TY - JOUR

T1 - Equilibrium of an Elastic Body with Closely Spaced Thin Inclusions

AU - Khludnev, A. M.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.

AB - Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.

KW - boundary conditions of mutual nonpenetration

KW - crack

KW - limiting models

KW - stiffness of inclusion

KW - thin inclusion

KW - CONTACT

KW - CRACK

KW - ASYMPTOTIC-BEHAVIOR

KW - SHAPE SENSITIVITY-ANALYSIS

KW - ENERGY INTEGRALS

KW - BODIES

KW - BOUNDARY

KW - NONPENETRATION

KW - PLATE

KW - RIGID INCLUSION

UR - http://www.scopus.com/inward/record.url?scp=85056094539&partnerID=8YFLogxK

U2 - 10.1134/S096554251810007X

DO - 10.1134/S096554251810007X

M3 - Article

AN - SCOPUS:85056094539

VL - 58

SP - 1660

EP - 1672

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 10

ER -