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.

Galerkin-Kantorovich variational method for solving saint venant torsion problems of rectangular bars

“…Finite Difference Method (FDM) was used to solve the resulting differential equations of their formulations. Guendouz et al [27] used an advanced and refined theory of one-dimensional (1D) and three dimensional (3D) beams to study unrestrained torsional analysis of composite bars with open cross-sections.…”

Free Vibration of Axially Functionally Graded Timoshenko Circular Arch

“…As mentioned above, free vibration studies of arches are still being actively conducted owing to the various applications of arch-framed structures. Studies on AFGMs include papers on stability analysis by Nieh et al [16] and Ranganathan et al [25]; nonlinear behavior analysis by Horibe and Mori [4]; stability optimization by Lee and Lee [26]; foundation structure by Sofiyev [27]; mechanical response of FGM beams by Boumezbeur et al [28]; static bending-torsion of FG cantilever beams by Guendouz et al [29]; and bending-torsion of 1D/3D beams based on the Saint-Venant's solution and taking into account the edge effects by Guendouz et al [30].…”