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Shape Derivatives for the Penalty Formulation of Elastic Contact Problems with Tresca Friction
- Source :
- SIAM Journal on Control and Optimization. 58:3237-3261
- Publication Year :
- 2020
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2020.
-
Abstract
- In this article, the shape optimization of a linear elastic body subject to frictional (Tresca) contact is investigated. Due to the projection operators involved in the formulation of the contact problem, the solution is not shape differentiable in general. Moreover, shape optimization of the contact zone requires the computation of the gap between the bodies in contact, as well as its shape derivative. Working with directional derivatives, sufficient conditions for shape differentiability are derived. %The problem is addressed in the general framework of two bodies with smooth boundaries. Then, some numerical results, obtained with a gradient descent algorithm based on those shape derivatives, are presented.<br />Comment: Preprint
- Subjects :
- 0209 industrial biotechnology
Control and Optimization
Level set method
Applied Mathematics
010102 general mathematics
Mathematical analysis
Linear elasticity
Unilateral contact
Numerical Analysis (math.NA)
02 engineering and technology
01 natural sciences
Projection (linear algebra)
020901 industrial engineering & automation
Optimization and Control (math.OC)
FOS: Mathematics
Penalty method
Shape optimization
Mathematics - Numerical Analysis
0101 mathematics
Mathematics - Optimization and Control
Mathematics
Subjects
Details
- ISSN :
- 10957138 and 03630129
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Control and Optimization
- Accession number :
- edsair.doi.dedup.....9d0c53e1d7528fa4a5a52148af54d357