Large Deflection Analysis of Functionally Graded Beams Resting on a Two-Parameter Elastic Foundation

Abstract

This paper presents a finite element procedure for the large deflection analysis of functionally graded (FG) beams resting on a two-parameter elastic foundation. The material properties of the FG beams are assumed to vary continuously in the thickness direction by a power-law distribution. Based on the strain energy expression, a shear deformable beam element, taking the effect of the material non-homogeneity and the foundation support into account, is formulated and employed in the analysis. An incremental/iterative procedure in combination with the arc-length control method is used for solving nonlinear equilibrium equations. The numerical results show that the convergence of the formulated element is fast, and the large displacements of the beams can be accurately assessed by using a few numbers of the elements. A parametric study is carried out to highlight the effect of the material non-homogeneity and the foundation support on the large deflection behavior of the beams. The influence of the aspect ratio on the large deflection response of the beam is also examined and highlighted.