Geodesic
A contact problem for an elastic plate with a~thin rigid inclusion
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 3, pp. 90-98

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An equilibrium problem for a plate under the influence of external forces is investigated. It is assumed that the plate contains a thin rigid inclusion that reaches the boundary under zero angle and is in partial contact with an undeformable solid. There is a delamination at one of the faces of the inclusion. A complete Kirchhoff–Love model is considered, where the unknown functions are the vertical and horizontal displacements of the points of the middle surface of the plate. We give a differential statement and a variational statement of the problem and prove the existence and uniqueness of a solution.
Keywords: plate, rigid inclusion, contact problem, fictitious domain. 
@article{SJIM_2016_19_3_a8,
     author = {I. V. Frankina},
     title = {A contact problem for an elastic plate with a~thin rigid inclusion},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {90--98},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2016_19_3_a8/}
}
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I. V. Frankina. A contact problem for an elastic plate with a~thin rigid inclusion. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 3, pp. 90-98. http://geodesic.mathdoc.fr/item/SJIM_2016_19_3_a8/