Exploring islands of stability in the design space of cylindrical shell structures

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Abstract

The structural stability of a simple benchmark problem – the snap through of a shallow cylindrical roof – is revisited. The problem is analysed in a robust manner using a technique known as generalised path-following, which combines the mathematical domains of finite element analysis and numerical continuation.
Using this technique, the well-known arc-length method for tracing equilibrium paths in load-displacement space is extended to explore other interesting paths on a two-dimensional solution manifold in three-dimensional load-displacement-parameter space. These paths include unconventional equilibrium paths traced by varying a model parameter, e.g. shell thickness, as well as critical paths that describe points where the tangential stiffness matrix is singular – that is where buckling, snap-through or other instabilities occur. For the chosen benchmark problem, a localised region of stable equilibrium exists on one of the unstable equilibrium branches. The evolution of this stable region with variations in shell thickness is explored by tracing the locus of critical
limit points that separate the stable and unstable portions of the equilibrium curve. Hence, without resorting to computationally expensive parametric studies, we establish a two-dimensional manifold of stable equilibria in displacement-load-thickness space, which can be graphically interpreted as an island of stability.
Original languageEnglish
Title of host publicationShell Structures: Theory and Applications Volume 4
Subtitle of host publicationProceedings of the 11th International Conference "Shell Structures: Theory and Applications, (SSTA 2017), October 11-13, 2017, Gdansk, Poland
EditorsWojciech Pietraszkiewicz, Wojciech Witkowski
PublisherRoutledge
Pages223-226
Number of pages4
ISBN (Print)9781138050457
Publication statusPublished - 25 Sep 2017
Event11th International Conference "Shell Structures: Theory and Applications" - Gdansk, Poland
Duration: 11 Oct 201713 Oct 2017

Conference

Conference11th International Conference "Shell Structures: Theory and Applications"
CountryPoland
CityGdansk
Period11/10/1713/10/17

Structured keywords

  • ACCIS Core Team

Keywords

  • Generalised path-following
  • Bifurcation
  • Buckling
  • Post-buckling
  • Nonlinearity

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