Localized wrinkling instabilities in radially stretched annular thin films |
| |
Authors: | C D Coman D M Haughton |
| |
Affiliation: | (1) Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW, Scotland, UK |
| |
Abstract: | Summary We investigate a pre-stressed annular thin film subjected to a uniform displacement field along its inner boundary. This loading
scenario leads to a variable stress distribution characterized by an orthoradial component that may change sign along a concentric
circle within the annular domain. When the intensity of the applied field is strong enough, elastic buckling occurs circumferentially,
leading to a localized wrinkling pattern near the inner edge. Using a linear non-homogeneous pre-bifurcation state, the eigenvalue problem describing this instability
is cast as a singularly-perturbed fourth-order linear differential equation with variable coefficients. The dependence of
the lowest eigenvalue on various non-dimensional quantities is numerically investigated using the compound matrix method.
These results are complemented by a WKB analysis which suggests that the qualitative and quantitative features of the full
model can be described by a simplified second-order eigenvalue problem which takes into account the finite stiffness of the
system. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|