Static Analysis of FG Beams via Complementary Functions Method

Static analysis of Functionally Graded (FG) beams is studied by the Complementary Functions Method (CFM). The material properties, Young’s modulus, of the straight beams, are graded in the thickness direction based on a power law distribution while the Poisson’s ratio is supposed to be constant. Governing equations of the considered problem are obtained with the aid of minimum total potential energy principle based on Timoshenko’s beam theory (FSDT). The main purpose of this paper is the infusion of the CFM to the static analysis of FG straight beams. The effectiveness and accuracy of the proposed method are confirmed by comparing its numerical results with those available in the literature. Application of this efficient method provides accurate results of static response for FGM beams with different variations of material properties in the thickness of the beam.