This work presents a detailed asymptotic description of the neutral stability envelope for the linear bifurcations of a shallow conical shell subjected to lateral pressure. The eighth-order boundary-eigenvalue problem investigated originates in the Donnell shallow-shell theory coupled with a linear membrane pre-bifurcation state, and leads to a neutral stability curve that exhibits two distinct growth rates. By using singular perturbation methods we propose accurate approximations for both regimes and explore a number of other novel features of this problem. Our theoretical results are compared with several direct numerical simulations that shed further light on the problem.
|Number of pages||21|
|Journal||Mathematics and Mechanics of Solids|
|Early online date||13 Feb 2017|
|Publication status||Published - 1 May 2018|
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- Department of Computer Science - Senior Lecturer in Mathematics
- School of Computing and Engineering
- Centre for Mathematics and Data Science - Member