| Title:
|
An equilibrium finite element method in three-dimensional elasticity (English) |
| Author:
|
Křížek, Michal |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
1 |
| Year:
|
1982 |
| Pages:
|
46-75 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates $O(h^2)$ in $L_2$-norm and $O(h^{1/2})$ in $L_\infty$-norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too. (English) |
| Keyword:
|
composite tetrahedral equilibrium element |
| Keyword:
|
two types of finite approximation |
| Keyword:
|
three-dimensional problem |
| Keyword:
|
polyhedral domain |
| Keyword:
|
Castigliano-Menabrea’s principle |
| Keyword:
|
minimum complementary energy |
| Keyword:
|
a priori error estimates |
| Keyword:
|
existence of strongly regular family of decompositions |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| MSC:
|
73K25 |
| MSC:
|
74B99 |
| MSC:
|
74H99 |
| MSC:
|
74P99 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 0488.73072 |
| idMR:
|
MR0640139 |
| DOI:
|
10.21136/AM.1982.103944 |
| . |
| Date available:
|
2008-05-20T18:18:22Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103944 |
| . |
| Reference:
|
[1] Л. Д. Александров: Выпуклые многогранники.H. - Л., Гостехиздат, Москва, 1950. Zbl 1157.76305 |
| Reference:
|
[2] J. H. Bramble M. Zlámal: Triangular elements in the finite element method.Math. Соmр. 24 (1970), 809-820. MR 0282540 |
| Reference:
|
[3] P. G. Ciarlet P. A. Raviart: General Lagrange and Hermite interpolation in $R^n$ with applications to finite element methods.Arch. Rational Mech. Anal. 46 (1972), 177-199. MR 0336957, 10.1007/BF00252458 |
| Reference:
|
[4] P. G. Ciarlet: The finite element method for elliptic problems.North-Holland publishing company, Amsterdam, New York, Oxford, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[5] G. Duvaut J. L. Lions: Inequalities in mechanics and physics.Springer-Verlag, Berlin, Heidelberg, New York, 1976. MR 0521262 |
| Reference:
|
[6] B. J. Hartz V. B. Watwood: An equilibrium stress field model for finite element solution of two-dimensional elastostatic problems.Internat. J. Solids and Struct. 4 (1968), 857-873. 10.1016/0020-7683(68)90083-8 |
| Reference:
|
[7] I. Hlaváček J. Nečas: Mathematical theory of elastic and elasto-plastic bodies.SNTL, Praha, Elsevier, Amsterdam, 1980. |
| Reference:
|
[8] I. Hlaváček: Convergence of an equilibrium finite element model for plane elastostatics.Apl. Mat. 24 (1979), 427-457. MR 0547046 |
| Reference:
|
[9] C. Johnson B. Mercier: Some equilibrium finite element methods for two-dimensional elasticity problems.Numer. Math. 30 (1978), 103-116. MR 0483904, 10.1007/BF01403910 |
| Reference:
|
[10] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha, 1967. MR 0227584 |
| Reference:
|
[11] : Энциклопедия элементарной математики - Геометрия книга 4, 5.Наука, Москва, 1966. Zbl 0156.18206 |
| . |
