Element Iterative Strategy

Force-based Element Type / Force-based Plastic-Hinge Elements Type

Individual force-based frame elements require a number of iterations to be carried in order for internal equilibrium to be reached [e.g. Spacone et al. 1996; Neuenhofer and Filippou 1997]. The maximum number of such element loop iterations, together with the corresponding (force) convergence criterion or tolerance, can be defined herein:

• Element Loop Convergence Tolerance. The default value is 1e-5 (users may need to relax it to e.g. 1e-4, in case of convergence difficulties)
• Element Loop Maximum Iterations (elm_ite). The default value is 300 (although this is already a very large value (typically not more than 30 iterations are required to reach convergence), users may need to increase it to 1000 in cases of persistent elm_ite error messages)

Whilst running an analysis, elm_inv and elm_ite flag messages may be shown in the analysis log, meaning respectively that the element stiffness matrix could not be inverted or that the maximum allowed number of element loop iterations has been reached. In both cases, the global load increment is subdivided, as described in Appendix A, unless the ‘Do not allow element unbalanced forces in case of elm_ite’ option discussed below has been deactivated by the user.

Users are also given the possibility of allowing the element forces to be output and passed on to the global internal forces vector upon reaching the maximum iterations, even if convergence is not achieved. This non-default option may facilitate the convergence of the analysis at global/structure level, since it avoids the subdivision of the load increment (note that the element unbalanced forces are then to be balanced in the subsequent iterations).

Displacement-based Plastic-Hinge Elements Type

Since the element consists of a series of three sub-elements (two links at the member edges and an elastic frame element in the middle) an iterative procedure is required, in order to achieve internal equilibrium.

The parameters required for the element iterative strategy are the maximum and the minimum iterations allowed, and the value for the convergence norm. It is noted that a relative small value is given as default for the maximum number of iterations, as it has been observed that typically convergence is achieved within a limited number of iterations. Hence, if convergence is not achieved relatively early, it is highly probable that no convergence will be achieved.