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A Modified Duality Scheme for Solving a 3D Elastic Problem with a Crack

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

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Abstract

We consider an equilibrium problem for a 3D elastic body with a crack. Inequality-type boundary conditions are considered at the crack faces to prevent mutual penetration between them. This leads to the formulation of a problem with an unknown contact area, which admits a variational formulation in the form of a problem of minimization of energy functional in a set of feasible displacements. To solve the problem, we consider the Uzawa algorithm based on the modified Lagrange functional and compare it with the classical analog. Numerical results illustrating the efficiency of the proposed algorithm are presented.

This study was supported by the Russian Foundation for Basic Research (Project 17-01-00682 A).

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Acknowledgements

This research was supported through computational resources provided by the Shared Facility Center “Data Center of FEB RAS” (Khabarovsk) [15].

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Authors and Affiliations

  1. Computing Center of Far Eastern Branch Russian Academy of Sciences, Kim Yu Chen 65, 680000, Khabarovsk, Russia

    Robert Namm & Georgiy Tsoy

Authors
  1. Robert Namm
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  2. Georgiy Tsoy
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Correspondence to Georgiy Tsoy .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Namm, R., Tsoy, G. (2019). A Modified Duality Scheme for Solving a 3D Elastic Problem with a Crack. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_41

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_41

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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