Abstract
The behavior of a tip-loaded anisotropic cantilever beam with an arbitrary cross-section is studied using Saint-Venant's semi-inverse method along with a power series solution for the local in-plane and out-of-plane deformation warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. Using the resulting three-dimensional displacement solutions, the shear deformation associated with applied tip loads is investigated as well as the shear center location. Two different definitions of the shear center are presented for anisotropic beams by extending existing approaches developed for isotropic sections. Both of the extended definitions reveal the linear dependency of the shear center location on beam length. Numerical results are presented for three different cross-sections (ellipse, triangle, NACA-0012 airfoil) and two different materials (Al 6061-T6, off-angle high strength graphite/epoxy fibers).
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