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.

从弯曲杆的Cosserat型模型开始，我们得出具有任意层数的多层复合梁的有效刚度系数的解析表达式。为此，我们将其与三维梁和杆的一些弯曲，扭转和延伸问题的解析解进行比较。复合梁的各层由不同的正交各向异性或各向同性非均质弹性材料组成。我们使用获得的一般公式来计算一些梁问题的精确解析解，并将它们与相应的数值模拟结果进行比较。数值研究表明，所得公式具有广泛的有效性和适用性。