Pseudodynamic testing of strain‐softening systems with adaptive time steps

Abstract

AbstractA structure may exhibit a severe strain‐softening behaviour when subjected to strong earthquake excitation. Pseudodynamic testing of such structures using an implicit time‐integration algorithm may be conceived of as a problem, since the Newton‐type iterations, which are often required when structural non‐linearity develops, may not converge under these circumstances. An unconditionally stable implicit time‐integration algorithm implemented with Newton‐type iterations is analysed to provide an insight into this problem. A simple convergence condition is derived to detect possible divergence. The condition is shown to be a sufficient criterion for convergence for general multiple‐degree‐of‐freedom structures, and it is used later on to develop an adaptive time‐stepping strategy to avoid divergence under severe strain‐softening conditions. The implementation of this technique for pseudodynamic testing is presented. As demonstrated by numerical examples, the algorithm proves to be effective and reliable.