Optimal Control of Rigidity Parameter of Thin Inclusions in Elastic Bodies with Curvilinear Cracks

2014 ◽  
Vol 203 (4) ◽  
pp. 591-604 ◽  
Author(s):  
V. V. Shcherbakov
Keyword(s):  
Optimal Control ◽  
Elastic Bodies ◽  
Rigidity Parameter ◽  
Curvilinear Cracks

Optimal Control of Inclusion and Crack Shapes in Elastic Bodies

2012 ◽  
Vol 155 (1) ◽  
pp. 54-78 ◽  
Author(s):  
A. Khludnev ◽  
G. Leugering ◽  
M. Specovius-Neugebauer
Keyword(s):  
Optimal Control ◽  
Elastic Bodies

Junction problem for rigid and Timoshenko elastic inclusions in elastic bodies

2015 ◽  
Vol 22 (4) ◽  
pp. 737-750 ◽  
Author(s):  
AM Khludnev ◽  
L Faella ◽  
TS Popova
Keyword(s):  
Rigid Inclusion ◽  
Existence Of Solutions ◽  
Elastic Inclusion ◽  
Joint Point ◽  
Elastic Bodies ◽  
Rigidity Parameter ◽  
Elastic Inclusions ◽  
Type Boundary ◽  
Crack Faces ◽  
Inequality Type

This paper concerns an equilibrium problem for a two-dimensional elastic body with a thin Timoshenko elastic inclusion and a thin rigid inclusion. It is assumed that the inclusions have a joint point and we analyze a junction problem for these inclusions. The existence of solutions is proved and the different equivalent formulations of the problem are discussed. In particular, the junction conditions at the joint point are found. A delamination of the elastic inclusion is also assumed. In this case, the inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. We investigate the convergence to infinity and zero of a rigidity parameter of the elastic inclusion. It is proved that in the limit, we obtain a rigid inclusion and a zero rigidity inclusion (a crack).

On modeling thin inclusions in elastic bodies with a damage parameter

2018 ◽  
Vol 24 (9) ◽  
pp. 2742-2753 ◽  
Author(s):  
A. M. Khludnev
Keyword(s):  
Optimal Control ◽  
Nonlinear Boundary ◽  
Equilibrium Problems ◽  
Control Function ◽  
Nonlinear Boundary Conditions ◽  
Energy Functional ◽  
Damage Parameter ◽  
Elastic Bodies ◽  
The Matrix ◽  
Crack Faces

In this paper, we analyze equilibrium problems for 2D elastic bodies with two thin inclusions in the presence of damage. A delamination of the inclusions from the matrix is assumed, thus forming a crack between the elastic body and the inclusions. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are discussed. The paper provides an asymptotic analysis with respect to the damage parameter. An optimal control problem is analyzed with a cost functional to be equal to the derivative of the energy functional with respect to the crack length, and the damage parameter being a control function.

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