Existence Theorems in the Geometrically Non-linear 6-Parameter Theory of Elastic Plates


In this paper we show the existence of global minimizers for the geometrically non-linear equations of elastic plates, in the framework of the general 6-parameter shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates.

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The first author (M.B.) is supported by the German state grant: “Programm des Bundes und der Länder für bessere Studienbedingungen und mehr Qualität in der Lehre”. Useful discussions with Professor V.A. Eremeyev are gratefully acknowledged.

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Correspondence to Patrizio Neff.

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Bîrsan, M., Neff, P. Existence Theorems in the Geometrically Non-linear 6-Parameter Theory of Elastic Plates. J Elast 112, 185–198 (2013). https://doi.org/10.1007/s10659-012-9405-2

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  • Elastic plates
  • Geometrically non-linear plates
  • Shells
  • Existence of minimizers
  • 6-parameter shell theory
  • Cosserat plate

Mathematics Subject Classification (2010)

  • 74K20
  • 74K25
  • 74G65
  • 74G25