The paper presents an explicit matrix algorithm to solve the problem of an elastic wedge with three loaded surfaces. The algorithm makes use of a recently published concept of transformation matrix, by which the original surface loads are converted to equivalent loads in half-space. The three loaded edges are considered simultaneously. The developed algorithm is used to study the effects of two free edges of a steel block and tapered rollers with different contact angles. The two load-free edges can substantially increase deformation if the two edges are close in distance. The results of the tapered roller simulation show that deformation is considerably sensitive to the contact angle of the tapered roller. The largest deformation appears at the big end of the roller. Furthermore, empirical formulae for correction factors for the calculation of block or quarter-space deformation based on half-space solutions are summarized.

中文翻译：

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考虑两个边缘效应的三维楔形问题的显式解

本文提出了一种显式矩阵算法来解决具有三个加载表面的弹性楔形问题。该算法利用了最近发布的转换矩阵的概念，通过该概念，原始表面载荷被转换为半空间中的等效载荷。同时考虑了三个加载的边。所开发的算法用于研究钢块的两个自由边缘和具有不同接触角的圆锥滚子的影响。如果两个无载荷边缘的距离很近，则这两个边缘会大大增加变形。圆锥滚子模拟的结果表明，变形对圆锥滚子的接触角相当敏感。最大的变形出现在辊的大端。此外，