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

Abstract

Beam finite elements for non linear plastic analysis of beam-like structures are formulated according to Displacement Based (DB) or Force Based (FB) approaches. DB formulations rely on modelling the displacement field by means of displacement shape functions. Despite the greater simplicity of DB over FB approaches, the latter provide more accurate responses requiring a coarser mesh. To fill the existent gap between the two approaches the improvement of the DB formulation without the introduction of mesh refinement is needed. To this aim the authors recently provided a contribution to the improvement of the DB approach by proposing new enriched adaptive displacement shape functions leading to the Smart Displacement Based (SDB) beam element. In this paper the SDB element is extended to include the axial force-bending moment interaction, crucial for the analysis of r/c cross sections. The proposed extension requires the formulation of discontinuous axial displacement shape functions dependent on the diffusion of plastic deformations. The stiffness matrix of the extended smart element is provided explicitly and shown to be dependent on the displacement shape functions updating. The axial force-bending moment interaction is approached by means of a fibre discretisation of the r/c cross section. The extended element, addressed as Fibre Smart Displacement Based (FSDB) beam element, is shown to be accurate and furthermore accompanied by the proposal of an optional procedure to verify strong equilibrium of the axial force along the beam element, which is usually not accomplished by DB beam elements. Given a fixed mesh discretisation the performance of the FSDB beam element is compared with the DB approach to show the better accuracy of the proposed element.

Targeted steel frames by means of innovative moment resisting connections

“…Improvement of the performance of the FEM both for uniform beams and, more significantly, for non-uniform discontinuous beams can be obtained by means of a preliminary mesh refinement or, alternatively, an a-posteriori sub-discretisation during the nonlinear analysis as well as an appropriate Gauss point refinement [34][35][36][37][38][39]. To overcome the latter problems some of the authors recently formulated a Smart Displacement Based (SDB) beam element, with uniform cross section, endowed with adaptive displacement shape functions able to update during the inelastic analysis [28,29]. The proposed adaptive displacement shape functions coincide, in the initial linear elastic state, with the classical Hermite polynomials and evolve subsequently in accordance with the stiffness decay evaluated at the Gauss cross sections.…”

“…The nonlinear elastic-plastic analysis of Frame 1, assuming an S235 steel grade, has been conducted by means of the FSDB model proposed in [29] through the software HiStrA [52] where the model has been implemented. A single finite element has been employed to simulate each frame element.…”

“…The advantage of such beam element consists in avoiding any FE mesh or Gauss point refinement during the analysis. The SDB beam element has been subsequently enriched with a fibre approach and denoted as Fibre Smart Displacement Based (FSDB) element [29].…”

A 2D beam‐column joint macro‐element for the nonlinear analysis of RC frames

“…[17][18][19] Critical reviews of the literature models are reported in Celik and Ellingwood 20 and Sharma et al 21 Typically, nonlinear joint elements are connected to nonlinear frame elements that account for the nonlinear response of the plastic zones at the ends of the beams and columns connected to the joint. [22][23][24] The beam-column joint models proposed to date can be classified into three categories: (i) lumped plasticity models; (ii) multispring models and (iii) finite element-based models. For frame analysis, only the first two categories are of interest.…”

“…Critical reviews of the literature models are reported in Celik and Ellingwood 20 and Sharma et al 21 . Typically, nonlinear joint elements are connected to nonlinear frame elements that account for the nonlinear response of the plastic zones at the ends of the beams and columns connected to the joint 22–24 …”