Nitsche-based isogeometric analysis of bending and free vibration of stiffened FGM plates with cutouts

Abstract

We have developed a coupled framework of Nitsche and isogeometric analysis for investigating the static bending and natural vibration of functionally graded material (FGM) plates reinforced with stiffeners and cutouts. The FGM plates are discretized using non-overlapping non-uniform rational B-splines (NURBS) patches, with stiffeners strategically positioned along the shared edges of neighboring patches. Consequently, the Nitsche technique is adopted to integrate these patches seamlessly. Our methodology, which combines the first-order shear deformation theory (FSDT) and Timoshenko beam theory, is utilized to examine the static bending and natural vibration of the perforated stiffened FGM plates. This approach eliminates the need for stiffener discretization and the localization of FGM plate elements at stiffener nodes. Initially, the convergence and accuracy of the present method are verified by the bending of an unstiffened FGM plate and free vibration of a stiffened FGM plate, respectively. Subsequently, the static bending behaviors of FGM plates are investigated by uniform and nonuniform loads, diverse gradient indices, and variable plate thicknesses. Furthermore, a thorough investigation is conducted on the free vibration of rectangular, skew, and circular FGM plates, considering the cutouts and stiffeners under various boundary conditions. The corresponding results of our method coincide with available data in literature.