In two recent papers, approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested, which provide explicit analytical relations for the force–approach relation, the size and the shape of the contact area, as well as for the pressure distribution therein. These solutions were derived for profiles, which only slightly deviate from the axisymmetric shape. In the present paper, they undergo an extensive testing and validation by comparison of solutions with a great variety of profile shapes with numerical solutions obtained by the fast Fourier transform (FFT)-assisted boundary element method (BEM). Examples are given with quite significant deviations from axial symmetry and show surprisingly good agreement with numerical solutions.

在最近的两篇论文中，提出了均匀幂律分级弹性体的紧凑非轴对称接触问题的近似解，它为力接近关系、接触区域的大小和形状提供了明确的分析关系，如下所示以及其中的压力分布。这些解决方案是针对轮廓导出的，仅略微偏离轴对称形状。在本文中，通过将各种轮廓形状的解与快速傅里叶变换（FFT）辅助边界元法（BEM）获得的数值解进行比较，对它们进行了广泛的测试和验证。给出的示例与轴对称性有相当大的偏差，并且与数值解显示出令人惊讶的良好一致性。