Abstract The purpose of this article is to analytically investigate the three-dimensional thermoelastic fields in a semi-infinite medium weakened by an annular crack. The crack faces are exposed to a prescribed temperature load and the external surface of the medium is kept at the reference temperature. The problem is formulated as a three-part mixed boundary value problem and is treated through Goodier’s thermoelastic potential and the Boussinesq harmonic functions. The Hankel transform method is employed to convert this problem into triple integral equations and a system of coupled ones. Using some integral relations and the Gegenbauer addition formula, the set of triple integral equations is ultimately reduced to an infinite system of linear algebraic equations. Closed-form formulas for various quantities of physical interest are derived and expressed in terms of the solution of the obtained infinite algebraic system. Moreover, the combined mechanical and thermal loading conditions are also considered. Numerical results for thermoelastic fields and mixed-mode thermal stress intensity factors are shown graphically to analyze their dependence on the radii and depth of the crack. Results for the thermoelastic problem of an infinite medium containing an annular crack are also obtained as a special case of this study.

中文翻译：

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热弹性半空间中的环状裂纹

摘要 本文的目的是分析研究被环形裂纹削弱的半无限介质中的三维热弹性场。裂纹面承受规定的温度载荷，介质的外表面保持在参考温度。该问题被表述为一个三部分混合边值问题，并通过 Goodier 的热弹性势和 Boussinesq 调和函数进行处理。Hankel变换方法被用来将这个问题转化为三重积分方程和耦合方程组。使用一些积分关系和 Gegenbauer 加法公式，三重积分方程组最终被简化为一个无限线性代数方程组。根据所获得的无限代数系统的解，推导出各种物理感兴趣量的闭式公式并表示。此外，还考虑了组合的机械和热载荷条件。热弹性场和混合模式热应力强度因子的数值结果以图形方式显示，以分析它们对裂纹半径和深度的依赖性。作为本研究的一个特例，还获得了包含环形裂纹的无限介质的热弹性问题的结果。热弹性场和混合模式热应力强度因子的数值结果以图形方式显示，以分析它们对裂纹半径和深度的依赖性。作为本研究的一个特例，还获得了包含环形裂纹的无限介质的热弹性问题的结果。热弹性场和混合模式热应力强度因子的数值结果以图形方式显示，以分析它们对裂纹半径和深度的依赖性。作为本研究的一个特例，还获得了包含环形裂纹的无限介质的热弹性问题的结果。