One- and two-dimensional analysis of large deformations of beams using continuum mechanics theory

In this paper, with the assumption of constant material properties, the nonlinear behavior of beams is studied using the finite element method. To this end, two approaches are represented: in the first approach, the beam is modeled by one dimensional elements of second order that is formulated according to continuum mechanics relationships based on the Lagrangian strategy, while in the second approach based on the Eulerian strategy the nonlinear behavior of the beam is investigated by making use of two dimensional elements. In both approaches, the second configuration, strains and stresses in the beam are obtained via the calculation of deformation gradient.