Shape Derivative for Penalty-Constrained Nonsmooth–Nonconvex Optimization: Cohesive Crack Problem Full article
| Journal |
Journal of Optimization Theory and Applications
ISSN: 0022-3239 |
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| Output data | Year: 2022, Volume: 194, Number: 2, Pages: 597-635 Pages count : 39 DOI: 10.1007/s10957-022-02041-y | ||||
| Tags | Destructive physical analysis; Free discontinuity problem; Lagrange method; Lavrentiev regularization; Non-penetrating crack; Optimal control; Penalization; Quasi-brittle fracture; Shape optimization; Variational inequality | ||||
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Abstract:
A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities 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.
Cite:
Kovtunenko V.A.
, Kunisch K.
Shape Derivative for Penalty-Constrained Nonsmooth–Nonconvex Optimization: Cohesive Crack Problem
Journal of Optimization Theory and Applications. 2022. V.194. N2. P.597-635. DOI: 10.1007/s10957-022-02041-y WOS Scopus РИНЦ OpenAlex
Shape Derivative for Penalty-Constrained Nonsmooth–Nonconvex Optimization: Cohesive Crack Problem
Journal of Optimization Theory and Applications. 2022. V.194. N2. P.597-635. DOI: 10.1007/s10957-022-02041-y WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000791053800002 |
| Scopus: | 2-s2.0-85129435781 |
| Elibrary: | 48581795 |
| OpenAlex: | W4229044232 |