Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||23|
|Published online||01 March 2021|
Shape derivatives for an augmented Lagrangian formulation of elastic contact problems*
Groupe Interdisciplinaire de Recherche en Éléments Finis de l’Université Laval, Départment de Mathématiques et Statistiques, Université Laval,
** Corresponding author: firstname.lastname@example.org
Accepted: 28 September 2020
This work deals with shape optimization of an elastic body in sliding contact (Signorini) with a rigid foundation. The mechanical problem is written under its augmented Lagrangian formulation, then solved using a classical iterative approach. For practical reasons we are interested in applying the optimization process with respect to an intermediate solution produced by the iterative method. Because of the projection operator involved at each iteration, the iterate solution is not classically shape differentiable. However, using an approach based on directional derivatives, we are able to prove that it is conically differentiable with respect to the shape, and express sufficient conditions for shape differentiability. Finally, from the analysis of the sequence of conical shape derivatives of the iterative process, conditions are established for the convergence to the conical derivative of the original contact problem.
Mathematics Subject Classification: 35J86 / 49K40 / 49Q10 / 74M15 / 74P15
Key words: Shape and topology optimization / unilateral contact / elliptic variational inequalities / conical differentiability / augmented Lagrangian method
© EDP Sciences, SMAI 2021
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