Three-field mixed beam-column finite element for geometric and material nonlinear analysis

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.