An integral equation formulation for a boundary value problem of elasticity in the domain exterior to an arc

  • George C. Hsiao
  • Ernst P. Stephan
  • Wolfgang L. Wendland
Conference paper

DOI: 10.1007/BFb0076269

Part of the Lecture Notes in Mathematics book series (LNM, volume 1121)
Cite this paper as:
Hsiao G.C., Stephan E.P., Wendland W.L. (1985) An integral equation formulation for a boundary value problem of elasticity in the domain exterior to an arc. In: Grisvard P., Wendland W.L., Whiteman J.R. (eds) Singularities and Constructive Methods for Their Treatment. Lecture Notes in Mathematics, vol 1121. Springer, Berlin, Heidelberg

Abstract

We consider here a Dirichlet problem for the two-dimensional linear elasticity equation in the domain exterior to an open arc in the plane. It is shown that the problem can be reduced to a system of boundary integral equations with the unknown density function being the jump of stresses across the arc. Existence, uniqueness as well as regularity results for the solution to the boundary integral equations are established in appropriate Sobolev spaces. In particular, asymptotic expansions concerning the singular behavior for the solution near the tips of the arc are obtained. By adding special singular elements to the regular splines as test and trial functions, an augmented Galerkin procedure is used for the corresponding boundary integral equations to obtain a quasi-optimal rate of convergence for the approximate solutions.

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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • George C. Hsiao
    • 1
    • 2
    • 3
  • Ernst P. Stephan
    • 1
    • 2
    • 3
  • Wolfgang L. Wendland
    • 1
    • 2
    • 3
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkU.S.A.
  2. 2.Department of MathematicsGeorgia Institute of TechnologyAtlantaU.S.A.
  3. 3.Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtFRG

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