Variational-Asymptotical Analysis of Initially Curved and Twisted Composite Beams

An asymptotically exact methodology, based on geometrically nonlinear, three-dimensional elasticity, is presented for cross-sectional analysis of initially curved and twisted, nonhomogeneous, anisotropic beams. Through accounting for all possible deformation in the three-dimensional representation, the analysis correctly accounts for the complex elastic coupling phenomena in anisotripic beams associated with shear deformation. The analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wave length of the deformation and to the minimum radius of curvature and/or twist. The resulting cross-sectional elastic constants exhibit first-order dependence on the initial curvature and twist. As is well known, the associated geometrically-exact, one-dimensional equilibrium and kinematical equations also depend on initial twist and curvature. Present numerical results show that it is insufficient to account for initial twist and curvature in the beam equations only. The corrections to the stiffness model derived herein are also necessary in general for proper representation of anisotropic beams.