A consistent total Lagrangian finite element for composite closed section thin walled beams

Abstract

This work presents a consistent geometrically exact finite element formulation of the thin-walled anisotropic beam theory. The present formulation is thought to address problems of composite beams with nonlinear behavior. The constitutive formulation is based on the relations of composite laminates and thus the cross sectional stiffness matrix is obtained analytically. The variational formulation is written in terms of generalized strains, which are parametrized with the director field and its derivatives. The generalized strains and generalized beam forces are obtained by introducing a transformation that maps generalized components into physical components. A consistent tangent stiffness matrix is obtained by parametrizing the finite rotations with the total rotation vector; its derivation is greatly simplified by obtention of the derivatives of the director field via interpolation of nodal triads. Several numerical examples are presented to show the accuracy of the formulation and also its frame invariance and path independence.