Shape optimization of elasto-plastic bodies

Zuzana Dimitrovová

Applications of Mathematics (2001)

  • Volume: 46, Issue: 2, page 81-101
  • ISSN: 0862-7940

Abstract

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Existence of an optimal shape of a deformable body made from a physically nonlinear material obeying a specific nonlinear generalized Hooke’s law (in fact, the so called deformation theory of plasticity is invoked in this case) is proved. Approximation of the problem by finite elements is also discussed.

How to cite

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Dimitrovová, Zuzana. "Shape optimization of elasto-plastic bodies." Applications of Mathematics 46.2 (2001): 81-101. <http://eudml.org/doc/33078>.

@article{Dimitrovová2001,
abstract = {Existence of an optimal shape of a deformable body made from a physically nonlinear material obeying a specific nonlinear generalized Hooke’s law (in fact, the so called deformation theory of plasticity is invoked in this case) is proved. Approximation of the problem by finite elements is also discussed.},
author = {Dimitrovová, Zuzana},
journal = {Applications of Mathematics},
keywords = {mixed boundary value problem; deformation theory of plasticity; shape optimization; cost functional; finite elements; shape optimization; deformation theory of plasticity; finite elements},
language = {eng},
number = {2},
pages = {81-101},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization of elasto-plastic bodies},
url = {http://eudml.org/doc/33078},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Dimitrovová, Zuzana
TI - Shape optimization of elasto-plastic bodies
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 2
SP - 81
EP - 101
AB - Existence of an optimal shape of a deformable body made from a physically nonlinear material obeying a specific nonlinear generalized Hooke’s law (in fact, the so called deformation theory of plasticity is invoked in this case) is proved. Approximation of the problem by finite elements is also discussed.
LA - eng
KW - mixed boundary value problem; deformation theory of plasticity; shape optimization; cost functional; finite elements; shape optimization; deformation theory of plasticity; finite elements
UR - http://eudml.org/doc/33078
ER -

References

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  1. Finite Element Approximation for Optimal Shape Design: Theory and Applications, John Wiley & Sons, Chichester, 1988. (1988) MR0982710
  2. Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier, Amsterdam-Oxford-New York, 1981. (1981) MR0600655
  3. Solution of Signorini’s contact problem in the deformation theory of plasticity by secant modules method, Apl. Mat. 28 (1983), 199–214. (1983) MR0701739
  4. Reliable solution of problems in the deformation theory of plasticity with respect to uncertain material function, Appl. Math. 41 (1996), 447–466. (1996) MR1415251
  5. 10.1007/BF01742734, Struct. Optim. 4 (1992), 133–141. (1992) DOI10.1007/BF01742734
  6. Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford, 1968. (1968) Zbl0164.26001MR0391679
  7. Inequalities of Korn’s type, uniform with respect to a class of domains, Appl. Math. 34 (1989), 105–112. (1989) MR0990298
  8. 10.1007/BF01447854, Appl. Math. Optim. 2 (1975), 130–169. (1975) MR0443372DOI10.1007/BF01447854

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