An Eulerian Finite Element with Finite Rotations for Thin-Walled Composite Beams

Abstract

An Eulerian beam finite element for composite thin-walled beams considering arbitrary displacements and rotations is presented. As a distinct feature, the virtual work equations are written as a function of generalized strain components, which are parametrized in terms of the director field and its derivatives. The generalized strains and forces are obtained via a transformation that maps generalized components into physical components. Finite rotations are parametrized with the incremental rotation tensor and an iterative multiplicative update of the director field is proposed. The formulation of the constitutive equation of the composite material is aided by a curvilinear transformation of the strain tensor. The proposed formulation is also valid for both isotropic and anisotropic beams. Different tests are performed to validate de formulation.