Summary
A problem in the linear theory of elasticity is considered wherein a layer with a circular cylindrical hole is subjected to a nonuniform axisymmetric radial displacement. The solution utilizes Navier's equations of elasticity which are sloved by means of extended Henkel transforms. A special case in which the readial displacement is a linear function of the axial coordinate is presented. Numerical results are given in graphical form for the case when hole radius and layer thickness are equal. The inversion integrals were evaluated numerically using Longman's technique for computing infinite integrals of oscillatory functions.
Zusammenfassung
Die Lösung des im Titel genannten Problem der linearen Elastizitätstheorie wird ausgehend von den Navierschen Gleichungen mit Hilfe von erweiterten Henkel-Transformationen gelöst. Eine Spezialfall (Radialverschiebung ist lineare Funktion der Axialkoordinate) wird erkläutert. Numerische Resultate des Falles bei dem Lochradius und Schichtdicke übereinstimmen werden in graphischer Form angegeben. Die Integrale der Rücktransformation werden numerisch, unter Verwendung der vonLongman angegebenen Methode zur Berechnung uneigentlicher Integrale oszillierender Funktionen ausgewertet.
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Grisson, D.S., Michalopoulos, C.D. The elastic layer with a cylindrical hole subjected to a nonuniform axisymmetric radial displacement. Acta Mechanica 17, 97–107 (1973). https://doi.org/10.1007/BF01260882
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DOI: https://doi.org/10.1007/BF01260882