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From:
Tomasz Kopecki (Rzeszów University of Technology, Faculty of Mechanical Engineering and Aeronautics, Rzeszów, Poland; e-mail: tkopecki@prz.edu.pl), “Chapter 8: Numerical Reproducing of a Bifurcation in the Stress Distribution Obtaining Process in Post-Critical Deformation States of Aircraft Load-Bearing Structures”, in the book, “Nonlinearity, Bifurcation and Chaos – Theory and Applications”, edited by Jan Awrejcewicz and Peter Hagedorn, ISBN 978-953-51-0816-0, October 21, 2012, DOI: 10.5772/48069
Kopecki's caption for this figure:
" Figure 2: Bifurcation points on a representative equilibrium path (u - representative geometric value, λ – control parameter related to load)."
Kopecki writes:
"In case of a large number of state parameters it is not possible at all to represent the character of bifurcation by applying a representative equilibrium path. Sometimes, changes of state parameters resulting from local bifurcation may show the lack of perceptible influence on the representative value, which results in non-occurrence of any characteristic points on the representative path. In general, however, these changes cause a temporary drop in the control parameter value (Figure 2)."
COMMENT: Often several successive and alternating nonlinear static and nonlinear dynamic finite element analyses are required to follow successive states of a nonlinearly deforming shell structure whenever the states of equilibrium at partiicular points on a load-deflection path change from stable to unstable and then back to stable, etc.
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