We rigorously establish the interesting result that in anti-plane elasticity an elastic epitrochoidal inhomogeneity can be made neutral to multiple uniform fields applied in the matrix via the insertion of two intermediate coatings. Using a two-term conformal mapping function, the simply connected domain occupied by the epitrochoidal inhomogeneity and its surrounding inner and outer coatings is mapped onto the interior of the unit circle in the image plane. The mismatch parameters are determined in an analytical manner by solving a set of two non-linear equations. An elastic inhomogeneity of arbitrary shape can be made neutral to multiple fields through the insertion of N coatings when the proposed mapping function for the simply connected domain occupied by the multicoated inhomogeneity is described in terms of a polynomial of finite degree containing N non-constant terms. In this case, the mismatch parameters are determined by iteratively solving a set of N non-linear equations.

我们严格地建立了一个有趣的结果，即在反平面弹性中，通过插入两个中间涂层，可以使弹性外旋轮线不均匀性与施加在基质中的多个均匀场保持中性。使用二项共形映射函数，由外摆线不均匀性及其周围的内外涂层占据的简单连接域被映射到图像平面中单位圆的内部。通过求解一组两个非线性方程以分析方式确定失配参数。通过插入N可以使任意形状的弹性不均匀性对多个场中性当提出的由多层不均匀性占据的简单连接域的映射函数根据包含N 个非常数项的有限次多项式描述时，涂层。在这种情况下，通过迭代求解一组N个非线性方程来确定失配参数。