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Structural Engineering and Mechanics
  Volume 79, Number 2, July25 2021, pages 211-222

Three-field mixed beam-column finite element for geometric and material nonlinear analysis
Miguel Ferreira, Paulo Providência, Ricardo Costa, Pedro Gala and João Almeida

    A mixed element (3fME) for geometric and material nonlinear finite element analysis of plane skeletal structures is presented, which can reach any predefined accuracy with only one element per structural member. This element is based on the 3-field approach−an application of the Hu-Washizu principle−directly approximating the fields of displacements, strains and stresses. The presented formulation considers both (i) geometrically nonlinear behavior−by including the second-order term in the strain-displacement relations and establishing equilibrium in the deformed configuration−and (ii) materially nonlinear elastoplastic behavior, at the fibre level, automatically handling the axial-bending interaction. The illustrative examples include both compression- and tension-bending interaction, and compare the accuracy of the novel finite element with published results.
Key Words
    3-field mixed finite element; beam-column finite element; geometric nonlinearity; modelling of skeletal structures; very coarse meshes
Miguel Ferreira: CERIS, Instituto Superior Técnico, University of Lisbon, 1049-001 Lisboa, Portugal
Paulo Providência: University of Coimbra, INESC Coimbra, DEC, 3030-290 Coimbra, Portugal
Ricardo Costa: Civil Engineering Department, ISISE, University of Coimbra, 3030-788 Coimbra, Portugal
Pedro Gala: DEC ESTG, INESC Coimbra, Polytechnic Institute of Leiria, 2411-901 Leiria, Portugal
João Almeida: DECivil, ICIST, CERIS, Instituto Superior Técnico, University of Lisbon, 1049-001 Lisboa, Portugal

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