing. arch 59, 445–455 (1989). https://doi.org/10.1007/BF00534311
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DOI: https://doi.org/10.1007/BF00534311