Etude dynamique des plaques nano composites fissurées par la méthode des éléments finis étendue (X-FEM). Dynamic study of cracked nanocomposite plates using the extended finite element method (X-FEM).

Abstract

This research investigates the free vibration behavior of cracked Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) plates using the Extended Finite Element Method (XFEM). The study examines the impact of different CNT distribution patterns (UD, FG-X, FG-A, and FG-O) on the vibrational characteristics, accounting for the influence of laminate stacking sequences. Using First-Order Shear Deformation Plate Theory (FSDT), a combined FEM-XFEM approach is implemented to effectively model cracks without remeshing. The effective elastic modulus of the composite is computed using the modified Halpin-Tsai model, and the elastic properties of CNTRC plies are predicted using the rule of mixtures. This analysis reveals the significant influence of crack length, crack position, width/thickness ratios, fiber volume fraction, and power law index on the natural frequencies and stiffness of FG-CNTRC plates. Key findings highlight the enhanced stiffness achieved with FG-X distributions due to strategic CNT placement, the reduction in natural frequencies with increasing crack length. The results demonstrate XFEM's accuracy and efficiency as a robust tool for the dynamic analysis of cracked FG-CNTRC structures, offering valuable insights for their design and optimization in demanding applications.