1. The obstacle problem for shallow shells in curvilinear coordinates
- Author
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Alain Léger, Bernadette Miara, Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Modélisation et Simulation Numérique (MOSIM), and École Supérieure d'Ingénieurs en Électronique et Électrotechnique
- Subjects
Curvilinear coordinates ,Plane (geometry) ,010102 general mathematics ,Mathematical analysis ,Unilateral contact ,Geometry ,General Medicine ,[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph] ,01 natural sciences ,law.invention ,010101 applied mathematics ,Inequation ,[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] ,law ,[PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph] ,Displacement field ,Obstacle problem ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Cartesian coordinate system ,0101 mathematics ,Signorini problem ,Mathematics - Abstract
International audience; 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.
- Published
- 2010