Contribution de l’approche en déformation pour l’analyse des structures

Abstract

The main objective of this work is to contribute to the modeling of the static , free vibration, and stability behavior of laminated composite plates and Functionally Graded Materials (FGMs). Firstly, a four-node rectangular finite element (SBRMP24), with six degrees of freedom per node, based on the strain approach and the First-Order Shear Deformation Theory (FSDT), has been developed for static, free vibration, and mechanical buckling analysis of FGM plates. FSDT provides a sufficiently accurate description for thin to moderately thick plates. However, it predicts constant transverse shear stresses across the thickness, necessitating a shear correction factor. Next,To overcome the limitations of FSDT, a new Trigonometric Shear Deformation Plate Theory (TrSDPT) model with five unknowns has been proposed for the analysis of FG plates behavior. This model accounts for the sinusoidal variation of transverse shear strains through the thickness and satisfies the zero shear stress boundary conditions on the top and bottom surfaces of the plate. A four-node quadrilateral finite element, based on this new model (HSBQP20), has been formulated to analyze the static and dynamic behavior of FGM plates. For both formulated finite elements, the displacement field includes higher-order terms, is based on assumed strain functions satisfying compatibility equations, and considers the position of the physical neutral surface. The performance and accuracy of the developed elements have been evaluated through validation tests. Additionally, the influence of various parameters on the behavior of FGM plates have been also studied. Finally, the element based on the trigonometric model has been also examinted for static and free vibration analysis of symmetric and antisymmetric laminated composite plates of different shapes. The results were compared with published analytical and numerical solutions, demonstrating excellent accuracy and efficiency in predicting both the bending behavior and free vibrations of laminated composite plates