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Shape Derivative for Penalty-Constrained Nonsmooth-Nonconvex Optimization: Cohesive Crack Problem
- Source :
- J. Optim. Theory Appl. (2022)
- Publication Year :
- 2022
-
Abstract
- A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities (VI) is studied with respect to its shape differentiability. The specific problem stemming from quasi-brittle fracture describes an elastic body with a Barenblatt cohesive crack under the inequality condition of non-penetration at the crack faces. Based on the Lagrange approach and using smooth penalization with the Lavrentiev regularization, a formula for the shape derivative is derived. The explicit formula contains both primal and adjoint states and is useful for finding descent directions for a gradient algorithm to identify an optimal crack shape from a boundary measurement. Numerical examples of destructive testing are presented in 2D.<br />Comment: 27 pages
- Subjects :
- Mathematics - Optimization and Control
35R37, 49J40, 49Q10, 74RXX
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Optim. Theory Appl. (2022)
- Publication Type :
- Report
- Accession number :
- edsarx.2204.04569
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10957-022-02041-y