A dynamic view of static instabilities
The implementation of a dynamic view of static stability is followed from concept to computer simulation in this work. The static view of (buckling) instabilities considers the structure under monotonic loading, and when the load reaches a critical value it displaces instantaneously to a new configuration. This new configuration could be another equilibrium state or it could be a collapsed state. The dynamic view makes two changes. First the independent variable is considered to be time—all variables, including the load are functions of time. Second, the complete state vector—both velocity and displacement—is monitored. The idea of stability is that if at some stage of the loading a small disturbance is given to the structure and the structure returns to the current loading path, then it is stable. At a critical point, however, a small disturbance (or a change in the load itself) will cause a dynamic process to ensue. Depending on the particular problem, a new equilibrium position may or may not be found. It is worth noting that if a new equilibrium position is found, it is not necessarily statically connected to the original equilibrium path; that is, we could not devise a proportional loading sequence (where the ratio of all the loads is kept constant) to connect the two equilibrium states. The analytical foundation for the view is developed based on a modal analysis of the non-linear dynamics of a general system. An example using a simple structure with an analytical solution is used to vet the view proposed in the theory. To determine the analysis tools needed to capture stability phenomenon two carefully chosen experimental set-ups are explored. ^
Major Professor: Graham C. Archer, Purdue University.