On Equilibrium Problem for Elastic Body with Neumann Boundary Condition and Delaminated Timoshenko Inclusion
- 1Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk 630090, Russia
Abstract
This paper addresses the investigation of an equilibrium problem describing an elastic body with an incorporated thin elastic Timoshenko inclusion, provided that the Neumann boundary condition is imposed on the external boundary of the body. The inclusion is delaminated from the elastic body, thus forming an interfacial crack. A restriction of the inequality type considered at the crack faces does not allow the opposite faces to penetrate each other. Moreover, the crack faces’ boundary conditions depend on a positive parameter characterizing the adhesion. We find the condition imposed on the external forces, proving the existence of a solution to the boundary value problem analyzed, and prove the solution’s existence. The asymptotic analysis of the solutions with respect to the adhesion parameter and the stiffness parameter of the inclusion is investigated. Limit models are analyzed. Both variational and differential statements of the considered problems are obtained, and a connection between them is established.
Related
- Carleman estimates for a nonconservative Timoshenko beam involving Dirichlet-Neumann boundary conditions and application to exact controllability
- Lack of exponential stability for thermoelastic Timoshenko and Bresse systems with full homogeneous Dirichlet boundary conditions
- Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning
- Equilibrium fluctuations of the weakly asymmetric inclusion process
- On the gauge invariant boundary condition in open XXZ chains: SoV bases, elementary blocks and overlaps
BibTeX
@article{khludnev2026equilibrium,
title = {{On Equilibrium Problem for Elastic Body with Neumann Boundary Condition and Delaminated Timoshenko Inclusion}},
author = {Alexander Khludnev and Evgeny Rudoy},
journal = {Axioms},
year = {2026},
month = oct,
doi = {10.3390/axioms15100780},
url = {https://www.mdpi.com/2075-1680/15/10/780},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - On Equilibrium Problem for Elastic Body with Neumann Boundary Condition and Delaminated Timoshenko Inclusion
AU - Alexander Khludnev
AU - Evgeny Rudoy
PY - 2026
DA - 2026/10/17
JO - Axioms
DO - 10.3390/axioms15100780
UR - https://www.mdpi.com/2075-1680/15/10/780
AB - This paper addresses the investigation of an equilibrium problem describing an elastic body with an incorporated thin elastic Timoshenko inclusion, provided that the Neumann boundary condition is imposed on the external boundary of the body. The inclusion is delaminated from the elastic body, thus forming an interfacial crack. A restriction of the inequality type considered at the crack faces does not allow the opposite faces to penetrate each other. Moreover, the crack faces’ boundary conditions depend on a positive parameter characterizing the adhesion. We find the condition imposed on the external forces, proving the existence of a solution to the boundary value problem analyzed, and prove the solution’s existence. The asymptotic analysis of the solutions with respect to the adhesion parameter and the stiffness parameter of the inclusion is investigated. Limit models are analyzed. Both variational and differential statements of the considered problems are obtained, and a connection between them is established.
SN - 2075-1680
ER -