A closed-form solution for accurate stress analysis of functionally graded Reddy beams

Abstract

In the present paper, a closed-form solution of the Reddy beam theory is developed and applied, for the first time, to investigate the bending behavior of straight and curved functionally graded (FG) beams, where the material properties change continuously from one surface to another in the thickness (or height) direction. The obtained closed-form solution, sum of polynomial and exponential terms, enriches the polynomial displacement field usually proposed in a finite element (FE) approach, with effects also on the derived strain and stress quantities, particularly relevant in FG beams. The adopted beam model is exploited to satisfy parabolic variation of the shear stress distribution along the thickness direction and does not require the use of shear correction factors, particularly difficult to obtain when the beam is inhomogeneous in the thickness direction. Comparative studies are carried-out to establish the robustness and the performance of the present model, and numerical results are presented and discussed in detail to investigate the effects of volume fraction index, radius of curvature, length-to-height ratio, and boundary conditions on the stress response of FG beams. The obtained results can serve as benchmarks for future research.