P. Helnwein, H.A. Mang:
"Der Blick über den Zaun - Lineare Stabilitätsuntersuchungen als Träger von Informationen über nichtlineares Strukturverhalten im Vorbeulbereich ";
Der Bauingenieur, 73 (1998), 5; 247 - 256.
``View over the fence" - on linear buckling analyses as a means for information on the nonlinear behavior of structures in the prebuckling domain
In engineering practice, determination of stability limits is usually based on the so-called second-order theory. It will be shown that this theory may yield significant overestimation of the critical load level related to snap-through. Moreover, based on von Karmán's theory, a strategy will be presented, leading to better estimations of stability limits at no significant additional computational costs. Possible errors and their reduction by means of the proposed strategy will be demonstrated and discussed in a comprehensive numerical study. The differential equations for a straight beam and a characteristic example for snap-through behavior serve as a vehicle for the explanation of the theoretical basis and of its consequences. The example shows the difference between the two theories used in this paper. Attention will be paid to the implementation of the proposed strategy into an existing program-code, permitting a view over the fence surrounding the linear theory.
Keywords: lineare Stabilitätsuntersuchung, Nichtlinearität, Strukturverhalten, Theorie 2. Ordnung, Knicken, Durchschlagen, konsistent linearisiertes Eigenw