TY - JOUR
AU - Nyurgun Lazarev
AU - Evgenii Sharin
AU - Galina Semenova
PY - 2021/07/19
Y2 - 2024/09/13
TI - Optimal location of a rigid inclusion for an equilibrium problem describing Kirchhoff-Love plate with nonpenetration conditions for known configurations of plate edges
JF - Mathematical notes of NEFU
JA - Math. notes NEFU
VL - 28
IS - 2
SE - Mathematics
DO -
UR - https://mzsvfu.ru/index.php/mz/article/view/optimal-location-of-arigid-inclusion
AB - A nonlinear model describing equilibrium of a cracked plate with a volume rigid inclusion is studied. It is assumed that under the action of certain given loads, plates have deformations with a certain predetermined configuration of edges near the crack. On the crack curve we impose a nonlinear boundary condition as a system of inequalities and an equality describing the nonpenetration of the opposite crack faces. For a family of variational problems, we study the dependence of their solutions on the location of the inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on a suitable Sobolev space. For this problem, the location parameter of the inclusion serves as a control parameter. We prove continuous dependence of the solutions on the location parameter and the existence of a solution to the optimal control problem.
ER -