Abstract The thermoelasticity problem of a coated polygonal hole subject to a point heat source is investigated herein. Based on conformal mapping, analytic continuation theorem, and alternation, temperature functions are obtained for any number of edges of a coated polygonal hole, while stress functions are obtained for a coated approximate triangle hole and a coated approximate square hole. Solutions of temperature contours and interfacial stresses agree well with the finite element results. Both the interfacial normal and shear stresses indicated an obvious concentration and a sudden jump across the corner of a coated polygonal layer, respectively. The present derived solutions can be considered as Green’s functions to study problems involving a crack interacting with a coated polygonal hole.

中文翻译：

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受点热源影响的带涂层多边形孔的界面应力

摘要 本文研究了涂层多边形孔在点热源作用下的热弹性问题。基于共形映射、解析连续定理和交替，获得了涂层多边形孔任意条边的温度函数，同时获得了涂层近似三角形孔和涂层近似方形孔的应力函数。温度等值线和界面应力的解与有限元结果非常吻合。界面法向应力和剪切应力都分别表明在涂层多边形层的拐角处有明显的集中和突然跳跃。当前导出的解决方案可以被视为格林函数来研究涉及裂纹与涂层多边形孔相互作用的问题。