Exact full-field analysis of strain and displacement for circular disks subjected to partially distributed compressions

The disk in diametral compression has been investigated frequently on developing experimental techniques, such as photoelasticity and Moiré interferometry, for several decades. Theoretically, the compression as a concentrated force is more conducive to analyze but it is impossible to achieve such loading condition experimentally. The distributed compression on a finite area at rim is important in many engineering applications and is relatively closer to actual testing conditions, but it is complicated to seek an analytical solution. This paper presents exact full-field solutions of strain and displacement of a circular disk subjected to partially diametral distributed compressions in explicit functional forms. Based on the theoretical solutions, full-field distributions of strain and displacement are easily provided in polar and Cartesian coordinates by numerical calculations. Interesting phenomena of strain and displacement are discussed in detail based on numerical results. The Saint-Venant's principle applied in circular disks subjected to diametral loadings is examined by comparing the full-field results for the concentrated load and the distributed compression with small angle. Experimental measurements of full-field displacement contours and isochromatic fringe patterns are used to compare with the theoretical predictions and good agreements of both results are found.