BIFURCATION BUCKLING OF SPHERICAL CAPS
NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES
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A nonlinear boundary value problem was considered for the axisymmetric buckling of thin spherical shells subjected to uniform external pressure. The uniformly compressed spherical state is a solution of this problem for all values of the pressure. It was proven, using Poincares method, that for pressures sufficiently near each simple eigenvalue of the linearized shell buckling theory, there is another buckled solution of the nonlinear problem. A convergent perturbation expansion was used to analyze the buckled solutions near the eigenvalues. For a limited range of caps, it was proven that one or three buckled solutions bifurcate from the multiple double eigenvalues depending on their order. The existence of a lowest intermediate buckling was established and precise upper and lower bounds were given on its magnitude.