The Wavelet Spectral Finite Element-based user-defined element in Abaqus for wave propagation in one-dimensional composite structures

A Wavelet Spectral Finite Element (WSFE)-based user-defined element (UEL) is formulated and implemented in Abaqus (commercial finite element software) for wave propagation analysis in one-dimensional composite structures. The WSFE method is based on the first-order shear deformation theory to yield accurate and computationally efficient results for high-frequency wave motion. The frequency domain formulation of the WSFE leads to complex-valued parameters, which are decoupled into real and imaginary parts and presented to Abaqus as real values. The final solution is obtained by forming a complex value using the real number solutions given by Abaqus. Four numerical examples are presented in this article, namely an undamaged beam, a beam with impact damage, a beam with a delamination, and a truss structure. A multi-point constraint subroutine, defining the connectivity between nodes, is developed for modeling the delamination in a beam. Wave motions predicted by the UEL correlate very well with Abaqus simulations. The developed UEL largely retains the computational efficiency of the WSFE method and extends its ability to model complex features.