Stochastic Assessment of Thermo-Elastic Wave Propagation in Functionally Graded Materials (FGMs) with Gaussian Uncertainty in Constitutive Mechanical Properties

Abstract

The main objective of this article is focused on stochastic analysis of wave propagation and effects of uncertainty in mechanical properties on transient behaviors of displacement and temperature fields in functionally graded materials under thermo-mechanical shock loading. The problem is studied in a cylindrical domain and the governing equations of a functionally graded thick hollow cylinder are solved. To assess the wave propagation, the generalized coupled thermoelasticty equations based on Green-Naghdi theory (without energy dissipation) are analyzed in a FG thick hollow cylinder. The FG cylinder is considered to have infinite length and axisymmetry conditions. The constitutive mechanical properties of FGM are assumed as random variables with Gaussian distribution and also the mechanical properties are considered to vary across thickness of FG cylinder as a nonlinear power function of radius. The FG cylinder is divided into many elements across thickness of cylinder and hybrid numerical method (Galerkin finite element and Newmark finite difference methods) along with the Monte Carlo simulation are employed to solve the statistical coupled equations. The effects of uncertainty in functionally graded materials on thermal and elastic waves, transient behaviors of radial displacement and temperature fields and variance and maximum values of displacement and temperature are discussed in details for various grading patterns in FGMs and various points on thickness at several times.