Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells

Non-linear buckling analyses of imperfect functionally graded truncated conical shells with simply supported boundary conditions and subjected to an axial compressive load have been presented in this work. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The non-linear prebuckling deformations and initial geometric imperfections of an FGM truncated conical shell are both taken into account. The fundamental relations, modified Donnell type non-linear stability and compatibility equations of an imperfect FGM truncated conical shell are obtained and are solved by superposition and Galerkin methods, and the upper and lower critical axial loads has been found analytically. The numerical illustrations concern the non-linear buckling response of FGM truncated conical shells with different values of truncated conical shell parameters, initial imperfections and compositional profiles. Comparing the results of this study with those in the literature validates the present analysis.

► Analytical solution of non-linear buckling analyses of imperfect functionally graded truncated conical shells is developed.
► The modified Donnell type non-linear stability and compatibility equations of imperfect FGM truncated conical shell are derived.
► The upper and lower critical axial loads has been found analytically.
► The effects of initial imperfections and compositional profiles on the non-linear critical axial load are studied numerically.