The multiple slope discontinuity beam element for nonlinear analysis of RC framed structures

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Abstract

The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoullibeam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of multiple discontinuities in the slope function was already solved by Biondi and Caddemi (Int J Solids Struct 42(9):3027–3044, 2005, Eur J Mech A Solids 26(5):789–809, 2007), who also found solutions in closed form. These solutions are now implemented in the new beam element respecting a thermodynamical approach, from which the state equations and flow rules are derived. State equations and flow rules are rewritten in a discrete manner tomatch up with the Newton–Raphson iterative solutions of the discretized loading process. A classic elastic predictor phase is followed by a plastic corrector phase in the case of activation of the inelastic phenomenon. The corrector phase is based on the evaluation of return bending moments by employing the closest point projection method under the hypothesis of associated plasticity in the bending moment planes of a Bresler’s type activation domain. Shapefunctions and stiffness matrix for the new element are derived. Numerical examples are furnished to validate the proposed beam element.
Lingua originaleEnglish
pagine (da-a)1469-1490
Numero di pagine22
RivistaMeccanica
Volume53
Stato di pubblicazionePublished - 2018

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Nonlinear analysis
plastic properties
Plasticity
discontinuity
slopes
bending moments
Bending moments
equations of state
Chemical activation
activation
static loads
stiffness matrix
iterative solution
concrete structures
Stiffness matrix
Concrete construction
Patient rehabilitation
numerical analysis
Reinforced concrete
Numerical models

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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title = "The multiple slope discontinuity beam element for nonlinear analysis of RC framed structures",
abstract = "The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoullibeam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of multiple discontinuities in the slope function was already solved by Biondi and Caddemi (Int J Solids Struct 42(9):3027–3044, 2005, Eur J Mech A Solids 26(5):789–809, 2007), who also found solutions in closed form. These solutions are now implemented in the new beam element respecting a thermodynamical approach, from which the state equations and flow rules are derived. State equations and flow rules are rewritten in a discrete manner tomatch up with the Newton–Raphson iterative solutions of the discretized loading process. A classic elastic predictor phase is followed by a plastic corrector phase in the case of activation of the inelastic phenomenon. The corrector phase is based on the evaluation of return bending moments by employing the closest point projection method under the hypothesis of associated plasticity in the bending moment planes of a Bresler’s type activation domain. Shapefunctions and stiffness matrix for the new element are derived. Numerical examples are furnished to validate the proposed beam element.",
author = "Giuseppe Giambanco and {Rezaee Hajidehi}, Mohsen and Antonino Spada",
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language = "English",
volume = "53",
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journal = "Meccanica",
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TY - JOUR

T1 - The multiple slope discontinuity beam element for nonlinear analysis of RC framed structures

AU - Giambanco, Giuseppe

AU - Rezaee Hajidehi, Mohsen

AU - Spada, Antonino

PY - 2018

Y1 - 2018

N2 - The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoullibeam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of multiple discontinuities in the slope function was already solved by Biondi and Caddemi (Int J Solids Struct 42(9):3027–3044, 2005, Eur J Mech A Solids 26(5):789–809, 2007), who also found solutions in closed form. These solutions are now implemented in the new beam element respecting a thermodynamical approach, from which the state equations and flow rules are derived. State equations and flow rules are rewritten in a discrete manner tomatch up with the Newton–Raphson iterative solutions of the discretized loading process. A classic elastic predictor phase is followed by a plastic corrector phase in the case of activation of the inelastic phenomenon. The corrector phase is based on the evaluation of return bending moments by employing the closest point projection method under the hypothesis of associated plasticity in the bending moment planes of a Bresler’s type activation domain. Shapefunctions and stiffness matrix for the new element are derived. Numerical examples are furnished to validate the proposed beam element.

AB - The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoullibeam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of multiple discontinuities in the slope function was already solved by Biondi and Caddemi (Int J Solids Struct 42(9):3027–3044, 2005, Eur J Mech A Solids 26(5):789–809, 2007), who also found solutions in closed form. These solutions are now implemented in the new beam element respecting a thermodynamical approach, from which the state equations and flow rules are derived. State equations and flow rules are rewritten in a discrete manner tomatch up with the Newton–Raphson iterative solutions of the discretized loading process. A classic elastic predictor phase is followed by a plastic corrector phase in the case of activation of the inelastic phenomenon. The corrector phase is based on the evaluation of return bending moments by employing the closest point projection method under the hypothesis of associated plasticity in the bending moment planes of a Bresler’s type activation domain. Shapefunctions and stiffness matrix for the new element are derived. Numerical examples are furnished to validate the proposed beam element.

UR - http://hdl.handle.net/10447/259335

UR - https://link.springer.com/article/10.1007%2Fs11012-018-0817-3

M3 - Article

VL - 53

SP - 1469

EP - 1490

JO - Meccanica

JF - Meccanica

SN - 0025-6455

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