Summary
In the first part of the paper an energy-consistent model for thick, elastic, isotropic plates based upon Jemielita's kinematical hypothesis is proposed. Since no assumptions on stresses are stipulated the model is free of the usual discrepancy between stress and displacement fields, viz. no one of the constitutive equations being violated. The objective of the second part of the paper is to perform a passage from the model obtained to the simplified one which is energy-inconsistent. This latter model proves far-reaching similarities to the first Reissner theory and, on the other hand, when an appropriate change of the function standing for the averaged plate deflection is made, — to the Kelkel's considerations.
Übersicht
Im ersten Teil der Arbeit wird ein energetisch konsequentes Modell einer dicken, isotropen Platte vorgeschlagen. Das Modell wird auf der Jemielita's kinematischen Hypothese gegründet. Da keine Voraussetzungen hinsichtlich der Spannungen aufgezwungen werden, ist das Modell von den in der Regel entstehenden Widersprüchen zwischen dem Spannungs- und Verschiebungsfeld frei, d. h. keine von den Gleichungen des Hooke'schen Gesetzes wird verletzt. Das Ziel des zweiten Teiles der Arbeit ist ein Übergang von dem hergeleiteten Modell zum energetisch inkonsequenten Modell. Die Gleichungen, die das letzte Modell beschreiben, zeigen weitgehende Ähnlichkeiten entweder mit den Gleichungen der ersten Reissnerschen Theorie, oder — nach entsprechender Umgestaltung der Funktion, die die Plattendurchbiegung beschreibt — mit den Kelkels Gleichungen.
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Lewiński, T. On refined plate models based on kinematical assumptions. Ing. arch 57, 133–146 (1987). https://doi.org/10.1007/BF00541387
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DOI: https://doi.org/10.1007/BF00541387