On the plane contact problem for a frictionless elastic layer
On the plane contact problem for a frictionless elastic layer
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DOI：
10.1016/0020-7683(73)90021-8
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发表时间：
1973-08
影响因子：
3.6
通讯作者：
M. Ratwani;F. Erdogan
中科院分区：
文献类型：
--
作者：
M. Ratwani;F. Erdogan
研究弹性层在弹性半空间上的平面接触问题。压缩载荷通过无摩擦刚性压痕施加于该层。假设层与子空间之间的接触也是无摩擦的，只有压缩的法向牵引力可以通过界面传递。因此，沿层-子空间界面的接触区域宽度是有限的，是未知的。该问题是用奇异积分方程组来表示的，其中未知函数是印痕与层之间的压力以及层与子空间之间的压力。首先对集中荷载的特殊情况进行了求解。然后研究了两种典型的邮票几何形状，即具有尖角的扁平邮票和弯曲邮票。在平面压痕的情况下，积分方程系统是齐次的，因此，层和子空间之间的接触面积的宽度与施加在压痕上的外部载荷的大小无关。然而，在弯曲冲压问题中，该接触区域的大小是外部载荷大小的函数。
The plane contact problem for an elastic layer lying on an elastic half space is considered. A compressive load is applied to the layer through a frictionless rigid stamp. It is assumed that the contact between the layer and the subspace is also frictionless and only compressive normal tractions can be transmitted through the interface. Hence, the width of the contact area along the layer-subspace interface is finite and is unknown. The problem is formulated in terms of a system of singular integral equations in which the unknown functions are the pressure between the stamp and the layer and that between the layer and the subspace. First the problem is solved for the special case of concentrated loads. Two typical stamp geometries, namely, a flat stamp with sharp corners and a curved stamp, are then investigated. In the case of flat stamp the system of integral equations is homogeneous and as a consequence the width of the contact area between the layer and the subspace turns out to be independent of the magnitude of the external load applied to the stamp. In the curved stamp problem, however, the size of this contact region is a function of the magnitude of the external load.