Secondary deformations due to axial shear of the annular region between two eccentrically placed cylinders
type: Item
instance of: scholarly article
title: Secondary deformations due to axial shear of the annular region between two eccentrically placed cylinders
zbMATH Open document ID: 0917.73017
DOI: 10.1023/A:1007484731059
published in: Journal of Elasticity
publication date: 1999-08-05T00:00:00Z
review text: For the title problem, the authors establish that if the driving shear force is not small, but the deviation of the cylinder from the axial symmetry is small, then the perturbation due to the secondary deformation can be characterized by the deviation from the axial symmetry. This follows by using a perturbation approach and by assuming an expansion of displacement in a small parameter and in terms depending on the cross-section and including the zeroth-order axial displacement, similarly to the analysis of the Poiseuille flow. The small parameter depends on the excentricity of the cylinders. The nonlinear kinematic analysis for a Green material leads to a nonlinear system of differential equations which is solved numerically by a Runge-Kutta scheme. The graphs show the axial deformation of zeroth order, the secondary displacement induced by the motion of the inner cylinder, and the pressure gradient for Mooney-Rivlin material. The authors also depict the appearance of boundary layers.
reviewed by: M. Mişicu
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 1176754
zbMATH Keywords: perturbation method
zbMATH Keywords: small parameter
zbMATH Keywords: zeroth-order axial displacement
zbMATH Keywords: nonlinear kinematic analysis
zbMATH Keywords: Green material
zbMATH Keywords: Runge-Kutta scheme
zbMATH Keywords: pressure gradient
zbMATH Keywords: Mooney-Rivlin material
author: Francesco Mollica
author: K. R. Rajagopal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1176754