Extended isogeometric analysis based on Bézier extraction for an FGM plate by using the two-variable refined plate theory

The static and dynamic analysis for the functionally graded material (FGM) plate is performed by using the extended isogeometric analysis (XIGA) based on the Bézier extraction and two-variable refined plate theory (RPT). The two-variable RPT using only four parameters for the displacement fields overcomes the shear locking without the shear correction factor. The isogeometric analysis (IGA) reduces the computational cost by avoiding multiple re-meshing steps and improves the accuracy of solutions due to approximating the exact geometry. The XIGA integrating the IGA with the extended FEM is capable of the general fracture analysis. By transforming Non-Uniform Rational B-Spline control meshes to Bézier elements with the Bézier extraction operator, we can implement the IGA in the familiar FEM framework. The theory presented in this paper is verified by comparing to the solutions of other methods. The effects of the side-to-thickness ratio, aspect ratio, ingredient fraction, and crack length on the static and dynamic behavior of the FGM plate are studied.