Augmented Lagrangian finite-elements for plate contact problems

The present work investigates the unilateral frictionless contact between a plate and a rigid obstacle. Two sets of problems are studied: a plate constrained through unilateral edge supports and a plate seating in its undeformed configuration at a given distance from a rigid support. The attention is concentrated on two augmented Lagrangian formulations. The algorithmic implementation within a finite‐element scheme is presented and discussed. The importance of using appropriate plate elements for the discretization of the structure is stressed. New gap elements compatible with a robust plate element are derived. Computational aspects are emphasized. A simple and effective numerical integration for the determination of the gap stiffnesses in partial contact with the support is proposed. Numerical results are carried out and compared with analytical solutions. The convergence to the solution of the perfectly constrained problem is numerically investigated. The inadequacy of the penalty method and the satisfactory performance obtained from only one augmented Lagrangian procedure are emphasized.