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

  • N. P. Lazarev
  • T. S. Popova
  • G. A. Rogerson


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.


Variational inequality Optimal control problem Non-penetration Nonlinear boundary conditions Crack Rigid inclusion 

Mathematics Subject Classification

49J30 49J40 74G55 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.North-Eastern Federal UniversityYakutskRussia
  2. 2.School of Computing and MathematicsKeele UniversityKeeleUK

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