Computational investigation of porosity effect on free vibration of cracked functionally graded plates using XFEM

The present work investigates the porosity effect on the vibration characteristics of the cracked functionally graded plate. Extended finite element method is employed to study the functionally graded plate with crack. A higher-order shear deformation theory (HSDT) is incorporated for the plate kinematics. The crack information in the functionally graded plate domain is collected by employing the level set method. The primary variable is enriched with additional functions by employing the partition of unity technique to address the crack in the functionally graded plate domain. The power-law distribution is employed to form functionally graded material (FGM) and a smooth gradation of material properties is achieved across the thickness direction. The porosity distribution in the FGM plate is determined by the porosity index. The convergence and comparative study have been done to check the current formulation's efficacy, accuracy, and reliability. Further, various numerical examples are presented. The effects of different influential parameters like porosity, crack, volume fraction and boundary condition on the vibration characteristics have been discussed in detail which can provide a reference for future research by researchers. Copyright (C) 2022 Elsevier Ltd. All rights reserved.