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Modelling and Simulation in Engineering
Volume 2017, Article ID 5246197, 19 pages
https://doi.org/10.1155/2017/5246197
Research Article

Modeling of Size Effects in Bending of Perforated Cosserat Plates

1Department of Mathematics, University of Puerto Rico at Aguadilla, Aguadilla, PR 00604, USA
2Department of Mathematical Sciences, University of Puerto Rico at Mayagüez, Mayagüez, PR 00681, USA

Correspondence should be addressed to Lev Steinberg; ude.rpu@grebniets.vel

Received 27 August 2016; Revised 20 November 2016; Accepted 1 December 2016; Published 30 March 2017

Academic Editor: Chung-Souk Han

Copyright © 2017 Roman Kvasov and Lev Steinberg. 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

This paper presents the numerical study of Cosserat elastic plate deformation based on the parametric theory of Cosserat plates, recently developed by the authors. The numerical results are obtained using the Finite Element Method used to solve the parametric system of 9 kinematic equations. We discuss the existence and uniqueness of the weak solution and the convergence of the proposed FEM. The Finite Element analysis of clamped Cosserat plates of different shapes under different loads is provided. We present the numerical validation of the proposed FEM by estimating the order of convergence, when comparing the main kinematic variables with an analytical solution. We also consider the numerical analysis of plates with circular holes. We show that the stress concentration factor around the hole is less than the classical value, and smaller holes exhibit less stress concentration as would be expected on the basis of the classical elasticity.