The conformal mapping, which transforms a half-plane into a unit disk, has been used widely in studies involving an isotropic elastic half-plane under anti-plane shear or plane deformation. However, very little attention has been paid to the possibility of utilizing this mapping in the study of an anisotropic elastic half-plane under the same deformation. In this paper, we discuss a general case of an arbitrarily located anisotropic elastic half-plane that corresponds to several affine counterparts (resulting from corresponding complex variable formalism). We show that this mapping is indeed applicable to each of the affine half-planes if and only if the key parameters in the mapping satisfy simple geometrical conditions. In addition, we introduce the application of this mapping with the corresponding geometrical conditions to the related study of anisotropic thin films under two-dimensional deformation.

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各向异性弹性中半平面到单位圆盘的共形映射及相关应用的讨论

将半平面转换为单位圆盘的共形映射已广泛用于涉及在反平面剪切或平面变形下的各向同性弹性半平面的研究。然而，很少有人关注在相同变形下的各向异性弹性半平面研究中利用这种映射的可能性。在本文中，我们讨论了一个任意定位的各向异性弹性半平面的一般情况，它对应于几个仿射对应物（由相应的复变量形式主义产生）。我们表明，当且仅当映射中的关键参数满足简单的几何条件时，这种映射确实适用于每个仿射半平面。此外，