A mixed finite element method for plate bending with a unilateral inner obstacle

Ivan Hlaváček

Applications of Mathematics (1994)

  • Volume: 39, Issue: 1, page 25-44
  • ISSN: 0862-7940

Abstract

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A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.

How to cite

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Hlaváček, Ivan. "A mixed finite element method for plate bending with a unilateral inner obstacle." Applications of Mathematics 39.1 (1994): 25-44. <http://eudml.org/doc/32867>.

@article{Hlaváček1994,
abstract = {A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.},
author = {Hlaváček, Ivan},
journal = {Applications of Mathematics},
keywords = {unilateral plate problem; inner obstacle; mixed finite elements; Herrmann-Johnson mixed model; fourth order variational inequality; fourth order variational inequality; saddle point theory; Herrmann- Johnson scheme; iterative procedure; existence; uniqueness; convergence},
language = {eng},
number = {1},
pages = {25-44},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A mixed finite element method for plate bending with a unilateral inner obstacle},
url = {http://eudml.org/doc/32867},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - A mixed finite element method for plate bending with a unilateral inner obstacle
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 1
SP - 25
EP - 44
AB - A unilateral problem of an elastic plate above a rigid interior obstacle is solved on the basis of a mixed variational inequality formulation. Using the saddle point theory and the Herrmann-Johnson scheme for a simultaneous computation of deflections and moments, an iterative procedure is proposed, each step of which consists in a linear plate problem. The existence, uniqueness and some convergence analysis is presented.
LA - eng
KW - unilateral plate problem; inner obstacle; mixed finite elements; Herrmann-Johnson mixed model; fourth order variational inequality; fourth order variational inequality; saddle point theory; Herrmann- Johnson scheme; iterative procedure; existence; uniqueness; convergence
UR - http://eudml.org/doc/32867
ER -

References

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  1. On the existence, uniqueness and approximations of saddle-point problems arising from Lagrange multipliers, vol. 8-R2, R. A. I. R. O., 1974, pp. 129–151. (1974) MR0365287
  2. Mixed finite element methods for 4th order elliptic equations, Topics in Numer. Anal., vol. III (ed. by J. J. H. Miller), Academic Press, London, 1977, pp. 33–56. (1977) Zbl0434.65085MR0657975
  3. Analyse convexe et problèmes variationnels, Dunod, Paris, 1974. (1974) Zbl0281.49001
  4. Numerical analysis of variational inequalities, North-Holland, Amsterdam, 1981. (1981) Zbl0463.65046MR0635927
  5. Mixed formulation of variational inequalities and its approximation, Apl. Mat. 26 (1981), 462–475. (1981) MR0634283
  6. Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  7. 10.1007/BF01389591, Numer. Math. 47 (1985), 435–458. (1985) Zbl0581.73022MR0808562DOI10.1007/BF01389591
  8. The finite element method for elliptic problems, North-Holland, Amsterdam, 1978. (1978) Zbl0383.65058MR0520174

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