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Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals

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Abstract

The paper is concerned with guaranteed and computable bounds of the limit (or safety) load, which is one of the most important quantitative characteristics of mathematical models associated with linear growth functionals. We suggest a new method for getting such bounds and illustrate its performance. First, the main ideas are demonstrated with the paradigm of a simple variational problem with a linear growth functional defined on a set of scalar valued functions. Then, the method is extended to classical plasticity models governed by vonMises and Drucker-Prager yield laws. The efficiency of the proposed approach is confirmed by several numerical experiments.

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Authors and Affiliations

  1. Department of Numerical Mathematics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Jaroslav Haslinger

  2. Institute of Geonics of the Czech Academy of Sciences, Department of Applied Mathematics and Computer Science & Department IT4Innovations, Studentská 1768, 708 00, Ostrava-Poruba, Czech Republic

    Jaroslav Haslinger & Stanislav Sysala

  3. St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 27, Fontanka, 191023, St. Petersburg, Russia

    Sergey Repin

  4. St. Petersburg Polytechnic University of Peter The Greate, Polytechnicheskaya 29, St. Petersburg, Russia

    Sergey Repin

  5. University of Jyväskylä, P.O. Box 35, 40014, Jyväskylä, Finland

    Sergey Repin

Authors
  1. Jaroslav Haslinger
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  2. Sergey Repin
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  3. Stanislav Sysala
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Corresponding author

Correspondence to Jaroslav Haslinger.

Additional information

This work was supported by The Ministry of Education, Youth and Sports of the Czech Republic from the National Programme of Sustainability (NPU II), project “IT4Innovations excellence in science-LQ1602”.

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Haslinger, J., Repin, S. & Sysala, S. Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals. Appl Math 61, 527–564 (2016). https://doi.org/10.1007/s10492-016-0146-6

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  • DOI: https://doi.org/10.1007/s10492-016-0146-6

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