Nurl-Based Isogeometric Analysis for Free Vibration of Functionally Graded Sandwich Plates Using Higher Order Formulations

The present research applies a 2D refined plate theory and isogeometric analysis (IGA) for free vibration analysis of functionally graded (FG) sandwich plates, whose governing equations are treated based on a unified formulation (UF), and nonuniform rational Lagrange (NURL)-based IGA technique. The constitutive model of FG materials is approximated via a Voigt's rule of mixture based on an equivalent single-layer (ESL) theory. The present framework offers several advantages, including high precision of vibration response by employing higher-order plate theory and the capability of NURL basis functions to capture the exact form of plate geometries. Moreover, higher-order theories postulated by the UF are exempt from the Poisson locking phenomenon and do not require a shear correction factor. Additionally, by employing UF, the effect of thickness stretching on vibration response is considered. Furthermore, higher-order NURL basis functions effectively mitigate shear locking. A large numerical investigation shows the accuracy of results and investigates the effects of several key parameters, such as gradient index, thickness-to-length ratios, layer-to-thickness ratios, and boundary conditions, on the vibration response of FG sandwich plates.