Transient dynamic analysis of porous functionally graded truncated conical shells under an asymmetric shock pressure

The paper is devoted to a hybrid three-dimensional (3-D) mathematical modeling to study transient dynamic response of porous functionally graded (FG) truncated conical shells subjected to an asymmetric shock pressure. The hybrid solution method is based on layerwise theory, differential quadrature method (DQM), and Fourier series expansion. Firstly, a Fourier series expansion is used for the displacement components and dynamic pressure in the circumferential direction. Then the layerwise theory is employed to approximate the displacement components in the radial direction. Finally, the DQM is applied to discretize the governing equations in both spatial and time domains. Five cases of different porous distribution along the thickness of the functionally graded shell are considered and the results are compared to the similar non-porous FG shell. The results reveal that the porosity distributions have significant effect on the magnitude of stress components created on the surfaces.