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Within the framework of the applied shell theory, an energetically consistent resolving system of equations is formulated and a complex numerical method is developed that allows solving both quasi-static and dynamic problems of nonlinear non-axisymmetric deformation and loss of stability of composite cylindrical shells within the framework of an explicit variational-difference scheme. The reliability and accuracy of the proposed method are justified by comparing numerical calculations with experimental data. For various reinforcement structures, the analysis of the characteristic spatial configurations and critical loads of the loss of stability of fiberglass cylindrical shells is carried out, depending on the amount of preloading by quasi-static internal pressure and subsequent loading by axial dynamic compression.

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