SUMMARYA 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 Newtontype 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-degreeof-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.
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