The buckling of functionally graded truncated conical shells under dynamic axial loading

The dynamic buckling of truncated conical shells made of functionally graded materials (FGMs) subject to a uniform axial compressive load, which is a linear function of time, has been studied. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the dynamic stability and compatibility equations of functionally graded truncated conical shells are obtained first. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equation with variable coefficient and critical parameters obtained using the Runge–Kutta method. The results show that the critical parameters are affected by the configurations of the constituent materials, compositional profile variations, loading speed variations and the variation of the shell geometry. Comparing the results of this study with those in the literature validates the present analysis.