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Torsion of an elastic half-space with a cylindrical cavity by a punch
European Journal of Mechanics - A/Solids ( IF 4.1 ) Pub Date : 2021-04-27 , DOI: 10.1016/j.euromechsol.2021.104308
P. Malits

Torsion of an elastic half-space with a vertical cylindrical cavity by a coaxial punch bonded to a flat boundary and rotated under action of the torque about the axis is considered in this article by employing Weber–Orr integral transforms. We suggest two novel methods reducing the problem to the regular integral equations of the second kind, which are effective for different intervals of geometric parameters and permit to derive a nearly exact approximate solution of the problem for all values of the parameters. The effect of the cavity on the mechanical characteristics in comparison with the well-known Reissner–Sagoci problem is studied in detail. In particular, it is shown that the discrepancies are very small if the punch radius is more than twice as large as the cavity radius and are large if the radii of the punch and cavity are close, that is, the strong edge effect is observed. Simple asymptotic formulas describing the edge effect and the case of a large radius punch are given. Results of this study can be helpful for theoretical modeling of borehole stress fields in structural and mechanical designs applications, for heapstead buildings foundations design as well as for a variety of other engineering problems of a medium with a similar geometry such as mineshafts, wells and boreholes.



中文翻译:

用冲头扭转带有圆柱腔的弹性半空间

在本文中,我们考虑采用韦伯-奥尔积分变换,通过同轴冲头将弹性半空间扭曲,该凹腔是通过同轴冲头结合到平坦边界并在绕轴的扭矩作用下旋转而产生的,该弹性半空间具有垂直圆柱腔。我们建议使用两种新颖的方法将问题简化为第二种规则积分方程,这对于几何参数的不同间隔有效,并允许针对所有参数值导出问题的几乎精确的近似解。与著名的Reissner-Sagoci问题相比,腔对机械特性的影响进行了详细研究。特别是表明,如果冲头半径是型腔半径的两倍以上,则差异非常小如果冲头和型腔的半径接近,则半径会很大,也就是说,会观察到强烈的边缘效应。给出了描述边缘效应和大半径冲头情况的简单渐近公式。这项研究的结果可为结构和机械设计应用中的井眼应力场的理论建模,堆垛建筑物基础设计以及具有类似几何形状的介质(如矿井,井眼和井眼)的各种其他工程问题提供帮助。 。

更新日期:2021-05-11
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