Dynamic Stability of Arches Impacted by Rigid Body

Abstract

The dynamic in-plane instability process of pin-ended arches under a central radial impact applied is analyzed with numerical simulation method. Based on energy characteristics of arch under impact, the method for determining the critical state of dynamic stability of both elastic arch and elastic–plastic arch under impact are discussed in this paper. The calculation results show that the strain energy of the elastic arch at dynamic stable critical state is consistent with that at a state after buckling under static load in which the bearing capacity of the arch drops to zero, and the difference between them are very small and no more than 3.6 %. When impact act on the arch with dynamic critical initial conditions, the converter efficiencies from initial kinetic energy possessed by the rigid body to elastic strain energy of arch approaches 100 %, therefore a feasible method is provided to determine the dynamic stability of elastic arch under impact on the energy method. Then the impact analysis of arch considering material nonlinearity is carried out, it is proposed that the instability of elastic-plastic arch can be judged by the forming of plastic hinges at about 1/4 on both sides of the arch. It is found that the elastic strain energy of elastic-plastic arch at dynamic stability critical state is very close to maximum elastic strain energy of the arch under static load, and the differences between them are no more than 3 %.