Modeling Spanwise Nonuniformity in the Cross-Sectional Analysis of Composite Rotor Blades

For the purpose of analyzing nonuniform rotor blades by beam theory, a general theory which properly models the effects brought on by spanwise nonuniformity to the cross-sectional analysis is presented. The variational-asymptotic method and the finite element method are combined to obtain an asymptoticallycorrect expression to the sectional strain energy based on a discretized warping field. This asymptoticallycorrect strain energy is then transformed into the form of a generalized Timoshenko beam theory for ease of use. The energy expressions identify the stiffness matrices. Recovery relations to the 3D displacement, stress, and strain fields are obtained with consistency to the energy. The effects of spanwise nonuniformity appear in the theory through derivatives of both pointwise and sectionwise quantities, so the derivatives are approximated by finite differences. The transformation to generalized Timoshenko form is validated for the case of a linearly tapered isotropic strip beam, but more validations are needed to validate the rest of the theory as well as to build confidence that the theory is appropriate for realistic composite rotor blades.