Alternating wavelet-time finite element method: Modeling and analysis of nonlinear wave propagation in one and two-dimensional waveguides

Abstract

In this paper, a novel method named the alternating wavelet-time finite element method (AWT-FEM) is proposed for studying elastic wave propagation in nonlinear structures. An alternating iterative procedure between the time-domain and a wavelet-domain combined with the spectral finite element method (SFEM) is employed to solve wave equations with general nonlinearities. The advantages of the proposed method are (1) the potential to provide high fidelity results for impacts with high frequency content through the use of the spectral finite element method; (2) nonlinear structures with physically realistic boundary conditions can easily be studied by circumventing wrap-around issues associated with Fourier-based methods;(3) the parallel computing compatible framework and the semi-analytical nature of SFEM make it more computationally efficient for nonlinear systems modeled with structural components. Simulations using the proposed method are conducted to demonstrate its applicability to study nonlinear wave propagation in one-dimensional and two-dimensional systems.

Progressive failure analysis on composite structures using a wave based method

“…The calculation of the scattering coefficients and the dynamic response of composite structures have been investigated using various numerical methods, including the spectral finite element method, [26][27][28][29] an enriched finite element method 30 and finite element method. 20,[31][32][33] The Finite Element Method is the most popular numerical tool to analyze wave propagation in discontinuous domains.…”