| Title:
|
Weight minimization of elastic plates using Reissner-Mindlin model and mixed-interpolated elements (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
107-121 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem to find an optimal thickness of the plate in a set of bounded Lipschitz continuous functions is considered. Mean values of the intensity of shear stresses must not exceed a given value. Using a penalty method and finite element spaces with interpolation to overcome the “locking” effect, an approximate optimization problem is proposed. We prove its solvability and present some convergence analysis. (English) |
| Keyword:
|
Reissner-Mindlin plate model |
| Keyword:
|
mixed-interpolated elements |
| Keyword:
|
weight minimization |
| Keyword:
|
penalty method |
| MSC:
|
49A22 |
| MSC:
|
49J20 |
| MSC:
|
65N30 |
| MSC:
|
73k40 |
| MSC:
|
74P99 |
| idZBL:
|
Zbl 0857.49003 |
| idMR:
|
MR1373476 |
| DOI:
|
10.21136/AM.1996.134316 |
| . |
| Date available:
|
2009-09-22T17:50:34Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134316 |
| . |
| Reference:
|
[1] Hlaváček, I.: Reissner-Mindlin model for plates of variable thickness. Solution by mixed-interpolated elements.Appl. Math. 41 (1996), 57–78. MR 1365139 |
| Reference:
|
[2] Hlaváček, I.: Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method.Appl. Math. 39 (1994), 375–394. MR 1288150 |
| Reference:
|
[3] Brezzi, F. – Fortin, M.: Mixed and Hybrid Finite Element Methods.Springer-Verlag, New York, Berlin, 1991. MR 1115205 |
| Reference:
|
[4] Brezzi, F. – Fortin, M. – Stenberg, R.: Error analysis of mixed-interpolated elements for Reissner-Mindlin plates.Math. Models and Meth. in Appl. Sci. 1 (1991), 125–151. MR 1115287, 10.1142/S0218202591000083 |
| Reference:
|
[5] Ciarlet, P.G.: Basic error estimates for elliptic problems. Handbook of Numer. Analysis, ed. by P. G. Ciarlet and J. L. Lions.vol. II, North-Holland, Amsterdam, 1991, pp. 17–352. MR 1115237 |
| . |
