Modeling of Functionally Graded structures behavior Modélisation du comportement des structures en Matériaux Fonctionnellement Gradués (FGM).

Abstract

A new class of composite materials known as "Functionally Graded Materials" (FGMs), has been designed by Japanese scientists to compensate for certain defects that occur in traditional laminated composites, such as stress concentration and delamination. FGMs are made from a mixture of metals and ceramics distinguished by a gradual change in composition and microstructure through the thickness, resulting in a smooth and continuous variation in material properties. FGMs have been widely used in many structural applications that differ from their first application as a thermal barrier for aerospace structures. The development of the use of FGMs in structures requires a good understanding of their mechanical behavior in order to provide an optimum profile to designers. The main aim of the present work is to contribute to the modeling of static, stability and dynamic behaviors of plates made of FGMs. First, a four-node rectangular finite element, with five degrees of freedom per node, based on First-order shear deformation theory (FSDT), has been adapted for static, mechanical buckling and free vibration analysis of FG single layer and sandwich plates. The FSDT provides a sufficiently accurate description of response for thin to moderately thick plates. However, it predicts constant transverse shear stresses across the thickness and a shear correction factor is needed. To overcome problems related to FSDT, a novel trigonometric shear deformation model with five unknowns has been proposed for the analysis of FG plates behavior. The model accounts for the sinusoidal variation of the transverse shear strains across the thickness and satisfies the shear stress-free boundary conditions on the top and bottom surfaces of the plate. A four-node rectangular finite element based on the proposed new model (R4SSDT), has been formulated to analyze the static, stability and dynamic behavior of FG single layer plates. For the two formulated finite elements, assumed natural shear strain and the physical neutral surface position procedures have been taken into consideration. The performance and accuracy of the developed elements have been evaluated through validation tests. The effects of various parameters on the behavior of FG plate have been also studied.