A thermo-mechanical analysis of functionally graded beams via hierarchical modelling

In this work, functionally graded beams subjected to thermal loadings are analysed. To this end, several beam models are hierarchically derived by means of a unified formulation that makes the formulation independent from the displacements polynomial approximation order over the cross-section. The temperature profile is determined by solving Fourier’s heat conduction equation. The governing equations are, then, derived from the Principle of Virtual Displacements considering the temperature field as an external load. A Navier-type, closed form solution is used. Simply supported beams are, therefore, considered. Functionally graded mono-layer and sandwich cross-section configurations are investigated. Numerical results in terms of temperature, displacement and stress distributions are provided for different beam slenderness ratios. Results are assessed towards three-dimensional finite element solutions demonstrating that accurate results can be obtained with reduced computational costs.