Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion

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Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion. / Khludnev, Alexander.

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 73, No. 2, 54, 04.2022.

Research output: Contribution to journal › Article › peer-review

Harvard

Khludnev, A 2022, 'Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion', Zeitschrift fur Angewandte Mathematik und Physik, vol. 73, no. 2, 54. https://doi.org/10.1007/s00033-022-01693-0

APA

Khludnev, A. (2022). Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion. Zeitschrift fur Angewandte Mathematik und Physik, 73(2), [54]. https://doi.org/10.1007/s00033-022-01693-0

Vancouver

Khludnev A. Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion. Zeitschrift fur Angewandte Mathematik und Physik. 2022 Apr;73(2):54. doi: 10.1007/s00033-022-01693-0

Author

Khludnev, Alexander. / Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion. In: Zeitschrift fur Angewandte Mathematik und Physik. 2022 ; Vol. 73, No. 2.

BibTeX

@article{e54cd1eb6164437aadd0280498519c17,

title = "Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion",

abstract = "In the paper, we consider a boundary value problem for an elastic plate with a thin rigid inclusion in a non-coercive case. Both vertical and horizontal displacements of the plate are considered in the frame of the considered model. The inclusion is assumed to be delaminated from the plate which provides a crack between the inclusion and the surrounding elastic body. To guarantee a mutual non-penetration between crack faces, we consider inequality type boundary conditions with unknown set of a contact. A solution existence of the equilibrium problems is proved. Displacements of the plate in the x3-direction can be fixed at one or two points. In these cases, we also prove a solution existence of the boundary value problems.",

keywords = "Crack, Elastic plate, Non-coercive boundary problem, Thin rigid inclusion, Variational inequality",

author = "Alexander Khludnev",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = apr,

doi = "10.1007/s00033-022-01693-0",

language = "English",

volume = "73",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "2",

}

RIS

TY - JOUR

T1 - Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion

AU - Khludnev, Alexander

PY - 2022/4

Y1 - 2022/4

N2 - In the paper, we consider a boundary value problem for an elastic plate with a thin rigid inclusion in a non-coercive case. Both vertical and horizontal displacements of the plate are considered in the frame of the considered model. The inclusion is assumed to be delaminated from the plate which provides a crack between the inclusion and the surrounding elastic body. To guarantee a mutual non-penetration between crack faces, we consider inequality type boundary conditions with unknown set of a contact. A solution existence of the equilibrium problems is proved. Displacements of the plate in the x3-direction can be fixed at one or two points. In these cases, we also prove a solution existence of the boundary value problems.

AB - In the paper, we consider a boundary value problem for an elastic plate with a thin rigid inclusion in a non-coercive case. Both vertical and horizontal displacements of the plate are considered in the frame of the considered model. The inclusion is assumed to be delaminated from the plate which provides a crack between the inclusion and the surrounding elastic body. To guarantee a mutual non-penetration between crack faces, we consider inequality type boundary conditions with unknown set of a contact. A solution existence of the equilibrium problems is proved. Displacements of the plate in the x3-direction can be fixed at one or two points. In these cases, we also prove a solution existence of the boundary value problems.

KW - Crack

KW - Elastic plate

KW - Non-coercive boundary problem

KW - Thin rigid inclusion

KW - Variational inequality

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UR - https://www.mendeley.com/catalogue/fd75e974-51b0-3ae9-a93c-b9fd8b8a132b/

U2 - 10.1007/s00033-022-01693-0

DO - 10.1007/s00033-022-01693-0

M3 - Article

AN - SCOPUS:85125013610

VL - 73

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 2

M1 - 54

ER -

ID: 35590435