MODÉLISATION NUMÉRIQUEDE L’EFFET DES VIEILLISSEMENTS DE POUTREEN BÉTON ARMÉ SOUS CHARGE MÉCANIQUE

Abstract

The objective of this thesis is to analyze beams made of functionally graded composite materials (FGM) under static bending, using a HSDT theory (higher order shear deformation), is considered. A mathematical model is established, for these composite beams of various limits, free, simple and fully clamped, in bending. New polynomial shear function is used. The edges of the section without stress are used in this study. No correction factor takes into account. The material properties are considered, a simple power law is taken into account. Illustrative cases of beams with simple supports and clamped ends subjected to a concentrated force at the center of the beam, and a uniformly distributed load with simple supports, respectively. Also, the cantilever beams are subjected to a concentrated shear force at the free end, and uniformly distributed load, respectively. The illustrative cases presented previously demonstrate the originality of this work in this investigation. The mathematical model is established by differential equations derived from the virtual work principle. The equilibrium equations and boundary conditions are presented. Based on the variational form to predict displacement fields. The solution of the analytical model is presented. The results in terms of displacement fields including section rotation and stress, deformation predicted from the proposed model are presented. Finally, the comparison between the current model and existing solution models in the literature showed better similarity and convergence