Numerical analysis of axisymmetric buckling of plates under radial compression

Nonlinear boundary-value problems of axisymmetric buckling of simply supported and clamped plates under radial compression are formulated for a system of six first-order ordinary differential equations with independent fields of finite displacements and rotations. Multivalued solutions are obtained by the shooting method with specified accuracy. Bifurcation of the solutions of the problem is studied, and a parametric bifurcation diagram is constructed for various values of the loading parameter. Curves of buckling modes are given for three branches of the solution. The numerical results agree with available theoretical data.