Influence of the mechanics of escape on the instability of von Mises truss and its control. (2017) - Orlando, Diego; Gonçalves, Paulo B.; Lenci, Stefano; Rega, Giuseppe
Abstract: The elastic von Mises truss model is a prototype for bi-stable structures. It allows a deep understanding of the static and dynamic buckling of several planar and spatial truss systems and shallow lattice shell structures, including the geodesic dome, and has a theoretical and practical interest. This structure has a highly nonlinear response in the presence of static and dynamic loads. The geometric nonlinearity is particularly significant even at low load levels when this structure is shallow. This paper presents an exact nonlinear formulation, which is used to investigate the mechanics of erosion and escape from the safe pre-buckling well. As the static pre-load increases, the probability of escape increases in a nonlinear manner. Permanent and transient escapes, as well as the influence of random noise, on the dynamic buckling load are investigated. To increase the load carrying capacity, a method for controlling the global nonlinear dynamics for the elastic von Mises truss is employed. The control method consists of the (optimal) elimination of homoclinic intersection by properly adding superharmonic terms to a given harmonic excitation. Permanent and transient basins of attraction are obtained. The results highlight the complex nonlinear dynamics of this class of structures and the effectiveness of the control method in increasing the integrity of the basins of attraction of the system and its practical safety.