Abstract
In standard stability investigations of structures applying the finite element method usually the bifurcation and snap-through points – so-called stability points – are detected. However, for practical design purposes not only the stable state of equilibrium itself is significant but also the robustness of the state against finite perturbations in contrast to infinitesimal perturbations. The sensitivity measure, which quantifies this robustness, can be investigated by introducing perturbations at certain load levels and considering the perturbed motion. Some sensitivity studies are performed for simple stability problems as well as for realistic structures (cylindrical shells) under different loading conditions. Further scalar parameters based on Liapunov Characteristic Exponents are developed to allow a better judgment of the motion after introducing perturbations and a more efficient analysis of the complex response (see Ewert/Schweizerhof[7]).
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Ewert, E., Schweizerhof, K. & Vielsack, P. Measures to judge the sensitivity of thin-walled shells concerning stability under different loading conditions. Comput Mech 37, 507–522 (2006). https://doi.org/10.1007/s00466-005-0733-y
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DOI: https://doi.org/10.1007/s00466-005-0733-y