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 VigdEli2019.
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.
