A simple and efficient numerical method for determination of deformations and stresses in rotating solid shafts with non-linear strain-hardening

摘要

A simple and efficient numerical method is proposed to investigate deformations and stresses in elastic-plastic rotating solid shafts. Using the assumption of plane strain, the governing equation is derived from the geometric relation, equilibrium equation, deformation theory, von Mises' yield criterion and non-linear stress-plastic strain relationship. By making use of the information of the second and third derivatives of the radial stress with respect to the radial co-ordinate and introducing a truncated Taylor's expansion, an iterative algorithm is presented which can solve elastic-plastic problems of rotating solid shafts quickly and effectively. Two numerical examples are given to demonstrate accuracy, efficiency and capacity of the proposed method in both fully elastic and non-linear strain-hardening elastic-plastic analyses of rotating solid shafts. Excellent agreement is found between this method and finite element approach.