Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method

Ivan Hlaváček

Applications of Mathematics (1994)

  • Volume: 39, Issue: 5, page 375-394
  • ISSN: 0862-7940

Abstract

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Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.

How to cite

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Hlaváček, Ivan. "Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method." Applications of Mathematics 39.5 (1994): 375-394. <http://eudml.org/doc/32892>.

@article{Hlaváček1994,
abstract = {Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.},
author = {Hlaváček, Ivan},
journal = {Applications of Mathematics},
keywords = {weight minimization; penalty method; unilateral plate bending; mixed finite elements; rigid obstacle; existence of optimal thickness; penalty method; Herrmann- Hellan finite element scheme; convergence},
language = {eng},
number = {5},
pages = {375-394},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method},
url = {http://eudml.org/doc/32892},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 5
SP - 375
EP - 394
AB - Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.
LA - eng
KW - weight minimization; penalty method; unilateral plate bending; mixed finite elements; rigid obstacle; existence of optimal thickness; penalty method; Herrmann- Hellan finite element scheme; convergence
UR - http://eudml.org/doc/32892
ER -

References

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  1. Mixed finite element methods for 4th order elliptic equations, J.J.H. Miller (ed.), Topics in Numer. Anal., vol. III, Academic Press, London, 1977, pp. 33–56. (1977) MR0657975
  2. 10.1007/BF01389591, Numer. Math. 47 (1985), 435–458. (1985) Zbl0581.73022MR0808562DOI10.1007/BF01389591
  3. Numerical analysis of variational inequalities, North-Holland, Amsterdam, 1981. (1981) MR0635927
  4. A mixed finite element method for plate bending with a unilateral inner obstacle, Appl. Math. 39 (1994), 25–44. (1994) MR1254745
  5. Functional analysis and numerical mathematics, Academic Press, New York, 1966. (1966) MR0205126
  6. Optimizacija v eliptičeskich graničnych zadačach s priloženijami v  mechanike, Nauka, Moscow, 1987. (Russian) (1987) MR0898435

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