Nitsche-based models for the unilateral contact of plates

Fabre, Mathieu; Pozzolini, Cédric; Renard, Yves

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S941-S967

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.

Classification : 65N22
Keywords: Contact problem, variational formulation, numerical scheme, Nitsche method

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