Nitsche based models for the unilateral contact of plates

This paper aims to present different Nitsche-based models for the unilateral contact of plate structures. Our analysis is based on the consideration of Nitsche’s method on a 3D structure with kinematic assumptions of thin or thick plate theories. This approach is compared to that of Gustafsson, Stenberg and Videman which consists of Nitsche’s method applied directly on a 2D plate model. To simplify the presentation, we focus on the contact of an elastic plate with a rigid obstacle. The different approaches are compared numerically in terms of reliability compared to the 3D elastic model. The aim of this paper is to present different Nitsche based models for the unilateral contact of plate structures. Our analysis is based on the consideration of Nitsche’s method on a 3D structure with kinematic assumptions of thin or thick plate theories. This approach is compared to the one of Gustafsson, Stenberg and Videman which consists of Nitsche's method directly applied on a 2D plate model. To simplify the presentation, we focus on the contact of an elastic plate with a rigid obstacle. The different approaches are numerically compared in terms of reliability compared to the 3D elastic model.