A multiresolution layerwise method with intrinsic damage detection capabilities for the simulation of guided waves in composite strips

A high-order layerwise multiresolution method that utilizes Daubechies wavelet and scaling functions for the approximation of state variables is presented for the enhanced simulation of guided waves in composite strips. The multiresolution approximation yields a hierarchical set of equations of motion involving the coarse component of generalized displacements, and finer components can be added on the coarse one, forming improved predictions until the desired precision is accomplished. The multiresolution approach is combined with a high-order layerwise laminate theory, enabling the accurate prediction of both symmetric and antisymmetric wave modes, the modeling of surface traction, and localized intra-ply and delamination damage types. Numerical results for the simulation of guided waves in laminated composite strips are presented, exhibiting significant reduction in computing times and remarkable convergence rates compared to single-resolution approaches and traditional finite element methods. Moreover, it is shown that each resolution can model specific bandwidths of wavenumbers, thus providing unique inherent capabilities to localize and isolate coexisting wave modes and detect converted and reflected waves, induced by degraded material regions and delaminations.