Shape sensitivity analysis of an elastic contact problem: Convergence of the Nitsche based finite element approximation

In a recent work, we introduced a finite element approximation for the shape optimization of an elastic structure in sliding contact with a rigid foundation where the contact condition (Signorini’s condition) is approximated by Nitsche’s method and the shape gradient is obtained via the adjoint stat...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2023-08, Vol.72, p.103836, Article 103836
Main Authors: Bretin, Élie, Chapelat, Julien, Douanla-Lontsi, Charlie, Homolle, Thomas, Renard, Yves
Format: Article
Language:English
Subjects:
Adjoint state method
Conical derivative
Engineering Sciences
Mathematics
Nitsche’s method
Numerical Analysis
Shape gradient
Shape optimization
Unilateral contact
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Summary:In a recent work, we introduced a finite element approximation for the shape optimization of an elastic structure in sliding contact with a rigid foundation where the contact condition (Signorini’s condition) is approximated by Nitsche’s method and the shape gradient is obtained via the adjoint state method. The motivation of this work is to propose an a priori convergence analysis of the numerical approximation of the variables of the shape gradient (displacement and adjoint state) and to show some numerical results in agreement with the theoretical ones. The main difficulty comes from the non-differentiability of the contact condition in the classical sense which requires the notion of conical differentiability.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2023.103836