Nonlinear low-velocity impact analysis of functionally graded shallow spherical shells in thermal environments

Abstract

This article presents the nonlinear dynamic response of functionally graded (FG) shallow spherical shells in thermal environments subjected to low-velocity impact by an elastic ball. The material properties of a FG shallow spherical shell vary continuously through the thickness according to a power law distribution of the volume fraction of the constituents. The temperature field is considered to vary along the thickness direction due to the steady state heat transfer. Based on the higher order shear deformation theory, the governing equations of motion for the shell, which account for geometric nonlinearity is obtained using Hamilton’s principle. The contact force between the shell and the impactor is relative to local deformation and calculated using a numerical method. Then, the governing equations of motion are solved numerically by the Chebyshev collocation method and Newmark scheme. This is a complete model that can not only fully model the dynamic behavior of the shell but also fully model the impactor’s dynamic behavior. In the numerical example, the effects of material properties, temperature, initial impact velocity and mass of the impactor on the dynamic behavior of the shells, and contact force are discussed in detail.