A higher-order spectral element for wave propagation analysis in functionally graded materials

Abstract

A new higher-order spectral element (SE) is developed for wave propagation analysis of a functionally graded material (FGM) beam in the presence of thermal and mechanical loading. The element is based on first order shear deformation theory (FSDT) and takes into account the depthwise contraction due to Poisson’s ratio. A new method of element formulation is employed, which is the most general one and devoid of all previous cumbersome wavenumber and wave amplitude computation. The beam can be subjected to temperature variation in depth direction. This variation is found by solving the one-dimensional heat conduction equation uncoupled from the elasticity equation. The effect of the computed temperature field is subsequently superimposed on the mechanical loading in the form of an equivalent nodal load. Numerical examples are directed towards highlighting the effect of the Poisson’s contraction on the structural response and stress wave. The spectrum and the dispersion relation are studied in detail. The stress field generated by the element and its difference from the FSDT stress field is outlined. The response of an FGM beam to thermo-mechanical loading is analysed and the effect of thermal loading on the overall response is elicited.