A spectrally formulated finite element for wave propagation analysis in layered composite media

Abstract

Wave propagation in orthotropic layered composite media due to high frequency impact loading is studied using a new spectral layer element (SLE). This novel element is formulated using the method of partial wave techniques (PWT) in conjunction with linear algebraic methodology. The matrix structure of finite element (FE) formulation is retained, which substantially simplifies the modeling of multi-layered structure. The developed SLE has an exact dynamic stiffness matrix, as it uses exact solution to the governing elastodynamic equation in frequency domain as its interpolation function. Due to this, the mass distribution is modeled exactly, and as a result, the element gives exact frequency response of each layer. Hence, one element may be as large as one complete layer and as a result system size is very small compared to conventional FE system sizes. The fast-Fourier transform (FFT) and Fourier series are used for inversion to the time/space domain. The formulated element is further used to study the stress distribution in a multi-layered media. As a natural application, Lamb wave propagation in composite plate is studied for different ply-angle and time domain description is obtained. Further, advantage of the spectral formulation in impulse force identification is demonstrated.