A consistent theory of finite stretches and finite rotations, in space-curved beams of arbitrary cross-section

Attention is focused in this paper on the development of a consistent finit e deformation beam theory, and its mixed variational formulation. The shear ing deformation, as well as cross-sectional warping displacement, are taken into account in this formulation. Beginning with the equilibrium equations of 3-D continuum body, we obtain the linear momentum balance (LMB), angula r momentum balance (AMB) and director momentum balance (DMB) conditions of the beam. The conjugate relationships between the strain and stress measure s are obtained through the stress power, in which the AMB condition plays a n important role. The use of the strain measures proposed herein, leads to the strain energy function which is invariant under a rigid-body motion. Th e present formulation is shown to be objective by using a numerical example . On the basis of Atluri's variational principle, we develop a mixed type v ariational functional for a space-curved beam, undergoing arbitrarily large rotations and arbitrarily large stretches. A choice of a proper finite rot ation vector, and unsymmetric curvature strains, makes it possible for cons tructing a consistent variational principle. The use of the present functio nal always leads to a symmetric tangent stiffness. The mixed variational fu nctional developed herein leads to a powerful tool for obtaining accurate n umerical results of 3-D space-curved beams, undergoing arbitrarily large st retches and rotations.