This work deals with finding the analytical displacements and stresses in thermoelasticity problems involving solid isotropic cylinders and spheres with an emphasis on stress-focusing phenomena relevant to the nuclear industry and high-temperature engineering. The study considers solid spheres and infinitely long solid cylinders with three different types of thermal loading: prescribed outer surface temperature, prescribed surface heat flux, and volumetric heat source. Both continuous and discontinuous thermal loading conditions are considered. It is shown that discontinuous loading, such as abrupt changes in prescribed surface temperature or heat flux prescriptions, results in unbounded stresses along the axis (in the case of an infinite cylinder) and the center (in the case of a solid sphere), while with continuous loading, we obtain finite stresses within the domains at all times.

中文翻译：

---

圆柱形和球形固体中热弹性应力聚焦的分析解决方案


这项工作涉及在涉及固体各向同性圆柱体和球体的热弹性问题中寻找分析位移和应力，重点是与核工业和高温工程相关的应力聚焦现象。该研究考虑了具有三种不同类型热载荷的实心球体和无限长的实心圆柱体：指定外表面温度、指定表面热通量和体积热源。考虑了连续和不连续的热载荷条件。结果表明，不连续载荷，例如规定表面温度或热通量规定的突然变化，会导致沿轴（在无限圆柱体的情况下）和中心（在实心球体的情况下）产生无限应力，而在连续载荷下，我们始终在域内获得有限应力。