| Title:
|
Finite elements methods for solving viscoelastic thin plates (English) |
| Author:
|
Růžičková, Helena |
| Author:
|
Ženíšek, Alexander |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
1984 |
| Pages:
|
81-103 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
viscoelastic bending |
| Keyword:
|
thin plates |
| Keyword:
|
finite elements in space |
| Keyword:
|
finite difference in time |
| Keyword:
|
rate of convergence |
| MSC:
|
65N30 |
| MSC:
|
73F15 |
| MSC:
|
73K25 |
| MSC:
|
74D99 |
| MSC:
|
74E10 |
| MSC:
|
74K20 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 0541.73090 |
| idMR:
|
MR0738495 |
| DOI:
|
10.21136/AM.1984.104073 |
| . |
| Date available:
|
2008-05-20T18:24:16Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104073 |
| . |
| Reference:
|
[1] K. Bell: A refined triangular plate bending finite element.Int. J. Numer. Meth. Engng. 1 (1969), 101-122. 10.1002/nme.1620010108 |
| Reference:
|
[2] J. H. Bramble M. Zlámal: Triangular elements in the finite element method.Math. Соmр. 24 (1970), 809-820. MR 0282540 |
| Reference:
|
[3] J. Brilla: Visco-elastic bending of anisotropic plates.(in Slovak), Stav. Čas. 17 (1969), 153-175. |
| Reference:
|
[4] J. Brilla: Finite element method for quasiparabolic equations.in Proc. of the 4th symposium on basic problems of numer. math., Plzeň (1978), 25-36. Zbl 0445.73060, MR 0566152 |
| Reference:
|
[5] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland, Amsterdam, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[6] V. Girault P.-A. Raviart: Finite Element Approximation of the Navier-Stokes Equations.Springer-Verlag, Berlin-Heidelberg-New York, 1979. MR 0548867 |
| Reference:
|
[7] J. Hřebíček: Numerical analysis of the general biharmonic problem by the finite element method.Apl. mat. 27 (1982), 352-374. MR 0674981 |
| Reference:
|
[8] V. Kolář J. Kratochvíl F. Leitner A. Ženíšek: Calculation of plane and Space Constructions by the Finite Element Method.(Czech). SNTL, Praha, 1979. |
| Reference:
|
[9] J. Kratochvíl A. Ženíšek M. Zlámal: A simple algorithm for the stiffness matrix of triangular plate bending finite elements.Int. J. Numer. Meth. Engng. 3 (1971), 553 - 563. 10.1002/nme.1620030409 |
| Reference:
|
[10] J. Nedoma: The finite element solution of parabolic equations.Apl. mat. 23 (1978), 408-438. Zbl 0427.65075, MR 0508545 |
| Reference:
|
[11] S. Turčok: Solution of quasiparabolic differential equations by finite element method.(in Slovak), Thesis, Komenský University Bratislava, (1978). |
| Reference:
|
[12] M. Zlámal: On the finite element method.Numer. Math. 12 (1968), 394 - 409. MR 0243753, 10.1007/BF02161362 |
| Reference:
|
[13] M. Zlámal: Finite element methods for nonlinear parabolic equations.R.A.I.R.O. Numer. Anal. 11 (1977), 93-107. MR 0502073 |
| Reference:
|
[14] A. Ženíšek: Curved triangular finite $C^m$-elements.Apl. Mat. 23 (1978), 346-377. MR 0502072 |
| Reference:
|
[15] A. Ženíšek: Discrete forms of Friedrichs' inequalities in the finite element method.R.A.I. R. O. Numer. Anal. 15 (1981), 265-286. Zbl 0475.65072, MR 0631681 |
| Reference:
|
[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).) MR 0743885 |
| Reference:
|
[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. MR 0555383 |
| . |
