Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 686421, 7 pages
http://dx.doi.org/10.1155/2014/686421
Research Article

Conservative Semidiscrete Difference Schemes for Timoshenko Systems

Department of Mathematics, Federal University of Pará, Augusto Corrêa Street 01, 66075-110 Belém, PA, Brazil

Received 2 December 2013; Accepted 5 February 2014; Published 7 May 2014

Academic Editor: Suh-Yuh Yang

Copyright © 2014 D. S. Almeida Júnior. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient Timoshenko systems considering shear deformation and rotatory inertia. We derive numerical energies showing the positivity, and the energy conservation property and we show how to avoid a numerical anomaly known as locking phenomenon on shear force. Our method of proof relies on discrete multiplier techniques.