Complex Variable Solutions for an Inhomogeneous Thick Plate Containing a Hole or a Crack
Complex Variable Solutions for an Inhomogeneous Thick Plate Containing a Hole or a Crack
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DOI：
10.1177/1081286504038670
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发表时间：
2004-10
影响因子：
2.6
通讯作者：
A. H. England
中科院分区：
文献类型：
--
作者：
A. H. England
求出了非均匀各向同性线弹性材料厚板的弹性方程的精确解，其中弹性系数是与板平面垂直的坐标的已知函数。假定板的上表面和下表面是无牵引力的。在以前的一篇文章中，这些解被表示为四个复势，它们是ζ=x+iy的解析函数，也就是板的中面坐标。虽然所得到的解不包含足够的一般性来满足板边缘周围的点边界条件，但可以在板边缘指定合力和力矩条件或平均位移。本文的目的是研究含有圆柱孔或贯穿厚度的线裂纹的板在无限远的均匀力场作用下的弹性场。
Exact solutions have been found to the equations of elasticity in a thick plate of inhomogeneous isotropic linearly elastic material in which the elastic moduli are known functions of the coordinate normal to the plane of the plate. The upper and lower surfaces of the plate are assumed to be traction free. In a previous paper these solutions were expressed in terms of four complex potentials that are analytic functions of ζ = x + iy, the coordinates in the mid-plane of the plate. Whilst the solutions obtained do not contain enough generality to satisfy the boundary conditions pointwise around the edge of the plate, resultant force and moment conditions or averaged displacements may be specified over the edge of the plate. The intention in this paper is to examine the elastic field in a plate containing a cylindrical hole or a through-thickness line crack under the action of a uniform force field at infinity.