Determination of effective stiffness properties of multilayered composite beams

Starting from a Cosserat-type model for curved rods, we derive analytical expressions for the effective stiffness coefficients of multilayered composite beams with an arbitrary number of layers. For this purpose, we employ the comparison with analytical solutions of some bending, torsion, and extension problems for three-dimensional beams and rods. The layers of the composite beam consist of different orthotropic or isotropic non-homogeneous elastic materials. We apply the obtained general formulas to calculate exact analytical solutions of some beam problems and compare them with corresponding results of numerical simulations. The numerical study shows a wide range of validity and applicability of the obtained formulas.