Abstract:
A two layer elastic body equilibrium problem is considered in this paper. One of the layers contains a crack. The other one is glued to the first one by its edge to cover one of the crack tips. The unique solvability of the problem with non-penetration condition on the crack faces is proved. A problem in the case when the second layer is rigid is studied. It is shown that a “rigid patch” problem could be obtained as a limit problem for a family of “elastic patch” problems when the rigidity parameter of the second layer tends to infinity. An optimal control problem is considered. The vector of exterior forces acting on two layers is chosen as a control function. Two aim functions are used. The first of them is a functional that characterizes potential energy change with respect to the crack length. The other one is a functional equal to an average opening of the crack along its length. The existence of solutions that minimize each of the functionals is proved.
Keywords:
elastic body, overlapping domain, crack with non-penetration optimal control problem.
Citation:
E. V. Pyatkina, “On control problem for two-layers elastic body with a crack”, Sib. J. Pure and Appl. Math., 16:4 (2016), 103–112; J. Math. Sci., 230:1 (2018), 159–166
\Bibitem{Pya16}
\by E.~V.~Pyatkina
\paper On control problem for two-layers elastic body with a crack
\jour Sib. J. Pure and Appl. Math.
\yr 2016
\vol 16
\issue 4
\pages 103--112
\mathnet{http://mi.mathnet.ru/vngu425}
\crossref{https://doi.org/10.17377/PAM.2016.16.410}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 230
\issue 1
\pages 159--166
\crossref{https://doi.org/10.1007/s10958-018-3735-y}
Linking options:
https://www.mathnet.ru/eng/vngu425
https://www.mathnet.ru/eng/vngu/v16/i4/p103
This publication is cited in the following 2 articles:
A. M. Khludnev, “Thin inclusion at the junction of two elastic bodies: non-coercive case”, Phil. Trans. R. Soc. A., 382:2277 (2024)
Alexey Furtsev, Hiromichi Itou, Evgeny Rudoy, “Modeling of bonded elastic structures by a variational method: Theoretical analysis and numerical simulation”, International Journal of Solids and Structures, 182-183 (2020), 100
Citation in format AMSBIB
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