Weight minimization of elastic plates using Reissner-Mindlin model and mixed-interpolated elements

Ivan Hlaváček

Applications of Mathematics (1996)

  • Volume: 41, Issue: 2, page 107-121
  • ISSN: 0862-7940

Abstract

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The problem to find an optimal thickness of the plate in a set of bounded Lipschitz continuous functions is considered. Mean values of the intensity of shear stresses must not exceed a given value. Using a penalty method and finite element spaces with interpolation to overcome the “locking” effect, an approximate optimization problem is proposed. We prove its solvability and present some convergence analysis.

How to cite

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Hlaváček, Ivan. "Weight minimization of elastic plates using Reissner-Mindlin model and mixed-interpolated elements." Applications of Mathematics 41.2 (1996): 107-121. <http://eudml.org/doc/32940>.

@article{Hlaváček1996,
abstract = {The problem to find an optimal thickness of the plate in a set of bounded Lipschitz continuous functions is considered. Mean values of the intensity of shear stresses must not exceed a given value. Using a penalty method and finite element spaces with interpolation to overcome the “locking” effect, an approximate optimization problem is proposed. We prove its solvability and present some convergence analysis.},
author = {Hlaváček, Ivan},
journal = {Applications of Mathematics},
keywords = {Reissner-Mindlin plate model; mixed-interpolated elements; weight minimization; penalty method; Reissner-Mindlin plate model; mixed-interpolated elements; weight minimization; penalty method},
language = {eng},
number = {2},
pages = {107-121},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weight minimization of elastic plates using Reissner-Mindlin model and mixed-interpolated elements},
url = {http://eudml.org/doc/32940},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Weight minimization of elastic plates using Reissner-Mindlin model and mixed-interpolated elements
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 2
SP - 107
EP - 121
AB - The problem to find an optimal thickness of the plate in a set of bounded Lipschitz continuous functions is considered. Mean values of the intensity of shear stresses must not exceed a given value. Using a penalty method and finite element spaces with interpolation to overcome the “locking” effect, an approximate optimization problem is proposed. We prove its solvability and present some convergence analysis.
LA - eng
KW - Reissner-Mindlin plate model; mixed-interpolated elements; weight minimization; penalty method; Reissner-Mindlin plate model; mixed-interpolated elements; weight minimization; penalty method
UR - http://eudml.org/doc/32940
ER -

References

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  1. Reissner-Mindlin model for plates of variable thickness. Solution by mixed-interpolated elements, Appl. Math. 41 (1996), 57–78. (1996) MR1365139
  2. Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method, Appl. Math. 39 (1994), 375–394. (1994) MR1288150
  3. Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, Berlin, 1991. (1991) MR1115205
  4. 10.1142/S0218202591000083, Math. Models and Meth. in Appl. Sci. 1 (1991), 125–151. (1991) MR1115287DOI10.1142/S0218202591000083
  5. Basic error estimates for elliptic problems. Handbook of Numer. Analysis, ed. by P. G. Ciarlet and J. L. Lions, vol. II, North-Holland, Amsterdam, 1991, pp. 17–352. (1991) MR1115237

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