A 2D multiresolution wavelet-based method for advanced simulations of highly transient responses in composite plates

Abstract

The efficient and robust simulation of transient responses in laminated plates, which may encompass numerous wave modes, is a challenging computational problem with multiple applications. In this direction, an advanced computational method with additional localization capabilities is developed by employing the multiresolution approximation, resulting in the 2D multiresolution finite wavelet domain (MR-FWD) method. Daubechies scaling and wavelet functions are utilized, formulating a novel set of mass-decoupled multiresolution discretized equations of motion that involve four solution components: the coarse, horizontal fine, vertical fine and diagonal fine solution. The multiresolution discretization is combined with the first-order shear laminated plate theory for the effective modeling of composite plates. Numerical case studies focus on guided wave propagation in three lamination cases of increased complexity, showing the remarkable computational efficiency of the MR-FWD method compared to single-resolution approaches and time-domain spectral finite elements. Most importantly, the advanced localization properties of the proposed method are demonstrated, especially in the multi-wave response of an asymmetric composite plate, where each fine solution captures different wave responses depending on their directivity and wavenumbers. This unique feature can pave the way towards a new numerical analysis framework, in which multiple solution components contribute critical information about the structural response.