Axisymmetric postbuckling and secondary bifurcation buckling of circular plates

The exact axisymmetric-postbuckling equilibrium path has been obtained by t he use of the power series method in solving the non-linear differential eq uations for the circular plates subjected to uniform radial compression. Th e problem of the asymmetric-bifurcation buckling from the axisymmetric-post buckling deformation state has been investigated according to the adjacent equilibrium criterion (Brush and Almroth, Buckling of Bars, Plates and Chel ls, McGraw-Hill, New York, 1975; Ziegler, Principles of Structural Stabilit y, Blaisdell Publishing Company, 1968) and the critical loads corresponding to the asymmetric-bifurcation point have been calculated for both simply s upported and clamped plates. The von Karman non-linear equations in the inc remental form have been solved by the use of the power-series expansion and the Fourier series expansion, and the postbuckling behaviour of the circul ar plate beyond the asymmetric-bifurcation point has been investigated. The given results show that in advanced axisymmetric-postbuckling stage, the h igh circumferential compressive stress can induce the circular plate to buc kle with an asymmetric mode, and the equilibrium of the circular plate at t he asymmetric-bifurcation point is unstable. (C) 1999 Elsevier Science Ltd. All rights reserved.