Reliability Analysis of Single-Degree-of-Freedom Elastoplastic Systems. II: Suboptimal Excitations

A method for constructing an approximation of the critical excitation that drives an elastoplastic system from rest to a target threshold at a specified time instant, referred to as the “suboptimal excitation,” is presented in this paper. It is based on the observations gained from study of the critical excitations in the companion paper. Essentially, for the usual case of interest where the failure time is not small compared to the natural period, the duration of the positive and negative pulses of the critical excitation are roughly equal to half of the natural period. This consideration allows for a simple intuitive approximation of the critical excitation. The amplitudes of the positive and negative pulses are obtained in closed forms using energy balance. Numerical investigations show that the critical excitations are well approximated by the suboptimal excitations.