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

Jaroslav Haslinger; Sergey Repin; Stanislav Sysala

Applications of Mathematics (2016)

  • Volume: 61, Issue: 5, page 527-564
  • ISSN: 0862-7940

Abstract

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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 von Mises and Drucker-Prager yield laws. The efficiency of the proposed approach is confirmed by several numerical experiments.

How to cite

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Haslinger, Jaroslav, Repin, Sergey, and Sysala, Stanislav. "Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals." Applications of Mathematics 61.5 (2016): 527-564. <http://eudml.org/doc/286786>.

@article{Haslinger2016,
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 von Mises and Drucker-Prager yield laws. The efficiency of the proposed approach is confirmed by several numerical experiments.},
author = {Haslinger, Jaroslav, Repin, Sergey, Sysala, Stanislav},
journal = {Applications of Mathematics},
keywords = {functionals with linear growth; limit load; truncation method; perfect plasticity; functionals with linear growth; limit load; truncation method; perfect plasticity},
language = {eng},
number = {5},
pages = {527-564},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals},
url = {http://eudml.org/doc/286786},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Repin, Sergey
AU - Sysala, Stanislav
TI - Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 5
SP - 527
EP - 564
AB - 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 von Mises and Drucker-Prager yield laws. The efficiency of the proposed approach is confirmed by several numerical experiments.
LA - eng
KW - functionals with linear growth; limit load; truncation method; perfect plasticity; functionals with linear growth; limit load; truncation method; perfect plasticity
UR - http://eudml.org/doc/286786
ER -

References

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