各向异性介质中的椭圆夹杂问题

THE PROBLEM OF TWO DIMENSIONAL DEFORMATION OF AN ELASTIC BODY WITH AN ELLIPTIC INCLUSION SUBJECTED TO POLYNOMIAL LOADING

本文研究了含椭圆夹杂的弹性体在多项式荷载作用下的二维变形问题，获得了介质和夹杂中的弹性场，证明了夹杂内部的应力变场以荷载的同阶多项式形式出现，而介质中的弹性场也能用椭圆坐标ζ＾－１２的多项式形式表示出来，并在此基础上，以受剪力作用的含夹杂或空孔的悬臂梁为例，求解了梁中的应力扰动现象，并获得了夹杂或空孔周转的环向应力。

In this paper, the two-dimensional deformation problem of an clastic body with an eliptic inclusion subjected to polynomial loadings are studied and from which the elastic fields in the inclusion and in the medium are obtained. Tn the investigation, it is verified that the stress field and the strain field in the inclusion are polynomials of the same order and that the field of the medium can be expressed as the polynomials with the elliptic coordinates ζ-1α. Based upon these results, an anisotropic elastic cantilever beam with an elliptic inclusion or with a hole subjected to a shear force is taken for an example, in which the stress disturbance in the beam and the hoop stress along the boundary of the inclusion or the hole are obtained.