Abstract Analytical solutions to the stress concentration factors (SCFs) for 3-D surfaces with small undulations are obtained by a boundary perturbation approach, with consideration of the boundary load ratio. And their applications are shown well to a number of shallow irregularities on surfaces. Moreover, the proposed analytical expression is applied to predict the SCFs of 3-D machined surface topography, which is reconstructed by two dimensional Fourier series. Besides, the prediction results are validated by finite element analysis, comparisons between analytical and numerical results suggest that our analytical solution can be used with assured confidence to calculate the SCFs of 3-D real machined surface topographies.

中文翻译：

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具有小起伏的 3-D 表面的应力集中：解析解

摘要 考虑边界载荷比的情况下，通过边界微扰方法获得了具有小起伏的 3-D 表面应力集中因子 (SCF) 的解析解。它们的应用在表面上的许多浅不规则处得到了很好的展示。此外，所提出的解析表达式用于预测 3-D 加工表面形貌的 SCF，该形貌由二维傅立叶级数重建。此外，通过有限元分析验证了预测结果，解析结果和数值结果之间的比较表明，我们的解析解可以放心地用于计算 3-D 真实加工表面形貌的 SCF。