Applications of Mathematics

, Volume 61, Issue 5, pp 527–564

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

  • Jaroslav Haslinger
  • Sergey Repin
  • Stanislav Sysala

DOI: 10.1007/s10492-016-0146-6

Cite this article as:
Haslinger, J., Repin, S. & Sysala, S. Appl Math (2016) 61: 527. doi:10.1007/s10492-016-0146-6


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.


functionals with linear growth limit load truncation method perfect plasticity 

MSC 2010

49M15 74C05 74S05 90C25 

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  • Jaroslav Haslinger
    • 1
    • 2
  • Sergey Repin
    • 3
    • 4
    • 5
  • Stanislav Sysala
    • 2
  1. 1.Department of Numerical MathematicsCharles UniversityPraha 8Czech Republic
  2. 2.Institute of Geonics of the Czech Academy of SciencesDepartment of Applied Mathematics and Computer Science & Department IT4InnovationsOstrava-PorubaCzech Republic
  3. 3.St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of SciencesSt. PetersburgRussia
  4. 4.St. Petersburg Polytechnic University of Peter The GreateSt. PetersburgRussia
  5. 5.University of JyväskyläJyväskyläFinland

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