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

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 crac...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2018-06, Vol.69 (3), p.1-11, Article 53
Main Authors: Lazarev, N. P., Popova, T. S., Rogerson, G. A.
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Cracks
Engineering
Mathematical Methods in Physics
Optimal control
Theoretical and Applied Mechanics
Two dimensional bodies
Two dimensional models
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Summary: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.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-018-0949-2