Transient Analysis of Functionally Graded Materials Plate using Reduced-Basis Methods

Understanding of the wave propagation behaviors in FGM structures and the non- destructive evaluation of the material property for quality assurance and reliability analysis are becoming increasingly important. This work deals with the development of fast methods for transient analysis of FGMs, that can significantly reduce the problem size and computational cost but still retain solution accuracy are highly desirable. Based on the hybrid numerical method, a reduced-basis method (RBM) is suggested to real-timely analyze the transient response displacement in functionally graded material (FGM) plate. In this method, the repeated large eigenvalue problems in wavenumber domain have been solved through off-line/on-line decomposition in a real-time manner. In off-line stage, the parameter independent matrices are projected onto the reduced-basis spaces constructed in terms of the solved eigenvalue problems in sample wavenumbers. In on-line stage, the reduced eigenvalue problems in arbitrary wavenumbers are gotten, subsequently the responses in wavenumber domain are obtained by the approximated eigenpairs. With the application of RBM, the computational cost of transient displacement analysis in FGM plate is saved significantly, while it still retains the accuracy of the solution and the physics of the structure. Numerical examples demonstrate the efficiency and accuracy of the present method.