Instability phenomena and their control in statics and dynamics: Application to deep and shallow truss and frame structures

In this paper we study the control for nonlinear geometric instability problem of a deep or a shallow truss or yet a frame structure. All the structural models are built with geometrically exact truss and beam finite elements. The proposed models can successfully handle large overall motion under static or dynamic conservative load. The control strategy considers adding a damping from either friction device or viscous damper. This kind of control belong to well-known concept of passivity. Different examples are presented in order to illustrate the proposed theoretical developments.