Finite elements methods for solving viscoelastic thin plates

Helena Růžičková; Alexander Ženíšek

Aplikace matematiky (1984)

  • Volume: 29, Issue: 2, page 81-103
  • ISSN: 0862-7940

Abstract

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The present paper deals with numerical solution of a viscoelastic plate. The discrete problem is defined by C 1 -elements and a linear multistep method. The effect of numerical integration is studied as well. The rate of cnvergence is established. Some examples are given in the conclusion.

How to cite

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Růžičková, Helena, and Ženíšek, Alexander. "Finite elements methods for solving viscoelastic thin plates." Aplikace matematiky 29.2 (1984): 81-103. <http://eudml.org/doc/15337>.

@article{Růžičková1984,
abstract = {The present paper deals with numerical solution of a viscoelastic plate. The discrete problem is defined by $C^1$-elements and a linear multistep method. The effect of numerical integration is studied as well. The rate of cnvergence is established. Some examples are given in the conclusion.},
author = {Růžičková, Helena, Ženíšek, Alexander},
journal = {Aplikace matematiky},
keywords = {viscoelastic bending; thin plates; finite elements in space; finite difference in time; rate of convergence; viscoelastic bending; thin plates; finite elements in space; finite difference in time; rate of convergence},
language = {eng},
number = {2},
pages = {81-103},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite elements methods for solving viscoelastic thin plates},
url = {http://eudml.org/doc/15337},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Růžičková, Helena
AU - Ženíšek, Alexander
TI - Finite elements methods for solving viscoelastic thin plates
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 2
SP - 81
EP - 103
AB - The present paper deals with numerical solution of a viscoelastic plate. The discrete problem is defined by $C^1$-elements and a linear multistep method. The effect of numerical integration is studied as well. The rate of cnvergence is established. Some examples are given in the conclusion.
LA - eng
KW - viscoelastic bending; thin plates; finite elements in space; finite difference in time; rate of convergence; viscoelastic bending; thin plates; finite elements in space; finite difference in time; rate of convergence
UR - http://eudml.org/doc/15337
ER -

References

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  2. J. H. Bramble M. Zlámal, Triangular elements in the finite element method, Math. Соmр. 24 (1970), 809-820. (1970) Zbl0226.65073MR0282540
  3. J. Brilla, Visco-elastic bending of anisotropic plates, (in Slovak), Stav. Čas. 17 (1969), 153-175. (1969) 
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  8. V. Kolář J. Kratochvíl F. Leitner A. Ženíšek, Calculation of plane and Space Constructions by the Finite Element Method, (Czech). SNTL, Praha, 1979. (1979) 
  9. J. Kratochvíl A. Ženíšek M. Zlámal, 10.1002/nme.1620030409, Int. J. Numer. Meth. Engng. 3 (1971), 553 - 563. (1971) Zbl0248.73029DOI10.1002/nme.1620030409
  10. J. Nedoma, The finite element solution of parabolic equations, Apl. mat. 23 (1978), 408-438. (1978) Zbl0427.65075MR0508545
  11. S. Turčok, Solution of quasiparabolic differential equations by finite element method, (in Slovak), Thesis, Komenský University Bratislava, (1978). (1978) 
  12. M. Zlámal, 10.1007/BF02161362, Numer. Math. 12 (1968), 394 - 409. (1968) MR0243753DOI10.1007/BF02161362
  13. M. Zlámal, Finite element methods for nonlinear parabolic equations, R.A.I.R.O. Numer. Anal. 11 (1977), 93-107. (1977) MR0502073
  14. A. Ženíšek, Curved triangular finite C m -elements, Apl. Mat. 23 (1978), 346-377. (1978) Zbl0403.65045MR0502072
  15. A. Ženíšek, Discrete forms of Friedrichs' inequalities in the finite element method, R.A.I. R. O. Numer. Anal. 15 (1981), 265-286. (1981) Zbl0475.65072MR0631681
  16. A. Ženíšek, Finite element methods for coupled thermoelasticity and coupled consolidation of clay, (To appear in R.A.I.R.O. Numer. Anal. 18 (1984).) (1984) Zbl0539.73005MR0743885
  17. E. Godlewski A. Puech-Raoult, Équations d'évolution linéaires du second ordre et méthodes multipas, R.A.I.R.O. Numer. Anal. 13 (1979), 329-353. (1979) MR0555383

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