Characteristic behavior of prismatic anisotropic beam via generalized eigenvectors

Elastic, anisotropic, non-homogeneous, prismatic beams are solved through a semi-analytical formulation. The resulting variational formulation is solved with a finite element discretization over the cross-section, leading to a set of Hamiltonian ordinary differential equations along the beam. Such a formulation is characterized by a group of generalized eigenvectors associated to null eigenvalues, which are shown to combine rigid body motions and the classical De Saint-Venant’s beam solutions. The related generalized deformation parameters are identified through the amplitude of the deformable generalized eigenvectors. Results obtained from the analysis of both isotropic and composite beams are presented.