This paper provides several solutions of the degenerate scale for some configurations with rigid line tips in antiplane elasticity. For solving the problem, it is necessary to investigate the conformal mapping function in advance. It is found that when a particular dimension reaches its critical value, a closed form solution for complex potential on the mapping plane can be found. This solution takes zero value for displacement along the boundary. However, it is not vanishing in the exterior region to the contour.

中文翻译：

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在反平面弹性或拉普拉斯方程中具有刚性线尖端的某些配置的退化尺度问题

本文针对在抗平面弹性方面具有刚性线尖端的某些配置，提供了退化尺度的几种解决方案。为了解决该问题，有必要预先研究保形映射功能。发现当特定尺寸达到其临界值时，可以找到映射平面上复杂电势的封闭形式解决方案。该解决方案沿边界的位移取零值。但是，它在轮廓的外部区域中不会消失。