Optimal control of the thickness of a rigid inclusion in equilibrium problems for inhomogeneous two-dimensional bodies with a crack

2015 ◽  
Vol 96 (4) ◽  
pp. 509-518 ◽  
Author(s):  
N. P. Lazarev
Keyword(s):  
Optimal Control ◽  
Rigid Inclusion ◽  
Equilibrium Problems ◽  
Two Dimensional

scholarly journals Optimal location of a rigid inclusion in equilibrium problems for inhomogeneous Kirchhoff–Love plates with a crack

2019 ◽  
Vol 24 (12) ◽  
pp. 3743-3752 ◽  
Author(s):  
Nyurgun Lazarev ◽  
Hiromichi Itou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Rigid Inclusion ◽  
Equilibrium Problems ◽  
Location Parameter ◽  
Continuous Functional ◽  
Existence Of A Solution ◽  
Crack Faces ◽  
Variational Statement

A non-linear model describing the equilibrium of a cracked plate with a volume rigid inclusion is studied. We consider a variational statement for the Kirchhoff–Love plate satisfying the Signorini-type non-penetration condition on the crack faces. For a family of 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 with respect to the location parameter and the existence of a solution of the optimal control problem.

scholarly journals Applied Optimization and Approximation

2014 ◽  
Vol 3 (4) ◽  
pp. 37-48
Author(s):  
Octav Olteanu
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Linear Function ◽  
Polynomial Approximation ◽  
Moment Problem ◽  
Quadratic Forms ◽  
Two Dimensional ◽  
Several Variables ◽  
Applied Optimization ◽  
The Moment

The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained cost function. Elementary notions of optimal control are considered as well. Finally, polynomial approximation results on unbounded subsets in several variables are applied to the moment problem. The existence of the solution of a two dimensional moment problem is characterized in terms of quadratic forms.

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