A A PARAMETRIC STUDY ON THE CENTRIFUGAL FORCE- INDUCED STRESS AND DISPLACEMENTS IN POWER-LAW GRADED HYPERBOLIC DISCS

Abstract

AN EXTENSIVE PARAMETRIC STUDY ON THE VARIATION OF THE CENTRIFUGAL-FORCE-INDUCED STRESS AND DISPLACEMENTS WITH THE INHOMOGENEITY AND PROFILE PARAMETERS AND BOUNDARY CONDITIONS IS CONDUCTED BASED ON THE AUTHOR’S RECENTLY PUBLISHED ANALYTICAL FORMULAS FOR RADIALLY FUNCTIONALLY GRADED ROTATING HYPERBOLIC DISCS. THE SIMPLE POWER MATERIAL GRADING RULE IS USED AS A MATERIAL GRADING RULE. THE RADIAL VARIATION OF THE THICKNESS OF THE DISC IS CHOSEN TO OBEY A HYPERBOLIC FUNCTION DEFINED EITHER CONVERGENT OR DIVERGENT. IN THE PRESENT WORK, CONTRARY TO THE PUBLISHED ONE, IT IS ASSUMED THAT BOTH YOUNG’S MODULUS AND DENSITY RADIALLY VARY WITH THE SAME INHOMOGENEITY INDEX. UNDER THIS ADDITIONAL ASSUMPTION, FOR THE VALUES OF THE CHOSEN SIMPLE POWER-LAW INDEXES Β=-5,0,5 FOR MATERIAL GRADING RULE , AND THE CHOSEN PROFILE PARAMETERS M=-1,-0.75,-0.5,-0.25,0.25,0.5,0.75,1 FOR HYPERBOLIC DISC; THE GRAPHS OF RADIAL STRESS, HOOP STRESS AND THE RADIAL DISPLACEMENT ARE ALL ILLUSTRATED GRAPHICALLY FOR A ROTATING DISC WHOSE BOTH SURFACES ARE STRESS-FREE, FOR A ROTATING DISC MOUNTED A RIGID SHAFT AT ITS CENTER AND ITS OUTER SURFACE IS STRESS-FREE, AND FINALLY FOR A ROTATING DISC ATTACHED A RIGID SHAFT AT ITS CENTER AND GUIDED AT ITS OUTER SURFACE (A RIGID CASING EXISTS AT THE OUTER SURFACE).