A method to determine a thermal-elastic-plastic stress-strain state of non-circular cylindrical shells has been developed. The mechanical properties of the material are considered as temperature-dependent. A non-linear shell theory, which is based on the Kirchhoff - Love hypotheses, is used. A modified method of successive elastic solutions is applied to linearize the equations of the theory of simple path-dependent processes of loading. To verify the proposed method, a solution for a cylindrical shell that is obtained by the numerical integration along the directrix is compared with a solution based on the application of the trigonometric Fourier series in cyclic coordinates.

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