Shape Derivative for Penalty-Constrained Nonsmooth–Nonconvex Optimization: Cohesive Crack Problem

Shape Derivative for Penalty-Constrained Nonsmooth–Nonconvex Optimization: Cohesive Crack Problem Научная публикация

Журнал

Journal of Optimization Theory and Applications
ISSN: 0022-3239

Вых. Данные

Год: 2022, Том: 194, Номер: 2, Страницы: 597-635 Страниц : 39 DOI: 10.1007/s10957-022-02041-y

Ключевые слова

Destructive physical analysis; Free discontinuity problem; Lagrange method; Lavrentiev regularization; Non-penetrating crack; Optimal control; Penalization; Quasi-brittle fracture; Shape optimization; Variational inequality

Авторы

Kovtunenko Victor A. ^1,2 , Kunisch Karl ²

Организации

1	Institute of Hydrodynamics SB RAS
2	Universität Graz

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.

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

Web of science:	WOS:000791053800002
Scopus:	2-s2.0-85129435781
РИНЦ:	48581795
OpenAlex:	W4229044232

БД	Цитирований
Scopus	7
OpenAlex	9
РИНЦ	9
Web of science	9