Reduction of a Coupled Dual Trigonometric Series to a Set of Singular Integral Equations and Their Solutions.

Abstract

In this paper we study a coupled pair of dual trigonometric series that arise in the study of contact problem of an inclusion as well as a set of curvilinear cracks. The dual series is reduced to a coupled pair of integral equations. Simple identities of the Kernel functions allow us to decouple these integral equations into a set of uncoupled singular integral equations. One of these integral equations has a logarithmic singularity and the other has a Cauchy type of singularity. The problem is then reformulated via a complex variable approach, and reduced to a Riemann-Hilbert problem leading to identical results. This equivalence may be useful in numerical computations if exact solutions cannot be obtained. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1975
Accession Number
ADA014187

Entities

People

  • M. A. Hussain
  • S. L. Pu

Tags

DTIC Thesaurus Topics

  • Complex Variables
  • Computations
  • Equations
  • Identities
  • Inclusions
  • Integral Equations
  • Integrals
  • Kernel Functions

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)