Modelling of wave propagation in composite plates using the time domain spectral element method

This paper presents results of numerical simulation of the propagation of transverse elastic waves corresponding to the A0 mode of Lamb waves in a composite plate. The problem is solved by the Spectral Element Method. Spectral plate finite elements with 36 nodes defined at Gauss–Lobatto–Legendre points are used. As a consequence of the selection of Lagrange polynomials for element shape functions discrete orthogonality is obtained leading to the diagonal form of the element mass matrix. This results in a crucial reduction of numerical operations required for the solution of the equation of motion by time integration. Numerical calculations have been carried out for various orientations and relative volume fractions of reinforcing fibres within the plate. The paper shows how the velocities of transverse elastic waves in composite materials depend on the orientation and the relative volume fraction of the reinforcement.