| Title:
|
Convergence of an equilibrium finite element model for plane elastostatics (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
24 |
| Issue:
|
6 |
| Year:
|
1979 |
| Pages:
|
427-457 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
An equilibrium triangular block-element, proposed by Watwood and Hartz, is subjected to an analysis and its approximability property is proved. If the solution is regular enough, a quasi-optimal error estimate follows for the dual approximation to the mixed boundary value problem of elasticity (based on Castigliano's principle). The convergence is proved even in a general case, when the solution is not regular. (English) |
| Keyword:
|
convergence |
| Keyword:
|
equilibrium |
| Keyword:
|
plane elastostatics |
| Keyword:
|
principle of minimum complementary energy |
| Keyword:
|
weak version of Castigliano principle |
| MSC:
|
35J20 |
| MSC:
|
49S05 |
| MSC:
|
65N30 |
| MSC:
|
73K25 |
| MSC:
|
74S05 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 0441.73101 |
| idMR:
|
MR0547046 |
| DOI:
|
10.21136/AM.1979.103826 |
| . |
| Date available:
|
2008-05-20T18:13:09Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103826 |
| . |
| Reference:
|
[1] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation.Apl. mat. 21 (1976), 43 - 65. MR 0398126 |
| Reference:
|
[2] B. Fraeijs de Veubeke M. Hogge: Dual analysis for heat conduction problems by finite elements.Inter. J. Numer. Meth. Eng. 5 (1972), 65 - 82. |
| Reference:
|
[3] V. B. Watwood, Jr. B. J. Hartz: An equilibrium stress field model for finite element solutions of two-dimensional elastostatic problems.Inter. J. Solids and Struct. 4 (1968), 857-873. |
| Reference:
|
[4] I. Hlaváček: Variational principles in the linear theory of elasticity for general boundary conditions.Apl. mat. 12 (1967), 425-448. MR 0231575 |
| Reference:
|
[5] G. Sander: Application of the dual analysis principle.Proc. of IUTAM Symp. on High Speed Computing of Elastic Structures, 167-207, Univ. de Liege, 1971 (ruský překlad - izdat. Sudostrojenije, Leningrad 1974). |
| Reference:
|
[6] B. Fraeijs de Veubeke: Finite elements method in aerospace engineering problems.Proc. of Inter. Symp. Computing Methods in Appl. Sci. and Eng., Versailles, 1973, Part 1, 224-258. |
| Reference:
|
[7] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[8] 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 |
| . |
