Elastoplastic deformations of rotating parabolic solid disks using Tresca’s yield criterion. (English) Zbl 1032.74578

Summary: Analytical solutions for the stress distribution in rotating parabolic solid disks are obtained. The analysis is based on Tresca’s yield criterion, its associated flow rule and linear strain hardening. It is shown that, the deformation behavior of the convex parabolic disk is similar to that of the uniform thickness disk, but in the case of concave parabolic solid disk, it is different. In the latter, the plastic core consists of three different plastic regions with different mathematical forms of the yield criteria. Accordingly, three different stages of elastic–plastic deformation occur. All these stages of elastic–plastic deformation are studied in detail. It is also shown mathematically that in the limiting case the parabolic disk solution reduces to the solution of rotating uniform thickness solid disk.


74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
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