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Buckling of an elastic hemispherical shell with an obstacle

Abstract

We study the buckling of an axially symmetric elastic hemispherical shell, uniformly compressed, subject to a constraint to the radial shifting of the equatorial circumference. The static equilibrium equations, using tensorial notations, are obtained applying the virtual displacements principle to the energy functional. The presence of a constraint does not modify the field equations with respect to the case of a constraint-free buckling, but only influences the boundary conditions, so that, instead of a boundary value problem, we deal with a problem with complementarity conditions on the boundary. We revisit and improve some previously obtained mathematical results, adapting them for the subsequent numerical treatment. Finally, by suitably using a delicate quasi-static shooting technique, numerical results are obtained, which complete the theoretical analysis and give an interesting insight into the behavior of the bifurcation branches.

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Correspondence to Alberto Maria Bersani.

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Communicated by Francesco dell’Isola and Samuel Forest.

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Bersani, A.M., Giorgio, I. & Tomassetti, G. Buckling of an elastic hemispherical shell with an obstacle. Continuum Mech. Thermodyn. 25, 443–467 (2013). https://doi.org/10.1007/s00161-012-0273-6

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  • DOI: https://doi.org/10.1007/s00161-012-0273-6

Keywords

  • Buckling
  • Elastic shell
  • Minimization of functionals
  • Nonlinear theory
  • Bifurcation
  • Shooting methods

Mathematics Subject Classification (2000)

  • 34B08
  • 34B15
  • 34B60
  • 74B15
  • 74G60
  • 74G65
  • 74K25