A regularized force-based beam element with a plastic-damage section model

law, to analyze the cyclic structural response of plane frames. Both displacement-based and forcebased approaches are used and compared, to demonstrate the significant advantages of the force-based formulation in the presence of material non-linearity. In order to overcome the pathological mesh dependent behaviour due to strain-softening, a classical non-local regularization procedure is adopted first, based on the integral definition of the associated variable governing the damaging process. Subsequently, for the force-based element, a new simple regularization technique is proposed based on a selected integration procedure along the element length, which predefines the location of the Gauss points in the beam region where the localization phenomena take place. As for the other computational aspects, an iterative element state determination is adopted for the force-based formulation and a local predictor-corrector algorithm is used to solve the incremental evolution problems of the plasticity and damage internal variables. Finally, some examples are shown on simple beams and frames, subjected to monotonic and cyclic loading conditions.