Numerical analysis of elastic–plastic rotating disks with arbitrary variable thickness and density

Abstract

A unified numerical method is developed in this article for the analysis of deformations and stresses in elastic–plastic rotating disks with arbitrary cross-sections of continuously variable thickness and arbitrarily variable density made of nonlinear strain-hardening materials. The method is based on a polynomial stress–plastic strain relation, deformation theory in plasticity and Von Mises’ yield condition. The governing equation is derived from the basic equations of the rotating disks and solved using the Runge–Kutta algorithm. The proposed method is applied to calculate the deformations and stresses in various rotating disks. These disks include solid disks with constant thickness and constant density, annular disks with constant thickness and constant density, nonlinearly variable thickness and nonlinearly variable density, linearly tapered thickness and linearly variable density, and a combined section of continuously variable thickness and constant density. The computed results are compared to those obtained from the finite element method and the existing approaches. A very good agreement is found between this research and the finite element analysis. Due to the simplicity, effectiveness and efficiency of the proposed method, it is especially suitable for the analysis of various rotating disks.