Certain contact problems must be treated as three-dimensional (3D) axial periodic problems, such as the contact of cylinders with rough surfaces and/or inhomogeneities in the materials, whose structural features in contact are confined in a finite domain in one direction but extended infinitely in the other direction. A novel numerical model for simulating the contact of machined cylindrical components containing inhomogeneities is developed via extending the concept of the 3D line-contact fast Fourier transform (FFT) algorithms. Due to the stochastic similarity of asperity and inhomogeneity distributions in the length direction, the cylinder is divided into N segments in the length direction while taking the roughness and inhomogeneities in one of these segments as representatives. The periodic convolution and FFT is used in the length direction, together with superposing the influence coefficients (ICs) of the N segments, while the discrete (circular) convolution and fast Fourier transformation (DC–FFT) is used in the non-periodic direction; this is named the DCS–FFT algorithm. The accuracy of the DCS–FFT algorithm is examined by the comparison of the numerical results for a degenerated cylindrical contact with the corresponding analytical solution, and its efficiency is evaluated through the comparison of its execution speed with that of two other FFT-based algorithms. The developed method is implemented to study the influence of inhomogeneities on subsurface stress distributions with/without the periodic length direction extension and superposition of inhomogeneity ICs. A criterion is provided to decide whether the DCS procedure is needed for the contact analysis of inhomogeneity-containing cylinders.

中文翻译：

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非均质材料三维接触影响系数求和的离散卷积和 FFT 方法 (DCS-FFT)

某些接触问题必须被视为三维 (3D) 轴向周期性问题，例如圆柱与粗糙表面和/或材料中的不均匀性接触，其接触的结构特征被限制在一个方向的有限域中，但扩展无限向另一个方向。通过扩展 3D 线接触快速傅里叶变换 (FFT) 算法的概念，开发了一种新的数值模型，用于模拟包含不均匀性的机加工圆柱部件的接触。由于长度方向的粗糙度和不均匀性分布的随机相似性，将圆柱体沿长度方向分为N个段，其中一个段的粗糙度和不均匀性为代表。长度方向使用周期性卷积和FFT，连同叠加N个片段的影响系数（IC），而在非周期方向上使用离散（圆形）卷积和快速傅立叶变换（DC-FFT）；这称为 DCS-FFT 算法。DCS-FFT 算法的准确性通过退化圆柱接触的数值结果与相应解析解的比较来检验，并通过其执行速度与其他两种基于 FFT 的算法的比较来评估其效率。所开发的方法用于研究不均匀性对具有/不具有周期性长度方向延伸和不均匀性 IC 叠加的地下应力分布的影响。