Meshless analysis of bi-directional functionally graded beam structures based on physical neutral surface

Abstract

More and more attention has been paid on the two-directional functionally graded materials (FGMs) applied in harsh heat environment. A novel meshless model is established for the bending analysis, based on the Smoothed Particle Hydrodynamics (SPH) method. To improve the prediction accuracy, the conventional SPH method is improved by the symmetric SPH method starting from the Taylor series expansion. Moreover, the neutral surface position of the bi-directional FG beam is determined and the third order Reddy-Bickford beam theory based on this exact neutral surface is adopted. The governing equations are deduced for FGB composed by two or four different materials and then discretized by the proposed method. The present model is verified by comparison of the deflection with the solution obtained in literature and a self-programmed finite element code. The deformation of the beam with different gradient indexes and boundary conditions is also investigated.