Interpolation non lineaire pour un element fini de poutre en grandes rotations tri-dimensionnelles - Mikdad, Mazen AI; lbrahimbegovic, Adnan (European Journal of Computational Mechanics, 1995)
We propose in this paper a finite element formulation for three-dimensional beams undergoing large displacement and large rotations but small strains, many structures of mechanical and civil engineering belong to this class of problems. The main feature of this formulation concerns the treatment of finite rotations : by using the orthogonal matrix parametrization of 3D finite rotations and a nonlinear finite element interpolation of linearized rotations, we are able to provide a symetric tangent stiffness matrix leading to quadratic convergence of the incremental solution procedure, and the consistent linearization being affected by this approach. Several numerical examples demonstrate the efficiency of this development.