Some coplanar punch and crack problems in three-dimensional elastostatics
Some coplanar punch and crack problems in three-dimensional elastostatics
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三维弹性静力学中的一些共面冲孔和裂纹问题
DOI：
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发表时间：
1963
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通讯作者：
W. D. Collins
中科院分区：
文献类型：
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作者：
W. D. Collins
弹性半空间和无限弹性固体的某些三维冲孔和裂纹问题分别归结为势理论中的狄利克雷或诺伊曼问题，其中势在无限三维空间的所有点上确定，给定其值或其在两个或多个共面圆形区域上的法向导数的值。这些问题是由无穷多的第二类Fredholm积分方程控制的，当圆区域之间的间距相对于半径足够大时，可以通过迭代近似求解。研究了由两个平端圆形冲头压痕的半空间和包含两个或多个共面便士形裂纹的无限固体在压力作用下的应力分布。
Certain three-dimensional punch and crack problems for an elastic half-space and an infinite elastic solid respectively reduce to Dirichlet or Neumann problems in potential theory in which the potential is to be determined at all points of an infinite three-dimensional space, given its values or the values of its normal derivative on two or more coplanar circular regions. These problems are shown to be governed by infinite sets of Fredholm integral equations of the second kind, which can be solved approximately by iteration when the spacing between the circular regions is sufficiently large compared with their radii. The stress distributions in a half-space indented by two flat-ended circular punches and in an infinite solid containing two or more coplanar penny-shaped cracks opened under pressure are thus investigated.