Vibration analysis of cracked functionally graded elliptical plates based on finite element phase-field model

This paper aims to perform the finite element phase-field analysis on the vibration of cracked functionally graded (FG) circular/elliptical plates. The mathematical model is under the shear deformation plate theory (SDPT) along with the phase-field model (PFM) through the variational formulation. The computational framework within the finite element analysis (FEA) is implemented to solve the problem. To simplify the application of FEA, the energy functional is developed by considering the PFM. Accordingly, the FEA and isoparametric formulation are employed to obtain the discretized finite element motion equations. several comparative and convergence demonstrations are provided to validate this approach. Then, the impacts of various involved parameters such as crack shape, FG material power-law index, plate aspect ratio and boundary support (BS) are investigated for the vibratory behavior of cracked circular/elliptical plates made of FG material. The reported results reveal the efficiency of the PFM in the dynamics of the cracked FG plates.