LAUSR

This study derived a full-field stress series solution to multi-loads with small contact area uniformly distributed around the circumference of a disk, and an analytical solution to concentrated forces spaced evenly around the circumference of a disk using the contribution of the full-field analytical solution of the Brazilian test model. Relative errors between the analytic solution and the series solution revealed that when $$2\alpha $$2α, the angle between the uniformly-distributed loads with small contact area, is less than $$5^{\circ }$$5∘, the full-field stress series solution can be reliably replaced with the full-field stress analytical solution. Based on a photoelastic experiment, we derived a formula by which to determine the full-field stress, resulting from concentrated forces isotopically arranged around the circumference of the disk. The numerical findings are in good agreement with those obtained in the photoelastic experiment, thereby verifying the efficacy of the simple theoretical formula derived in this study. This study provides a full-field stress analytical solution for forces evenly spaced around the circumference of a disk. This solution can be used to evaluate the internal stress distribution of disk structures and optical components clamped at the edges.