New boundary integral equation formalism for elastic wave scattering

• Published in: AIP conference proceedings Vol. 2102; no. 1
• Main Author: Schafbuch, Paul J.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Melville American Institute of Physics 08.05.2019
• Subjects: Boundary conditions; Boundary integral method; Cracks; Elastic scattering; Elastic waves; Finite difference method; Finite element method; Formalism; Free boundaries; Free surfaces; Integral equations; Kernels; Nondestructive testing; Numerical integration; Plane waves; Reciprocity; Stress distribution; Ultrasonic testing; Wave scattering
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.5099857

Boundary integral equations methods are inherently advantageous for infinite medium problems such as elastic wave scattering for ultrasonic Nondestructive Testing. The reduction in dimensionality of the problem (e.g., volume to surface) also leads to computational advantages versus finite element or finite difference methods for homogeneous media. However, numerical integration of the strongly singular (1/r2) kernels of the traditional BIE formalism has been a challenge in implementation; although successful functioning codes have long existed. Still, methods to incrementally minimize this difficulty have been the subject of research for three decades. This new BIE method utilizes an analytical representation for the incident plane wave’s stress field and Betti reciprocity to eliminate the strongly singular kernel integration that is required by scatterers with stress-free boundary conditions (such as voids, open cracks, and any nearby free surfaces). An associated weakly singular (1/r) BIE is readily solved instead.