The application of analytical methods to solve the problem of an anisotropic semi-infinite plane with a hole has not been observed thus far. This paper presents an analytical solution for an orthotropic semi-infinite plane with an arbitrary-shaped hole, considering the condition of a uniform stress applied at the hole boundary. First, the shapes of holes on the [Formula: see text]- and [Formula: see text]-planes are determined based on the shape of the hole on the z-plane. Next, the regions outside the holes on these physical planes are mapped to the rings on the [Formula: see text]- and [Formula: see text]-planes, respectively. Therefore, the boundary conditions with [Formula: see text] and [Formula: see text] as independent variables are established. Then, the boundary collocation method is used to solve the stress boundary conditions along the upper boundary and the hole boundary, thereby obtaining two analytical functions for calculating the stress and displacement of the structure. Finally, the correctness of the proposed method is verified by conducting boundary condition checks and comparing the stress and displacement results obtained by the proposed method with those obtained from ANSYS, and further investigates the influence of anisotropic parameters on normal stress and displacement.

中文翻译：

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具有任意形状孔的正交各向异性半无限平面的解析解

迄今为止尚未观察到应用解析方法来解决带孔的各向异性半无限平面问题。本文提出了具有任意形状孔的正交各向异性半无限平面的解析解，考虑了在孔边界施加均匀应力的条件。首先，根据z平面上的孔的形状确定[公式：见正文]-和[公式：见正文]-平面上的孔的形状。接下来，这些物理平面上孔洞外部的区域分别映射到[公式：见正文]平面和[公式：见正文]平面上的环。因此，建立了以[式：见正文]和[式：见正文]为自变量的边界条件。然后采用边界搭配法求解沿上边界和孔边界的应力边界条件，从而得到计算结构应力和位移的两个解析函数。最后，通过边界条件校核，并将该方法得到的应力和位移结果与ANSYS得到的应力和位移结果进行比较，验证了该方法的正确性，并进一步研究了各向异性参数对法向应力和位移的影响。