Secondary deformations due to axial shear of the annular region between two eccentrically placed cylinders
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.
scientific article; zbMATH DE number 1176754