Nonlocal steady-state thermoelastic analysis of functionally graded materials by using peridynamic differential operator

Abstract

In this study, a nonlocal model is presented for the steady-state thermoelastic analysis of functionally graded materials (FGM) by using peridynamic differential operator. The displacement–temperature equations of coupled thermo-elasticity and boundary conditions for a two-dimensional FGM square plate under mechanical and thermal loads are converted from classical local differential forms into nonlocal integral forms with peridynamic differentical operator. The temperature, displacement and stress fields are solved by introducing Lagrange multiplier and employing variational analysis. A comparison study is conducted to validate the accuracy and convergence of this nonlocal model by comparing the nonlocal analysis results with finite element results as well as analytical solutions in literature. The effects of different material gradients and loads on the physical fields of FGM plates are investigated further by introducing the Mori-Tanaka method to estimate the effective properties, and the influences of the degree of nonlocality on the stress singularity at the crack tip in FGM plates are analysed finally.