Stability of statically and periodically loaded structures

In this thesis different kinds of stability phenomena are analysed. Firstly the quasi-static behaviour of an elastic structure is studied for increasing loading. The post-buckling behaviour is studied numerically with a path-following method where limit points and bifurcation points can be determined with good accuracy and the solutions may be followed out on the secondary branches. Secondly, an axially loaded beam, both when the deflection is unconstrained and when the transversal motion is limited by constraints. The beam is periodically loaded and the dynamic effects as well as the damping effects are taken into account for the analysis. The regions of stability in the loading parameter space are determined using Floquet theory and a finite element formulation for the unconstrained beam and this is verified experimentally.

The constrained system turns out to be very sensitive of initial conditions and chaotic motions are detected both in the numerical simulations and in the experiments. The modelling of the impacts and damping effects turns out to be crucial and great effort is made for developing numerical models where a good correspondence between experiments and computations is reached.