Interaction between snap-through and Eulerian instability in shallow structures

The multifold nature of structural instability problems necessitates a number of different kinds of analytical and numerical approaches. Furthermore, instability collapses of large-span roof sensitized the global community to reduce the effects of geometrical imperfections, then some limiting recommendations have been recently proposed. This study provides new insights into the interaction between the two different categories of structural instability and, for the first time, a unified theoretical evaluation of the critical load due to interaction is proposed. The snap-through phenomenon of 2D Von Mises arches was investigated by an incremental-displacement nonlinear analysis. At the same time, the equilibrium paths were considered in relation to the Eulerian buckling loads for the same structural systems. For each structural scheme the effect of the two governing parameters was investigated: slenderness and shallowness ratios. For these purposes, several original theoretical and numerical snap-through versus buckling interaction curves were obtained. These curves provide indications about the prevailing collapse mechanism with regards to the geometric configuration of the structure. Consequently, this innovative method is able to predict the actual instability of a wide range of mechanical systems. With this approach, it is possible also to establish the connection between the magnitude of structural imperfections (defects) and instability behavior. The proposed procedure is able to provide the effective critical load given by the interaction effect and to correlate the instability behavior to the maximum tolerable imperfection sizes.