Three-dimensional Green's functions for a multilayered half-space in displacement potentials

Ronald Y.S. Pak, Bojan B. Guzina

Research output: Contribution to journalArticlepeer-review

105 Scopus citations


To advance the mathematical and computational treatments of mixed boundary value problems involving multilayered media, a new derivation of the fundamental Green's functions for the elastodynamic problem is presented. By virtue of a method of displacement potentials, it is shown that there is an elegant mathematical structure underlying this class of three-dimensional elastodynamic problems which warrant further attention. Constituted by proper algebraic factorizations, a set of generalized transmission-reflection matrices and internal source fields that are free of any numerically unstable exponential terms common in past solution formats are proposed for effective computations of the potential solution. To encompass both elastic and viscoelastic cases, point-load Green's functions for stresses and displacements are generalized into complex-plane line-integral representations. An accompanying rigorous treatment of the singularity of the fundamental solution for arbitrary source-receiver locations via an asymptotic decomposition of the transmission-reflection matrices is also highlighted.

Original languageEnglish (US)
Pages (from-to)449-461
Number of pages13
JournalJournal of Engineering Mechanics
Issue number4
StatePublished - Apr 2002
Externally publishedYes


  • Boundary element method
  • Displacement
  • Elasticity
  • Green's function
  • Layered systems
  • Viscoelasticity
  • Wave propagation


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