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首页> 外文期刊>International Journal of Solids and Structures >Effective approach to the contact problem for a stratum
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Effective approach to the contact problem for a stratum

机译：解决阶层接触问题的有效方法

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摘要

A novel effective algorithm for the problem of the circular punch in contact with a stratum rested on a rigid base is suggested in this paper. The problem is reduced to the Fredholm integral equations of the second kind. In contrast to the Cooke-Lebedev method and the moments method, which are traditionally employed, the operators of these integral equations are strictly positive definite even in the limiting case of the zero thickness. The latter provides efficient applications of numerical methods. It is also shown that a special approximation enables to obtain an approximate solution via a finite system of linear algebraic equations. As example, the well-known problem for a homogeneous layer is studied. An approximate analytical solution is found with a certain iterative method for a flat punch. This solution is remarkable accurate and possesses the right asymptotic behavior for both a very thin and a very thick layers. Asymptotic formulas for the thin inhomogeneous stratum indented by an indenter of arbitrary profile are pointed out. (C) 2004 Elsevier Ltd. All rights reserved.
机译：提出了一种新的有效算法，解决了圆形冲头与刚性基体接触的问题。该问题被简化为第二类Fredholm积分方程。与传统上使用的Cooke-Lebedev方法和矩量方法相反，即使在零厚度的极限情况下，这些积分方程的算子也严格是正定的。后者提供了数值方法的有效应用。还显示了一种特殊的近似方法，可以通过线性代数方程的有限系统来获得近似解。例如，研究了均质层的众所周知的问题。对于平冲头，使用某种迭代方法可以找到近似的解析解。该解决方案非常精确，并且对于非常薄和非常厚的层都具有正确的渐近行为。指出了由任意轮廓的压头压入的不均匀薄地层的渐近公式。 （C）2004 Elsevier Ltd.保留所有权利。

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