Analysis of FGM Cantilever Beams under Bending-torsional Behavior Using a Refined 1D Beam Theory

Abstract

The static bending-torsion problem of functionally graded cantilever beams is studied using a refined 1D/3D beam theory (Refined beam theory RBT and Refined beam theory with distortion modes RBT*) built on the 3D Saint-Venant (SV) solution. In these theories, the displacement models include Poisson's effects, out-of-plane deformations and distortions. For a given section, the sectional displacement modes are derived from the computation of the particular 3D Saint-Venant’s solution. These modes, which reflect the mechanical behavior of the cross-section, lead to a beam theory that actually corresponds to the cross-section type in terms of shape and material. In addition, the models take into account edge effects to predict a 3D solution in a larger internal region to better describe the overall behavior of FGM beams. The models examined are implemented on the CSB (Cross-Section and Beam Analysis) tool. It is based on the RBT/SV (Refined Beam Theory based on the 3D SV’s solution) theory of FGM beams. The mechanical and physical characteristics of the FGM beams vary continuously, according to a power-law distribution, through the thickness of the beams. The numerical and 3D results obtained with homogeneous and FGM beams are systematically compared with other models in the literature and those provided by the full Saint-Venant beam theory (SVBT) calculations.