Theory and numerics of three-dimensional beams with elastoplastic material behaviour

A theory of space curved beams with arbitrary cross-sections and an associated nite element formulation is presented. Within the present beam theory the reference point, the centroid, the centre of shear and the loading point are arbitrary points of the cross-section. The beam strains are based on a kinematic assumption where torsion-warping deformation is included. Each node of the derived nite element possesses seven degrees of freedom. The update of the rotational parameters at the nite element nodes is achieved in an additive way. Applying the isoparametric concept the kinematic quantities are approximated using Lagrangian interpolation functions. Since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric sti ener of shells. Due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load-carrying capacity of beam structures