Abstract
Based on the modified Hu-Washizu variational principle, a three-dimensional system of homogeneous linearized differential equations of stability of non-thin anisotropic cylindrical shells is obtained. The anisotropy type of shells is characterized by one plane of elastic symmetry. Reducing the system to a one-dimensional one is carried out using the Bubnov-Gal'orkin method, which approximates the functions of unknown systems of equations along the generatrix and takes into account their periodicity in the circumferential direction. The numerical solution of the obtained one-dimensional system of equations is carried out using the discrete orthogonalization method. 
 The problem of stability of a non-thin anisotropic cylindrical shell for a different number of cross-laid composite layers against the action of axial pressure is solved. The nature of the dependence of critical forces on the number of layers is analyzed.
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