A Frame Invariant and Path-Independent Geometrically Exact thin Walled Composite Beam Element

Abstract

A geometrically exact, frame invariant and path independent beam finite element for
composite thin-walled beams is presented. In the proposed formulation 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 by introducing a transformation that maps generalized components into physical components. Finite rotations are parametrized with the total rotation vector and a multiplicative update of the directors is performed via the total rotation tensor. A curvilinear transformation is applied to the strain vector and the transformed deformations are used to write the constitutive relations. As a result, the proposed formulation is valid for both isotropic and anisotropic beams. The frame invariance and path independence of the presented formulation is ensured by the use of interpolation to obtain the derivatives of the director field.