Analysis on the Establishment of Angular Displacement and Stresses for Pure Azimuthal Deformation in an Incompressible Hollow Cylindrical Gent Material
Okujagu Tamunobarachueye Edward
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Nwagwu Isaac Ogazie *
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
Julius Bassey Effiong
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This project work is concerned with the study of an Isotropic, Incompressible hollow cylinder deforming under pure azimuthal shear loading. The analysis resulted into a non-linear second order ordinary differential equation for the determination of the angular displacement. The resulting solution of the boundary value problem gave an equation which needed the wolfram Alpha software for the determination of the analytic solution of the angular displacement. Relationship between the displacement, stress components and the material parameter for hardening and softening is shown and the effect of change on the material parameter on the angular displacement is illustrated.
Keywords: Angular displacement, deformed radius, shear strain, displacement gradient, shear stresses