Elastic Stress Analysis of Hyperbolic Rotating Disks via Optimal Homotopy Asymptotic Method

Abstract

This study, it is aimed to use an effective approximation method, called Optimal Homotopy Asymptotic Method (OHAM) for elastic stress analysis. This study is carried out with the idea that utilizable of the considered method in many areas and having advantages will add a new perspective to the rotating disc problems that can provide convenience and practicality. The considered disk is an annular disk with both free ends and is subjected to centrifugal force. The thickness variation is assumed as hyperbolic. Deformations occurred on the disk, and radial and tangential stresses are calculated with the proposed method. The approximate solutions are in very good agreement with the exact solution. It is observed that the results converge to exact solutions faster than other approximate methods, like the Improved Adomian Decomposition method, in the literature. The results of this study show that OHAM is a very practical method with fast results for rotating disk problems. The study also shows the advantages of OHAM being directly applicable to differential equations of rotating disks without any transform function. Results by the comparison of approximate results and exact solutions indicated that OHAM can effectively be used in the analysis of rotating variable thickness disks.