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Study of geometric non-linear instability of 2D frame structures. (English) Zbl 1344.74032
Summary: In this work, we deal with the geometric instability problem of the two-dimensional (2D) elastic frame structures undergoing large overall motion. The geometrically exact beam model with total Lagrangian formulation is used to obtain the solution to non-linear instability problems with large pre-buckling displacements. We propose, in particular, a study of dynamic analysis that can deal with instability problems of this kind with no need for any load decrease. The dynamics approach provides a more realistic post-buckling behaviour for the case of snap-through or snap-back. The material damping is necessary when a classical time integration scheme like Newmark is used. The principal novelty in this work is to consider non-linear damping to avoid the vibration around the equilibrium point when a classical scheme as Newark is used. The efficiency of the damping model and methodology analysis are illustrated by a number of numerical simulations.
74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics
74H55 Stability of dynamical problems in solid mechanics
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