Shape Derivative for Penalty-Constrained Nonsmooth-Nonconvex Optimization: Cohesive Crack Problem
| Autor: | Kovtunenko, Victor A., Kunisch, Karl |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | J. Optim. Theory Appl. (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10957-022-02041-y |
| Popis: | 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. Comment: 27 pages |
| Databáze: | arXiv |
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