TY - JOUR

T1 - Equilibrium problem for elastic plate with thin rigid inclusion crossing an external boundary

AU - Khludnev, Alexander

AU - Fankina, Irina

N1 - Funding Information: This work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2021/6

Y1 - 2021/6

N2 - The paper concerns an equilibrium problem for an elastic plate with a thin rigid inclusion. Both vertical and horizontal displacements of the plate are considered in the frame of the model. It is assumed that the inclusion crosses the external boundary of the plate. Moreover, the inclusion is delaminated from the plate which leads to appearance of a crack between the inclusion and the plate. To provide a mutual nonpenetration between crack faces, we consider nonlinear boundary conditions with unknown set of a contact. We prove a solution existence of the equilibrium problem and analyze an inverse problem with unknown elasticity tensor. To formulate the inverse problem, additional data are imposed to be determined from a boundary measurement. An existence of a solution to the inverse problem is proved, and stability properties are established.

AB - The paper concerns an equilibrium problem for an elastic plate with a thin rigid inclusion. Both vertical and horizontal displacements of the plate are considered in the frame of the model. It is assumed that the inclusion crosses the external boundary of the plate. Moreover, the inclusion is delaminated from the plate which leads to appearance of a crack between the inclusion and the plate. To provide a mutual nonpenetration between crack faces, we consider nonlinear boundary conditions with unknown set of a contact. We prove a solution existence of the equilibrium problem and analyze an inverse problem with unknown elasticity tensor. To formulate the inverse problem, additional data are imposed to be determined from a boundary measurement. An existence of a solution to the inverse problem is proved, and stability properties are established.

KW - Crack

KW - Elastic plate

KW - Free boundary problem

KW - Inverse problem

KW - Thin rigid inclusion

KW - Variational inequality

UR - http://www.scopus.com/inward/record.url?scp=85106252858&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=46094075

U2 - 10.1007/s00033-021-01553-3

DO - 10.1007/s00033-021-01553-3

M3 - Article

AN - SCOPUS:85106252858

VL - 72

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 3

M1 - 121

ER -