Nonlinear flexural and vibration response of geometrically imperfect gradient plates using hyperbolic higher-order shear and normal deformation theory

This paper investigates the sensitivity of nonlinear flexural and vibration response of shear deformable functionally graded material (FGM) plates to the initial geometrical imperfections. The formulations are based on recently developed non-polynomial higher-order shear and normal deformation theory by authors. The theory accounts for nonlinear variation in the in-plane and transverse displacement through the thickness. It also accommodates thickness stretching effect without employing shear correction factor. The novelty of this theory is that it contains only four unknowns, unlike several other shear deformation theories which contain five or more unknowns. The equations of motion are derived using variational principle. The initial geometric imperfections have been incorporated using generic imperfection function. Material properties of the FGM plates are assumed to be varying continuously in the thickness direction according to a simple power law and exponential law. Convergence and comparison studies have been carried out to establish the authenticity and reliability of the solution. The numerical results are highlighted with various geometric imperfections and system parameters.