The problem as to whether an inclusion when embedded in an elastic infinite matrix with a perfectly bonded interface could achieve uniform internal stress has been studied extensively in the literature. It has been shown that in almost all cases ellipsoidal shape (including elliptical shape for two-dimensional deformation) is the only inclusion shape ensuring the uniformity of the stress inside the inclusion if the external loading exerted remotely on the edge of the matrix is uniform. From a practical point of view, this result remains valid for a non-uniform remote loading imposed on the matrix provided the product of the inclusion's size and the gradient of the non-uniform loading is small enough (as compared with the overall level of the stress field induced by the non-uniform loading at the inclusion's position). In this paper, we explore the possibility of designing an inclusion enclosing uniform internal stress in an elastic infinite plane under anti-plane shear deformation for a non-uniform remote loading with arbitrary gradients. We derive the equations with respect to the parameters describing the configuration of the inclusion leading to a uniform internal stress inside the inclusion for a general polynomial remote loading, and establish the analytic and numerical solutions for the shape of the inclusion which are illustrated via several examples.

文献中广泛研究了夹杂物嵌入具有完美结合界面的弹性无限基体时是否可以实现均匀内应力的问题。已经表明，在几乎所有情况下，如果远程施加在基体边缘的外部载荷是均匀的，椭圆形（包括二维变形的椭圆形）是唯一确保夹杂物内部应力均匀的夹杂物形状。从实际的角度来看，如果夹杂物的尺寸和非均匀载荷梯度的乘积足够小（与整体水平相比），这个结果对于施加在基体上的非均匀远程载荷仍然有效。由夹杂物位置的非均匀载荷引起的应力场）。在本文中，我们探索了在具有任意梯度的非均匀远程加载的反平面剪切变形下设计包含均匀内应力的夹杂物的可能性。我们推导出了关于描述在一般多项式远程加载的夹杂物内部产生均匀内应力的夹杂物配置的参数的方程，并建立了夹杂物形状的解析和数值解，通过几个例子来说明.