Contribution à la modélisation par MEF des structures en FGM

Abstract

In this work, we present a torsional-bending analysis of different homogeneous or FGM beams using a refined beam theory built on 3D Saint-Venant’s solution (RBT/SV) and taking into account the edge effects. In this theory, the displacement models include Poisson's effects, out-of-plane deformations and distortions extracted from 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 (shape and materials). To implement this approach, a tool called CSB (Cross-Section and Beam analysis) is provided and is based on a first cross-section analysis solved by 2D-FEM computations to get the sectional deformation modes, and then the equilibrium beam problem is solved by 1D-FEM computation according to the displacement model. The results obtained for RBT models are systematically compared with other models in the literature, 3D-FEM which we also consider as a reference, and those provided by the full Saint-Venant beam theory (SVBT) calculations. The results clearly show the efficiency of RBT by greatly improving the internal solution, and at the same time, a detailed 3D solution is obtained in the edge region.