Mixed formulation and locking in path-following nonlinear analysis Original Research Article

The arc-length Riks strategy has rapidly become a standard tool for path-following analysis of nonlinear structures due to its theoretical ability to surpass limit points. The aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle ‘locking’ effect intrinsic to the nonlinear nature of the problem. As a consequence, its sanitization has to be pursued within a reformulation of the structural model. The use of a mixed (stress-displacement) variant of the algorithm, in particular, appears very promising in this respect. The topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in [39]. It is shown that, with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation, it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the