Abstract
Some approaches to solving nonlinear boundary-value problems of the theory of flexible shells described by ordinary and partial differential equations are presented. One-dimensional problems for a system of anisotropic shells of rotation in the subcritical and supercritical regions of deformation, as well as two-dimensional problems for shells of canonical and noncanonical forms, are considered. The solution of nonlinear problems is performed on the basis of numerical and numerical-analytic methods with the use of discrete orthogonalization and Fourier discrete series.
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