Dynamic Stability of Single Layer Reticulated Dome under Step Load

Abstract

A single layer reticulated dome is an imperfect sensitive structure, which may lose its stability under strong earthquake action and strong wind load. Several methods have been adopted by numerous investigators to solve latticed dome static stability but few concerned with dynamic stability. Dynamic stability means structural stability under dynamic disturbance, which is a research field closely related to stability theory and vibration theory. This chapter presents that the members of reticulated dome are assumed as three-dimensional beam element and the nonlinearity of latticed domes include geometric nonlinearity caused by joint large displacement, large rotation, and nonlinear material constitutive relation. The updated Lagrangian formulation is employed to develop a three-dimensional beam element geometry nonlinear analysis, which includes joints with large displacements and large rotations. Trial calculation is the only valid method for a structure's dynamic stability critical load analysis. By increasing the load step-by step,then calculating the structure nonlinear dynamic response, the structure vibration amplitude increased with the load. When the structure vibration time history curve bifurcate and diverge and at the same time the structure stiffness matrix is negative definite, the structure vibrates from stable to unstable state and the load is called dynamic stability critical load.