The obstacle problem for shallow shells in curvilinear coordinates

Alain Leger (1) , Bernadette Miara (2)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 MOSIM - Modélisation et Simulation Numérique

Starting from the 3D Signorini problem in presence of a plane obstacle, we justify the limit inequation of unilateral contact posed in a 2D domain. In particular, we show that we can uncouple the three covariant components of the limit Kirchhoff-Love displacement field so that the non-penetrability condition involves only the "transverse" component as this is the case in Cartesian framework.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]

Alain Leger, Bernadette Miara. The obstacle problem for shallow shells in curvilinear coordinates. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2010, 348 (21-22), pp.1235-1239. ⟨10.1016/j.crma.2010.09.013⟩. ⟨hal-00617838⟩