N. V. Neustroeva, “Rigid Switching on in the Contact Problem for Elastic Plates”, Sib. Zh. Ind. Mat., 12:4 (2009), 92–105; J. Appl. Industr. Math., 4:4 (2010), 526

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Sibirskii Zhurnal Industrial'noi Matematiki, 2009, Volume 12, Number 4, Pages 92–105 (Mi sjim585)

This article is cited in 36 scientific papers (total in 36 papers)

Rigid Switching on in the Contact Problem for Elastic Plates

N. V. Neustroeva

Institute of Mathematics and Informatics, Yakutsk State University, Yakutsk

Full-text PDF (352 kB) Citations (36)

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Abstract: We consider a family of problems describing the contact of elastic plates located at a fixed angle to each other and, in the natural state, touching along a line. The plates are subjected only to bending. We study passage to the limit from elastic switching on to rigid switching on. We show that the limiting problems describe exactly the contact of an elastic plate with a rigid bar and the problem of the equilibrium of an elastic plate with rigid switching on. We establish the solvability of the problems, find the boundary conditions holding on the possible contact set and their precise interpretation.

Keywords: Kirghoff–Lyav model, contact problem, rigid switching on.

Received: 27.02.2009

English version:
Journal of Applied and Industrial Mathematics, 2010, Volume 4, Issue 4, Pages 526–538
DOI: https://doi.org/10.1134/S1990478910040071

Bibliographic databases:

UDC: 517.95

Language: Russian

Citation: N. V. Neustroeva, “Rigid Switching on in the Contact Problem for Elastic Plates”, Sib. Zh. Ind. Mat., 12:4 (2009), 92–105; J. Appl. Industr. Math., 4:4 (2010), 526–538

Citation in format AMSBIB

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\jour J. Appl. Industr. Math.

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Linking options:

https://www.mathnet.ru/eng/sjim585

https://www.mathnet.ru/eng/sjim/v12/i4/p92

This publication is cited in the following 36 articles:

N. A. Nikolaeva, “Plastina Kirkhgofa — Lyava s ploskim zhestkim vklyucheniem”, Chelyab. fiz.-matem. zhurn., 8:1 (2023), 29–46
N. P. Lazarev, V. A. Kovtunenko, “Asymptotic analysis of the problem of equilibrium of an inhomogeneous body with hinged rigid inclusions of various widths”, J. Appl. Mech. Tech. Phys., 64:5 (2024), 911–920
Lazarev N., “Inverse Problem For Cracked Inhomogeneous Kirchhoff-Love Plate With Two Hinged Rigid Inclusions”, Bound. Value Probl., 2021:1 (2021), 88
Lazarev N.P. Semenova G.M. Romanova N.A., “On a Limiting Passage as the Thickness of a Rigid Inclusions in An Equilibrium Problem For a Kirchhoff Love Plate With a Crack”, J. Sib. Fed. Univ.-Math. Phys., 14:1 (2021), 28–41
Lazarev N. Romanova N. Semenova G., “Optimal Location of a Thin Rigid Inclusion For a Problem Describing Equilibrium of a Composite Timoshenko Plate With a Crack”, J. Inequal. Appl., 2020:1 (2020), 29
Furtsev A.I., “the Unilateral Contact Problem For a Timoshenko Plate and a Thin Elastic Obstacle”, Sib. Electron. Math. Rep., 17 (2020), 364–379
Fankina V I., “on the Equilibrium Problem For a Two-Layer Structure With the Upper Layer Covering a Defect Tip”, Sib. Electron. Math. Rep., 17 (2020), 141–160
N. P. Lazarev, G. M. Semenova, “Optimal control of the location of a thin rigid inclusion in the equilibrium problem of an inhomogeneous two-dimensional body with a crack”, J. Appl. Industr. Math., 13:1 (2019), 76–84
A. I. Furtsev, “A contact problem for a plate and a beam in presence of adhesion”, J. Appl. Industr. Math., 13:2 (2019), 208–218
N. A. Nikolaeva, “On equilibrium of the elastic bodies with cracks crossing thin inclusions”, J. Appl. Industr. Math., 13:4 (2019), 685–697
I. V. Frankina, “On the equilibrium of a two-layer elastic structure with a crack”, J. Appl. Industr. Math., 13:4 (2019), 629–641
Lazarev N.P. Everstov V.V. Romanova N.A., “Fictitious Domain Method For Equilibrium Problems of the Kirchhoff-Love Plates With Nonpenetration Conditions For Known Configurations of Plate Edges”, J. Sib. Fed. Univ.-Math. Phys., 12:6 (2019), 674–686
Fankina V I., “The Equilibrium of a Two Layer Structure in the Presence of a Defect”, Sib. Electron. Math. Rep., 16 (2019), 959–974
A. I. Furtsev, “On Contact Between a Thin Obstacle and a Plate Containing a Thin Inclusion”, J Math Sci, 237:4 (2019), 530
A. M. Khludnev, “Equilibrium of an elastic body with closely spaced thin inclusions”, Comput. Math. Math. Phys., 58:10 (2018), 1660–1672
Lazarev N.P., Popova T.S., Rogerson G.A., “Optimal Control of the Radius of a Rigid Circular Inclusion in Inhomogeneous Two-Dimensional Bodies With Cracks”, Z. Angew. Math. Phys., 69:3 (2018), 53
A. M. Khludnev, “Asymptotics of anisotropic weakly curved inclusions in an elastic body”, J. Appl. Industr. Math., 11:1 (2017), 88–98
Khludnev A.M., Popova T.S., “Timoshenko Inclusions in Elastic Bodies Crossing An External Boundary At Zero Angle”, Acta Mech. Solida Sin., 30:3 (2017), 327–333
I. V. Frankina, “A contact problem for an elastic plate with a thin rigid inclusion”, J. Appl. Industr. Math., 10:3 (2016), 333–340
N. P. Lazarev, “Optimal control of the size of rigid inclusion in equilibrium problem for inhomogeneous Timoshenko-type plate with crack”, J. Math. Sci., 228:4 (2018), 409–420

Citing articles in Google Scholar: Russian citations, English citations
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