From sequentially linear analysis to incremental sequentially linear analysis: Robust algorithms for solving the non-linear equations of structures of quasi-brittle materials

It is difficult to accurately predict the strength of masonry and concrete structures. The most widely used method for simulating their behaviour is finite element analysis with the Newton-Raphson method and arch length control. However, the Newton-Raphson method can diverge and not produce a result, for example in bifurcations or during snap...

Incremental sequentially linear analysis to control failure for quasi-brittle materials and structures including non-proportional loading

Quasi brittle materials, such as un-reinforced masonry or concrete are difficult to analyse because often the traditional Newton–Raphson (N-R) procedure fails to converge. Many solutions have been proposed such as Sequentially Linear Analysis (SLA), but these may fail in case of non-proportional loading with a large prestress. In this paper a...