Cross-sectional analysis of composite beams including large initial twist and curvature effects

Abstract

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. 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 wavelength of the deformation and to the minimum radius of curvature and/or twist. The final one-dimensional strain energy per unit length exhibits asymptotically correct second-order dependence of the initial curvature and twist parameters. Cross-sectional constants of the one-dimensional theory are obtained via finite element discretization over the cross-sectional plane. Numerical results obtained for both isotropic and composite beams are compared with published results from special purpose analyses for initially twisted, straight beams, as well as initially curved, untwisted beams. The agreement with previously published results is excellent.