<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the dimension of the problem inside the inclusion is decreased by one. For the numerical solution of this problem we propose an iterative domain decomposition algorithm (Dirichlet-Neumann scheme). This approach allows us to decouple problems in both parts and preserve the structure of the corresponding matrices. We investigate the convergence of the aforementioned algorithm and prove that the problem is well-posed.</p></abstract>

We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the dimension of the problem inside the inclusion is decreased by one. For the numerical solution of this problem we propose an iterative domain decomposition algorithm (Dirichlet-Neumann scheme). This approach allows us to decouple problems in both parts and preserve the structure of the corresponding matrices. We investigate the convergence of the aforementioned algorithm and prove that the problem is well-posed.

On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion

Faculty of Applied Mathematics and Informatics, Department of Applied Mathematics, Ivan Franko Lviv National University, Universytetska,1, 79000, Lviv, Ukraine

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain...

On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion

Published Online: May 15, 2015

Page range: 27 - 32

DOI: https://doi.org/10.1515/ama-2015-0006

© Bialystok University of Technology

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.