Hybrid Numerical-Analytical Scheme for Locally Inhomogeneous Elastic Waveguides

Abstract

Numerical simulation of guided wave excitation, propagation, and diffraction in laminate structures with local inhomogeneities (obstacles) is associated with high computational cost due to the need for a mesh-based approximation of extended domains with a rigorous account for the radiation conditions at infinity. To obtain computationally efficient solutions, hybrid numerical-analytical approaches are currently being developed, based on linking a numerical solution in a local vicinity of the source and/or obstacles with an explicit analytical representation in the external semi-infinite domain. However, the developed methods are generally not widely spread because the possibility of such coupling with an external multimode wave field is generally not provided in standard finite-element (FE) software. We propose a scheme that allows the use of the FE software as a black box for the required correct matching of local numerical and global analytical solutions (FEM-An). The FEM is used to obtain a set of local numerical solutions that serve as a basis in the inner domain. These solutions satisfy the boundary conditions induced by guided wave modes so that they fit correctly with the modal expansion in the outer region. The expansion coefficients of both FE and modal decompositions are determined then from the condition of stress and displacement continuity at the interface between the inner and outer domains. This scheme was numerically validated against analytical solutions to test problems and FE solutions for long waveguide sections with perfect match layer absorbing conditions at the ends (FEM-PML). Along the way, it turned out that the FEM-PML approach gives an incorrect result in the backward-wave bands and at high frequencies. The application of the FEM-An hybrid scheme is illustrated by examples of Lamb wave diffraction by elastic inclusions and delaminations.