Elastic wave propagation in a functionally graded nanocomposite reinforced by carbon nanotubes employing meshless local integral equations (LIEs)

The transient dynamic analysis of displacement field and elastic wave propagation in finite length functionally graded nanocomposite reinforced by carbon nanotubes are carried out using local integral equations (LIEs) based on meshless local Petrov–Galerkin (MLPG) method. The distribution of the aligned carbon nanotubes (CNTs) is assumed to vary as three kinds of functionally graded distributions as well as uniform distribution (UD) through radial direction of axisymmetric reinforced cylindrical composites. The mechanical properties are simulated using a micro-mechanical model in volume fraction form. A unit step function is used as a test function in the local weak form, which leads to local integral equations (LIEs). The analyzed domain is divided into small subdomains with a circular shape. The radial basis functions are used for approximation of the spatial variation of field variables. For treatment of time variations, the Laplace-transform technique is utilized. The 2D propagation of elastic waves through 2D domain is illustrated for various kinds of carbon nanotubes distributions. The time histories of displacement fields are studied in detail for various kinds of carbon nanotube distributions in reinforced cylindrical composites.