Summary
The deformations of a simply supported rectangular plate are calculated when a uniaxial inplane compressive load is applied to it by means of a rigid platen of a testing machine. This kind of loading enforces a uniform in-plane displacement of the loaded edge and has the consequence that the distribution of the load along the edge becomes increasingly nonuniform as the buckling of the plate becomes more pronounced. The equilibrium, constitutive and compatibility equations are written for a material that deforms elastically and in consequence of steady-state creep but the numerical solution is given for a material that can deform only because of creep. The solution shows that the critical time of the simpler theory in which the load is distributed uniformly does not exist in the case treated here. Nevertheless the critical time is a good indicator of danger because the deformations of the plate increase much more rapidly after the critical time than before.
Übersicht
Es werden die Deformationen einer einfach gelagerten rechteckigen Platte berechnet, die über den starren Balken einer Prüfmaschine auf einachsigen Druck in der Plattenebene belastet wird. Der belastete Rand erleidet dabei eine gleichmäßige Verschiebung, jedoch wird die Lastverteilung längs dieses Randes um so ungleichförmiger, je mehr die Platte ausbeult. Zustandsgleichungen und die Bedingungen für Gleichgewicht und Verträglichkeit werden für elastisch verformbares und stationär kriechendes Material aufgestellt, wobei die numerische Lösung nur für den letztgenannten Fall angegeben wird. Die Ergebnisse zeigen, daß im vorliegenden Fall die kritische Zeit der einfachen Theorie, bei der eine gleichförmige Lastverteilung angenommen wird, nicht existiert. Dennoch ist die kritische Zeit ein gutes Gefahren-Kriterium, weil die Deformationen der Platte nach der kritischen Zeit erheblich rascher anwachsen als davor.
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Dedicated to Professor Dr. H. Görtier on the occasion of his 60th birthday.
The work reported here was carried out under Contract AF 33 (615) 5115 awarded to Stanford University by the Air Force Flight Dynamics Laboratory at Wright-Patterson Air Force Base, Ohio.
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Levi, I.M., Hoff, N.J. The postcritical behavior of compressed plates that creep. Ing. arch 38, 329–342 (1969). https://doi.org/10.1007/BF00536175
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DOI: https://doi.org/10.1007/BF00536175