# 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

## Access Full Article

top## Abstract

top## How to cite

topRůžičková, 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

top- K. Bell, 10.1002/nme.1620010108, Int. J. Numer. Meth. Engng. 1 (1969), 101-122. (1969) DOI10.1002/nme.1620010108
- J. H. Bramble M. Zlámal, Triangular elements in the finite element method, Math. Соmр. 24 (1970), 809-820. (1970) Zbl0226.65073MR0282540
- J. Brilla, Visco-elastic bending of anisotropic plates, (in Slovak), Stav. Čas. 17 (1969), 153-175. (1969)
- J. Brilla, Finite element method for quasiparabolic equations, in Proc. of the 4th symposium on basic problems of numer. math., Plzeň (1978), 25-36. (1978) Zbl0445.73060MR0566152
- P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. (1978) Zbl0383.65058MR0520174
- V. Girault P.-A. Raviart, Finite Element Approximation of the Navier-Stokes Equations, Springer-Verlag, Berlin-Heidelberg-New York, 1979. (1979) Zbl0413.65081MR0548867
- J. Hřebíček, Numerical analysis of the general biharmonic problem by the finite element method, Apl. mat. 27 (1982), 352-374. (1982) Zbl0541.65072MR0674981
- V. Kolář J. Kratochvíl F. Leitner A. Ženíšek, Calculation of plane and Space Constructions by the Finite Element Method, (Czech). SNTL, Praha, 1979. (1979)
- 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
- J. Nedoma, The finite element solution of parabolic equations, Apl. mat. 23 (1978), 408-438. (1978) Zbl0427.65075MR0508545
- S. Turčok, Solution of quasiparabolic differential equations by finite element method, (in Slovak), Thesis, Komenský University Bratislava, (1978). (1978)
- M. Zlámal, 10.1007/BF02161362, Numer. Math. 12 (1968), 394 - 409. (1968) MR0243753DOI10.1007/BF02161362
- M. Zlámal, Finite element methods for nonlinear parabolic equations, R.A.I.R.O. Numer. Anal. 11 (1977), 93-107. (1977) MR0502073
- A. Ženíšek, Curved triangular finite ${C}^{m}$-elements, Apl. Mat. 23 (1978), 346-377. (1978) Zbl0403.65045MR0502072
- 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
- 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
- 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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.