Michell–Fourier analytical treatment of stresses in the ring test under parabolic compression

TL;DRAbstract

This paper attempts to provide a simple analytical solution for the calculation of stress tensors induced in a linear elastic ring of a brittle material subjected to parabolic loading over two symmetric strips of its outer perimeter. Using the Michell-Fourier series technique and Airy stress functions, stress components are investigated in a tensile positive fashion. Results are obtained in series form to facilitate parametric studies on the influence of the loading angle and geometric characteristics of the ring on the maximum tensile stress. Results indicate that for a ring with a small hole, the type of the imposed stress is crucial in determining the distributions of the stress components inside the ring domain, although it becomes almost negligible for a ring with a relatively large hole. In contrast, a large inner to outer ratio influences significantly the stress values at critical points of the ring experiencing the maximum tensile stress.

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