Abstract

Analytical solutions are obtained for an uncoupled quasi-static cyclic thermoelasticity problem for regular solids: a half-space, a plate, a space with a cylindrical channel, a cylinder, a space with a spherical cavity, and a sphere. The solutions, which are trigonometric Fourier series of temporary variable, are transformed by changing the spatial variable into a form convenient for analysis of temperature oscillations and thermocyclic stresses in the thermal layer. For the solutions found, simple asymptotic dependences are established, suitable for large radii of curvature of the surface and body size. The influence of the solid shape on temperature oscillations and thermocyclic stresses in the thermal layer has been studied.

中文翻译：

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固体形状对热层中非耦合准静态循环热弹性问题解的影响（以常规固体为例）

摘要

对于常规固体的非耦合准静态循环热弹性问题，获得了解析解：半空间，板，带圆柱通道的空间，圆柱，带球腔的空间和球体。通过将空间变量更改为便于分析热层中的温度振荡和热循环应力的形式，可以将临时变量的三角傅里叶级数转换为求解。对于找到的解决方案，建立了简单的渐近依赖关系，适用于较大的表面曲率半径和主体尺寸。研究了固体形状对热层中温度振荡和热循环应力的影响。