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The investigations were financed within the framework of the Lublin University of Technology – Regional Excellence Initiative project, funded by the Polish Ministry of Science and Higher Education (contract no.030/RID/2018/19).
The behavior of FGM cylindrical shells with imperfections under compression was analyzed. Two cases of the ceramics-metal phase arrangement regarding the shell thickness, as well as a case where the coupling matrix determined according to the classical laminate plate theory equaled zero, owing to which the shell was homogenous transversely, was assumed in the analytical–numerical calculations. Cylindrical shell edges were simply supported. Thermal loads were neglected in this study. Within the first-order approximation of the non-linear Byskov-Hutchinson theory, a value of the ultimate load-carrying capacity corresponding to the critical load of the actual structure with imperfections was determined. This approach allows one to determine the imperfection sensitivity surface as well. It was assumed in the numerical calculations that the material of cylindrical shell gradients complied with Hooke’s law. The critical load of real shells (i.e., with imperfections) is treated as the failure load in standard provisions, design and verifications calculations. An analytical–numerical method (ANM) developed by the authors was applied in the calculations. In this approach, Lagrange’s description, precise strains for thin-walled panels and the second Piola-Kirchhoff’s stress tensor, the exact transition matrix method and the numerical method of the transition matrix using Godunov’s orthogonalization are used. All results were validated with the finite element method.
