Abstract A unified semi-analytical solution based on graphical conformal mapping and complex variable methods is proposed to calculate the in-plane stress around an arbitrarily-shaped hole in isotropic or anisotropic materials. The method requires only the outline coordinates of the hole, the elastic moduli of the material, and the magnitude and direction of the far-field stresses. Comparison with many published results for a wide range of shapes, such as triangles, squares, ovaloids, and ellipses, has been carried out to validate the method. The method has also been applied to a highly irregular geometry that has been observed in a breakout of a subsurface borehole. The solution is essentially closed-form, in the sense that it can be explicitly expressed in terms of the mapping coefficients, and parameters that depend only on the elastic moduli of the materials. With such a degree of flexibility, the method will be useful to study the effect of hole geometry on the stress distribution around holes in isotropic or anisotropic materials.

中文翻译：

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计算各向同性或各向异性材料中任意形状孔周围应力的统一方法

摘要 提出了一种基于图形共形映射和复变量方法的统一半解析解，用于计算各向同性或各向异性材料中任意形状孔周围的面内应力。该方法只需要孔的轮廓坐标、材料的弹性模量以及远场应力的大小和方向。已针对各种形状（如三角形、正方形、椭圆形和椭圆形）与许多已发表的结果进行比较，以验证该方法。该方法还应用于在地下钻孔的突破中观察到的高度不规则的几何形状。该解基本上是封闭形式的，因为它可以用映射系数明确表示，和仅取决于材料弹性模量的参数。由于具有如此高的灵活性，该方法将有助于研究孔几何形状对各向同性或各向异性材料中孔周围应力分布的影响。