On the boundary integral-equations for the crack opening displacement of flat cracks

DOI10.1007/BF01200328zbMath0753.45005OpenAlexW1975183790MaRDI QIDQ1194221

Tuong Ha-Duong

Publication date: 27 September 1992

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01200328

zbMATH Keywords

solvabilityHelmholtz equationpseudodifferential operatorcrack opening displacementsymbolLamé systemhypersingular operatoracoustic and elastic scatteringcoerciveness estimatefirst kind boundary integral equationsflat cracks

Mathematics Subject Classification ID

Systems of singular linear integral equations (45F15) Fracture and damage (74R99) Wave scattering in solid mechanics (74J20) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Pseudodifferential operators (47G30)

Related Items

On the identification of the flatness of a sound-hard acoustic crack ⋮ A Wiener-Hopf approach for the scattering by a disk ⋮ The factorization method for cracks in elastic scattering ⋮ Well-Posed PDE and Integral Equation Formulations for Scattering by Fractal Screens ⋮ Gemischte Fourier‐Randelementmethoden zur Berechnung zeitharmonischer Streufelder an Schirmen ⋮ Numerical simulations on resonance poles -- the trapping case of two plane cracks ⋮ Sobolev spaces on non-Lipschitz subsets of \(\mathbb {R}^n\) with application to boundary integral equations on fractal screens ⋮ An integral equation method for the electromagnetic scattering from a scatterer on an absorbing plane ⋮ A space-time variational formulation for the boundary integral equation in a 2D elastic crack problem ⋮ Inverse scattering for a plane screen. ⋮ Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The explicit solution of elastodynamical diffraction problems by symbol factorization
• A regularized boundary integral equation method for elastodynamic crack problems
• Bifurcation of a running crack in antiplane strain
• Curved finite element methods for the solution of singular integral equations on surfaces in \(R^3\)
• Numerical Analysis of the Exterior Boundary Value Problem for the Time- Harmonic Maxwell Equations by a Boundary Finite Element Method Part 1: The Continuous Problem
• A new method for calculating scattering with particular reference to the circular disc
• Diffraction of elastic waves by a penny-shaped crack: analytical and numerical results
• Some applications of a galerkin‐collocation method for boundary integral equations of the first kind
• A boundary integral equation method for three‐dimensional crack problems in elasticity
• Scattering From Three-Dimensional Planar Cracks by the Boundary Integral Equation Method
• On boundary integral equations for crack problems
• On the transient acoustic scattering by a flat object