A multisegment method is developed for the solution of two-point boundary-value problems governed by a system of first-order ordinary nonlinear differential equations. By means of this method, rotationally symmetric shells of arbitrary shape under axisymmetric loads can be analyzed with any available nonlinear bending theory of shells. The basic equations required by the method are given for one particular theory of shells, and numerical examples of a shallow spherical cap and a complete torus subjected to external pressure are presented in detail. The main advantage of this method over the finite-difference approach is that the solution is obtained everywhere with uniform accuracy, and the iteration process with respect to the mesh size, which is required with the finite-difference method, is eliminated.

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