Elastic stress analysis of partially loaded hollow discs

Analysis of cracked and un-cracked semicircular rings under symmetric loading

“…and found SCF for different ratios of radii. Serati et al [4] solved the ring under uniform pressure acting partially on inner and outer boundaries symmetric to an in-plane axis. Durelli and Lin [5] gave the stresses and displacements at the boundaries of a circular ring for different ratios of inner to outer radii obtained using Nelson's equations.…”

Stiffness and Strength of Rock Cutting and Drilling Tools – Drag Bit and Roller Disc Cutters

“…Consequently, the compatibility equations are excluded as they are not formally needed for the general system, and the system of elasticity equations reduces to fifteen linearly independent partial differential equations [22,194,199,200,216]. However, in many cases, especially in three-dimensional (3D) domains, solving for the full system of equations makes the problem very complicated.…”

“…Replacing the new non-zero stress terms A 03 θ, A 12 r θ sin(θ) and A 14 r θ cos(θ) with null stress terms in Eqs. (3.11), (3.12) and (3.13) and sorting for the constants, the general Michell solution is then expressed as [22,138,194,199,216,218]…”

“…(3.30) into Eqs. (3.28) and (3.29), A 12 and A 14 can then be directly calculated from the boundary conditions as [194,199,216]:…”

“…(3.20) responsible for multi-valued displacements. Since they depend on the characteristics of the problem, these constraints need to be identified at the beginning of the analysis [199]. Consequently, when using the Airy stress function method, additional constraint relations are to be introduced, either for the constant determination in Eq.…”