On the Sapondzhyan-Babuska Paradox

Authors: Chechkin, Gregory¹; Lukkassen, Dag¹; Meidell, Annette²

Source: Applicable Analysis, Volume 87, Number 12, December 2008 , pp. 1443-1460(18)

Abstract:

We consider the Lame form of the elasticity system and demonstrate the famous paradox, which can be obtained by the limit passage in the polygonal plates with very small sides as the length of sides goes to zero. The phenomenon is that boundary conditions in the original problem and the limit problem are different. We provide the asymptotic and numerical analysis for the approximation of displacements, energies and moments, demonstrating the paradox.

Keywords: plate theory; oscillating boundary; homogenization

Document Type: Research article

DOI: 10.1080/00036810802140632

Affiliations: 1: Narvik University College, N-8505 Narvik, Norway,Norut Narvik, N-8504 Narvik, Norway 2: Narvik University College, N-8505 Narvik, Norway

Links for this article

http://www.ingentaconnect.com/tandf/gapa/2008/00000087/00000012/art00011
http://openurl.ingenta.com/content?genre=article&issn=0003-6811&volume=87&issue=12&spage=1443&epage=1460
http://dx.doi.org/10.1080/00036810802140632