Abstract and Applied Analysis
Volume 2005 (2005), Issue 8, Pages 889-899
Stable and unstable bifurcation in the von Kármán problem for a circular plate
1Department of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, Gdańsk-Oliwa 80–952, Poland
2Department of Technical Physics and Applied Mathematics, Gdańsk University of Technology, ul. Gabriela Narutowicza 11/12, Gdańsk 80–952, Poland
Received 20 February 2004
Copyright © 2005 Andrei Borisovich and Joanna Janczewska. 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.
In this work, we study bifurcation in the von Kármán
equations for a thin circular elastic plate which lies on the
elastic base and is simply supported and subjected to a
compressive force along the boundary. Applying analytical methods,
we prove the existence of stable and unstable simple bifurcation
points in the solution set of these equations.