Existence of an optimal size of a rigid inclusion for an equilibrium problem of a Timoshenko plate with Signorini-type boundary condition

被引：0
作者：
Nyurgun Lazarev
Tatiana Popova
Galina Semenova
机构：
[1] North-Eastern Federal University,
来源：
Journal of Inequalities and Applications | / 2016卷
关键词：
crack; plate; rigid inclusion; nonpenetration condition; variational inequality; 74G55; 49J40; 49J30;
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摘要：
We study the contact problems for elastic plates with a rigid inclusion. We consider the case of frictionless contact between the rigid part of the plate and a rigid obstacle. The contact is modeled with the Signorini-type nonpenetration condition. The deformation of the transversely isotropic elastic part of the plate is described by the Timoshenko model. We analyze the dependence of solutions to the contact problems on the size of rigid inclusion. The existence of a solution to the optimal control problem is proved. For that problem, the cost functional characterizes the deviation of the displacement vector from a given function, whereas the size parameter of rigid inclusion is chosen as the control function.
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