Circular bars are widespread elements in building and mechanical engineering. They allow one to enhance the strength of the multilayer composite materials along with their weight reduction. However, their analytical modeling is developed rather poorly, which creates additional obstacles in their efficient design. The paper presents the results of the exact analytical solution to the plane bending task of elasticity theory for the multilayer beam with a circular axis under normal uniform loading on its longitudinal surfaces considering the cylindrical orthotropy of its layers’ materials. The problem has been solved using the methods of linear elasticity theory based on the continual approach where the circular bar is considered as a solid with the elastic characteristics varying in the radial direction. The solution for the shear stresses is assumed using the known distribution in the cross section. Therefore, the solution to the problem is reduced to the determination of two unknown functions of stress distribution throughout the section height. The system of linear differential equations has been obtained for the determination of the sought functions and unknown functions of integration in the process of the solution to the equations of plane theory considering the variable elastic characteristics. General analytical solutions for uniform and discontinuous-nonuniform layers from cylindrically orthotropic and isotropic materials have been developed. The influence of transverse shear deformation and compression on the characteristics of the stress-strain state of a cantilever three-layer beam with a semicircular axis is theoretically investigated. The obtained relations allow us to predict the stress-strain state of circular multilayer beams, as well as to build applied methods for solving problems of strength, rigidity, and optimal design of such structural elements.

圆棒是建筑和机械工程中广泛使用的元素。它们允许人们在减轻重量的同时增强多层复合材料的强度。但是，他们的分析模型开发得很差，这在他们有效的设计中造成了其他障碍。本文给出了多层圆梁在纵向方向上正常均布载荷下考虑圆柱层材料的正交各向异性的弹性理论的平面弯曲任务的精确解析解的结果。使用基于连续方法的线性弹性理论方法解决了该问题，其中将圆棒视为具有沿径向方向变化的弹性特征的实体。假定使用横截面中的已知分布来求解剪切应力。因此，该问题的解决方案简化为确定整个截面高度上两个未知的应力分布函数。已经获得了线性微分方程系统，用于在考虑可变弹性特征的平面理论方程的求解过程中确定寻找的函数和未知的积分函数。已经开发了由正交各向异性和各向同性圆柱材料制成的均匀和不连续非均匀层的一般分析解决方案。理论上研究了横向剪切变形和压缩对半圆轴悬臂三层梁的应力-应变状态特性的影响。所获得的关系使我们能够预测圆形多层梁的应力-应变状态，并建立用于解决强度，刚度问题以及此类结构元件的最佳设计的应用方法。