Implementation of a hybrid numerical-analytical approach for solving the problems of SH-wave diffraction by arbitrary-shaped obstacles

Abstract

Guided waves propagation and diffraction are considered in elastic waveguides with arbitrary shaped local inhomogeneities. Both analytical and numerical approaches are widely used to calculate and analyze displacement fields. This paper presents the implementation of a hybrid numerical-analytical approach. A numerical approach is utilized in the internal domain containing local inhomogeneity. It is based on the decomposition by the set of basic solutions obtained by the finite element method. Meanwhile, the solution in the outer semi-infinite domains has an analytical form and is based on the decomposition by the normal modes. Unknown decomposition coefficients are derived from the imposed interface conditions between the domains. The numerical computation of the basis finite-element solutions can be carried out on a specialized software. Nevertheless, a more efficient implementation is proposed based on the fact that multiple basic finite element problems share a single global stiffness matrix, which can be inverted once. The algorithm is tested by comparison with the COMSOL model which utilises perfectly matched layers. The developed package allows not only to calculate the displacement fields in the local domain containing the inhomogeneity, but also to obtain analytical representations of the waves travelling to infinity, which yield a physically descriptive representation of the solution. In addition, the presented package allows a parametric analysis of the dependence of the wave field characteristics on various medium properties and inhomogeneity geometry.