Stability of saddle-like deformed configurations of plates and shallow shells

Abstract

Studied in this paper are circular and square plates and shallow shells with circular and square bases subjected to certain transverse loadings which, according to the classical linear theory, will produce saddle-like deformed configurations. The analysis shows that the vastly different non-linear behavior is characterized by non-linear bifurcation, the existence of multiple equilibrium configurations and jump phenomenon in deformation, and it involves questions of stability. Moreover, the results demonstrate that when the deformation is appreciable the saddle-like configurations are unstable, and the square plates subjected to four corner forces and the circular plates under periodic edge loadings of cos 2θ type will take on configurations which are more or less cylindrical in shape. This paper is a sequel to [1] where much simpler problems of plates and shallow shells of infinite size are treated.