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Optimal control of the radius of a rigid circular inclusion in inhomogeneous two-dimensional bodies with cracks

Optimal control of the radius of a rigid circular inclusion in inhomogeneous two-dimensional bodies with cracks Thumbnail


Abstract

A two-dimensional model describing the equilibrium state of a cracked inhomogeneous body with a rigid circular inclusion is investigated. The body is assumed to have a crack that reaches the boundary of the rigid inclusion. We assume that the Signorini condition, ensuring non-penetration of the crack faces, is satisfied. We analyze the dependence of solutions on the radius of rigid
inclusion. The existence of a solution of the optimal control problem is proven. For this problem, a cost functional is defined by an arbitrary continuous functional, with the radius of inclusion chosen as the control parameter.

Citation

(2018). Optimal control of the radius of a rigid circular inclusion in inhomogeneous two-dimensional bodies with cracks. Zeitschrift für Angewandte Mathematik und Physik, https://doi.org/10.1007/s00033-018-0949-2

Acceptance Date Mar 22, 2018
Publication Date Apr 11, 2018
Journal Zeitschrift fur angewandte Mathematik und Physik
Print ISSN 0044-2275
Publisher Springer Verlag
DOI https://doi.org/10.1007/s00033-018-0949-2
Keywords variational inequality, optimal control problem, nonpenetration, non-linear boundary conditions, crack, rigid inclusion
Publisher URL https://doi.org/10.1007/s00033-018-0949-2

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