Method of fundamental solutions without fictitious boundary for plane time harmonic linear elastic and viscoelastic wave problems

• The SBM solution of plane linear viscoelastic wave problems is first presented.
• The SBM origin intensity factors of harmonic viscoelastic wave are derived.
• Five cases with different materials and geometric boundaries are tested.
• The SBM produces accurate solutions and performs more stable than the MFS.

This study makes the first attempt to apply a recently developed modified method of fundamental solutions (MFS) without fictitious boundary, which is named as the singular boundary method (SBM), to the solution of plane linear elastic and viscoelastic wave problems. Like the standard MFS, the SBM applies the fundamental solutions of the governing equations of interest as the basis functions. Unlike the standard MFS, the SBM, however, does not require the fictitious boundary outside physical domain to avoid the singularity of the fundamental solution and instead directly places the source points on the physical boundary coinciding with collocation points via the concept of origin intensity factors. To demonstrate the effectiveness of the SBM for plane elastic and viscoelastic wave problems, several numerical examples are given in comparison with analytical solutions, and numerical results of the MFS and the finite element method.