Report
Shape optimization involving the Tresca friction law in a 2D linear elastic model
| العنوان: | Shape optimization involving the Tresca friction law in a 2D linear elastic model |
|---|---|
| المؤلفون: | Bourdin, Loïc, Caubet, Fabien, Jacob de Cordemoy, Aymeric |
| المساهمون: | XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et de leurs Applications Pau (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) |
| المصدر: | https://hal.science/hal-04785047 ; 2024. |
| بيانات النشر: | CCSD |
| سنة النشر: | 2024 |
| المجموعة: | HAL e2s UPPA (Université de Pau et des Pays de l'Adour) |
| مصطلحات موضوعية: | Shape optimization, shape sensitivity analysis, contact mechanics, Tresca's friction law, Signorini's unilateral conditions, variational inequalities, twice epi-differentiability, AMS Classification: 49Q10, 49Q12, 49J40, 74M10, 74M15, 74P10, [MATH]Mathematics [math] |
| الوصف: | The aim of this work is to analyse a shape optimization problem in a mechanical friction context. Precisely we perform a shape sensitivity analysis of a Tresca friction problem, that is, a boundary value problem involving the usual linear elasticity equations together with the (nonsmooth) Tresca friction law on a part of the boundary. We prove that the solution to the Tresca friction problem admits a directional shape derivative which moreover coincides with the solution to a boundary value problem involving tangential Signorini's unilateral conditions. Then an explicit expression of the shape gradient of the Tresca energy functional is provided (which allows us to provide numerical simulations illustrating our theoretical results). Our methodology is not based on any regularization procedure, but rather on the twice epi-differentiability of the (nonsmooth) Tresca friction functional which is analyzed thanks to a change of variables which is well-suited in the two-dimensional case. The obstruction in the higher-dimensional case is discussed. |
| نوع الوثيقة: | report |
| اللغة: | English |
| الاتاحة: | https://hal.science/hal-04785047 https://hal.science/hal-04785047v1/document https://hal.science/hal-04785047v1/file/Shape_optimization_in_a_two_dimensional_linear_elastic_model_involving_the_Tresca_friction_law.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.74CF52FE |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |