Summary
An aid to the solution of the displacement equations of motion in the linear theory of homogeneous and isotropic elastic solids is the decomposition of the displacement field into a rotational and irrotational part, the so-calledLamé scalar and vector potentials. Previous works have required the vector potential to be divergence free in order to insure completeness of this representation of the displacement field. The purpose of the present paper is to broaden the class of functions that define displacement fields that are complete to include all displacement fields defined in terms of theLamé potentials, requiring only that theLamé potentials satisfy the two wave equations resulting from the displacement equations of motion.
Zusammenfassung
Bei der Lösung derNavierschen Bewegungsgleichungen der linearen Theorie homogener und isotroper elastischer Körper wird gewöhnlich die Aufspaltung des Verschiebungsfeldes in einen drehungsfreien Anteil und einen Drehungsanteil, die sogenanntenLaméschen Skalar- und Vektorpotentiale, benützt. Frühere Arbeiten verlangten die Quellfreiheit des Vektorpotentials, um die Vollständigkeit dieser Darstellung des Verschiebungsfeldes sicherzustellen. Zweck der vorliegenden Arbeit ist, die Klasse der imLaméschen Sinne vollständigen Verschiebungsfunktionen zu erweitern, wobei nur verlangt wird, daß dieLaméschen Potentiale die beiden aus den Bewegungsgleichungen folgenden Wellengleichungen befriedigen.
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Long, C.F. On the completeness of theLamé potentials. Acta Mechanica 3, 371–375 (1967). https://doi.org/10.1007/BF01181496
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DOI: https://doi.org/10.1007/BF01181496