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Boundary Variational Inequalities in the Theory of Interface Cracks

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Book cover Operator Theoretical Methods and Applications to Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 147))

Abstract

We formulate three-dimensional interface crack problems in terms of Signorini conditions. With the help of potential theory we reduce these to variational inequalities which are employed on the two-dimensional boundary of a domain occupied by two homogeneous elastic anisotropic bodies. For the boundary variational inequalities, we prove uniqueness and existence. For a corresponding boundary element Galerkin approximation we also show convergence and asymptotic error estimates.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Georgian Technical University, Pfaffenwaldring 57, Tbilisi, 380075, Georgia

    David Natroshvili

  2. Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, Stuttgart, D-70550, Germany

    Wolfgang L. Wendland

Authors
  1. David Natroshvili
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  2. Wolfgang L. Wendland
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, IL - Ramat Aviv, 69978, Israel

    Israel Gohberg

  2. Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Wolfgang Wendland

  3. Departamento de Matemática, Instituto Superior Técnico, U.T.L., Avenida Rovisco Pais, 1049-001, Lisboa, Portugal

    António Ferreira dos Santos , Frank-Olme Speck  & Francisco Sepúlveda Teixeira ,  & 

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Natroshvili, D., Wendland, W.L. (2004). Boundary Variational Inequalities in the Theory of Interface Cracks. In: Gohberg, I., Wendland, W., Ferreira dos Santos, A., Speck, FO., Teixeira, F.S. (eds) Operator Theoretical Methods and Applications to Mathematical Physics. Operator Theory: Advances and Applications, vol 147. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7926-2_36

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  • DOI: https://doi.org/10.1007/978-3-0348-7926-2_36

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9623-8

  • Online ISBN: 978-3-0348-7926-2

  • eBook Packages: Springer Book Archive

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