Numerical simulation of elastic wave propagation in functionally graded cylinders using time-domain spectral finite element method

Functionally graded material is a new class of composite materials with gradually varying material contents. In this article, a two-dimensional axisymmetric time-domain spectral finite element method is proposed for the analysis of elastic wave propagation in functionally graded cylinders. The stiffness and mass matrix of an arbitrary quadrilateral axisymmetric spectral element is developed. The element nodes are collocated at Gauss-Lobatto-Legendre points. High-order Lagrangian polynomials are used as shape functions and the Gauss-Lobatto-Legendre quadrature rules are applied. They provide the capability to model spatial varying material properties and lead to a diagonal mass matrix. The effectiveness of the proposed model is verified by comparing with published data. Elastic wave propagation in a functionally graded cylinder subjected to an impulsive loading is studied detailed. The effect of material grading pattern is analyzed. The results demonstrate the effectiveness of the present method for the analysis of elastic wave propagation in functionally graded solids with axial symmetry and the material composition variation has an important effect on structural wave propagation behavior.