Abstract:
Under consideration are the variational problems concerning the equilibrium of plates containing a crack. Two new mathematical models are proposed in which the nonpenetration conditions define the corresponding nonconvex sets of admissible functions.
The first model describes the equilibrium of a Timoshenko plate with a crack, and the second corresponds to a composite plate containing a crack along a Kirchhoff—Love elastic inclusion. The proposed approach is substantiated by an explicit example.
We prove the existence of solutions for the corresponding variational problems
and show that the equilibrium equations are satisfied for each of the problems.
Citation:
N. P. Lazarev, G. M. Semenova, “Equilibrium problem for a Timoshenko plate
with a geometrically nonlinear condition of nonpenetration
for a vertical crack”, Sib. Zh. Ind. Mat., 23:3 (2020), 65–76; J. Appl. Industr. Math., 14:3 (2020), 532–540
\Bibitem{LazSem20}
\by N.~P.~Lazarev, G.~M.~Semenova
\paper Equilibrium problem for a Timoshenko plate
with a geometrically nonlinear condition of nonpenetration
for a vertical crack
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 3
\pages 65--76
\mathnet{http://mi.mathnet.ru/sjim1099}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.306}
\elib{https://elibrary.ru/item.asp?id=45184950}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 3
\pages 532--540
\crossref{https://doi.org/10.1134/S1990478920030126}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85094665535}
Linking options:
https://www.mathnet.ru/eng/sjim1099
https://www.mathnet.ru/eng/sjim/v23/i3/p65
This publication is cited in the following 5 articles:
Victor A. Kovtunenko, Nyurgun P. Lazarev, “Variational inequality for a Timoshenko plate contacting at the boundary with an inclined obstacle”, Phil. Trans. R. Soc. A., 382:2277 (2024)
N. P. Lazarev, D. Ya. Nikiforov, N. A. Romanova, “Zadacha o ravnovesii dlya plastiny Timoshenko, kontaktiruyuschei bokovoi i litsevoi poverkhnostyami”, Chelyab. fiz.-matem. zhurn., 8:4 (2023), 528–541
N. P. Lazarev, G. M. Semenova, E. D. Fedotov, “An Equilibrium Problem for a Kirchhoff–Love Plate, Contacting an Obstacle by Top and Bottom Edges”, Lobachevskii J Math, 44:2 (2023), 614
Nyurgun P. Lazarev, Victor A. Kovtunenko, “Signorini-Type Problems over Non-Convex Sets for Composite Bodies Contacting by Sharp Edges of Rigid Inclusions”, Mathematics, 10:2 (2022), 250
N. Lazarev, “Inverse problem for cracked inhomogeneous Kirchhoff-Love plate with two hinged rigid inclusions”, Bound. Value Probl., 2021:1 (2021), 88
Citation in format AMSBIB
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