This article is cited in 12 papers

Differentical equations, dynamical systems and optimal control

On modeling elastic bodies with defects

A. M. Khludnev<sup>ab

a</sup> Lavrentyev Institute of Hydrodynamics of SB RAS pr. Lavrentieva, 15, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova str., 1, 630090, Novosibirsk, Russia

Abstract: The paper concerns a mathematical analysis of equilibrium problems for 2D elastic bodies with thin defects. The defects are characterized with a damage parameter. A presence of defects implies that the problems are formulated in a nonsmooth domain with a cut. Nonlinear boundary conditions at the cut faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are analyzed. The paper provides an asymptotic analysis with respect to the damage parameter. We obtain invariant integrals over curves surrounding the defect tip. An optimal control problem is investigated with a cost functional equal to the derivative of the energy functional with respect to the defect length, and the damage parameter being a control function.

Keywords: defect, damage parameter, non-penetration boundary conditions, variational inequality, optimal control, derivative of energy functional.

UDC: 517.958,539.3

MSC: 35Q74,35Q93

Received December 29, 2017, published February 15, 2018

Language: English

DOI: 10.17377/semi.2018.15.015

Bibliographic databases:

•