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首页> 外文期刊>International Journal of Solids and Structures >Symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating
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Symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating

机译：多层弹性涂层轴对称压痕问题的符号和数值解

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This paper is concerned with a semi-analytical approach to the solution of the axisymmetric indentation problem for a multilayered elastic half-space. The stress and displacement fields for each layer and the substrate are derived in closed form by using the Papkovich-Neuber potentials and the Hankel transform. The bonded or sliding interface conditions between the sub-layers are handled by the use of the appropriate transfer matrix, and then the mixed boundary value problem is reduced to a Fredholm integral equation. Symbolic and numerical computations of the solution are implemented in the symbolic software Mathematica in the form of a fast and efficient numerical algorithm, allowing rapid determination of the load-displacement curves and composite elastic properties for an arbitrary rigid indenter shape. A series of results for different indenters (flat, conical, spherical and blunted conical punch shapes) and different multilayered composites is presented and discussed. The complete set of symbolic and numerical computations are provided as supplementary resources with the paper.
机译：本文涉及一种半解析方法，用于求解多层弹性半空间的轴对称压痕问题。通过使用Papkovich-Neuber势和Hankel变换以闭合形式导出每一层和基板的应力和位移场。通过使用适当的传递矩阵来处理子层之间的键合或滑动界面条件，然后将混合边界值问题简化为Fredholm积分方程。该解决方案的符号和数值计算在符号软件Mathematica中以快速高效的数值算法的形式实现，从而可以快速确定载荷-位移曲线和任意刚性压头形状的复合弹性。提出并讨论了针对不同压头（扁平，圆锥形，球形和钝头圆锥形冲头形状）和不同多层复合材料的一系列结果。本文提供了完整的符号和数值计算集作为补充资源。

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