The Three-Dimensional Beam Theory: Finite Element Formulation based on Curvature

Abstract

A new finite element formulation of the 'geometrically exact finite-strain beam theory' is presented. The formulation employs the generalized virtual work principle in which the main role is played by the pseudo-curvature vector. The solution of the governing equations is obtained by using a combined Galerkin-collocation algorithm. The collocation assures that the equilibrium and the constitutive internal force and moment vectors are equal at a set of the chosen discrete points. A special update procedure for the pseudo-curvature and rotation vectors is employed in Newton's iteration because of the non-linearity of the configuration space. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples.