| Title:
|
A finite element analysis for the Signorini problem in plane elastostatics (English) |
| Author:
|
Hlaváček, Ivan |
| Author:
|
Lovíšek, Ján |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
22 |
| Issue:
|
3 |
| Year:
|
1977 |
| Pages:
|
215-228 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Signorini unilateral boundary value problem describes the equilibrium of an elastic body resting on a rigid and frictionless support. A displacement finite element method, using piecewise linear polynomials on the triangulation, can be applied to obtain an approximate solution. Assuming that the solution is sufficiently regular, the optimal rate of convergence is proved. Moreover, the convergence is justified even without any regularity assumption. () |
| MSC:
|
49R50 |
| MSC:
|
65N30 |
| MSC:
|
74B99 |
| MSC:
|
74H99 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 0369.65031 |
| idMR:
|
MR0446014 |
| DOI:
|
10.21136/AM.1977.103694 |
| . |
| Date available:
|
2008-05-20T18:07:14Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103694 |
| . |
| Reference:
|
[1] Signorini A.: Questioni di elasticità non linearizzata о semi-linearizzata.Rend. di Matem. e delle sue appl. 18 (1959). MR 0127587 |
| Reference:
|
[2] Fichera G.: Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno.Mem. Ace. Naz. Lincei, s. VIII., 7, f. 5 (1964). Zbl 0146.21204, MR 0178631 |
| Reference:
|
[3] Fichera G.: Boundary Value Problems of Elasticity with Unilateral Constraints.Encycl. of Physics (ed. by S. Flügge), vol. VIa/2. Springer, Berlin 1972. |
| Reference:
|
[4] Hlaváček I.: Dual Finite Element Analysis for Unilateral Boundary Value Problems.Apl. Mat. 22 (1977), 14-51. MR 0426453 |
| Reference:
|
[5] Nečas J.: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
|
[6] Scarpini F., Vivaldi M.: Error Estimates for the Approximation of Some Unilateral Problems.R.A.I.R.O. (1977). Zbl 0358.65087, MR 0488860 |
| Reference:
|
[7] Céa J.: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892 |
| Reference:
|
[8] Frémond M.: Dual Formulations for Potential and Complementary Energies.Mathematics of Finite Elements and Appl. (ed. by J. R. Whiteman), Academic Press, 1973. |
| Reference:
|
[9] Panagiotopoulos P. D.: Unilateral Problems in the Theory of Elasticity.Ing. Archiv. 44, (1975), 421-432. MR 0426584 |
| Reference:
|
[10] Mosco U., Strang G.: One-sided Approximations and Variational Inequalities.Bull. Amer. Math. Soc. 80 (1974), 308-312. MR 0331818, 10.1090/S0002-9904-1974-13477-4 |
| . |
