Summary
This paper proposes to use Helmholtz's representation of displacement component for the formulation of flat plates in extension. This is an alternative formulation equivalent to the classical formulation using Airy's stress function. On the other hand, by means of Southwell's analogies, it is possible to introduce some new quantities called stress-function potentials which lead to an another alternative formulation of flat plates in flexure. Some simple examples for stretching and bending case illustrate the merits of the above mentioned formulation.
Übersicht
Zur Bestimmung des ebenen Spannungszustandes elastischer Medien wird die von Hehnholtz angegebene Darstellung verwendet, die eine Alternative zum üblichen Vorgehen unter Verwendung der Airyschen Spannungsfunktion bietet. Unter Verwendung der Southwellschen Analogie lassen sich als neue Größen die „Potentiale der Spannungsfunktionen” einführen, so daß eine Theorie der Plattenbiegung ähnlich wie die von Lagrange und Kirchhoff gewonnen wird. Das wird an einigen einfachen Beispielen erläutert.
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The author is grateful to Professor Ch. Massonet for his interest and encouregement during the course of this work.
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Dang Hung, N. Displacement potentials for membranes in stretching and stress-function potentials for plates in bending. Ing. arch 45, 41–53 (1976). https://doi.org/10.1007/BF00534245
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DOI: https://doi.org/10.1007/BF00534245