Augmented Lagrangian Finite-Elements for Plate Contact Problems

Abstract

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.

Static modes switching in gear contact simulation

“…4. Augmented Lagrangian approach: This approach combines the main ideas of the two previous methods and can be interpreted as an interative penalty method [12]. As noted in [11] the method keeps the number of variables reduced leading to algorithms of similar complexity with respect to penalty formulations while providing increased robustness.…”

“…Step 3: Based on the frequency range of interest only a few vectors are chosen as dynamically responding and the rest to respond quasi-statically, see Eq. (12). If the suggested set of vectors is adopted, the eigenmodes are chosen to respond dynamically while the residual attachment vector space is chosen to respond statically…”

Algorithms and Strategies for Treatment of Large Deformation Frictional Contact in the Numerical Simulation of Deep Drawing Process

“…However, due to the supplementary term associated with the formulation proposed in [17], the two formulations behave differently, even when an Uzawa type algorithm is applied to both. In [111] this comparison is done for plate contact problems, showing that the formulation proposed in [18] may not always result in the exact solution. In fact, when using an Uzawa algorithm, the Lagrange multipliers become constant.…”