Limit elastic speeds of functionally graded annular disks

Abstract

Based on Variational principle, the limit elastic angular speed of rotating disk made of functionally graded material is reported. Assuming a series approximation following Galerkin's principle, the solution of the governing equation is obtained based upon von Mises failure criterion. The elasticity modulus, density and yield stress are assumed to vary according to power law with grading index in the range of -3.0 to 3.0. At grading index, n = 0.0, the disk assumes isotropic material behavior. The investigation reports the variation of limit elastic speed with grading parameter for a different ratio aspect of the annular disk and establishes the existence of optimum grading index at each ratio aspect. The location of yield initiation is also reported in each case and is observed to play a significant role in optimizing limit elastic speed. Further, the displacement, strain and stress states of the disks at limit elastic speed is also reported. The results are validated with benchmarks for the appropriate system parameter values. Due to Variational nature of the solution and ease of handling the non-linear failure criterion, the solution methodology is observed to be stable, simple and robust.

Keywords

• limit elastic speed
• annulus
• von-mises criterion
• fgm