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Buckling of an elastic hemispherical shell with an obstacle

Continuum Mechanics and Thermodynamics volume 25, pages 443–467 (2013)Cite this article

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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Authors and Affiliations

  1. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, via A. Scarpa 16, 00161, Rome, Italy

    Alberto Maria Bersani & Giovanna Tomassetti

  2. International Research Center for Mathematics and Mechanics of Complex Systems (M&MoCS), Palazzo Caetani, 04012, Cisterna di Latina, LT, Italy

    Alberto Maria Bersani & Ivan Giorgio

  3. Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, via Eudossiana 18, 00184, Rome, Italy

    Ivan Giorgio

Authors
  1. Alberto Maria Bersani
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  2. Ivan Giorgio
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  3. Giovanna Tomassetti
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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