Vibration Analysis of Curvilinearly-Stiffened Functionally Graded Plate Using Element Free Galerkin Method

摘要

The element free Galerkin (EFG) method is developed for the free vibration of a functionally-graded plate with curvilinear stiffeners. The governing equations for the plate and stiffeners are derived by using the first order shear deformation theory. The in-plane deformation, transverse deflection and rotations of the plate and stiffener are expressed using moving least square (MLS) approximation. The penalty method is used to impose the boundary conditions. Material properties of the plate are assumed to vary continuously through the thickness, according to a power law, in terms of the volume fractions of the constituents. The formulation can model stiffeners having arbitrary orientation, curvature, and eccentricity. Several numerical examples for various material compositions and boundary conditions are compared with the other results available in the literature, illustrating the accuracy of the present approach. Finally, the influences of material composition, stiffener's number, and size on natural frequency is investigated.