Choosing an Optimal Shape of thin Rigid Inclusions in Elastic Bodies
V. V. Shcherbakov1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: thin rigid inclusion, crack, nonlinear boundary conditions, variational inequality, optimal control
Abstract
The optimal control problem for a three-dimensional elastic body containing a thin rigid inclusion as a surface is studied. It is assumed that the inclusion delaminates, which is why there is a crack between the elastic domain and the inclusion. The boundary conditions on the crack faces that exclude mutual penetration of the points of the body and inclusion are considered. The cost functional that characterizes the deviation of the surface force vector from the function prescribed on the external boundary is used; in this case, the inclusion shape is considered as a control function. It is proven that a solution of the described problem exists.
DOI: http://dx.doi.org/10.1134/S0021894415020182
|
