Axisymmetric postbuckling and secondary bifurcation buckling of circular plates

Abstract

The exact axisymmetric-postbuckling equilibrium path has been obtained by the use of the power series method in solving the non-linear differential equations for the circular plates subjected to uniform radial compression. The problem of the asymmetric-bifurcation buckling from the axisymmetric-postbuckling deformation state has been investigated according to the adjacent equilibrium criterion (Brush and Almroth, Buckling of Bars, Plates and Chells, McGraw-Hill, New York, 1975; Ziegler, Principles of Structural Stability, Blaisdell, 1968), and the critical loads corresponding to the asymmetric-bifurcation point have been calculated for both simply supported and clamped plates. The von Karman non-linear equations in the incremental form have been solved by the use of the power-series expansion and the Fourier series expansion, and the postbuckling behaviour of the circular plate beyond the asymmetric-bifurcation point has been investigated. The given results show that in advanced axisymmetric-postbuckling stage, the high circumferential compressive stress can induce the circular plate to buckle with an asymmetric mode, and the equilibrium of the circular plate at the asymmetric-bifurcation point is unstable.