Geometrically nonlinear vibrations of FG-GPLRC cylindrical panels with cutout based on HSDT and mixed formulation: a novel variational approach

Based on Reddy’s third-order shear deformation theory and mixed formulation, a new numerical approach in the variational framework is developed to analyze the geometrically nonlinear free vibration behavior of cylindrical panels having cutouts with various shapes (e.g., square, circular, elliptical) under arbitrary boundary conditions. It is also assumed that the panel is made of functionally graded graphene platelet-reinforced composite with various patterns for the distribution of GPLs along the thickness direction whose effective properties are estimated using the modified Halpin–Tsai model in conjunction with the rule of mixture. The proposed approach can be named VDQFEM as it utilizes the VDQ and FE methods. Efficient matrix formulation, being free from the locking problem, computational efficiency and being able to solve problems with concave and polygon domains are the main features of VDQFEM. Selected numerical results are given to investigate the influences of geometrical parameters and weight fraction/distribution pattern of GPLs on the large-amplitude vibration response of panels with various cutouts and boundary conditions.