The present work aims to investigate the effect of an edge crack on the stress concentration around the circular hole surrounded by Functionally Graded Material (FGM) in an infinite plate subjected to uniaxial tensile load. The numerical investigation has been carried out using Extended Finite Element Method (XFEM). Two cases have been analysed in this work, i.e. the whole plate made up of radial FGM and homogeneous material plate having radial FGM layer around the hole. Young’s modulus of FGM varies according to exponential and power law function. The relations of stress intensity factor (SIF) and stress concentration factor (SCF) with normalised crack length, Young’s modulus ratio, FGM layer thickness and power law index have been presented. It has been observed that the FGM layer case has low SCF around hole than FGM plate case in presence of an edge crack.

This paper deals with free vibrations of the axially functionally graded (AFG) horseshoe arch. The modulus of elasticity and the mass density of AFG material of arch are chosen as a univariate quadratic function. The differential equations with the boundary conditions that govern the free vibration of such arch are derived and numerically solved to calculate natural frequencies and mode shapes. Natural frequencies of this study agree well with those of the finite element ADINA. Parametric studies of the geometrical and mechanical properties of the arch on frequencies and mode shapes are performed and extensively discussed.

In this paper, harmonic forced vibration of circular functionally graded plate integrated with two uniformly distributed actuator faces made of piezoelectric material is studied. The material properties of the functionally graded substrate layers are assumed to be graded in the thickness direction according to the power-law distribution, also the distribution of electric potential field along the thickness direction of piezoelectric layers is modeled by a quadratic function. The governing equations are solved for simply supported boundary condition of the sandwich circular plate and the solutions are presented by elementary Bessel functions. The performance of the present model is compared with that of ?nite element analyses as well as other available literature by the presentation of comparative results obtained for several examples encompassing different power indexes and vibration modes. The results show that thickness of piezoelectric layer and changing the power index in FG material has a significant influence on the deflection and natural frequencies of system.