On the Sapondzhyan–Babuška Paradox

Abstract

We consider the Lamé 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

Acknowledgements

The work of G. A. Chechkin was partially supported by RFBR grant and by the program ‘Universities of Russia’.