Wave propagation in functionally graded materials by modified smoothed particle hydrodynamics (MSPH) method

We use the modified smoothed particle hydrodynamics (MSPH) method to study the propagation of elastic waves in functionally graded materials. An artificial viscosity is added to the hydrostatic pressure to control oscillations in the shock wave. Computed results agree well with the analytical solution of the problem. It is shown that, for the same placement of particles/nodes the MSPH method gives better results than the finite element method when the initial smoothing length in the MSPH method is 1.1 times the distance between two adjacent particles. Effects of the artificial viscosity are also examined, and the optimum value of the linear artificial viscosity that minimizes the relative error in computed stresses is found.