A regularized force‐based beam element with a damage–plastic section constitutive law

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Abstract
A new beam finite element is presented, with a generalized section constitutive law based on damage mechanics and plasticity, to analyse the cyclic structural response of plane frames. Both displacement‐based and force‐based (FB) approaches are used and compared, to demonstrate the significant advantages of the FB formulation in the presence of material non‐linearity. In order to overcome the analytical problems and the pathological mesh dependency of the numerical response in the presence of strain‐softening post‐peak behaviour, a classical non‐local regularization procedure is adopted first, based on the integral definition of the associated variable governing the damaging evolution process. Subsequently, for the FB 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 FB formulation and a local predictor–corrector algorithm is used to solve the incremental evolution problems of the damage and plastic internal variables. Finally, some examples are shown on simple beams and frames, subjected to monotonically increasing and cyclic loading conditions. Copyright © 2006 John Wiley & Sons, Ltd.

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