Shape sensitivity analysis of an elastic contact problem: Convergence of the Nitsche based finite element approximation
| Autor: | Élie Bretin, Julien Chapelat, Charlie Douanla-Lontsi, Thomas Homolle, Yves Renard |
|---|---|
| Přispěvatelé: | Renard, Yves |
| Rok vydání: | 2023 |
| Předmět: |
Nitsche's method
Applied Mathematics finite element method General Engineering General Medicine [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] conical derivative Computational Mathematics shape gradient sensitivity analysis shape optimization linearized elasticity adjoint state method General Economics Econometrics and Finance Analysis unilateral contact |
| Zdroj: | Nonlinear Analysis: Real World Applications. 72:103836 |
| ISSN: | 1468-1218 |
| DOI: | 10.1016/j.nonrwa.2023.103836 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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