The use of variable scalar step-lengths can significantly improve the convergence characteristics of iterative procedures. These step-lengths can be calculated in two different ways; in a corrector sense using `line searches' or in a predictor sense using some acceleration scheme. Both versions are considered in the present report and the resulting variable step-lengths are applied to non-linear finite element analyses implementing the Newton-Raphson and modified Newton-Raphson iterative solution procedures. The variable step-length algorithms are incorporated in incremental formulations using both load control and the more versatile `arc-length' method. (A)

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