Based on the Timoshenko theory the approach is presented for calculation of the stability of anisotropic cylindrical shell due to the geometrical prebuckling non-linear stress-strain state. The relevant properties of the coating material are symmetrical according a plane which can coincide with the central surface. Numerical study was performed using the method of discrete orthogonalization. A graph is illustrating the effect of the angle of layering of the fiber composite for the critical stress to axial compression.

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