Summary
After a brief review on a theory of stress and stress functions in three-dimensional elastostatics, the author attempts to extend his consideration into the problem of elastodynamics. The stress is represented by the Riemann-Christoffel curvature tensor of a four-dimensional Riemannian space having the stress functions as the components of its metric tensor. From this basic recognition, a representation for stresses by ten stress functions is given. As one of the special cases, the expression for the stress the author used in the analysis of stress fields by moving dislocations is derived. Elementary expressions of the forms which are extensions of Morera's and Maxwell's stress functions are also derived from the general principle.
Zusammenfassung
Nach einem kurzen Überblick über die Theorie der Spannungsfunktionen in der dreidimensionalen Elastostatik werden die Überlegungen auf Probleme der Elastodynamik erweitert. Das Tensorfeld der Spannungen wird mit Hilfe des Krümmungstensors eines vierdimensionalen Riemannschen Raumes beschrieben, in welchem die Komponenten des Maßtensors als Spannungsfunktionen verwendet werden. Als Sonderfälle erhält man die Darstellung des Spannungsfeldes in Nähe bewegter Versetzungen und die Erweiterungen der Moreraschen und Maxwellschen Spannungsfunktionen.
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Minagawa, S. On the stress functions in elastodynamics. Acta Mechanica 24, 209–217 (1976). https://doi.org/10.1007/BF01190371
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DOI: https://doi.org/10.1007/BF01190371