Combined effects of heterogeneity and non-linearity on the critical time parameters of orthotropic conical shells

The work is devoted to the non-linear dynamic stability of heterogeneous orthotropic truncated conical shells subjected to the combined static and time-dependent axial loads. The basic equations are derived using the finite deflection theory with von Karman–Donnell-type of kinematic non-linearity and reduced to a non-linear differential equation with the time variable coefficient using the superposition principle and Galerkin method. The resulting equation is solved numerically using Runge–Kutta method for variety of an axial loading speed, heterogeneity of features, orthotropic material properties and conical shell characteristics to obtain the non-linear critical time parameters. Finally, the influences of the axial loading speed, non-linearity, heterogeneity and orthotropy on the dimensionless critical time parameters are discussed in detail.