An exact analytical solution is obtained for the extension problem in the case of an infinitely long continuous round cylinder attached to an external hollow round cylinder. This mechanical system is considered as a composite rod whose components are made of elastic materials with different mechanical characteristics. The method of solving this problem is based on the approach proposed by the author of this paper to solve the plane stress state problem in a spatial formulation, which allows one to integrate the equilibrium equations in finite form. The distribution of displacements and stresses in the rod is discussed.

中文翻译：

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分段均匀复合杆的延伸

在将无限长的连续圆柱体连接到外部空心圆柱体的情况下，可以获得有关扩展问题的精确解析解。该机械系统被认为是一种复合杆，其部件由具有不同机械特性的弹性材料制成。解决此问题的方法是基于本文作者提出的以空间公式解决平面应力状态问题的方法，该方法允许以有限形式集成平衡方程。讨论了杆中位移和应力的分布。