An asymptotic strain gradient Reissner-Mindlin plate model

Michèle Serpilli (1) , Françoise Krasucki (2) , Giuseppe Geymonat (3)

1 Department of Civil and Building Engineering, and Architecture [Ancona]
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 LMS - Laboratoire de mécanique des solides

In this paper we derive a strain gradient plate model from the three-dimensional equations of strain gradient linearized elasticity. The deduction is based on the asymptotic analysis with respect of a small real parameter being the thickness of the elastic body we consider. The body is constituted by a second gradient isotropic linearly elastic material. The obtained model is recognized as a strain gradient Reissner-Mindlin plate model. We also provide a mathematical justification of the obtained plate model by means of a variational weak convergence result.

Mots clés: Asymptotic analysis; Strain gradient elasticity; Plate models; Micro-plates

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Michèle Serpilli, Françoise Krasucki, Giuseppe Geymonat. An asymptotic strain gradient Reissner-Mindlin plate model. Meccanica, 2013, pp.1-13. ⟨10.1007/s11012-013-9719-6⟩. ⟨hal-00757357⟩