Stress-minimizing holes with a given surface roughness in a remotely loaded elastic plane

We proposed a new form of modeling the boundary roughness effects on the stress distribution and stress concentration around a single hole in a loaded thin elastic plate. The shape irregularities are simulated as periodic patterns of notch-like deviations from an "ideal" shape (mostly from a circle). These are assessed with two relative measures: their maximum peak-to-valley height and the average slope. At given hole shape, all expressions for stress fields are derived in explicit form. This analysis serves as a basis to formulate and numerically solve the optimization problem of finding the stress-minimizing hole shape under fixed irregularities levels. In doing so, the surface topography need not be shallow as was supposed in previous studies. Methodologically, this study continues the previous work of the authors in detecting the "worst" hole shape under certain extremizing conditions [Vigdergauz and Elishakoff 2019]. The performance of the proposed scheme is verified via instructive numerical examples. The results obtained are presented graphically and may be analyzed visually. They have a practical relevance for optimal design problems in mechanical engineering.