Abstract:
The work is devoted to the calculation of the geometry of an equi-strength annular disk taking into account the anisotropy and strength differential effect. The disk is under centrifugal forces and tractions on the inner and outer surfaces. The problem statement is based on the anisotropic elasticity theory and the plane stress assumption. General quadratic failure criterion is used, the only requirement for which is ellipticity. In particular cases, the used condition is reduced to many known strength criteria (Tsai–Wu, Hill, Drucker–Prager, von Mises, etc.).
The governing system of equations consists of the compatibility equation, the equilibrium equation and the condition of constant equivalent stress. This condition is satisfied by a trigonometric substitution and an introduced auxiliary function. The two remaining equations are solved sequentially in an implicit form, in which the auxiliary function is treated as independent variable. The found analytical solution allows to construct the geometry of the disk (profile and inner radius of the disk) of equal strength, and also to determine the distribution of stresses in it. It is established that the solution may not exist and be non-unique. In particular cases, the solution is reduced to solutions for many known failure criteria, as well as to the classical solution of Rabotnov. Comparison of calculations obtained for the Tsai–Wu and von Mises criteria showed that anisotropy and different strengths under tension and compression can have a significant effect on the geometry of a disk of equal strength and the stress state in it.
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