A smart displacement based (SDB) beam element with distributed plasticity

A Fibre Smart Displacement Based (FSDB) beam element for the nonlinear analysis of reinforced concrete members

“…The closed form solutions in terms of axial and transversal displacement of a stepped beam presented in the previous section can be conveniently adopted to formulate an extension of the Smart Displacement Based (SDB) beam element as formulated in [Pantò et al 2017] for the analysis of inelastic beams under flexural behaviour only. In this section a DB beam finite element able to account for the flexural and axial behaviour is proposed.…”

“…The above discussion convinced, in the past, some of these authors to devote attention to the study of beams with stepped variations of the bending stiffness Caddemi 2005, Biondi andCaddemi 2007] and also to formulate linear two node finite elements with different types of singularities also by adopting the classical Timoshenko theory to account for the shear deformations [Caddemi et al 2013a, Caddemi et al 2013b]. The governing equations of the flexural behaviour of stepped beams has been successfully applied for the plastic analysis of beam elements [Pantò et al 2017], however, in the latter work plastic deformations in axial direction have not been accounted for and the effect of the related axial stiffness decay has not been taken into account. Due to the above limitation the theory therein presented is not applicable to frame structures.…”

“…With respect to the classical Hermite cubic polynomials, the proposed shape functions contain additional terms (formulated by means of generalised functions) that update during the inelastic analysis being dependent on stiffness decay of the cross sections according to a reference stepped beam model as diffusion of plastic deformations occurs. The resulting element, formulated in a pure flexural state and according to a sectional approach for homogeneous sections, was called Smart Displacement Based (SDB) beam element [Pantò et al 2017]. Given the efficacy of the smart displacement shape functions introduced in [Pantò et al 2017], within the same framework, however in the context of concentrated plasticity, shape functions endowed with additional terms, able to capture the occurrence of plastic hinges during the analysis at any beam cross section, have been adopted in [Hajidehi et al 2018 to improve the DB formulation of concentrate plasticity inelastic beams.…”

“…The resulting element, formulated in a pure flexural state and according to a sectional approach for homogeneous sections, was called Smart Displacement Based (SDB) beam element [Pantò et al 2017]. Given the efficacy of the smart displacement shape functions introduced in [Pantò et al 2017], within the same framework, however in the context of concentrated plasticity, shape functions endowed with additional terms, able to capture the occurrence of plastic hinges during the analysis at any beam cross section, have been adopted in [Hajidehi et al 2018 to improve the DB formulation of concentrate plasticity inelastic beams. In this paper the SDB beam element is improved and some of the original limitations removed.…”

A New Discrete Macro-Node Element for the Seismic Behaviour Modelling of Reinforced Concrete Frames

“…A reliable nonlinear model of a reinforced concrete building should include efficient simulation of beams, columns as well as beam-to-column joints. Many advanced numerical models have been proposed in the literature to simulate static, cyclic and dynamic behaviour of beams-columns elements also subjected to axial-moment-shear interactions [1,2,3] and some of these models have already implemented in advanced software largely used in engineering practice, however efficient models of beam-column joints still represent an academic issue whose results have not been made available to engineering community. In this paper a new discrete macro-node element is proposed.…”