Analysis of boundary layer effects due to usual boundary conditions or geometrical defects in elastic plates under bending: an improvement of the Love-Kirchhoff model

Andrés Alessandro León Baldelli (1) , Jean-Jacques Marigo (2) , Catherine Pideri (3)

1 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
2 LMS - Laboratoire de mécanique des solides
3 IMATH - Institut de Mathématiques de Toulon - EA 2134

We propose a model of flexural elastic plates accounting for boundary layer effects due to the most usual boundary conditions or to geometrical defects, constructed via matched asymptotic expansions. In particular, considering a rectangular plate clamped at two opposite edges while the other two are free, we derive the effective boundary conditions or effective transmission conditions that the two first terms of the outer expansion must satisfy. The new boundary value problems thus obtained are studied and compared with the classical Love-Kirchhoff plate model. Two examples of application illustrate the results.

Mots clés: Dimension reduction; Plate theory; Boundary layers; Matched asymptotic expansions

Domaines: Mécanique des solides [physics.class-ph]; Mathématiques [math]

Andrés Alessandro León Baldelli, Jean-Jacques Marigo, Catherine Pideri. Analysis of boundary layer effects due to usual boundary conditions or geometrical defects in elastic plates under bending: an improvement of the Love-Kirchhoff model. Journal of Elasticity, In press, ⟨10.1007/s10659-020-09804-6⟩. ⟨hal-03053520⟩