A Vectorial Approach for the Formulation of Finite Element Beams in Finite Rotations

Two vectorial finite element approaches to formulate models, for three-dimensional elastic beams, in cases of small strains in the large displacement and rotation regime are presented. These two approaches differ in the finite element local frame of reference where rigid and deformative modes are referred. In both of these geometrically nonlinear formulations, based on the total Lagrangian description, the use of the rotation parameters is bypassed. Complex manipulations required to obtain conservative descriptions and well-posed transformation matrices are avoided. In particular, slopes and distances are used instead of rotation parameters to compute the nonlinear representations of the strain measures in the inertial frame of reference. Numerical tests have been carried out to validate the developed technique in the frame structure context.