A modification of Newton’s method is applied to the solution of the nonlinear differential equations for clamped, shallow spherical caps under uniform pressure. The linear form of Newton’s method or quasi-linearization breaks down at limit points of the differential equations. A simplified “quadratic form” is derived in the paper and shown to be satisfactory for continuing the solution past the limit point and into the postbuckling region. Results for the buckling pressures defined by the limit points agree with published results for perfect caps. New results are presented for imperfect caps that check experiment.

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