Composite Beam Analysis Linear Analysis of Naturally Curved and Twisted Anisotropic Beams

The aim of this report is to present a consistent theory for the deformation of a naturally curved and twisted anisotropic beam. The proposed formulation naturally extends the classical Saint-Venant approach to the case of curved and twisted anisotropic beams. The mathematical model developed under the assumption of span-wise uniform cross-section, curvature and twist, can take into account any kind of elastic coupling due to the material properties and the curved geometry. The consistency of the math-model presented and its generality about the cross sectional shape, make it a useful tool even in a preliminary design optimization context such as, for example, the aeroelastic tailoring of helicopter rotor blades. The advantage of the present procedure is that it only requires a two-dimensional discretization thus, very detailed analyses can be performed and interlaminar stresses between laminae can be evaluated. Such analyses would be extremely time consuming if performed with standard finite element codes that prevents their recursive use as for example when optimizing a beam design. Moreover, as a byproduct of the proposed formulation, one obtains the constitutive law of the cross-section in terms of stress resultant and moment and their conjugate strain measures. This constitutive law takes into account any kind of elastic couplings, e.g. torsion-tension, tension-shear, bending-shear, and constitutes a fundamental input in aeroelastic analyses of helicopter blades. Four simple examples are given in order to show the principal features of the method.