A Boundary-Field Formulation for Elastodynamic Scattering

George C. Hsiao, Tonatiuh Sánchez-Vizuet, Wolfgang L. Wendland

Research output: Contribution to journalArticlepeer-review

Abstract

An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By applying a boundary-field equation method, we are able to formulate a nonlocal boundary problem (NBP) in the Laplace transformed domain, using the field equations inside the obstacle and boundary integral equations in the exterior elastic medium. Existence, uniqueness and stability of the solutions to the NBP are established in Sobolev spaces for two different integral representations. The corresponding results in the time domain are obtained. The stability bounds are translated into time domain estimates that can serve as the starting point for a numerical discretization based on Convolution Quadrature.

Original languageEnglish (US)
JournalJournal of Elasticity
DOIs
StateAccepted/In press - 2022

Keywords

  • Convolution quadrature
  • Elastodynamics
  • Time-dependent boundary integral equations
  • Transient wave scattering

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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